Nuclear structure studies of neutron rich isotopes of 129 131ag, 130 133cd, 131 135in and 134 138sn via Β delayed neutron measurements using the briken detector system

In recent decades, research in nuclear physics has expanded from stable nuclei toward the short-lived rare isotopes or alternatively exotic nuclei In most cases, exotic nuclei are characterized by an unbalanced ratio between neutron number (N) and proton number (Z) Nuclei with an excess of protons compared to their stable isotopes are called proton-rich nuclei, while neutron-rich nuclei are those with an excess of neutrons.

Proton-rich nuclei are unstable against the β + decay, while neutron-rich nuclei are unstable against the β − decay A variety of new phenomena associated with exotic nuclei has been revealed recently, such as the formation of nuclear halo [160], the appearance of new magic numbers [169, 155] in neutron-rich nuclei, or two-proton radioactivity phenomena in proton-rich nuclei [47].

In order to improve current knowledge on structures and reactions of such exotic nuclei, constructions of radioactive isotope beam (RIB) facilities are demanded, and the experimental results obtained on the produced RIB are used to guide the development of the theoretical models Presently, the numbers of RIB facilities in developed countries exist Several of them are being upgraded to increase the production yield of the RIB.

Experimental studies using radioactive isotopes (RIs) are among the frontier areas of modern physical research and play an important role in enhancing our knowledge of atomic nuclei One of the earliest applications of the radioactive isotope studies was the use of α-emitted radioactive isotope of polonium in the Rutherford scattering experiment, which has led to the first experimental evidence of the atomic nucleus.

Since then, various methods for producing RIs have been developed in parallel with the development of modern nuclear physics With such development in the last three decades, there is a growing number of newly discovered RIs, from about 2200 in 1981 to 3252 in 2017 [124, 95], out of about 6000-7000 isotopes predicted to exist Figure 1.1 shows a summary of the discovered isotopes using various methods.

The extension of the nuclear chart toward extreme isospin, both in proton and neutron-rich side is an experimental challenge [39] Such exotic nuclei are mostly unstable, with short half-lives and their production yields are typically very low There- fore, there is a need for efficient methods to produce exotic nuclei with a sufficiently high yield In general, there are two methods to produce exotic nuclei: the so-called in-flight projectile fragmentation/fission method and the isotope separation on-line(ISOL) method.

Figure 1.1: The chart of nuclides showing a large area of the unknown neutron-rich nuclei towards the neutron drip-line Image adapted from

In the isotope separation online technique, a nuclear reaction is used to produce the radioactive nuclei, such as the spallation of the accelerated proton beam The productions are separated by chemical or laser ionization processes and post-accelerated by an independent accelerator This method has been first demonstrated at Louvain- la-Neuve in 1989, where the 13 N beam was successfully produced for an experiment to study the astrophysical (p, γ) reaction Nowadays, there are several operating ISOL- based facilities in Europe and North-America, such as SPIRAL II at GANIL in France [141], REX-ISOLDE at CERN in Switzerland [78], MAFF in Germany [54], ISAC-II at TRIUMP in Canada [90], HRIBF at ORNL in USA [21].

The in-flight method has been utilized to produce the nuclei of interest within the scope of this work This method is known as an efficient method to produce a wide range of the exotic nuclei by direct reaction mechanisms, such as projectile- fragmentation or in-flight fission of a heavy-ion on light target A detailed review of this method can be found in Ref [114] The method was first demonstrated in the pioneered experiment carried out at Lawrence Berkeley National Laboratory(LBNL) in 1970s, where unstable 11 Be and 11 Li beam was created for the first time from a projectile fragmentation of 1-GeV/nucleon 20 Ne beams This experiment has led to the discovery of the halo structure in neutron-rich nuclei in 1985 [160] Later, the in-fight fission of 238 U was carried out successfully in 1994 at the Gesellschaft fur Schwerionenfoschung (GSI) [22] Nowadays, many large-scale facilities in the world, such as GANIL in France, MSU/NSCL in the USA, GSI in Germany and RIBF in Japan, are utilizing this method to produce a broad range of isotopes for nuclear physics experiments such as reaction, decay, laser spectroscopy,

One major advantage of the in-flight method compared to ISOL method is that all of the elements and short-lived nuclei can be accessed This is because, in the in-flight method, RIs are separated by a physical process using a magnetic spectrometer rather than a chemical process, thus the production of RIs are faster However, purification of the in-flight radioactive beam is more difficult due to the large emittance of the secondary beam before the magnetic spectrometer Therefore, event-by-event particle identification (PID) and tracking techniques are usually used.

1.2.1 Application of the Independent Particle Shell Model

There are many theoretical models used to predict various aspects of the structure of atomic nuclei, including their macroscopic and microscopic properties [1] In the view of the shell model, protons and neutrons in the atomic nucleus are arranged in a defined shell structure with a large energy gap between the shells This structure arises from the quantum nature of nucleons Due to the Pauli principle, there are only a limit number of nucleons occupying a shell The so-called closed shell nucleus is when all energy levels within and bellow a shell are completely filled with neutrons or protons.

In the present thesis, the focused nuclei are in the near closed-shell region, which is better described by the shell model.

A large number of experimental evidence supports the concept of the nuclear shell structure One of the clear evidence was based on the systematic of the neutron or proton separation energies S n or S p (the amount of energy needed to remove a neutron or proton from the nucleus), which shows sharps peak at particular numbers: 2, 8, 20, 28, 50, 82 and 126 As a result, the nuclei with magic number of proton or neutron, or both (doubly magic) are usually more stable than others, such as 4 2 He, 16 8 O, 48 20 Ca,

Similar behavior was also observed in the systematic of the first excitation energy of the even-even nuclei (shown in Fig 1.2).

Figure 1.2: Energy of first excited states in even-even nuclei, as a function of neutron number Sharp peaks are located at the neutron magic number of N=8,20,28,50, 82 and 126 Image source: Ref [133]

The solar abundance pattern also contains imprints of the nuclear magic numbers, where double magic and stable nuclei such as 4 2 He, 16 8 O, 40 20 Ca and 208 82 Pb are located at abundance peaks, as shown in Fig.1.3.

Figure 1.3: Relative solar abundance pattern as a function of mass number Image source: Ref [68]

Another experimental clue of the nuclear shell structure can be inferred from the zero electrical quadrupole moment of doubly magic nuclei, which proves a spherical distribution of the charges inside the nucleus This evidence has been later used for the simple assumption of the shell models based on the movement of nucleons in a central mean-field potential describing the system with spherical symmetry: Us.p(r)≡Us.p(r).

The nuclear shell model was first constructed with similar consideration as for the electron shell in the atom Shells of electrons are filled from lower to higher energy levels, each has a limited number of occupied electrons due to the Pauli principle (electron is a fermion) The atomic properties are determined by the valance electron and the fully occupied shells are considered as an inert core.

The so-called independent particle shell model was originated from the early development of the shell model In this model, nucleons are confined in a central potential with a strong attractive spin-orbit term The starting point of the model was a central potential in the form of a harmonic oscillator Further inclusion of spin-orbit potential terms and more elaborate form of nuclear potential such as Woods-Saxon (WS) [178] allows physicists to predict the experimentally observed nuclear magic numbers, where nucleons completely filled a shell In details, the number of nucleons occupying a shell is dictated by it’s degeneracy Each shell (orbit) l has parity of (−1) l and degenerates into 2(2l+ 1) magnetic substates The (2l+ 1) factor is originated from the z-component m l and the factor of 2 is from the projection of spin m s With the presence of the spin-orbit interaction, the orbit l is split into two subshells with total angular momentum j =l±1/2 There are 2j + 1 possible substates with m j values: m j = ±1/2,±3/2, ±j In this case m l and m s can not be considered as "good" quantum number Each substate can only be occupied by one proton or neutron due to the Pauli exclusion principle: no two fermions may occupy the same substrate at the same time As a result, no more than 2j + 1 neutrons or protons may exist in a subshell with a total angular momentum j This rule is used to calculate the set of nuclear magic numbers, corresponding to the number of nucleons completely filled a shell (called closed shells).

The independent particle model predicts the ground and excited states of nuclei with a single nucleon outside a closed shell Closed shells have 2j+1 degenerate magnetic substates, resulting in a total magnetic quantum number of zero and positive parity This implies a ground state with angular momentum J=j and parity π=(-1)l The closed shell acts as an inert core, with the last nucleon being referred to as the "valence" nucleon.

41 20Ca 21 should have a 7/2 − ground state because it has one neutron outside of N closed shell, while the Z shell is fully occupied This neutron resides in the 1f 7/2 orbit, having a parity ofπ = (−1) 3 =−1.

The independent particle picture can be extended to account for nucleus with a single proton or neutron "hole", i.e all but one nucleon fill the outermost j-orbit of a closed shell For example, the case of 39 20 Ca 19 , also with Z shell fully occupied.

SinceJ~ f ullshell = 0, we haveJ~f ullshell−1+j = 0 and an orbit with a proton or neutron hole must have J = j, which means the single hole or single-particle state must has the same spin.

The independent particle model is also applicable in the case of three particles in a j-shell, where particles 1 and 2 can be coupled by anti-align angular momenta so that J 12 = 0 giving J =j This corresponding to an empirically lowest energy of the system Another result of the spin coupling of two particles is that the ground state of nuclei with 2 nucleons outside of the doubly-magic core is always J π = 0 + This is also true with the ground state of all even-even nuclei.

Single-particle energies in nuclei are influenced by the number of nucleons and the resulting changes in the single-particle potential Heavier nuclei exhibit more compressed energy levels due to potential modifications Additionally, residual interactions contribute to these energy shifts.

