Exclusive measurement of isospin mixing at high temperature in 32s

Exclusive measurement of isospin mixing at high temperature in 32S Physics Letters B 763 (2016) 422–426 Contents lists available at ScienceDirect Physics Letters B www elsevier com/locate/physletb Exc[.]

Contents lists available atScienceDirect

www.elsevier.com/locate/physletb

Debasish Mondala,b, Deepak Pandita, S Mukhopadhyaya,b, Surajit Pala,

Srijit Bhattacharyac, A Ded, Soumik Bhattacharyaa,b, S Bhattacharyyaa,b, Balaram Deye,

Pratap Roya,b, K Banerjeea,b, S.R Banerjeea,b, ∗

aVariable Energy Cyclotron Centre, 1/AF-Bidhannagar, Kolkata-700064, India

bHomi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai-400094, India

cDepartment of Physics, Barasat Government College, Kolkata-700124, India

dDepartment of Physics, Raniganj Girls’ College, Raniganj-713358, India

eTata Institute of Fundamental Research, Mumbai-400005, India

a r t i c l e i n f o a b s t r a c t

Article history:

Received 5 August 2016

Received in revised form 5 October 2016

Accepted 25 October 2016

Available online 2 November 2016

Editor: V Metag

Keywords:

Isospin mixing in nuclei

Isovector giant dipole resonance

Statistical theory of nucleus

BaF 2 detectors

Exclusivemeasurementofisospin(I)mixingin32Sathightemperature(T)hasbeenperformedutilizing the γ-decay ofisovectorgiant dipole resonance (IVGDR).The degree of isospinmixing was deduced fromthe ratioofhighenergyγ-raycross-sectionsof32Sand31P populatedatthesametemperature and angular momentum (J) Precise temperature was determined by simultaneous measurement of nuclearleveldensity(NLD)parameterandangularmomentum.ThemeasuredCoulombspreadingwidth (↓) seemsto be independentof temperatureand angular momentum.The isospin becomes agood

quantumnumberwithincreaseintemperature However,whencomparedwiththecalculationathigh temperature,measuredisospinmixingisunderpredictedbythecalculations

©2016TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense

(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3

formalized via theconcept of isospinquantum numberI[1,2].It

is fullypreserved by the charge independent part ofnuclear

in-teraction However, the presence of electromagnetic interactions

andthe chargedependentshortrangepotentialbreaktheisospin

symmetry innuclei;the mostimportantpartbeingthe isovector

Coulombinteraction whichmixesstatesseparatedby I = 1[3]

Despitebeingasmalleffect,isospinmixingisimportantin

connec-tionwithtwobasicphenomenainphysics,namely,thespreading

widthof isobaric analog states (IAS) [4–6] andthe superallowed

Fermiβ-decay[7–10] The spreadingwidth oftheIAS isdirectly

relatedtotheisospin mixingin theparentnuclei[5,6].While, in

caseofsuperallowed Fermiβ-decay,themeasured lifetimeis

re-latedtothevectorcouplingconstantG V whichinturniscrucialin

determiningtheu-quarktod-quarktransitionmatrixelementV ud

measured f t valueneedsseveralcorrections[7];one ofthem

be-ingδc,whichisrelatedtotheisospinmixing[9].Inrecentyears,

* Corresponding author at: Variable Energy Cyclotron Centre, 1/AF-Bidhannagar,

Kolkata-700064, India.

E-mail address:srb@vecc.gov.in (S.R Banerjee).

experimental advances have put the theoretically calculated cor-rectionsunderintensescrutiny

Ingeneral,isospinmixingcanbestudiedbyutilizingthe transi-tionswhichwouldhavebeenforbiddenifisospinmixingdoesnot take place.Forexample,a) electricdipoletransitioninself conju-gate nuclei[11],b) Fermi β-decay[12,13],c) splittingofthe IAS studied by β delayed γ-rays [14] and d) evaporated E1 γ-rays fromthedecayofIVGDR[15]

Atmoderateexcitationenergiesthe γ-raysassociatedwiththe decayofIVGDRareemittedmostlyfromthefirststageofthe com-pound nuclear decay It is, therefore, an ideal tool to study the isospin mixingin self conjugate (N = Z) nucleiin the excitation energy range where the statistical model of nuclei can be ap-plied.Owingtotheisovectornatureofthedecay,the γ-transitions

Consequently, if a self-conjugate nucleus is populated by bom-barding aself-conjugateprojectileona self-conjugatetarget,only

