SPALLATIONREACTIONS WITHNEUTRON-RICHAND
NEUTRON-POORNUCLEI
TH.AOUST
SCK-CEN,Boeretang200,B-2400Mol,Belgium
and
UniversityofLiege,Physi sDepartment
alleedu 6Ao ^ut17, b^at. B5,B-4000Liege1,Belgium
E-mail: taousts k en.be
J.CUGNON
UniversityofLiege,Physi sDepartment
alleedu 6Ao ^ut17, b^at. B5,B-4000Liege1,Belgium
E-mail: ugnonplasma.theo.phys.ulg.a .be
Arenewed interest inspallationrea tions inthe GeV range has arisen, dueto
the re ent advent of ADSproje ts fortransmutationof nu learwaste. Mostof
investigationshavedealtwithproton-indu edrea tionsonstablenu lei.Here,an
exploratorytheoreti al investigation ofspallationrea tions onunstable nu lei is
presented.Themainissueisthedependen eofthemeasurablequantitieswiththe
isospinofthetarget.
1. Introdu tion
Spallationrea tionsareveryimportantforthedevelopmentofradioa tive
beams 1
, in astrophysi s 2
and in osmi -ray physi s 3
. In re ent years,
therehasbeenarenewedinterestinproton-indu edspallationrea tionsin
theGeVin identenergyrange,duetotheadventofproje tsof
a elerator-drivensystems(ADS) fortransmutationofnu learwastes(seee.g. Ref. 4
),
leadingto moresystemati and morepre ise measurements. Inparallel,a
realimprovementofthetheoreti altoolshastakenpla e,espe iallyin the
frame of the EU HINDAS proje t 5
. These e ortshave ontributed to a
more ompleteunderstandingofthespallationpro esses,strengtheningthe
intranu lear- as ade(INC)plusevaporationapproa h. Thepro ess anbe
dividedinto twostages. Inthe rstonethein identparti leexpellsafew
theremaining,randomized,ex itationenergyisreleasedbyan
evaporation-likepro ess. Inparti ular,itappearedthatoneofthebesttheoreti altools
isprovidedbytheLiegeintranu lear as ademodelINCL4 oupledtothe
K.-H.S hmidt ABLA evaporation- ssionmodel. This approa h, whi h is
basi allyparameter-free,owingtoa\self- onsistent"determination ofthe
stopping time, was shown re ently to yield parti ularly good results for
a large set of data for in ident energies ranging from 200 MeV to a few
GeV 6
. These data in lude total rea tion ross-se tions, in lusive light
parti le produ tion ross-se tions, multipli ity distributions, residue
pro-du tion ross-se tionsandre oildistributions. Lateron,thisapproa hwas
shownto belargelysu essfulin thedes riptionofspallation rea tionsat
lower in identenergy, down to afew tens of MeV,after small hanges in
thetreatmentofthePauliprin iple 7
.
TheHINDAS proje thas onsiderably improved themeasurementsof
the isotopi ross-se tions. Usually, the latter are performed in
proton-indu edrea tionsbya tivity(basi ally -ray)measurements. Inthe
HIN-DASproje t,reversekinemati s experimentshavebeenperformed: stable
nu lei bombard an hydrogen target and forward- ying residues are
ana-lyzedbyamagneti isotopi spe trometer. Individual isotopeprodu tion
ross-se tion anbedetermined,in onstrasttothea tivitymethodwhi h
anonlya essto umulated ross-se tions.
This method ould in prin iple be extended to a eleratednon-stable
nu lei, provided the intensity of the beam is suÆ iently large. Here, we
present anexploratory theoreti al investigation of spallation rea tionson
neutron-ri handneutron-poornu lei. Wewillusethesameapproa hasin
Ref. 6
,ex eptforanimprovedtreatmentofthenu learmean eld. Themain
issue is to know whether there are qualitative di eren es with spallation
rea tionsonordinarynu lei. Inparti ular, thefollowingquestions willbe
studied: (i) What is the evolution of the neutron multipli ities with the
target neutron (or proton) ex ess? (ii) Is the shape of the residue mass
spe traqualitativelymodi ed?