1.2.2 The Multi-particle Shell Model

To understand excited states in nuclei, the residual interaction between nucleons must be considered This interaction, absent in the independent particle model, is present in the Hamiltonian for an A-nucleon system It affects the excitation properties and higher-lying excited states of nuclei with multiple particles or holes outside a doubly magic core.

Where ~pi, mi, ~ri is the momentum, mass and position vector of i th nucleon V ik represents potential induced by two-body interaction U i is the one-body nucleon potential that overall contributes to the mean-field potential similar to the independent particle picture Outside of the inert doubly magic core, the interaction of valence nucleons can be associated with the two-body matrix elements (TBME) of the residual interactionH res The effect of residual interaction shifts the energy level of the excited state Figure1.4 illustrates some examples of energy shifts due to residual interactions of two particles configuration, in which identical nucleons (n-n or p-p multiplets) with angular momentumj 1 andj 2 are coupled to form states with integer values of angular momentum J

Figure 1.4: Examples of excited states produced residual interactions of identical nucleons Upper panels show examples for equivalent orbits (n 1 l 1 j 1 =n 2 l 2 j 2 ) Lower panel shows examples of non-equivalent orbits.

In fact, only a certainJ values are allowed due to the Pauli principle For example, the excited states originated from a coupling of two identical nucleons in an equivalent orbit of the samenlj always has even value of total angular momentumJ The effect of residual interaction would lower the smallJ the most in this case, as shown in the upper panels of Fig 1.4 For identical nucleons resided in non-equivalent orbits, a general rule arising from residual interaction follows that for positive parity configuration only even J level is lowered, while only odd J levels are lowered for negative parity.

The parity of the multi-particle system is multiplicative: π = ((−1) l ) n , with n is the number of particles For example a configuration of (f 5/2 ) n produces states with parity of π= ((−1) 3 ) n = (−1) n

The multi-particle configuration under the effect of residual interaction leads to the parabolic rule for energies of states when extended to account for non-identical nucleons This rule expresses energy shifts as a function of J(J + 1), where J is the total angular momentum.

The parabolic rule can be used to obtain approximately the lowest-lying excited state (largest energy shift) This can be also applied in the particle-hole p-n configurations Fig 1.5 shows some examples of the parabolic rule applied for particle-particle and particle-hole configurations For particle-hole configuration as in 48 Sc and 116 In, the parabolic behavior of the excitation energy is evidenced, except the parabola is in- verted compared to the particle-particle configuration in 122 Sb This can be explained by the fact that the residual interaction has the opposite sign of a particle-particle or hole-hole Another example of the π0g −1 9/2 N ν1f 7/2 multiplet (proton subshell 0g 9/2 and neutron subshell1f 7/2 ) in 132 In, which will be discussed later in the present thesis, forms a parabolic shape in J(J + 1) with spin from 1 − to 8 − , and the 5 − , 6 − and 7 − states are the possible lowest-lying members (ground state) according to the parabolic rule Indeed, the detail shell model calculation predicts 7 − to be the ground state of

1.2.3 Shell structure south-east of doubly magic 132 Sn

Shell structure far-off stability The parabolic rule in the multi-particle configuration is an important result of the multipole decomposition of the residual interaction acting between non-identical

1.3.1 Gamma-ray decay and Weisskopf estimates γ-rays spectroscopy offers an indispensable tool to study nuclear structure The nuclei in excited states (for example, following a nuclear reaction) often decays to the ground state through emission of electromagnetic radiation (photons) by either directly or through a sequence of intermediate-energy states The γ-rays energies are typically in the range of 0.1 to 10 MeV and equal to the energy difference between the initial (Ei) and final states (E f ) of the excited nuclei: ∆E =E f −Ei The photon also carries the angular momentum λ (referred to as multipolarity) characterized by the difference of spin (angular momenta) between initial J i and final states J f

The above equation reflects angular momentum conservation in γ-decay, and the amount of angular momentum carried by the photon is ¯hλ The emission of γ-ray can be treated either as a classical wave phenomenon or a quantum phenomenon In the classical picture, nucleons generate a radiation field when its charge and current distribution vary with time Transitions followed by emission γ-rays are classified as electric if the radiation field is generated by a change in charge distribution, or as magnetic if it is due to a change in the current distribution Transitions are further restricted by the selection rules on the parity change

Here, for a given value of λ, electric and magnetic multipoles have opposite parity.

For a transition, several possible multipoles may be possible according to the selection rules The intensity of the de-excited γ-rays is also governed by the selection rules, which depend on the momentum of initial and final states.

In the quantum mechanical point of view, theγ transition probabilities are governed by the nuclear matrix elements that connect the initial and final nuclear states, which represents as reduced transition strength B(σλ) The independent-particle estimates (B(M λ)) for the transition strength on the shell model basis (called Weisskopf single particle estimates) can be writen as [41]:

WhereR= 1.2×10 −13 A 1/3 cm is the nuclear radius The electromagnetic transition rate, when converted from the classical to quantum mechanical theory of electromagnetic radiation, takes the form:

Where E γ is the gamma-rays energy and the constants are: hc¯ = 197.327×10 −10 keV cm, ¯h = 6.58212 ×10 −19 keV s, e 2 = 1.440 −10 keV cm, the nuclear magneton à 2 N = 1.5922 −38 keV cm 3 and b = 10 −24 cm 2 (barn) The Wiesskopf single-particle estimates can be used to predict which multipole is more likely by comparing with the experimentally deduced transition strength Lower multipole is dominant with greater transition probability Also, electric radiation has transition probability greater than that of magnetic radiation, given the same multipole order.

The Wiesskopf single-particle estimates can predict electromagnetic transitions but not de-excitation rates of excited states This is due to the competition between γ-ray emission and internal conversion, where an atomic electron is emitted carrying kinetic energy (T e) equal to the transition energy (∆E) minus its binding energy (B e) The binding energies of the electrons determine the discrete energy spectrum of internal conversion electrons, containing peaks corresponding to electrons from different atomic orbitals.

We denote the total internal conversion coefficient as the ratio of the transition rate of an electron (W e ) and a γ-ray emission (W γ ) αic= W e

Therefore, the total transition rate of W tot =W e +W γ of an excited state must be scaled by αic in the following manner

When severalγ-rays transition deexcited a nuclear state, the transition strength of a particularγ-ray with branching ratio br can be described as:

The electron transition probabilities W e depends on which atomic shell the electron came from The total internal conversion coefficient must be obtained as a summation of partial coefficients of all atomic shells (and subshells). α=α K +α L +α M (1.14) α L =α L I +α L II +α L III (1.15)

The internal conversion coefficient is multipolarity dependence A non-relativistic calculation for the internal conversion coefficient gives: α Eλ ≈ Z 3 n 3 λ λ+ 1 e 2 4π 0 ¯hc

Where Z is the atomic number, n is the principal quantum number of the atomic electron, e 2

4π 0 ¯hc is fine structure constant, and E is the transition energy One can infer from this expression that the internal conversion process strongly dominates at low excitation energies, high multipole orders and heavy nuclei with high Z.

By taking into account more sophisticated atomic effects, the internal conversion coefficient can be accurately estimated using the BrIcc tool [79], which is available at [32].

Isomeric states are nuclear excited metastable states with half-life orders of magnitude higher than10 −12 s Such long-lived excited states are caused by the hindrance of the γ-rays transition due to the spin difference of initial and final states Isomeric states (or isomer) provides first insights into intrinsic and collective behavior in a nucleus, while other short-lived states are difficult to be observed experimentally with standard detectors The transition probability of an isomeric state includes contributions from all the γ-ray that depopulates the isomeric state, as well as the internal conversion electrons.

A combination of the two processes results in a faster decay than theγ-rays emission alone Then given the multipolarity σλ, the transition energy E γ , the half-life T 1/2 ln(2)/W tot and the branching ratio br, the electromagnetic transition strength B(σλ) of an isomericγ decay can be determined according to the equations1.7,1.8, 1.9, 1.10 and 1.12.

The experimental B(σλ) values then can be used to compare with the shell model calculation and to estimate the order of nuclear collectivity involved in the transition.

In this context, B(σλ) values are usually expressed in Weisskopf units (W.u.) OneWeisskopf unit for a given multipolarityσλcorresponds to the Weisskopf single-particle estimate given in the equations1.7 and 1.8.

1.4.1 Beta decay theory β decay is a consequence of weak interaction, which is one of the most fundamental processes taking place in the universe In this process, one proton or neutron in atomic nucleus decays into neutron or proton, emitting electrons and antineutrinos: p→n+e + +v e (1.18) n →p+e − + ¯v e (1.19)

Here e + , v e and ¯v e denote a positron, neutrino, and anti-neutrino, respectively.

Another weak interaction process involves orbital electron interaction with the atomic nucleus, where an electron is absorbed by a proton in the atomic nucleus, converted it into a neutron and an electron anti-neutrino is emitted. p+e − →n+ ¯ve (1.20)

In nuclear β decay, the total released energy, the Q value, is always positive if this decay is energetically possible The β particle and neutrino will share this energy because the mass of the recoil nucleon is much larger than that of an electron Therefore, the energy spectrum of β particle has a continuous form up to some maximum value of E max

Where m(A, Z) is the atomic mass of nucleus A Z X For proton rich nuclei, an electron capture (EC) process is energetically possible, leaving the Q EC value of

Where m e and E b is the electron mass and binding energy of captured electron in an atom.

Depending on the total angular momentum L and spin parityπofβand neutrino,β- decay is classified as an allow transition if L=0 andπ = +1 and a forbidden transition if L 6= 0 and π = (−l) L For the allowed transition, β decay can be further sub- categorized based on total spin S of emitting β particle and neutrino: The Fermi transition corresponds to an S=0 (anti-parallel) and Gamow-Teller (GT) transition with S=1 (parallel).