I = 0 states are populated in the compound nucleus (CN) with the assumption that the isospin is fully conserved Due to the abovementionedisospinselectionrule γ-transitionsonlybetween states I = 0 to I = 1 are allowed But, at moderate excitation energies there are not many I = 1 final states to be populated

by IVGDR γ-decay This results in the suppression of the yield

of γ-rays decaying from self-conjugatenuclei populated through

http://dx.doi.org/10.1016/j.physletb.2016.10.065

0370-2693/©2016 The Authors Published by Elsevier B.V This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) Funded by

3

I=0 entrance channelascomparedtoI= 0nucleiforwhichall

γ-transitions are allowed However, in presence ofan admixture

ofI=1statesintheinitialcompoundnucleus,theIVGDR γ-yield

isenhancedastheseI=1statescandecaytoI=0states

Theabovetechnique was firstproposedby Harakehetal.[15]

and was later modified by Behr et al [16] who formalized the

isospinmixingasprescribedinRef.[17].Itwasshown,byinclusive

high energy γ-ray measurement, that for 28Si isospin gradually

becomes agood quantumnumberasexcitation energyincreases

Recently,isospinmixinghasbeenmeasuredfor80Zr[18,19].They

concludedthattheCoulombspreadingwidth(↓),infact,remains

constantwithtemperatureandisospinmixingdecreases withthe

increaseintemperature.Theresultwas comparedwiththe

calcu-lationofSagawaetal.[6]whoproposedthatthespreadingwidth

oftheIASarisesduetothecouplingofisovectormonopole(IVM)

statesandtheyconnectedtheisospinmixingintheparentnucleus

tothespreadingwidthoftheIAS.Interestingly,theresultmatches

wellwiththecalculation;alsowhenextrapolatedtozero

temper-ature,the result agrees quite well with the recentcalculation of

Satulaet al [20] However, at lower mass regions the measured

isospinmixingvaluesseem tobea bithigherathigher

tempera-tures[21].Itcouldalsobementionedherethatinallthe

measure-mentswhichappliedtheformalism ofRef.[16] toextractisospin

mixing, heavy ion fusionreaction was usedto ensure the

statis-ticalnatureofthe evaporated γ-rays However, insuch reactions

whichinturnaffectthehighenergy γ-ray spectrum[22],

partic-ularlyat lower mass regions [23] It should also be pointed out

thatin allthe previous measurements inlower massregions the

nuclearleveldensity(NLD)parameter,whichisvitalforstatistical

modelcalculationsaswell asforprecisedeterminationofnuclear

temperature,wasnotmeasured

In thisletter, we report on the measurement of isospin

mix-ing in 32S for which only one measurement exists at 58.3 MeV

[24].Ourprimalobjectivesweretoa)populatethecompound

nu-cleuswith light ion(α) induced fusionreaction to minimize the

angularmomentum effect; thesereactions have beenextensively

usedto study thelow temperatureproperties ofIVGDR [25–27],

mea-suringthe low energy γ-ray multiplicity, c) measure the crucial

NLD parameter, for the first time in this context, by measuring

theevaporated neutron energyspectrum, d)determine theexact

andNLDparameter,e)compareourresultwiththecalculationsof

Ref.[6]andattempttoextrapolatetheresulttowardszero

temper-ature

Cy-clotronCentre(VECC),Kolkata Thecompoundnuclei31Pand32S

werepopulatedatthesameexcitationenergy(E*=40.2MeV)and

angularmomentum(<J> =12h)¯ throughI=1/2 and I= 0

en-trancechannelsbybombardingself-supporting27Al(I=1/2) and

28Si(I=0)targetnucleiwith α-beam(I= 0)ofenergies35 MeV

and38 MeV,respectivelyfromK-130Cyclotron The target

thick-nesseswere 7.1 and10.8 mg/cm2 for 27Al and28Si,respectively

Here31Pwaspopulatedasareferencenucleus(populatedthrough

differententrance channel isospin but atsame E* and <J>) to

findtheIVGDRparameters(energy,widthandstrength)tobeused

fortheanalysisof32S.Asthemassesofthetwocompoundnuclei

arenearlysameandtheyarepopulatedatthesameexcitation

besameforboththenuclei.Itshouldalsobementionedthatthe

criticalangular momentum ( J c) [28],above whichnoticeable

ef-fectonIVGDRwidthisobserved,is11h for¯ 32S.Consequently,the

highenergy γ-rayspectraareexpectedtobesensitiveto

temper-atureonly

Fig 1 (Coloronline.) (a) Experimental fold distributions along with the simulated one (b) The total fusion cross-section (arb unit) (green solid triangles with red dot-dashed line) and the selected angular momentum distribution (solid blue line) for CASCADE calculations.

