Energetic Light Fragment Production Capability in MCNP6

0.13 MB·

by  Leslie M. Kerby

EnergeticLightFragmentProductionCapabilityinMCNP6
LeslieM.Kerby,∗,†StepanG.Mashnik,†KonstantinK.Gudima,‡ArnoldJ.Sierk,†JeffreyS.Bull,†andMichaelR.James†
∗IdahoStateUniversity,Pocatello,ID
†LosAlamosNationalLaboratory,LosAlamos,NM
‡InstituteofAppliedPhysics,AcademyofScienceofMoldova,Chis¸ina˘u,Moldova
[email protected]
INTRODUCTION De-excitation of light nuclei with A ≤ A remain-
Fermi
ingaftertheIntra-NuclearCascadeisdescribedinCEMand
The Monte Carlo Methods, Codes, and Applications LAQGSMonlywiththeFermibreakupmodel,whereA
Fermi
group within the Computational Physics Division at Los isa‘cut-offvalue’fixedinthemodels. ThevalueofA isa
Fermi
6 AlamosNationalLaboratoryhasledthedevelopmentofthe modelparameter,notaphysicalcharacteristicofnuclearreac-
1 transport code MCNP6 (Monte Carlo N-Particle transport tions. Actually,theinitialversionoftheFermibreakupmodel
0 code,version6)[1].MCNP6isageneral-purpose,continuous- incorporatedintoCEMandLAQGSMusedA≤ A =16,
Fermi
2 energy,generalized-geometry,time-dependent,Monte-Carlo justas A = 16isusedcurrentlyinGEANT4[5]andin
n radiation-transportcodedesignedtotrackmanyparticletypes SHIELD-FHermITi [6].ButthatinitialversionoftheFermibreakup
a over broad ranges of energies. It is used around the world model had some problems and code crashes in some cases.
J inapplicationsrangingfromradiationprotectionanddosime- Toavoidunphysicalresultsandcodecrashes, wechosethe
1 try,nuclear-reactordesign,nuclearcriticalitysafety,detector expedientofusingA = 12inbothCEMandLAQGSM.
Fermi
1 designandanalysis,decontaminationanddecommissioning, Later,theproblemsintheFermibreakupmodelwerefixed,
acceleratorapplications,medicalphysics,spaceresearch,and andwestudiedhowthevalueofAFermiaffectedthefinalresults
] beyond. Atlowerenergies,thecodeusestablesofevaluated ofthosecodes.
h
t nucleardata,whileforhigherenergies(>150MeV),MCNP6 We found that the performance of MCNP6, CEM, and
- usesthecascade-excitonmodel,version03.03(CEM03.03) LAQGSMinsimulatingfragmentationreactionsatintermedi-
l
c [2,3],andtheLosAlamosquark-gluonstringmodel,version ateenergiesfortargetswithA<13providereasonablygood
u 03.03(LAQGSM03.03)[3,4]tomodelnuclearreactions. predictionsforallreactionstested,althoughafine-tuningof
n Emission of energetic heavy clusters heavier than 4He theA cut-offparameterintheFermibreakupmodelmight
[ Fermi
from nuclear reactions play a critical role in several appli- provideabetterdescriptionofsomeexperimentaldata. How-
1 cations,includingelectronicsperformanceinspace,human ever,insomecasesA =12providedthebestagreement
Fermi
v radiation dosages in space or other extreme radiation envi- withexperimentaldata,andsowedidnotfindsufficientev-
7 ronments, proton- and hadron-therapy in medical physics, idencetochangetheFermicut-offvalueinMCNP6, CEM,
3 accelerator and shielding applications, and more. None of andLAQGSMatthattime. SeeRef.[7]forcompleteresults.