The total transition strength of the GT and Fermi allowed transitions includes the phase space integralf that depends on theQ β and the partial decay half-life t [61] f t= K

Where G V and G A are the vector and axial-vector weak coupling constants, B F và B GT is Fermi and GT transition strength The ft value can be experimentally obtained (usually given in logarithmic scale) and is a standard measure of the strength of a particular decay transition.

The Fermi transition strength is determined by the square of the nuclear matrix element, which connects the initial nuclear state |Ψi> to the final nuclear state |Ψf> via the isospin transition operator τ±.

The isospin transition operator τ ± only changes the projection on the Z direction of isospin but not its absolute value Therefore, the Fermi transition follows the decay selection rules: ∆T = 0, ∆J = 0, ∆π = 0 and ∆L = 0, which follows that the isospin, nuclear spin, parity, and orbital angular momentum remain unchanged As a consequence, Fermi decay sometime feeds to the isobaric analogue states (IAS) in proton-rich daughter nuclei.

The Gamow-Teller transition is characterized by the Pauli spin matrix operator~στ ±

Which leads to the following selection rules

• ∆J = 0,±1 : Nuclear spin unchanged or up to one unit changed (but not 0 + → 0 + )

• ∆T = 0, ±1 : Isospin unchanged or up to one unit changed.

• ∆L= 0 : The orbital angular momentum unchanged.

Gamow-Teller transition is more popular across the chart of nuclei than the Fermi transition.

Despite its moniker, the "forbidden transition" exhibits a non-zero likelihood of occurrence and can prevail over permissible transitions that may be suppressed by selection rules The forbiddenness of these transitions is dictated by the total angular momentum of the beta particle and neutrino (L total), with L total values of 1, 2, and 3 corresponding to the first, second, and third forbidden decays Unlike allowed transitions, the transition strength of forbidden transitions is calculated using distinct transition matrix forms and statistical gross theory.

Table 1.1 summarized the categorization of β decay transition based on the forbiddenness The distribution of log(f t)values, shown in Fig 1.7, demonstrates that it is not trivial to distinguish the forbidden and allowed transition due to a large overlap in their log(f t)distributions.

The equation 1.24 allows one to determine the f t value, a representative value of β decay transition The physical interpretation of this quantity can be inferred from

Table 1.1: Classification of β decay and selection rules in orbital angular momentum L, the change in nuclear momentum∆land the parity

First forbidden 1 0,1 yes 6-10 First forbidden unique 1 2 yes 8-10 Second forbidden 2 1,2 no 10-13 Second forbidden unique 2 3 no ≈13 the Fermi theory ofβ decay, in whichf value is given by a phase-space integral called Fermi integral f(Z 0 , E e max ) = 1 m 5 e c 7 Z p max

Figure 1.7: Distribution of the experimentallog(f t) values for supper allowed, allowed (a) and forbidden (b) transitions Image adapted from

Where p is the momentum of the emitted electron (or positron), Ee is the electron energy, E e max = Q β −E f is the maximum energy of the electron (or positron), which is a subtraction ofQ β value and the energy level of the final state in daughter nucleus.

The Fermi integral is taken over all the possible excitation energies in daughter nucleus with the correction factor F(Z 0 , p)for the Coulomb interaction between the emitted β particle and the daughter nucleus F(Z 0 , p)is referred to as Fermi function and can be calculated numerically and tabulated in [50] The measurement of theβ decay half-life,together with the calculation of the Fermi integralf allow one to derive thef t-value, or often its logarithmic value (logf t), which purely depend on the nuclear matrix element that connects the parent and daughter nuclear wave functions.

In β decay of neutron-rich nuclei, Gamow-Teller allowed transition is the dominant one, therefore the total decay constant, according to Equation1.24 is given as λ= ln(2) T 1/2 =X f m 5 e c 4 2π 3 ¯h 7 G 2 A B GT f(Z 0 , Q β −E f ) (1.28)

Where f(Z 0 , Q β −E f ) can be determined from Equation 1.27 Equation 1.28 can be rearranged into a shorten formulation

Where S(β)E f is called β strength function [60] This function is extended to account for not only GT transition but also forbidden transition And the Equation 1.29is an integration over all the final states in the daughter nucleus that are populated through these two transitions The population of the final states in the nucleus in β decay is illustrated in Fig 1.8.

Figure 1.8: Illustration of aβ decay process, followed by the emission of one or two neutron The level structure in daughter nuclei is arbitrary.

Figure 1.8 also indicates another decay mode accompanied with β decay in very neutron-rich nuclei This decay mode called β-delayed neutron emission that occurs when the neutron separation energy (S 1n ,S 2n S xn ) in daughter nuclei is smaller than the Q β value Such a decay process is as follow

Beta decay in neutron-rich nuclei often results in the spontaneous emission of neutrons due to the dominance of strong interactions over electromagnetic decay This occurs when the decay process populates excited states above the neutron separation energy, leading to beta-delayed neutron emission (βxn) The probability of βxn emission is determined by the location of the x-neutrons separation energy (S xn ).

Experimental studies on exotic nuclei produced by radioactive isotopes beam factories are among frontier areas of modern nuclear physics, which lead to discoveries of new phenomena in atomic nuclei and unprecedented development of nuclear theories, in an attempt to explain experimental observations In particular, the doubly magic regions far from stability are of interest in nuclear structure studies because they can provide unique benchmarks for the shell model, from the simple independent particle picture to the more sophisticated multi-particle picture Recently, nuclear physicists have at- tempted to perform experimental studies on the neutron-rich nuclei around the region south-east of doubly magic nucleus 132 Sn, the heaviest double-magic nuclei that are experimentally accessible, using both ISOL and in-flight facilities However, only limited experimental information has been obtained (Section 1.2.1) Most of the experimental data in this region were obtained using β-decay spectroscopy β-decay and γ-decay are among comprehensive tools to access nuclear excitation levels and study structure of nuclei in this region (Sections 1.3, 1.4) The β decay properties such as β-decay half-lives and β-delayed neutron emission probabilities are sensitive to the excitation structure within the Q β windows Therefore, these observables can be first means to access nuclear structure information and provide important inputs to improve the theoretical models Furthermore, β-decay properties of nuclei around the neutron magic numbers are among important nuclear physics data for the r-process, as those nuclei are responsible for matter accumulation during the nucleosynthesis, forming the r-process abundance peaks The β-delayed neutron emission probabilities of nuclei south-east of 132 Sn are expected to have large impacts on final r-processes abundance according to the recent r-process sensitivity study assuming various astrophysical scenarios (Sec- tion 1.4.3) Various experimental techniques can be used to measure the β-delayed neutron emission probabilities The direct technique that involves the construction of neutron counter arrays is a more popular one.

Based on discussions in this chapter, the primary objective of the present thesis is to perform experimental studies on the nuclear structure of the neutron-rich isotopes in the vicinity of classical doubly-magic nuclide 132 Sn: 129-131 Ag, 130-133 Cd, 131-135 In and

134-138Sn via β-delayed neutron measurements The second objective of the present thesis is to measure isomeric states of the nuclei in this region.

The production of neutron-rich nuclei around the neutron number N region was conducted at the Radioactive Isotope Beam Factory (RIBF), a state-of-the-art facility comprising 5 cyclotron and 1 Linac accelerators Various experimental devices harness the primary beam from these accelerators to explore the properties of exotic nuclei These devices include BigRIPS, RIPS, GARIS, SAMURAI, Rare-RI Ring, and SHARAQ, each dedicated to different beam-lines and research objectives.

OEDO, Biology Beamline, Material Beamline, CRIB, KISS To accelerate the primary

238U beam used in this work, the 5-stages acceleration scheme involving 5 accelerators was used.

Figure 2.1 gives a schematic overview of the experimental setup in this work, starting from the entrance of the Superconducting Ring Cyclotron (SRC) accelerator The primary beam exiting the SRC was transported to a thick production target made by Beryllium, a low Z material having large production cross-section of neutron-rich fragments via abrasion-fission reaction The production fragments, having large angular and momentum spread due to the use of the thick target, were transported to the Big RIKEN Projectile Fragment Separator (BigRIPS) Thanks to the large acceptance design of the BigRIPS, a large amount of incoming secondary ions from the target was accepted and transported through a tandem (or 2 stages) separator Iden- tification of the fragments was carried out in the second stage of the BigRIPS after the focal plane F3 by using beam-line detectors such as plastic scintillator, ParallelPlate Avalanche Counter (PPAC) and ionization chamber (IC) The identified cocktail beam was then transported to the decay station located at last focal plane F11, where the AIDA detector (Advanced Implantation Detector Array), an active stopper of 6 double-sided silicon-strip detectors (DSSDs) was placed at the center position to stop and measure subsequent beta-decays of implanted ions The implant-associated and β-delayed processes that emit gamma-rays and neutrons were measured by the High purity-germanium (HP(Ge)) Clover detectors and neutron counters surrounding the active stopper Detail drawing of the experimental setup at the F11 focal plane is given in Fig 2.2.

The primary Uranium beam was initially produced by a SuperConducting ElectronCyclotron Resonance (SC-ECR) [64,181] Uranium material was ejected from a water- cooled metallic rod by the sputtering method and ionized into a plasma state inside the

Figure 2.1: Schematic overview of the experimental setup The secondary beam produced by production target were separated and identified using BigRIPS instruments such as dipole magnets D1-D8 forBρ selection, quadrupole magnets to focus the beam at the focal planes F1- F11, where beam-line detectors such as Parallel Plate Avalanche Counter (PPAC), MUlti-Sampling Ionization Chamber (MUSIC) are placed The BRIKEN setup comprising neutron and beta counting systems is located at the F11 focal plane.