The highenergy γ-rayspectrafromthe decayofIVGDRwere measuredusingapartoftheLAMBDAspectrometer[29].Atotalof

49 BaF2 detectors,each havingdimension of3.5×3.5×35 cm3, were arrangedina7×7 matrix.Thedetectorsystemwasplaced

atadistanceof50 cmfromthetargetandatanangleof90◦with

respect to the beam axis The geometrical efficiency of the sys-tem was 1.8% It was surrounded by a 10 cm thick passive lead shield toblock the γ-ray backgrounds.A50element multiplicity filter(BaF2detectoreachhavingdimensionof3.5×3.5×5.0 cm3) was alsoutilizedforprecise measurementofangularmomentum populatedaswell as totake start triggerfortime of flight(TOF) measurements The multiplicity filterwas divided intotwo parts

of25elements each andtheywere placed ontop andbottom of thetargetchamberin5×5 matrixatadistanceof5 cmfromthe target Toensureequal solid angleforeach detector,each matrix wasconfiguredinastaggeredcastletypegeometry.Thedatawere acquired usinga VMEbased data acquisition system Onlythose eventsforwhichatleastonedetectorfromboththetopand bot-tom multiplicityfiltersfiredin coincidencewithone ofthe BaF2

detectorsof LAMBDA spectrometerabove a thresholdof4.0 MeV were recorded This coincidence technique, despite selecting the higher angular momentum phase space (Fig 1b), guarantees the selection ofstatisticaleventsaswell asasignificant reduction in backgroundevents.TheneutroneventswererejectedbyusingTOF techniqueandthepulseshapediscrimination(PSD)techniquewas utilizedto getridofthepile-upeventsineach detectorby mea-suringthechargedepositionovertwointegratingtimeintervalsof

50 nsand2 μs.Thetimespectrumofthecyclotronradiofrequency (RF)wasalsorecordedwithrespecttothemultiplicityfilterto fur-therensuretheselectionofbeamrelatedevents.Thehighenergy

γ-rayspectrawerereconstructedusingclustersummingtechnique

[29] in which each detector was required to satisfy the prompt time gate and PSD gate The events were so selected that they shouldliewithinthepromptgateofRFtimespectrum

The evaporatedneutron energyspectrawere measured,in co-incidence with the multiplicity γ-rays, using a liquidscintillator basedneutronTOFdetector[30].Itwasplacedatanangleof150◦

withrespect tothe beamaxisandata distanceof150 cm from thetarget.Then− γ discriminationwasdoneusingPSDtechnique comprising ofTOF and zerocrossover time (ZCT) The TOF spec-tra were converted to neutron energy spectra using the prompt

γ-peaks in the TOF as time reference The energy spectra were convertedfromlaboratoryframetocenter ofmass(CM)frame.The energyresolutionofthepresentset-upis∼17%at1 MeV.The de-tailedenergydependentneutrondetectionefficiencycanbefound

inRef.[30]

The angular momenta populated in the reactions studied do

not affecttheIVGDR parametersconsiderably However, to

deter-minethe temperatureofthecompound nuclei,it isimportantto

determine the angular momentum accurately; also the selection

only those events for which both of the top and bottom

multi-plicity filters firedin coincidence) is crucial for statisticalmodel

calculations Thus the experimentally measured fold distribution

GEANT3simulations[31].Thedetailedprocedurecanbe obtained

in Ref [32] The experimental fold distributions for 31P and 32S

along with the simulated one are shown in Fig 1a, while the

selected angular momentum phase spaceis shown in Fig 1b It

distributionswereproperlynormalizedwiththeinputchannel

fu-sioncross-sectionobtainedfromthePACE4 codefor31Pand32S

ItisinterestingtonotefromFig 1athatfolddistributions for31P

and32Swerethesameassertingthefactthattheangular

momen-tumpopulationsforboththenucleiwerethesame

The experimental spectrawere analyzed with amodified

ver-sion of CASCADEcode [33] inwhich isospin was properly taken

careof[16].TwotypesofpureisospinstatesI<=Iz andI>=Iz+1

wereconsidered.Thefractionof≷statesthatmixeswith≶states

wasdefinedas[17]

