STUDY OF THE REACTIONS BETWEEN LIGHT NUCLEI IN THEASTROPHYSICAL ENERGY REGION USING THE PLASMA HALL ACCELERATOR Vyach.M.Bystritsky1, Vit.M.Bystritskii2, L.D.Butakov3, V.V.Gerasimov1, G.
Trang 1STUDY OF THE REACTIONS BETWEEN LIGHT NUCLEI IN THE
ASTROPHYSICAL ENERGY REGION USING THE PLASMA HALL ACCELERATOR
Vyach.M.Bystritsky1, Vit.M.Bystritskii2, L.D.Butakov3, V.V.Gerasimov1, G.N.Dudkin3, A.R Krylov1, B.A.Nechaev3, V.M.Padalko3, S.S.Parzhitskii1 , A.V.Petrov3, N.M.Polkovnikova3,
J.Wozniak4
AGH, University of Science and Technology, Cracow, Poland
Abstract Using the plasma accelerator based on the pulse Hall ion source, the first
measurements of the astrophysical S-factor of the d+d3He + n reaction were performed for deuteron energies 9.1 and 9.9 keV The observed values of the S-factor and effective cross sections ~dd for dd reaction are in agreement with the results obtained by us earlier in the experiments at liner plasma accelerators (in a configuration of both direct and inverse Z-pinch) The preliminary results have confirmed the fact that the proposed technique can be effective to study nuclear reactions between light nuclei in the astrophysical energy region
I Introduction
Interest in studying reactions between light nuclei (pd , dd, d3He and d6Li reactions) in the region
of astrophysical energies 2-12 keV is caused by a possibility of verifying symmetries in strong interactions, determining the contribution to interaction from exchange currents, checking the standard Solar model [1] Research of the given processes in the indicated energy region is rather problematic since intensity of the beams of the accelerated particles produced by classical accelerators are extremely low (I 1012 – 1013 1/s ), and cross sections of nuclear reactions in thes ), and cross sections of nuclear reactions in the astrophysical energy region are extremely small (10-39 - 10-33 сm2) An impetus to the current intensive study of reactions between light nuclei has become the possibility of using for these purposes pulsed high-current plasma accelerators and energy-precise linear ion accelerators of energy 4-100 keV [2-4] Plasma accelerators with the liner plasma formation in the direct and inverse Z-pinch configuration allowed quantitative information on the astrophysical S-factors and effectivecross sections of the pd and dd reactions (pd3He + ; dd3He + n) in the ultralow energy region to be obtained for the first time [2,4] The results obtained for the first time have confirmed the fact that the proposed technique can be effectively used to study nuclear reactions
in the astrophysical energy region It is necessary to note that highly accurate measurement of cross sections of the pd, dd and d3He reactions with the use of the plasma in the Z-pinch configuration is rather problematic The absence of reproducibility of the experimental conditions from "shot" (the act of the accelerator operation) to "shot" caused by the specificity of the work of accelerators of this class imposes certain restrictions on accuracy of measurement of parameters of the investigated processes
This stimulated development of alternative methods for formation of intense charged-particles beams in the ultralow energy region For further research of reactions with light nuclei we developed and built a pulsed ion source with the closed Hall current allowing acceleration of plasma ions H +, D + and 3He + in the energy range 2-12 keV In this work the preliminary results
of measuring the astrophysical S-factor and effective cross sections for the dd reaction in the experiment at the created accelerator
2 Measurement method
Experimental determination of the astrophysical S-factor and effective cross section of the dd reactions is based on measurement of the neutron output and parameterizationof the dependence
of the cross section reaction ~dd on the deuteron collision energy:
Trang 2
0
2
0
exp
) , ( )
(
)
(
x d x E E
e dE E f n
N
N E
S
n t d
n
, (1) ~dd N nexp /s ), and cross sections of nuclear reactions in theN d n t n l~
where exp
n
N is the yield of the detected neutrons, Nd is the number of deuterons hit in the target, Z1 = Z2 = 1 is the deuteron charge, = md is the reduced mass of the colliding particles, nt is the deuteron density of the target, (E) = Z1Z2e2 (µ/s ), and cross sections of nuclear reactions in theE)1/s ), and cross sections of nuclear reactions in the2 , n is the efficiency of the neutron registration, E are the collision energies of deuterons with the target nuclei after passage of a target layer of thickness x , E is the average energy of the deuteron collision, f (E) is the energy distribution of the deuterons hitting the target, l~ is the effective target thickness defined from