Figure 2.2: Schematic view of the experimental setup at the F11 focal plane Light particles (proton, deuterium, triton ) and background neutrons coming with beam were suppressed by a lead wall and a wall of polyethylene plus cadmium absorber The RI beam was slowed down by the aluminum degraders, the plastic and∆E silicon detectors before entering the AIDA DSSD stack Details explanation on the detectors system can be found in the text (Courtesy from Dr Iris Dillmann, a collaborator of the present experiment)

The 28 GHz microwave's RF electromagnetic field extracted uranium ions optimized for high charge states These ions were accelerated through a multi-stage cascade involving RILAC and four cyclotrons (RRC, fRC, IRC, SRC) Charge strippers utilizing He gas and graphite carbon were strategically positioned after RRC and fRC to strip Uranium ions to charge state 92+ prior to final acceleration at SRC The resulting fully-stripped Uranium beam, possessing a kinetic energy of 345 MeV/u (approximately 70% of the speed of light), was transported to the experimental area for further studies.

Figure 2.3: Schematic view of the acceleration of 238 U beam at the

RIBF accelerator complex Image source: Ref [136]

2.1.2 Production and separation of secondary beam

The 345 MeV/u 238 U beam from the SRC accelerator impinged on a 4 mm Beryllium target at the entrance of the BigRIPS spectrometer, the F0 focal plane The collision of energetic U beam on a low-Z Be target induced in-flight abrasion-fission reactions, resulting in two fragments of neutron-rich nuclei having a similar proton-to-neutron ratio as of the primary beam The use of heavy beam impinged on a light target allows for the extraction of reaction fragments in a forward angle, although the angular and momentum spread is typically large (dp/p≈10%and 100msr, respectively) due to the use of the thick target The BigRIPS spectrometer was designed to compensate for such effect by introducing a large entrance aperture and superconducting quadrupole magnet, which has a momentum acceptance of 6% and an angular acceptance of 80 msr [87].

In the BigRIPS spectrometer, the two stages separation scheme allows separation of various ion species according to their mass-to-charge ratio and charge state [86] As shown in Fig.2.4, the first stage of ion separation features two dipole magnets D1 andD2 The differing bending radiusρof ions through the dipole magnets under a uniform magnetic field B provides spatial separation depending on their mass-to-charge ratio

A Q The following equation describes the relation between mass-to-charge ratio (A/Q) and the so-called magnetic rigidity (Bρ) value

Where c is the speed of light,m0is the mass unit andβis the ion velocity According to this equation, the selection of ion species with the desired range Bρ value can be realized by tuning the magnetic field B and the X-axis slits that limit the bending radius ρ Further separation of ion species with the same A/Q value but different Z number was realized by placing a wedge-shape aluminum degrader in between D1 and D2 The energy loss at the degrader, which is proportional to the Z 2 , further deflects ions species with different atomic number Z after the D2 magnet This method of separation is known as Bρ−∆E −Bρ method In the second stage of the tandem separation scheme, D3 and D4 dipole provides further A/Q selection for purification of the beam.

2.1.3 Beam-line Detectors for Particle identification

In parallel with the separation of a cocktail beam usingBρ−∆E−Bρmethod, several detectors were placed along the beamline of BigRIPS and Zero-degree spectrometer for identification of fragments of interested Ionizing chambers, plastic scintillators, and position-sensitive detectors provided information on the atomic charge, the time- of-flight, and the position/trajectory, respectively Combining such information, each ion in the cocktail beam can be identified on an event-by-event basis.

The schematic view of BigRIPS and Zero-degree spectrometer with the locations of beamline detectors is shown in Fig 2.4.

Plastic scintillators (Saint-Gobain BC-420) were employed to measure the time-of-flight (TOF) of particles within the BigRIPS and Zero-degree spectrometers, allowing for the estimation of mass-to-charge ratios Detectors at focal points F3, F7, and F11 measured TOF from F3 to F7 in BigRIPS and from F7 to F11 in the Zero-degree spectrometer.

With active areas measuring 100×100mm2 and a thickness of 0.2mm, F3 and F7 plastics enhance TOF measurements' timing resolution due to their thinness Conversely, F11 plastic employs a thicker design (1mm) to optimize its detection capabilities for light particles, while maintaining an active area of 100×100mm2.

When heavy ions parsing through the plastic material, their deposited energy is released in a form of photons, which were then converted into electrical signals by using two photomultipliers (PMTs) The intrinsic properties of the organic scintillation materials allow for a precise timing measurement, of the order of picoseconds to nanoseconds precision Besides, usage of two photomultipliers helps to reduce the noise and unwanted event by applying coincidence conditions between two PMTs A comparison between signals amplitudes of two PMTs can also be used to extract the transverse position information.

Parallel plate avalanche counters (PPAC)

Wedge degrader Beam from SRC

D8 Beam delivered to BRIKEN setup

Zero-degree spectrometer: Beam transport, additional particle identification Production target

Figure 2.4: Schematic figure of the BigRIPS and Zero-degree spectrometers and associated beam-line detectors.

The Bρ values of the fragments after the magnetic analyzer (dipole magnet) can be measured precisely by tracking their trajectories using a position-sensitive detector.

In the present experiment, parallel plate avalanche counters with the capability of two-dimensional position measurement were used The exploded view of a PPAC used in the present experiment is shown in Fig.2.5a Basic principle of the PPAC is demonstrated in Fig.2.5b Incident particles ionize a gas between two parallel electrodes (cathode and anode) Under a uniform electric field applied between electrodes, an avalanche of electrons produces fast cathode signals For position determination, the detector was designed with one anode and two stripped cathodes in the X (horizontal) and Y (vertical) dimension The cathode strips were uniformly fabricated by vacuum deposition of 150 thick Al material on a thin polyester film The strip pitch is 2.4 mm and the spacing between the strips is 0.15 mm The active volume of the PPACs used in the present experiment is 240×150mm 2 and the gap between electrodes was 4.3 mm

To reduce the number of readout channels for both X and Y cathodes, the strip signals are fed into a chain of delay-lines connecting between the strips The delayed signal is readout on both sides of the delay-line chain The position information is obtained from the time difference between signals from two readout channels, where the reference time is from the anode signal For this time measurement, analog signals were fed to the constant fraction discriminator (CFD) to obtain digital timing signals which are amplitude-independent These signals were then read by a Time-to-Digital converter (TDC) In an optimum condition, the detection efficiency as large as 99 %, the position resolution of 0.9 mm and timing resolutions of 1.2 ns can be achieved [88].

Multi-sampling ionization chamber (MUSIC)

Figure 2.5: a) An exploded view of a delay line PPAC b) Principle of avalanche Image source: Ref [89]

The Multi-sampling Ionization Chambers (MUSIC) employed in this study, located at the F7 and F11 focal planes, measured energy loss to determine the atomic number of heavy ions Designed to reduce dead-time, the MUSIC chamber features a parallel stack of 24 plate ionization chambers with tilted anode and cathode plates to minimize recombination effects The chamber was contained in an aluminum vessel filled with a 90% argon and 10% methane gas mixture, ensuring high purity (>99%).

) Two 50 àm thick Kapton sheets were used as the entrance and exit windows of the MUSIC chamber The area of the entrance/exit windows is about150×150 mm 2

The energy loss of ions across the MUSIC chamber is taken as a geometric mean of signals from the anodes, which collect electrons liberated from the interaction of charged particles with gas molecules.

The transported ions, separated and identified by the BigRIPS spectrometer, were implanted into the active stopper AIDA (Advanced Implantation Detector Array) at the last focal plane F11 Unlike passive stoppers, AIDA serves the dual purpose of stopping the ion beam and detecting both the ions and their subsequent β decays.

Figure 2.6: An cross-sectional view of a MUSIC chamber Image adapted from Ref [80]

The AIDA detector is composed of six double-sided silicon strip detectors (DSSDs) Developed at the UK's Science and Technology Facilities Council and the University of Edinburgh, the detector utilizes advanced DSSD and ASIC technologies Its compact instrumentation density allows for high detector segmentation, reducing background interference when correlating ions with β decays This is particularly beneficial when dealing with high implantation rates, as it minimizes the implantation rate per pixel.

The DSSD of AIDA is of n-type (i.e bulk volume of DSSD is made from n-type silicon with extra electrons by doping), which is segmented in one dimension (called p-side or front side) by p + type silicon strip in one side of the n-type silicon bulk forming a p + n junction, whereas segmentation in another dimension (called n-side or backside) is provided by n + strips with ohmic contact to the n-Si bulk p + and n + strips are connected to electrodes for applying bias to the detector When detector bias is supplied, the depletion zone expands from the p-n junction towards the backside.

The energy deposit of ionizing particles such asβ and heavy ions induces small current signals in p + and n + strips with a magnitude proportional to the deposited energy.

The conceptual drawing of a DSSD is shown in Fig 2.7a and the technical drawing of the DSSD used in this experiment (Micron semiconductor BB18(DS) 2M/2M [20]) is presented in Fig 2.7b The DSSD has 128 strips along the X-axis and 128 strips along the Y-axis, each with 560 àm pitch (560 àm per strip) covering an active area of 71.63×71.63cm 2

Figure 2.8 shows a picture of six silicon detectors, which were closely packed inside an aluminum enclosure with a section of 10 cm x 10 cm Four long Ti rods attached to the enclosure were used to support the DSSD stack by suspending the PCB (Printed

Figure 2.7: (a) Scheme of a DSSD Image source: Ref [94] (b) Technical drawing of the DSSD used in the present experiment [20].

The Double-Sided Silicon Detector (DSSD) is separated by 1 cm plastic spacers adhered to a titanium rod The aluminum enclosure's beam-facing window is sealed with a thin aluminized Mylar foil This prevents ambient light and environmental interference The foil also transforms the enclosure into a Faraday cage, shielding the system from external electronic noise.