2. The theoreti alapproa h
Our INC+evaporation model ombines the INCL4 version of the Liege
intranu lear- as ade model 6
and the ABLA evaporation- ssion ode of
K.-H. S hmidt 8;9
. It is des ribed in Ref. 6
. We brie y re all the main
su es-The fate ofall parti lesis followedastime evolves. Parti lestravelalong
straight-line traje tories until twoof them rea h their minimum distan e
ofapproa h,in whi h asethey anbes atteredprovidedthevalueofthis
distan e issmallenough,oruntiltheyhittheborderofthepotentialwell,
supposedtodes ribethenu leartargetmean eld. Additionalfeaturesare:
(1)initialpositionsoftargetnu leonsaretakenatrandominthespheri al
nu lear target volume with asmoothsurfa e; (2) an improved treatment
of the Pauli blo kingis introdu ed; (3) inelasti ity is introdu ed through
rea tionsinvolvingpion'sanddelta's(4)isospindegreesoffreedomare
in-trodu edforalltypesofparti les;(5)the as ade odeisstoppedatatime
determinedbythe odeitself,whentheemissionpatternbe omes
evapora-tive;(6)theABLA odehasasophisti atedevaporation- ssion ompetition
withvis ositye e ts.
InthestandardINCL4version,althoughneutronandprotons are
dis-tinguished, theyexperien ethesamenu learaveragepotential,ex ept,of
ourse, for the Coulomb external potential. Here, we introdu ed isospin
andenergy-dependentpotentials,followingtheopti al-model
phenomenol-ogy(details anbefoundin Ref. 10
).
3. Observablequantities
3.1. Introdu tion
We present al ulations for parti le and residue ross-se tions. Altough
spallations rea tionswith unstable nu lei will probably berealized in
re-versekinemati s,wepresentresultsasindire tkinemati s,forthesakeof
omparison. Wewill onsider twotypesoftargets: PbandSnisotopes.
3.2. Parti le produ tion ross-se tion
Averageprotonandneutronmultipli itiesaregiveninTable1forp-indu ed
rea tionson Snand Pb rea tionsat 1GeV.Inea h ase, aneutron-poor
andaneutron-ri htargetsare omparedwithastableisotope.
Themost remarkable,but ratherexpe ted, result is theenhan ement
(redu tion) of the neutron multipli ity for the neutron-ri h (-poor)
iso-topes. Less obviously, this enhan ement (redu tion) is less marked, even
proportionally,for theemissionduring the as ade stage (mainly E
n 20
MeV). Thelarge partof the e e t is oming from the evaporationstage.
afewneutronsbeforerea hingtheso- alled\evaporation orridor"onthe
proton-ri hsideofthevalleyofstability,paralleltothestabilityline,where
abalan e betweenproton emission (favouredby smaller separation
ener-gies) andneutron emission (favouredbythe absen e ofCoulomb barrier)
settles.
Table1. Parti lemultipli itiesinproton-indu edrea tionsat
1GeV.ThequantitiesSn andSp arethe neutronand proton
separationenergies,respe tively.
p+Sn 100 Sn 124 Sn 134 Sn <n>,En<2MeV 0.34 1.87 2.92 <n>,2MeV <E n <20MeV 1.41 5.19 8.01 <n>,En>20MeV 1.71 2.25 2.64 <n> 3.42 9.30 13.57 <p> 7.40 3.30 2.50 Sn (MeV) 17.65 9.10 3.90 S p (MeV) 2.80 10.70 16.2 p+Pb 182 Pb 208 Pb 212 Pb <n>,En<2MeV 1.39 3.50 3.80 <n>,2MeV <E n <20MeV 3.44 7.87 8.50 <n>,En>20MeV 2.20 2.61 2.73 <n> 7.10 13.98 15.03 <p> 5.90 3.10 2.90 Sn (MeV) 11.75 7.40 5.10 Sp(MeV) 1.30 8.00 8.80
There is, of ourse,asymmetri e e t onthe protonmultipli ities. It
islessdramati in absolutevalues,but moredramati in proportion.