5 theavailablemodelsareabletoaccuratelypredictemission
2 oflightfragments(LF)fromarbitraryreactions. TheCEM PREEQUILIBRIUM
0
andLAQGSMeventgeneratorsinMCNP6describequitewell
1. thespectraoffragmentswithsizesupto4Heacrossabroad Thepreequilibriuminteractionstageofnuclearreactions
0 rangeoftargetmassesandincidentenergies(upto∼5GeV isconsideredbythecurrentCEMandLAQGSMintheframe-
6 forCEMandupto∼1TeV/AforLAQGSM).However,they work of the latest version of the modified exciton model
1 donotpredictthehigh-energytailsofLFspectraheavierthan (MEM) [8, 9]. At the preequilibrium stage of a reaction,
v: 4Hewell. MostLFwithenergiesaboveseveraltensofMeV CEM03.03andLAQGSM03.03takeintoaccountallpossible
i areemittedduringtheprecompoundstageofareaction. The nuclear transitions changing the number of excitons n with
X 03.03 versions of CEM and LAQGSM do not account for ∆ =+2,-2,and0,aswellasallpossiblemultiplesubsequent
n
r precompoundemissionofLFlargerthan4He. emissions of n, p, d, t, 3He, and 4He. The corresponding
a
ThegoalofthisresearchistoenableMCNP6toproduce systemofmasterequationsdescribingthebehaviorofanu-
high-energylightfragments. TheseenergeticLFmaybeemit- cleusatthepreequilibriumstageissolvedbytheMonte-Carlo
ted by our models through three processes: Fermi breakup, technique. Improvements to the preequilibrium stage were
preequilibrium,andcoalescence. Weexploretheemissionof three-fold:extensionofpreequilibriumtoincludeLFemission
lightfragmentsthrougheachofthesemechanismsanddemon- upto28Mg,adoptionoftheNASAreactioncrosssectionas
strateanimprovedagreementwithexperimentaldataachieved theinversecrosssection,andthecreationofanewmodelfor
by extending precompound models to include emission of thecondensationprobabilityγ .
j
fragmentsheavierthan4He.
Preequilibriumextension
FERMIBREAKUP
CEM03.03doesnothavethecapabilitytooutputcross
TheFermibreakupmodelisusedinCEMandLAQGSM sectionsforfragmentslargerthan4He. Therefore,oneofthe
forresidualnucleiwithatomicmassnumberA≤12,making firstthingsdonewastoaddthiscapability. Wealsocreated
itparticularlyimportantforreactionswithlighttargetnuclei. thecapabilitytooutputbyisotope,Znumber,ormassnumber.
ExtendingtheMEMtoproduce66fragmenttypes,upto formacomplexparticleoftype jintheexcitedresidualnu-
28Mg,involvesextendingthecalculationofemissionwidths cleus. Weexploretheformulationofanewmodelforγ ,one
j
(Eq.(1))toall66fragmenttypes. TheemissionwidthΓ ,(or whichisenergy-dependent,andwhichprovidesimprovedfits
j
probabilityofemittingparticlefragment j),isestimatedas toexperimentalfragmentspectra.
Thecondensationprobabilityγ couldbecalculatedfrom
(cid:90) E−Bj first principles, but such a calculatjion is not feasible. γ is,
Γ (p,h,E)= λ (p,h,E,T)dT, (1) j
j j therefore,estimatedastheoverlapintegralofthewavefunc-
Vc
j tionofindependentnucleonswiththatofthecomplexparticle
wherethepartialtransmissionprobabilities,λ ,areequalto (seedetailsin[2]),asshowninEq.(5).
j
λj(p,h,E,T)=γj2πsj2(cid:126)+31µj(cid:60)(p,h)ω(pj,0g,T +Bj) γj ≈ p3j(pAj)pj−1. (5)
j (2)
ω(p−p ,h,E−B −T) Eq.(5)isarathercrudeestimate.InCEMweapproximate
× j j Tσinv(T), γ bymultiplyingtheestimateprovidedbyEq.(5)byempirical
ω(p,h,E) j j
coefficients F . Valuesof F ford, t, 3He, and4Heneedto
j j
for complex particles and fragments. This extension there- be re-fit after the upgrades to the inverse-cross-section and
foreentailscalculatingCoulombbarriers, bindingenergies, coalescencemodels,andnewvaluesofFjneedtobeobtained
reducedmasses,inversecrosssections,andcondensationprob- forheavyclustersupto28Mg.