Flat cables with copper shielding that connect the DSSD connectors to the front-end electronics were arranged tightly along with the aluminum enclosures This design was dedicated to compactness, easy mounting, and replacement of the DSSD.

Dual-gain electronics is a common design for readout electronics of an implantation detector since the signal from heavy-ion implantation are several orders of magnitude larger than the β decay signal In the case of AIDA, the dual gain electronics were implemented in ASIC (Application-Specific Integration Circuit) module, where DSSD signals are split into the low and high energy branches, which sensitive to the energy range of 0-20 MeV and 0.1-20 GeV, respectively A major advance in AIDA ASIC is the Diode and CMOS switching circuit that controls the flow of the DSSD signal to a low or high gain branch The design of the switching circuit minimizes the overload recovery time originated from heavy-ion induced signals The design of an AIDA ASIC channel is depicted in Fig 2.9 The low energy range branch is equipped with a high gain preamplifier with a feedback capacitor of about 1 pF and a feedback stabilization circuit The processed signal from the preamplifier is fed into a shaper with variable shaping time (from 0.5 to 5 às) In this experiment, an optimum value of 3.2às of shaping time was chosen to suppress the high-frequency noise The signal is then amplified by a slow amplifier with controllable gain before inputting to the multiplexer to be combined with signals from other channels and form an analog output signal The timing information of the signal is recorded by both slow and fast discriminators, having two different threshold settings The fast discriminator input is taken directly from the preamplifier, while the amplified signal after the slow amplifier is fed into the slow

Figure 2.8: Picture of the DSSD stack, its support structures and cabling discriminator Owning the fast-rising edge of the raw input signal after preamplifier, fast discriminator provides good timing resolution compared with the slow discriminator The preamplifier, shaper and fast discriminator of high energy range branch are similar to those of low energy range branches, except that the design of the preamplifier is optimized for 1 nF feedback capacitor.

The AIDA data acquisition system processed the output signals from the ASIC module using the 64 channels Front End Electronics card (so-called FEE64) The FEE64 card, as illustrated in Fig.2.10, features the 16-bit 200 kSPS waveform sampling flash Analogue to Digital converters (ADC) model AD976A and the sliding scale ADCs (16 bits) The digitized data from the ADCs and discriminators is processed with the Xilinx Virtex 4FX FPGA chip This chip also provides functionality for controlling the ASIC and recording signal time-stamp A computer processor running a LINUX operating system, which integrated into the FEE64 card, controls the FPGA, acquires processed data from FPGA, buffers, and transfers the data to the Gigabit ethernet output.

Independent self-contained DAQ systems implemented in 24 FEE64 cards operate in parallel to record the data from six DSSDs detectors with 1536 read-out channels.

The FEE64 cards are synchronized using the digitized time-stamp reference module called MACB [12], which is design-compatible with the DAQ synchronization standard developed by CERN collaborators under the White Rabbit project [144] SeveralMACB modules are linked and a master MACB module is responsible to distribute a 50 Mhz clock as well as the correlation trigger signals to other slave MACB modules The purpose of the correlation signal is to monitor the synchronization betweenFEE64 cards The signals from each MACB module are sent to the time-stamping unit in each FEE64 card to record the timing information of crossing-threshold signals from

Figure 2.9: Schematic diagram of an AIDA ASIC channel Image source: Ref [12]

Figure 2.10: Conceptual design of the AIDA FEE card Image source:

DSSDs In the present experiment, a MACB unit was employed as a master clock to distribute clock signals to other independent DAQ systems of the BRIKEN 3 He array and BigRIPS spectrometer.

The recorded data from FEE64 cards was transferred to the main DAQ computer where the MIDAS (Multi-Instance Data Acquisition System) DAQ software [131] is installed This software was built around the use of Web technologies with a graphical interface as shown in Fig 2.11 The MIDAS DAQ software combined the recorded data including ADC output, time-stamp, waveform and channel information from all FEE64 cards into a "Merger" program This contains specially designed subroutines to receive the data from FEE64 cards through Gigabit Ethernet connection and sort the data in time order using the time-stamp information The sorted data was then parsed to a Tape server, which manages on-line monitoring and off-line data recording using shared memory buffers Other features of MIDAS software include controlling the parameters of the ASIC and the FEE64 cards as well as monitoring of the data recorded in the FEE64 card.

For the present experiment, the waveform information has been disabled to reduce the data size By disabling the waveform information makes it more difficult to debug the system since the shape of the signals can be monitored with waveform information.

However, since only one electronics setting is required throughout the experiment, the use of waveform information is not necessary Eventually, the data stream from the Tape server contains only the time-stamp, ADC output, and channel identification.

Figure 2.11: Front page of the MIDAS data acquisition software

The BRIKEN neutron detector array surrounds axially the active stopper AIDA to detect the delayed neutron originated from the β decay of the implanted RIs With experiences gained from previous experiments at GSI (Germany) [28], JYFL (Finland) [9], ORNL (USA) [53] and NSCL-MSU (USA) [122], the BRIKEN detector was built with the aims to increase the neutron detection efficiency to the level that has never been achieved before and to exploit the high-intensity beam available at RIBF, thus improve the statistics of measuredβ-delayed neutrons emitted from most neutron-rich nuclei of which production yields are limited.

The 3 He proportional counters were used in this experiment for neutron detection The counter operates in the proportional mode and indirectly detect neutrons via charged particles produced by the neutron-induced reaction The principle of neutron detection for such a counter is based on a large cross-section for neutron-induced reaction with

3He, as shown in Fig 2.12 as a function of neutron energy The reaction products, following the reaction presented in equation 2.3, are tritium and proton with a total kinetic energy of 765 keV. n+ 3 He→ 3 H+ 1 H+ 765 keV (2.3)

Figure 2.12: Reaction cross section of 3 He(n,p) reaction as a function of neutron energy [36]

The deposited energy of reaction products depends on the location of the reaction in the 3 He tube If a reaction occurs near the wall of the 3 He tube, the deposited energy is a part of the total kinetic energy since the remaining energy can be absorbed outside in the wall or outside This represents a so-call wall effect and emerges in the energy spectrum as a long plateau region at low energies with two edges at 191 keV and 574 keV, which related to the tritium and proton, respectively (see Fig 2.13) In case that the kinetic energy of tritium and proton are fully absorbed in the counter, the deposited energy is equal to the total kinetic energy of 765 keV that corresponds to the full energy peak in Fig 2.13.

Figure 2.13: Integrated neutron pulse height spectrum obtained with

BRIKEN neutron detector for all runs in 130 Ag setting

The 3 He counter is more sensitive to the thermal neutron as evidence from the reaction cross-section shown in Fig 2.12 However, in the measurement of β-delayed neutrons emitters at the very neutron-rich region, higher energy neutrons up to the order of MeV are emitted Therefore, neutrons need to be moderated before being detected by the 3 He counter by an efficient moderation material In the present experiment, a high-density polyethylene (HDPE) matrix was used as the moderator.

Fig 2.14 illustrates the moderation process of neutrons in a 3 He-based detectors with HDPE moderator The figure is taken from a GEANT4 simulation model Details about the simulation will be described in Sec 2.3.2.

2.3.2 Design of the BRIKEN neutron detectorThe experimental determination of the Pn values requires coincidence measurement of neutrons with the β decay of radioactive isotopes For β-delayed single neutron

GEANT4 simulation models can visually track neutron behaviors in 3He counters embedded within an HDPE moderator The slowing down of neutrons in the moderator and their subsequent capture by the counters are depicted Equations such as P 1n = N β /N n are employed to calculate the P 1n value based on the number of detected beta decay (N β ) and neutron (N n ) in coincidence.

P 1n = ¯nNn ¯ β N β (2.4) where ¯ β and ¯n is the average β and neutron detection efficiency, which is, in general, neutron-energy-dependent Moreover, for the measurements of neutron-richβ- delayed neutron emitters, one expects an increased possibility of high energyβ delayed neutrons as a consequence of a widening Q βn window To compensate for the effect of neutron energy on the detection efficiency, the design goal of the BRIKEN neutron detector is to achieve maximum and constant neutron detection efficiency over a wide range of neutron energy by optimizing the distribution of 3 He counters inside the HPDE moderator The design of the BRIKEN neutron detector is complicated by numbers of available 3 He counters, which are of different size and gas pressure Such 3 He counters were contributed by 5 institutions including ORNL in the USA, RIKEN in Japan, UPC in Spain, GSI in Germany and JINR in Russia The available 3 He is listed in Table2.1.

The design of the BRIKEN neutron detector makes use of GEAN T4 program to select an optimum arrangement of 3 He counters in the moderator A general approach for such design, outlined in Ref [166] based on optimization of two parameters of merit: the average neutron detection efficiencyη(E max )and the flatness factor up to a given maximum energy limit E max , as a function of a reduced number of geometrical variables The flatness factorF(E max )is the ratio between the maximum and minimum detection efficiency Those parameters were obtained by extensive MC simulations varying a set of geometrical variables to find an optimum set of parameters of merit.

Table 2.1: Lists of available 3 He counters and their dimensions

Owner Pressure Diameter Length Number of and type (atm) (inch/cm) (cm) tubes

Neutron density distributions, weighted by neutron capture cross-sections, were examined to optimize detection efficiency in a moderator Simulations revealed that dense regions enhance efficiency, making a closely packed configuration favorable However, this setup hinders uniform efficiency across energy ranges A square distribution of weighted neutron density emerged, highlighting the potential advantage of a square arrangement of 3 He detection tubes over a ring arrangement.

Based on the aforementioned approach, several possible configurations have been proposed before the installation of the BRIKEN detector, which is categorized into the hybrid and compact setup The only difference between the two setups is the implementation of two large volume germanium detectors (clovers) for the hybrid setup.