α2

≷= 

↓

≷/ ≷↑

1+ ≷↓/ ↑

≷+ ≶↓/ ↑

≶

(1)

where↑ isthestatisticaldecaywidthoftheCN.Themixed

pop-ulationsofthecompoundnuclearstatesweredefinedas

˜

σ<= (1− α<2) σ<+ α2>σ> (2)

˜

σ>= (1− α>2) σ>+ α2<σ< (3)

where σ< and σ> are the population of the pure isospin states

Theleveldensityofeachtype ofisospinstateswasaccountedfor

andthe transmission coefficient was divided intoisospin

depen-dent andindependentparts Thecalculation contains only ↓

> as thefreeparameter(tobederivedfromtheexperimentaldata).The

detailsofthecalculationcanbeobtainedinRef.[16,34]

The statisticalmodelanalysisfor31Pwas performedwiththe

assumptionthattheisospinisfullyconserved(↓

>=0).The CAS-CADE neutron spectrum (after correcting for detector efficiency)

mini-mization was done in the energyrange 4.0–10.0 MeV The

Reis-dorf level density prescription [35] was used and the best fit

was obtained for a˜ =4.2±0.3 MeV Similar analysisresulted in

˜

a=3.9±0.1 for32S.Theevaporatedneutronenergyspectraalong

theIVGDRparameters were extractedbycomparing thehigh

en-ergy γ-ray spectrumof 31PwiththeCASCADEcalculationsalong

σ (0)e−E γ / 0.The slopeparameter E0=4.9 MeV whichis

consis-tentwiththeparametrizationE0=1.1[(Elab−Vc)/A ]0.72[36].The

deducedparameters were E G D R=17.8±0.2 MeV, G D R=8.0±

0.4 MeV and S G D R=1.00±0.03.Theuncertaintieswereobtained

by χ2 minimization procedure in the energy range 14–21 MeV

Theexperimental highenergy γ-ray spectrumfor31Palong with

theCASCADE spectra,properlyfolded withthedetectorresponse

function,areshowninFig 3a.Inordertoemphasize ontheGDR

regionthe corresponding linearizedspectraare showninFig 3b,

usingthe quantity F(Eγ)Y exp(Eγ)/Y cal(Eγ), where Y exp(Eγ) and

Y cal(Eγ) are the experimental and the CASCADE spectra, while

F(Eγ)istheLorentzianhavingtheabovementionedparameters

Fig 2 (Coloronline.) Experimental neutron spectra (green filled circles) along with the CASCADE predictions (red solid lines) for (a) 31 P and (b) 32 S.

Fig 3 (Color online.) Experimental high energy γ-ray spectra (green filled cir-cles) along with CASCADE calculations for  >↓=0 keV (blue dashed line) and

 >↓=24 keV (red solid line) for 31 P (a) and 32 S (c) The corresponding linearized plots are also shown for 31 P (b) and 32 S (d).

Finally, the isospin mixingparameters were deduced utilizing theIVGDRparametersextractedfrom31P.Inordertoincreasethe sensitivity ofisospin mixingand minimize theeffects of statisti-cal modelparameters,isospinmixingwas deducedfromtheratio

of γ-raycross-sectionsof32Sand31PintheGDRregion(Fig 4b)

Weremarkherethatthoughwecouldsimulatetheresponse func-tion ofLAMBDA spectrometer, theabsoluteefficiency ( in) ofthe array isnot known.So, wehavetakenthe ratioof[σγ × in]for both the nuclei andcompared withthe ratio ofCASCADE cross-sections properly folded with the detector response function It should be highlighted herethat ↓

> was theonly parameter that wasvariedtomatchtheexperimentalratiowiththeCASCADE pre-diction As ↓ remains nearly temperature independent [17,37],

Fig 4 (Coloronline.) (a) Experimentalσγ× infor 31 P (green open circles) and 32 S

(blue filled circles) (b) Experimental ratio (pink filled circles) of the high energy

γ-ray cross-sections of 32 S and 31 P along with the CASCADE predictions for

differ-ent >↓.↓>=0 keV for blue dashed line (zero mixing), >↓=24 keV for red dashed

line and↓>=10 MeV for black dashed line (full mixing).χ2 as a function of >↓

(inset Fig b).