3.3. Residue produ tion ross-se tion
Theresiduemassspe traforp-indu edrea tionsonSntargetsaregivenin
Fig.1. Theabs issaxisequalto120minusthemassloss.Itisappropriate
to omparetheso- alledfragmentationpeaks, orrespondingtotheresidues
whi hare reatedbyevaporation(x&70). Asexpe ted,thefragmentation
peak is broader for 134
Sn, mainly be ausestarting from theneutron-ri h
sideofthevalleyofstability,thesystem anevaporatemorenu leonsbefore
rea hingtheevaporation orridor. The ssion ontributionisverysmallin
this ase. It orrespondsto the x . 70 part of the spe trum. It is only
1. e+00
1. e+01
1. e+02
1. e+03
1. e+04
1. e+05
20
40
60
80
100
120
140
Counts
A+(120-A
T
)
p(1GeV)+Sn
100
Sn
120
Sn
134
Sn
Figure1. Residuemassspe traforproton-indu edrea tionsonthreeSntargetsat1
GeV.Notethatthehorizontals alehasbeen hosensu hthattheisobars orresponding
tothesamemasslossappearatthesamepla eforthethreesystems.
1. e+00
1. e+01
1. e+02
1. e+03
1. e+04
1. e+05
50
100
150
200
Counts
A+(208-A
T
)
p(1GeV)+Pb
182
Pb
208
Pb
212
Pb
Figure2. SameasFig.1forthreePbtargets.
theyare pra ti allyidenti al for 208
Pb and 212
Pb. Theshape is di erent
for 182
Pb,but thisismainly linkedwiththemoststrikingresultof Fig.2,
namely the large ssion ross-se tion for this target. This, of ourse, is
due to the large ssility parameter of the remnants and leads to a large
depopulation of the mass spe trum around mass loss 5-6. As for the
othertargets,apeakexistsformasslossofonemassunit. Thispeakarises
be ause peripheral ollisions lead to small ex itation energy; for smaller
impa t parameters, more ex itation energy is left in the target remnant
andleads,eitherto importantevaporationor,asinthis parti ular aseof
182
Pb,to ssion.
4. Con lusion
We have presented here exploratory al ulations for spallation rea tions
onneutron-ri handneutron-poornu lei.Neutronandprotonmultipli ities
anbesubstantially hanged. Theshapeoftheresiduemassspe traisnot
drasti allydi erentfrom theordinarytarget ase,ex eptfor ssion.
Referen es
1. I.Tanihata,Onthepossibleuseofse ondaryradioa tivebeams,inTreatise
onHeavy-IonS ien e,vol.8,ed.byD.A.Bromley,PlenumPress,(1989).
2. T.K.Gaiser,Cosmi RaysandParti lePhysi s,CambridgeUniversityPress,
(1992).
3. M. Longair, HighEnergy Astrophysi s, vol. 1and 2,CambridgeUniversity
Press, (1997).
4. W.Gudowski,Nu l.Phys.A654,436 (1999).
5. A.Koningetal,HINDAS,AEuropeanNu learDataProgramfor
A eleratr-Driven Systems, Tsukuba Conferen e, 2002; J.-P. Meulders et al, HINDAS
nalreport,tobepublishedinEUpubli ations2004.
6. A. Boudard, J. Cugnon, S.Leray and C. Volant, Phys. Rev. C66, 044615
(2002).
7. J.CugnonandP.Henrotte,Eur.Phys.J.A16,393(2003).
8. J.-J.GaimardandK.-H.S hmidt,Nu l.Phys.,A531709(1991).
9. A.R. Junghans,M. de Jong, H.G.Cler , A. V.Ignatyuk, G.A.Kudyaev
andK.-H.S hmidt,Nu l.Phys.A629,635(1998).