Two possible compact configurations, proposed by the author of the present thesis, are displayed in Fig 2.16 Two geometrical parameters, namely the distance from the center of the first group of tubes next to the beam hole and the separation parameter were selected for the optimization procedure The results of the optimization achieved a rather flat and high neutron detection efficiency of over a neutron energy range up to 5 MeV with only 136 3 He tubes, as can be seen in Fig 2.16.

The flexibility of the BRIKEN setup to switch between hybrid and compact configurations is also an optional requirement This can be achieved by removing the HP(Ge) clover detector and filling up space with HDPE plugs with holes, allowing for additional

3He tubes to be plugged in One of these designs, proposed by authors in Ref [166],has been chosen as the final design of the BRIKEN neutron detector In hybrid mode,this setup employed 148 3 He tubes and two clover detectors with a resolution of 1% at1.33 MeV, whereas 166 3 He tubes are used for the compact mode after transforming from the hybrid mode For the single β-delayed neutron with energy less than 1 MeV,the average neutron detection efficiency estimated from GEANT4 simulation in the hybrid and compact mode is 68.6% and 75.8 %, respectively [166] Fig 2.17 shows the

Figure 2.15: An axial projection (beam view) of the neutron density distribution, weighted on the neutron capture cross-section of 3 He

Figure 2.16: Two proposed compact configurations of 3 He tubes arrangement in the HDPE moderator Left panel figures represent the geometrical distribution The corresponding efficiency curves for each configuration are shown on the right panel Each color represents a different type of the 3 He listed in 2.1 The blue square hole at the center position represents the insertion hole for the active stopper AIDA. neutron response and the distribution of the 3 He tubes in the final design.

Nuclei of interest produced by in-flight fission are unstable against the β decay and may exist in a meta-stable form (isomer) with a relatively short half-life in the order of ns to ms Under such conditions,γ-rays may emit around the implanted position in AIDA detector, following theβ-decay or de-excitation from the isomeric states of such radioactive nuclei In the present experiment, γ-rays were measured by two HP(Ge) Clover-type detectors installed from two sides of the stack of AIDA DSSD detector in the plane perpendicular to the beam Each Clover detector is segmented into 4 HP(Ge) crystals arranged in a clover shape The four crystals have a diameter of 50 mm and a length of around 80 mm They are assembled at 10 mm from the front face inside an Aluminum closure with a section of10.1cm×10.1cm The crystals, cryogenic structure, and preamplifiers were from the CLARION array of Oak Ridge National Laboratory [52] The high voltage of typically 3500 V was provided by the versatile high-voltage system MPOD from Wiener with ISEG HV cards [176], which were also used to supply high voltage for 3 He tubes and auxiliary detectors Signals from the preamplifier installed closed to the HP(Ge) crystal were directly sent to the digitizer channels of the previously described Gasific DAQ system to obtain time and energy information.

In addition to the main detectors measuring β, neutrons, γ emitted from the decay of implanted radioactive isotopes, several auxiliary detectors were installed in theBRIKEN setup to detect unwanted events such as light particles (including neutrons) traveling with the beam A plastic scintillation detector with a thickness of 1 mm was installed at the F11 focal plane (F11 plastic) in front of the DSSD stack to detect the heavy ions and other unwanted products punching through Another 10 mm thick plastic scintillator (called AIDA plastic) is positioned at the downstream of the AIDADSSD stack, designed to veto the light particles traveling with beam, which deposit energy in the DSSD stack Also, a thin large area Si detector was added in between F11 plastic and the DSSD stack This ∆E detector with better energy resolution than theAIDA DSSD stack provides the energy loss information (∆E) of ions before entering the DSSD stack This information can be used for confirmation of the atomic number of the ions just before entering the DSSD stack, since nuclear reaction may occur in the Aluminium degrader that change the atomic number Z of the ions.

In this chapter, analysis methods applied to the experimental data are presented The identification of RIs in the BigRIPS spectrometer, the analysis of active stopper AIDA,calibration of detector and data merging method are followed by the analytical method to obtain the β decay half-lives and β delayed neutron emission probabilities (For example Ref [134]) The computer scripts for analyzing the data are stored at [25].

The present experiment aims at measuringβ decay and isomeric decay of a wide range of nuclei species around mass A = 130 Therefore, the BigRIPS spectrometer was tuned for the large acceptance mode that accepted a variety of ion species around the mass number A = 130 with a large range of Bρ values Before the implantation of such a cocktail beam into the BRIKEN setup at the F11 focal plane, event-by- event identification of nuclei of interested was necessary for the subsequent analysis.

The particle identification (PID) provided the information on atomic number Z and the mass-to-charge ratio A/Q of the fragments using a so-called ∆E −Bρ −T OF method utilizing several beamline detectors as described in Section 2.1 The method is presented below.

Velocity measurement using Time-of-flightThe speed of each ionβ =v/c, the first piece of information to determine the PID parameters (Z and A/Q), was deduced by the measurement of time-of-flight (TOF) using two plastic scintillators arranged in a far path length L: β = L c×T OF (3.1)

In BigRIPS and Zero-degree spectrometers, two pairs of plastics scintillators F3-F7 and F7-F11 were used The flight path of F3-F7 plastics was46.96m.

Determination of atomic number ZThe information on atomic number Z was obtained from the measurement of energy loss using ionization chamber (see Section.

2.1) In the present experiment, either MUSIC ionization chambers at F7 and F11 can be used In the present analysis, the F7 MUSIC chamber was used, owning to its good stability and sufficient energy resolution compared with F11 MUSIC (F7 MUSIC was placed inside a vaccum chamber while F11 MUSIC was not) The energy loss in the MUSIC chamber can be well described by the Bethe-Bloch formula:

Where dx is the thickness of counter gas,e is the atomic charge,m e is the electron mass, N a is the Avogadro number ρ is the density, Z m is the atomic number and A m is the mass number of the counter gas, respectively I is the design value of the MUSIC chamber representing the average excitation energy and ionization potential of the counter gas material.

After combining the constants in Eq 3.2 one gets.

Where A 1 and A 2 are parameters deduced from experimental calibration using a primary beam with known Z.

Determination of mass-to-charge ratio The mass-to-charge ratio was determined using combined information of the magnetic rigidityBρand velocityβas follows

Here γ is the relativistic velocity γ = 1/p

1−β 2 , c is the speed of light, m u 931.494 MeV is the atomic mass unit.

Bρ 0 values at center of the magnetic dipoles were deduced using Nuclear Magnetic Resonance (NMR) measurements, while the extractBρvalue for each ion with different trajectory along a dipole magnet was determined from a trajectory measurement using a pair of PPAC detectors (see Sec 2.1) located at the exit of the dipole magnet This measurement was combined with the transmission optical matrices of the BigRIPS dipole magnet to give the momentum dispersion δ, and thus a precise Bρ value is determined

An event by event particle identification (PID) of the implanted ion was provided by the BigRIPS team Fig 3.1 shows the particle identification (PID) plot for the present experiment In this PID plot, thanks to the high A/Q resolution, the fully strips ions and several hydrogen-like charge states contamination were visible.

3.2.1 Energy calibration of AIDA detector

The energy calibration of the AIDA detector is an important step and should be carried out at the beginning of the analysis In the case of a highly segmented implantation detector with dual-gain preamplifier like AIDA, the calibration should be done for both high and low energy range for a large number of strips (1536 channels in total) For

Figure 3.1 presents a particle identification plot For low energy ranges, energy calibration is necessary for energy determination and noise suppression For high energy ranges, calibration helps identify implantation positions, particularly when energetic heavy ions produce signals in multiple DSSD pixels.

The absolute energy calibration of DSSDs detector (both high and low energy range) is referred to as a set of calibration coefficients for each strip (channel) that translates the measured ADC amplitude to the unit of energy By analyzing the energy spectra collected for all the channels of the detector using calibration source with known energy, such as α or conversion electron sources, these sets of coefficients can be obtained.

However, in the present experiment, due to the design of the support structure, the enclosure and cabling of the DSSDs stack, also due to a large number of the strip, it is not possible to perform absolute calibration using calibration sources To tackle this problem, two methods have been employed in the present experiment to calibrate the low energy and high energy branches in AIDA.

For the high energy branch, the so-called "automatic intrinsic calibration" method was used The calibration data, in this case, was taken directly from the experimental data of heavy ions The idea of this method, which was described in Ref [135], relied on the mutual energy consistency between p-side and n-side strip When a heavy-ion deposits energy within a crossing area between n and p-side strip, which is referred to a pixel (i,j), the same amount of charge is assumed to be collected for both sides.

This charge creates signals in both n and p-side strips with corresponding amplitude A n and A p corresponding to the same amount of deposit energy.

E p =s p A p +o p , E n =s n A n +o n , E p =E n (3.6) where s p , s n is the slope of p-side and n-side strip, and o p , o n is the offset of the p-side and n-side strip, respectively From this equation, it is clear that the signal amplitude of p and n side strips for the event that deposit in single-pixel are related as a linear function

A p =O pn +S pn A n , S pn = s n s p , O pn = on−op s p (3.7) withO pn andS pn being the offset and slope parameters, which were determined for each pixel of the DSSD in the first step of calibration procedure by a least-square fitting to the distribution of p/n side amplitude pairs (A p , A n ) The choice of the least square fitting method is for the sake of simplicity An example of such a fit for measured data is shown in Fig 3.2.

Figure 3.2: A fit of the measured amplitude pairs (Ap, An) from experimental data of a single pixel in an DSSD

In the second step, a set of calibration parameters for all strips can be calculated by minimizing the following equation [135] χ 2 =X p,n

(3.8)Minimization of the χ 2 value is done with the Minuit2Minimizer minimizing algorithm provided in the ROOT package [26].