same↓

> was usedforallthe decaysteps Thebestvalue for↓

>

was obtainedby χ2 minimization technique inthe energyrange

α2

<=3.5±1.8% at T=2.7 MeV The experimental high energy

γ-rayspectrumfor32SalongwiththeCASCADEfitfor↓

>=0 keV and↓

>=24 keV areshowninFig 3candthecorresponding

lin-earized plots are shown in Fig 3d We emphasize here that the

presentations(Fig 3cand3d)dependonthenormalizationpoint;

however,theextracted↓

> fromtheratioofthecrosssectionsof

32Sand31Piscompletelyindependentofthenormalizationpoint

Itshouldbementionedthat α2

<dependsonJandourquotedvalue correspondstoJ=11¯h,thepeakoftheJdistribution.The

temper-aturewas calculatedusingthe relation T=  (E∗−E rot− P )/a,˜

where E rot isthe rotationalenergyandP isthepairingenergy

Weremarkherethatthequotederrorscorrespondtothe

statisti-calerrors aswell asthesystematicerrors owingto thepresence

ofisotopicimpurity in the28Sitarget andthe uncertaintyinthe

determinationofbremsstrahlungcomponent

Itis interesting to compare ourresult withthe onlyreported

measurementfor32S[24]forwhich↓

> was 20±25 keV and α2

<

was1.3±1.5%atT= 2.85 MeV[21].Itemphasizesthefact that

↓

>indeedremainsconstantwithtemperature.Itisalsofascinating

tonote fromFig 5athat α2

< decreases withthe increasein tem-perature.This isowing to thefact that the competitionbetween

thetimescalesassociatedwiththeCoulombspreadingwidth(↓)

and the compound nuclear decay width (↑) leads towards the

restorationofisospinsymmetry[38,39].Theintrinsicdecaywidth

ofthecompound nuclear state becomes solarge ascompared to

theCoulombspreadingwidththatthestatedoesnotgetsufficient

differentanditwouldbeinterestingtodisentangletheeffectsofJ

andTon α2

<.Itcouldalsobeconjecturedthat↓

>doesnotchange

Itwould be appealing to compareour measured α2

> at mini-mum angularmomentum (1h)¯ withthe calculationof Sagawaet

al.[6].Accordingtotheformalism

α>2= 1

I A S

C N+ I V M

(4) where I A S is the spreading width of IAS, which is equivalent

to ↓

>, C N is the compound nuclear decay width and I V M is

the width of the isovector monopole (IVM) state at the energy

Fig 5 (Coloronline.) (a) Measuredα2

<for 32 S at different temperatures The blue solid circle is the present measurement and the red filled circle is adopted from Ref [24] (b) Comparison of our measuredα2

>at J=1¯h withthe calculation ofα2

>

with T [6].α2

>at T=0 imposed from Ref [20] (red dot dashed line),α2

>at T=0 calculated using the formalism of Ref [9] by imposingδ cvalue from Ref [7] (green solid line).

of IAS. α2

> was set at 0.7% at T=0 from the recent calculation

of Satulaet al.[20].This results in I V M=3.4 MeV as C N=0

at T=0 Next, C N was calculated using the CASCADE code at different temperatures using our best fit parameters The result-ingcalculationisshowninFig 5b(reddotdashedline).Itshould

bementionedherethatI V M wasassumedtemperature indepen-dent and ↓

> was given a weak linear dependence [6] on T as

↓

>(T) = >↓(0)(1 +cT)wherec=0.2 MeV−1.Theparametercwas calculatedbyassumingthat↓

>(T =2.7 MeV)=37 keV i.e.↓

> re-mained within the experimental error bar As can be seen from

Fig 5bthatourmeasured α2

>=3.5±1.9% remainswellabovethe calculatedvalue

Thevalueof α2

>atT=0 hasalsobeenextractedusingthe cal-culatedvalueofδc=0.65% in34Clwhichreproducesthecorrected

> is extracted utilizing the formalism of Ref [9]

withtheassumptionthatδc issamefor34Cland32S.Accordingto thisformalism α2

>isdefinedas

α>2= 41ξA2/3

where V1=100 MeV, ξ =3 [9] Equation (5) yields α2

>=2.0% which in turn yields I V M=1.2 MeV. α2

> was extrapolated to higher temperatures using the same procedure described before

As can be seen from Fig 5b the calculation (solid green line), thoughunderpredicts,betterexplainsourmeasureddata.Itshould

behighlightedinthiscontextthatMelconianetal.[40]havefound

δctobeashighas5.3±0.9% whichwasattributedtothepresence

ofcloselyingI=0 andI=1 statesnear7.0 MeVexcitationenergy

in32Sanditwascorroboratedbytheshellmodelcalculations.So,

it would be interesting to perform the statistical model analysis withthelocaleffectsbutisbeyondthescopeofthepresentwork