n
n
N is the yield of neutrons from the dd reaction in the case
of an the infinitely thick target)
3 Experimental procedure
The experimental setup (Fig.1) includes the plasma accelerator on the basis of the Hall ion source, a solid-state CD2 target from installed in the accelerator chamber, two detectors for detection of 2.5 MeV neutrons, diagnostic equipment for collecting information on parameters of the accelerated-ion flow generation process, an electrostatic multigrid mass-spectrometer of charged particles for measurement of the deuteron energy distribution
The CD2 solid-state target was of the 25 cm2 area Neutrons were detected by two detectors of thermal neutrons, each being an assembly of 10 proportional 3He counters [5] Current of accelerated ions at the output of the Hall source was measured by means of the Rogovsky belt, and the current density in various sections of the beam hitting the target surface was determined with the collimated Faraday cylinders The energy distribution of ions was measured by our electrostatic multigrid mass-spectrometer of the charged particles whose operation was based on the braking potential method
4 Analysis of the results
Figure 2 shows the energy distribution of deuterons measured by the mass-spectrometer during data taking in the experiment on the study of the dd reaction Using the function describing the given energy distributions, the values describing the experimental conditions (Ed =9.10.3 keV,
Ed =9.90.3 keV, FWHM =1.3 keV, Nd (9.1) = (4.10.5)·1014, Nd (9.9) = (7.950.3)·1014 , n t
=(8.000.08)·1022 , n =(1.270.11)10 -2, exp
n
N (9.1)=4 and exp
n
N (9.9) = 12), and formulas (1) and (2) we determined the values of the astrophysical S-factor and the effective dd-reaction cross:
Fig 1 Experimental setup: (1) Hall ion
source plasma accelerator, (2) CD2
deuterium target, (3) electrostatic mass
spectrometer, (4) 3He detector of thermal neutrons
Fig 2 Deuteron energy distribution
S~(4.7) = (31.916.9 3.2) keV b, ~dd(4.3 < Ecoll <5.1) = (3.2 1.7 0.3) 10-31 сm2 ;
Trang 3S~(5.1) = (38.911.7 3.1) keV b, ~dd(4.7 < Ecoll <5.5) = (6.6 2.0 0.5) 10-31 сm2
The first errors here are the statistical errors and the second are the systematical ones
These valuesof theS(Ē ) and ~dd agree within measurementerrorswith the results of the direct and inverse Z-pinch experiments and with the calculations by the model of the interaction of a low-energy deuteron beam with the deuterium-containing solid-state target (see fig 3)
Fig 3 Dependence of the reaction
astrophysical S-factor on the deuteron
collision energy: ●, ○ are the results of the
experiments with the inverse Z-pinch [2]; ■,
are the results of [7] and [6] respectively; □ is
the present work
Fig 4 Dependence of the dd reaction cross section on the deuteron collision energy The curve – calculated dependence obtaining with
S = 53.8 keV·b: ■ – [6]; ●, ○ – are the results
of the experiments with the inverse Z-pinch [2]; □ – is the present work
The experimental results obtained with the plasma Hall accelerator indicate that, the developed technique holds promise for detailed study of reaction mechanisms between light nuclei in the region of ultralow energies
This work was supported by the Russian Foundation for Basic Research, Grant No 06-02-17182 and the grant of Plenipotentiary of Poland in JINR
References
1 A new approach in the experimental studies of nuclear reactions at ultralow energies, V.M.Bystritsky et al., Nucleonika 42 (1997) 775 - 793
2 Measurement of the astrophysical S-factor for dd interaction at ultralow deuteron – collision energies using the inverse Z pinch, V.M Bystritsky , V.V Gerasimov, A.R Krylov et al., Physics of Atomic Nuclei 66 (2003) 1731- 1738
3 First measurement of the d(p,γ))3He cross section down to the soar Gamow peak, C Casella,
H Costantini, A Lemut et al., Nucl Phys A706 (2002) 203 - 216 and references there in
4 Study of the pd reaction at ultralow energies using hydrogen liner plasma V.M Bystritsky , Vit.M Bystritskii, G.N Dudkin, V.V Gerasimov, A.R Krylov, G.A Mesyats, B.A Nechaev, V.M Padalko, S.S Parzhitskii, F.M Pen`kov, N.A Ratakhin, J.Wozniak, Physics
of Atomic Nuclei 68 (2005) 1777- 1786
5 3He detectors in experiments at the powerful pulsed accelerators, V.F.Boreiko, V.M.Bystritsky, V.M Grebenyuk et al., NIM A 490 (2002) 344- 355
6 Low-energy fusion cross sections of D + D and D + 3He reactions, A Krauss, H.W Becker,
H.P Trautvetter et al., Nucl Phys A 465 (1987) 150 - 172
7 Differential cross sections at low energies for 2H(d,p)3H and 2H(d,n)3He, R.E Brown and N
Jarmie, Phys Rev C 41 (1990) 1391-1400.