It is important to note that the unique solution of equation3.8can only be obtained by providing two calibration parameters, either for a p-side or n-side strip Because of this, the method can only provide a precise relative energy matching for all the strip, rather than an absolute energy calibration However, it is sufficient to use this method to obtain the interaction position of heavy ion and reject noise events.

After calibration, it is expected that the energy spectra between channels are well matched To demonstrate this, the calibrated energy of high energy events is plotted in Fig 3.3over the strip number and compare with uncalibrated cases with an assumption of a common gain of 20 GeV/32768 ADC channels that apply for all the strips Without calibration, the channel-by-channel variation of the energy is observed After applying calibration using this method, the energy spectra of all strips are well aligned This confirms that the calibration method works correctly.

Figure 3.3: The energy deposit of single pixel events versus strip number: (a) the uncalibrated n-strips energy assuming E n = 0.61A n , (b) the calibrated n-strips energy, (c) the uncalibrated p-strips, (d) the calibrated p-strips

To correctly identify the decay events, calibration for low energy range in AIDA is a vital step in the analysis It is possible to utilize a similar method as it was applied for the high energy range In this case, the experimental data of β and light particles,which induced signals in the low energy branch, can be used Along with this method,pulser can also be used to inject charges in the first stage of readout electronics, which includes shaping preamplifier and amplifier, for the calibration purpose In the case of AIDA, there is an assumption that the gain introduced by readout electronics for any channel i is a common value of s i = 20M eV /32768ADCchannel because of the feedback capacitances and resistors, which determines the signal amplification, is uniformly fabricated With such an assumption, the energy calibration is straightforward.

The measured energy spectrum with different sets of the pulser amplitude P injected in channeliwas used to determining the "ADC offset"o adci , that is, the ADC channel number at zero energy The corresponding amplitude of the signals is related to the pulser amplitude by following the relation

The ADC offset value was then used to determine the energy offset parameter using the following relation sio adci +oi= 0 (3.10)

A computer subroutine written in C++ was used to perform the fit and calculation of the calibration coefficient automatically One example of the fit is shown in Fig.3.4.

The calibration procedure for pulser data entails determining the peak position in the energy spectrum, which corresponds to the pulser's setting value A computer subroutine identifies this peak position By fitting the peak position against the pulser's setting value, the calibration constant is established This constant enables accurate energy measurements based on the pulser data.

Figure 3.5 exhibits the energy matching between channels after applying the ADC calibration coefficients (s pi , o adci ) to the pulser data The right figure shows the projection on the horizontal axis(all channels) of the left histogram in the logarithmic scale.

Figure 3.5 demonstrates the precision of the calibration, with peak positions aligning seamlessly across channels The parallel bands observed in the left panel of Fig 3.5 highlight this alignment, indicating that the projection of the 2D spectrum along the amplitude axis reveals no misalignment-induced peaks.

A pair of calibration coefficients (s i , o i ) for all channels was then applied to the experimental data In Fig.3.6a, the results of this calibration are evaluated by plotting

Figure 3.5: The calibration data were taken from run RIBF127/R28, R29 The left panel shows a histogram plotting signal amplitude against the channel number The histogram on the right is a projection of the left histogram on all the strips. the disagreement between the calibrated Y and X strips energy over the calibrated X strips energy A direct comparison of the performance of the pulser method with the

The design of AIDA readout system is based on the concept of self-trigger Unlike the conventional triggered readout system where the event structure is retained and defined by an external logic circuit, each strip is readout whenever there is a crossing-threshold signal, regarding as an ADC item, and an event can be defined by the off-line analysis using their time-stamp information The event reconstruction is accomplished by theAIDA sorting software prepared by the author of this thesis This software, developed

Figure 3.17: a) Two dimensional histogram of time versus energy with a fit to the corresponding energy-time matrix obtained by the procedure described in the text b) Two dimensional histogram of time versus energy before applying time slew correction c) Two dimensional histogram of time versus energy after applying time slew correction by the author of the present thesis and available at [11], has been utilized as the main near-line analysis code during the BRIKEN experimental campaigns.

Events in the article are categorized as heavy-ion implantation events or β-like events, requiring timing, position, and energy data extraction from time-stamped data Event definition is based on channel energy threshold, with an event occurring when a pair of n and p-side strip channels with signal amplitude crossing the threshold in a short time period determined by system timing resolution In AIDA FEE systems, timing resolution is influenced by the readout process of ASICS units with multiplexed readout, with each unit handling 16 strips on either the n or p-side of a DSSD.

Therefore, an event is defined as a group of low or high energy ADC items, of which time-stamps are within 2àof each other The geometrical information for each event is stored in a collection of the so-called "cluster", which are defined by a group of fired X strips (X cluster) or Y strips (Y cluster) in any DSSD layer that is next to each other.

Low and high energy cluster is formed by low and high energy ADC items (represented by channels with an ADC value in data-stream), respectively.

An implantation event is defined when there is at least one paired high energy X-Y clusters in any DSSD layer The last DSSD layer (looking from beam direction) with paired X-Y clusters is defined as the implantation layer Also, there is an option to assign the implantation layer that have only Y or X high energy clusters, or a strip with and overflow ADC value in low energy An example of a reconstructed implantation event is illustrated in Fig 3.18, in which heavy-ion punches through first and second DSSD layers and stopped at the third DSSD layer, leaving energy deposit in three DSSD layers and triggers high energy range in both X and Y strips along its track.

DSSD No 3 is the implantation layer as no high-energy ADC items are present in the subsequent DSSD (DSSD No 4) Delta rays induced by the heavy-ion produce low-energy ADC items in neighboring strips along its track in DSSD No 3, as well as in DSSD No 4.

Figure 3.18: An event viewing plot showing fired strips for both low and high energy range in X and Y dimension for six DSSDs, the calibrated energy for both ranges is projected in the colored axis A schematic view of the event is shown in the bellow panel (see explanation in the text)

A β-like event is identified by the presence of at least one low-energy X-Y cluster in a DSSD layer without any high-energy clusters Physically, this type of event corresponds to light particles traversing the BigRIPS spectrometer or β decay of implanted ions In both scenarios, a single paired cluster is expected in each DSSD layer.

However, under the presence of low energy electronics noises, there is a possibility to find multiple paired clusters Such conditions are depicted in Fig 3.19a, from which clusters in a DSSD layer are categorized based on the number of X and Y clusters and shown with the respective percentage of total events One should emphasize more on the event of category B, which accounts for more than half of the total number of events For such an event, the real hit position is presumably assigned to the cluster that has the largest total energy of the X and Y cluster (EX+EY) The reason for this assignment is shown in Fig.3.19b, from which an energy correlation between X and Y clusters is plotted for single paired cluster in category A, which most likely to be free of electronics noise issue, and compared with the same plot for paired clusters that has largest sum energy of X and Y clusters EX+EY and that for all other paired clusters in category B A similar correlation can be clearly seen for the paired cluster in category A and that with largest sum energy in category B, indicating the real hit position, while the other clusters in category B do not show a clear correlation This method to find a real hit position is further checked by comparing the decay curves obtained for clusters in category B, as shown in Fig.3.20 Details about the construction of the decay curves will be described in the Sec 3.5 From this figure, more decay components for clusters with the largest EX+EY were found, which further confirm the effectiveness of this method in removing noise events.

Figure 3.19: (Left four panels: Categorization of low energy events.

Right two panels: Two dimensional histograms showing calibrated energy of X cluster versus calibrated energy of Y cluster for paired-cluster with largest EX+EY (upper panel) and others paired cluster (lower panel) in Category B The inset in upper panel shows similar histogram for a single cluster in Category A.

The energy and timing information of each cluster can be provided from both Y andX strips, called TY and TX, EY and EX Physically the electrons with a continuum energy up to theQ β value, which is expected from the decay of neutron-rich isotopes in the present experiment, travel by a zig-zag track (i.e its direction changed drastically) and deposit energy in one or more strips in X and Y dimension depending on the energy and the path of travel In addition, if the energy deposition takes place in the junction area, inter-strips charge collection may occur resulting in multiple neighboring strips fired Therefore, for the events with energy loss shared between neighboring strips,an addback algorithm need to be applied, where the energy of neighboring strips of a cluster was summed up to derive the total energy The event timing is defined as the earliest time-stamps among all fired strips on both sides This is to cancel the effect of

Figure 3.20: Decay curves for two type of paired clusters in Category

B the 2às channel conversion time.

Position determination of implant and decay events is crucial for subsequent analysis, as it enables the extraction of decay curves with reduced background Typically, the position is inferred from the fired strips in the Y and X dimensions For events spanning multiple strips, a common approach is to calculate the energy-weighted mean position for both implantation and decay events, as outlined in Ref [111]: x β Pm i=nE i x i / Pm.

(3.14) with x i and E i being the position of the i th strips (either X or Y) that fired and the corresponding measured energy The summation runs over all the strips within a cluster.

When applying to find β decay position, this method relies on the fact that the Bragg curve of electrons peaks around the original position To demonstrate this, the interaction of expected β particles from the decay of 130 Cd isotope (measured in the present experiment) in the DSSD detector is modeled by a GEANT4 simulation (Fig.

3.21a and the results are depicted in Fig 3.21b, where a histogram of energy weighted mean position of multi-strips events with respect to the emission position ofβparticles is plotted In this simulation, β particles is emitted isotropically from the center pixels with an energy spectrum that follow the Fermi theory (described in Sec 1.4.1) for an intense allowed transition (with I β = 74.2(67)% [72]) from β decay of 130 Cd g.s (J π = 0) to the 2120 keV state in 130 In (J π = 1−), taking into account a β-decay energy ofQ β = 8350(160)keV [174] (Qb30 keV) According to the histogram shown in Fig 3.21b, most of theβpositions determined by the energy weighted mean method are distributed around 2 mm from the original position (zero value in the histogram) of the β particles.