Itshould alsobe highlightedherethat,asmentionedtherein,the formalismofSagawaetal.[6]maybevalidinmedium-heavyand heavy nuclei.However,moredataare requiredatstill lower tem-peraturestounderstandthesystematicbehaviorofisospinmixing

inlowermassregion

In summary,we havemeasured the isospin mixing in 32S by utilizing α-induced fusion reactions.Precisetemperaturewas

angularmomentum.Coulombspreadingwidth↓ wasfoundtobe

More-over,isospinbecomes a goodquantumnumberwiththeincrease

intemperature.However, α2

>,whenextrapolatedtohigher temper-atures, by imposing its value at zero temperature, underpredicts

ourmeasuredvalue

Acknowledgements

The authors would like to thank A Corsi for providing the

M Kicinska-Habior Debasish Mondal sincerely acknowledges the

discussionswithJ.A.Behr

References

[1] W Heisenberg, Z Phys 77 (1932) 1.

[2] E.P Wigner, Phys Rev 51 (1937) 106.

[3] D.H Wilkinson, Isospin in Nuclear Physics, North-Holand Publishing Company,

Amsterdam, 1969.

[4] J Janecke, et al., Nucl Phys A 463 (1987) 571.

[5] T Suzuki, et al., Phys Rev C 54 (1996) 2954.

[6] H Sagawa, et al., Phys Lett B 444 (1998) 1.

[7] J.C Hardy, et al., Phys Rev C 91 (2015) 025501.

[8] V Rodin, Phys Rev C 88 (2013) 064318.

[9] N Auerbach, Phys Rev C 79 (2009) 035502.

[10] H Sagawa, et al., Phys Rev C 53 (1996) 2163.

[11] E Farnea, et al., Phys Lett B 551 (2003) 56.

[12] N Severijns, et al., Phys Rev C 71 (2005) 064310.

[13] P Schuurmans, et al., Nucl Phys A 672 (2000) 89.

[14] Vandana Tripathi, et al., Phys Rev Lett 111 (2013) 262501 [15] M.N Harakeh, et al., Phys Lett B 176 (1986) 297.

[16] J.A Behr, et al., Phys Rev Lett 70 (1993) 3201.

[17] H.L Harney, et al., Rev Mod Phys 58 (1986) 607.

[18] A Corsi, et al., Phys Rev C 84 (2011) 041304(R).

[19] S Ceruti, et al., Phys Rev Lett 115 (2015) 222502.

[20] W Satula, et al., Phys Rev Lett 103 (2009) 012502.

[21] M Kicinska-Habior, Acta Phys Pol B 36 (2005) 1133.

[22] A Bracco, et al., Phys Rev Lett 74 (1995) 3748.

[23] Deepak Pandit, et al., Phys Rev C 81 (2010) 061302(R).

[24] M Kicinska-Habior, et al., Nucl Phys A 731 (2004) 138.

[25] S Mukhopadhyay, et al., Phys Lett B 709 (2012) 9.

[26] Deepak Pandit, et al., Phys Lett B 713 (2012) 434.

[27] Balaram Dey, et al., Phys Lett B 731 (2014) 92.

[28] Dimitri Kusnezov, et al., Phys Rev Lett 81 (1998) 542.

[29] S Mukhopadhyay, et al., Nucl Instr Meth A 582 (2007) 603 [30] K Banerjee, et al., Nucl Instr Meth A 608 (2009) 440.

[31] R Brun, et al., GEANT3, CERN-DD/EE/84-1, 1986.

[32] Deepak Pandit, et al., Nucl Instr Meth A 624 (2010) 148 [33] F Puhlhofer, Nucl Phys A 280 (1977) 267.

[34] J.A Behr, Ph.D thesis, University of Washington, 1991, unpublished [35] W Reisdorf, et al., Z Phys A 300 (1981) 227.

[36] H Nifennecker, et al., Annu Rev Nucl Part Sci 40 (1990) 113 [37] E Kuhlmann, Phys Rev C 20 (1979) 415.

[38] H Morinaga, Phys Rev 97 (1955) 444.

[39] D.H Wilkinson, Philos Mag 1 (1956) 379.

[40] D Melconian, et al., Phys Rev Lett 107 (2011) 182301.