Although commonly used for analysis of the active stopper in the fast radioactive beam facility [111, 121, 162, 180], the energy weighted-mean method for position determination was found to be less effective when applying to the data from highly

After presenting the calibration and event reconstruction in each DAQ system, a brief introduction about the data processing is now given.

3.4.1 Pre-sorting of the data from individual DAQ system

As the first step of data processing, the ordinary data from three independent DAQ systems in the different binary formats need to be sorted into ROOT-files containing the necessary information for extracting the physical quantity of interests Specific sorting programs have been developed by an individual group responsible for each detector system.

For BigRIPS detector, the raw binary RIDF file produced from the RIBF DAQ system was sorted by using the common analysis tool ANAROOT developed at RIBF The sorting of the BigRIPS data includes decoding of the binary file, calibration of beamline detectors and event reconstruction to derive the A/Q and Z value in the event-per-event basis The ANAROOT software also provides capabilities for further refinement of the reconstructed data, as it was briefly shown before The resulting output ROOT-Files containing the calculated A/Q and Z values for each event with an assigned synchronized time-stamp were then provided.

The BRIKEN detection system's data is sorted within the Gasific DAQ system, with the binary file structured to include three key elements: the geometrical assignment of readout channels for spatial resolution, the synchronized time-stamp for temporal analysis, and the ADC information representing the magnitude of threshold-crossing signals, providing information on the intensity and arrival time of detected particles.

Providing a configuration file containing the mapping and calibration factors for all the readout channels, the data was then reconstructed and stored as a form of ROOT-file, which contains three branches of data for each kind of detector, namely the BRIKEN

3He counters, Clover detectors and auxiliary detectors.

For a completed analysis, the specific information of an event measured by three DAQ systems system need to be combined This is realized by matching the "absolute" time-stamp of the events seen by each DAQ system, thanks to a common clock shared between them AMerger program has been developed for this purpose, where the data is ordered by time before being matched, thanks to the implementation of the C++ multimap library The program are divided into several steps which are shown in Fig.

Since each DAQ system has a certain constant offset of timestamp with respect to the master clock, representing the propagation time of the synchronization clock signal through the cables and time-processing units, the program needs to find the relative offset (∆T S) between DAQ systems before merging the data Such relative offset values between DAQ systems are determined by plotting the correlation histogram of the time-stamp difference An example of such a plot is displayed in Fig.3.21, where a prominent correlation peak was observed from the time difference between F11 plastic signals recorded by the BRIKEN DAQ and the F7 plastic signals from BigRIPS DAQ.

The observation of this correlation peak directly demonstrates the matching between events seen by two DAQ systems and the displacement of the peaks represents the relative time offset value Fig 3.22 is another example of such timing correlation histogram for BRIKEN DAQ and AIDA DAQ After finding the correlation peak, by applying a time gate within the correlation peak to the∆T Sbetween the DAQ systems, the event detected from the system can be associated with another The correlation window is chosen based on the width of the correlation peak, which reflects the timing resolution of each detector and its associated electronics, as well as the physical delayed time of the associated events.

After matching the events based on the time-stamp, the events were categorized into those associated with the implantation of heavy-ion, theβ decay in AIDA and the neutrons detected in BRIKEN detector Three data containers with respective vectors of time-correlated events are used in this step:

• The implant correlated data container contains the implantation events in AIDA recorded by the AIDA DAQ system, together with the calculated Z and A/Q values in BigRIPS spectrometer and the HP(Ge) Clover detector information for checking isomeric γ-rays emitted from implanted isotopes Here a double coincidence between implantation events and γ-rays events was performed In addition, this container has the information from the F11 plastic detector, the

∆E silicon detector and the downstream veto plastic detector, those which are acquired by the BRIKEN DAQ system and sensitive to the heavy-ion.

• In the β-decay correlated data container, the identified low energy β-like events in AIDA and its associated information in F11 plastic, the downstream veto plastics, the HP(Ge) Clover and the BRIKEN neutron detector are stored The use of auxiliary plastics information is necessary for applying veto conditions to reject light particle events, which will be described later, whereas the associated information from Clover detectors is needed for checking theβ-delayedγ-rays At this step, the accompanied delayed neutron emitted from each β decay event is also contained in the associated information from the BRIKEN neutron detector.

The data processing scheme (Figure 3.23) utilizes synchronized timestamps to integrate data from three acquisition systems It begins with the extraction of raw data from the systems Next, the data is synchronized, aligned, and merged Finally, the ROOT-file is created as the output, containing the combined and harmonized data.

Figure 3.24: Distribution of∆TS between F11 plastic signals recorded in BRIKEN DAQ and the F7 plastic signals in BigRIPS DAQ

• In the neutron correlated data container, the identified neutron events detected by the BRIKEN neutron detector are stored together with associated information in the F11 plastic detector and the downstream veto plastics detector The main purpose of associating with those plastic detectors is to veto some beam-related neutron contaminants, mainly from the heavy-ion and light particle-induced reaction.

Each data container can be written into independent ROOT-trees for the purpose of checking the individual type of events or can be used as inputs for the second step of data merging which will be described in Sec 3.5.

A selection of fission fragments is an important step in the analysis to pick up the RI of interest among others and must be carried out before obtaining the decay properties of selected RIs In the present experiment, the BigRIPS spectrometer was running in the large acceptance mode to accept a variety of RIs at the same time Those RIs identified event-by-event in BigRIPS spectrometer with respective Z and A/Q values before being implanted in AIDA detector Therefore, after merging the AIDA and BigRIPS data, the particle identification (PID) plot as a form of a histogram of Z versus A/Q value can be obtained for all implantation events recorded in AIDA detector Such PID plot is drawn in Fig.3.25 By fitting the Z-projected PID plot (Fig.3.25b), an average relative resolutionσ Z /Z of 0.4 % was achieved Similarly, A/Q axis projection gives an average absolute rms A/Q resolution of 0.0014, corresponding to a relative rms A/Q of 0.05% This is sufficient to identify and separate the hydrogen-like contamination with A/Q = A−3 Z−1 (having one electron not fully striped) from the fully-stripped fragments withA/Q= A Z The selection of the implanted RI of interest among others was carried out by an elliptic gate centered at the expected (Z, A/Q) The width of the elliptic gate in the Z direction (vertical) was chosen as±3σ of the average resolution and that in A/Q direction (horizontal) was ±3σ of the average resolution The portion of real events included in this gate according to the Gaussian distribution is estimated to be 99.7% The amount of main contamination from the hydrogen-like peak was estimated by fitting the Y-axis-projected PID plot for a given range of X-axis to a function of superimposed Gaussian peaks, as shown in Fig 3.25c The amount of charge state contamination was estimated to be as low as 1.2% for the nuclei of interest in the present thesis, equivalent to a purity of 99.6 %.

Figure 3.25: A PID plot of Atomic number Z versus Mass-to-charge ratio A/Q (c) and the projection on the A/Q direction (a) of Sn isotope, where projection area is limited between the red lines in panel (c) In panel (a), estimations of the main component of isotopes of interest are shown in red, whereas those of charge state contaminants are shown in green Panel (b) shows a projected histogram on Z direction for all isotopes together with a superimposed Gaussians fit shown in red.

Utilizing the delayed coincidence method, the experiment determined β-decay half-lives This technique involves recording the production time of the radionuclide and the subsequent β-decay time, which are then plotted as a time correlation spectrum (decay curve) The decay curve reflects the exponential decay rate and allows for the extraction of the initial activity of the decaying nucleus By gating on detected neutrons, the decay activity in the neutron emission mode can be obtained, which aids in determining P n values.

The decay curve has, in general, an exponential shape if all events that look like decay is registered after the production of any nucleus This shape is not, however, hold true for the present experiment with complex backgrounds, consisting decay of descendant nuclei in the decay chain, the parasitic events with a constant rate, the other decaying nuclei and the decay of previously produced nuclei The latter two can be greatly reduced by employing highly segmented detectors like AIDA, where the registered events are distributed to many small segments, equivalent to separated measurements in each segment at lower rate In this case, the produced nuclei and subse- quence decay recorded in the segmented detector are associated via spatial correlation.

Depending on the direction and the energy of the emitted electrons, energy deposition may take place in the same or surrounding segment with the produced nuclei.

The association by spatial correlation was applied by gating on the position difference between in x and y direction while constructing the decay curve For each of the observed β decay in time correlation with an implant RI, the position difference in x and y dimension were calculated as: δx x β −x implant δy y β −y implant

By gating on theβ-like events occurring within 2 s after each implanted event, a histogram showing theδx−δy pattern is obtained in Fig.3.26after being subtracted with that obtained for uncorrelatedβ-like events recorded within the same time windows of 2 s before each implant event (backward in time) From this background-subtracted histogram, as shown in Fig 3.26, one observes that the position difference can be as large as 4 pixels distance Therefore, to increase the β detection efficiency it is needed to limit a spatial correlation window on the x-y plane toδx

Tiêu đề	Nuclear Structure Studies of Neutron-Rich Isotopes of 129-131Ag, 130-133Cd, 131-135In And 134-138Sn Via β-Delayed Neutron Measurements Using The Briken Detector System
Tác giả	Vi Ho Phong
Người hướng dẫn	Le Hong Khiem, Prof. Dr., Shunji Nishimura, Dr.
Trường học	VNU University of Science
Chuyên ngành	Nuclear Physics
Thể loại	Doctoral Thesis
Năm xuất bản	2020

Định dạng
Số trang	164
Dung lượng	14,9 MB