abilitiesforall66fragmenttypes. InanalyzingthefittedFjdatasetwecreatedmathematical
TheextendedMEMprovidesdramaticallyimprovedabil- modelsforboththefragment-specificequationsforFjanda
ity to describe light-fragment production at intermediate to generalizedFjmodel. ThegeneralFjmodelis:
highenergiesacrossmostreactionstested,whilemaintaining
goodresultsforfragments≤4He. Fj(T0,Aj,Zj,At)=(cid:20)7800(2.5)Aje−T0/20+ T0.22τ(4+)τ100(cid:21)
0
InverseCrossSections (6)
×e−30100−0At,
Total-reaction-cross-sectionmodelshaveasignificantim- τ= A −(Z −3).
j j
pactonthepredictionsandaccuracyofspallationandtransport
codes. Forexample,CEMusestotalreactioncrosssections Forthefragment-specificF ,discussionofthephysicalmean-
j
asinversecrosssections,σijnv,tocalculatetheprobabilitiesof ingofthemodel,andresults,seeRef.[13].
emissionofpossiblenucleonsandfragments.
TheinversecrosssectionsinCEM03.03aretakenfrom COALESCENCE
theDostrovskyetal. model[10]. Itsgeneralformis:
CEM03.03 is capable of producing light fragments up
σ =πr2A2/3α (1− Vj). (3) to4Heinitscoalescencemodel. Weextendthecoalescence
Dost. 0 j T modeltobeabletoproduceupto7BeinCEMandupto12C
inLAQGSM.
TheDostrovskymodelwasnotintendedforuseaboveabout
Whenthecascadestageofareactioniscompleted,CEM
50MeV/nucleon,andisnotverysuitableforemissionoffrag- uses the coalescence model to create high-energy d, t, 3He,
ments heavier than 4He. Better total-reaction-cross-section and4Hefragmentsbyfinal-stateinteractionsamongemitted
modelsareavailabletoday. Wecomparedresultsfromseveral
cascadenucleonsoutsideofthetargetnucleus. Themagnitude
totalreactioncrosssectionmodelsanddeterminedtheNASA
ofthemomentum, p,ofeachcascadenucleoniscalculated
(orTripathietal.) model[11]providedthebestgeneralagree-
relativistically from its kinetic energy, T. We assume that
mentwithexperimentaldata. AsshowninEq.(4),theNASA allthecascadenucleonshavingdifferencesintheirmomenta
crosssectionattemptstosimulateseveralquantum-mechanical
smallerthan p andwiththecorrectisotopiccontentforman
effects,suchastheopticalpotentialforneutrons(withthepa- c
appropriatecompositeparticle.
rameterX )andcollectiveeffectslikePauliblocking(through
m Thecoalescencemodelfirstchecksallnucleonstoform
thequantityδ ).
T 2-nucleonpairs,theirmomentapermitting. Itthentakesthese
2-nucleonpairsandthesinglenucleonsleftandforms4He,
B
σ =πr2(A1/3+A1/3+δ )2(1−R T )X . (4) 3He,and/ortritium,theirmomentapermitting. Theextended
NASA 0 P T T cT m
cm coalescencemodelfurthertakesthesetwo-nucleonpairs,tri-
ResultsofimplementingtheNASAinverse-cross-section tium,3He,and4Hetoseeiftheycancoalescetoformheavier
modelintotheextendedMEMshowimprovedagreementwith clusters: 6He,6Li,7Lior7Be.
experimentaldata. SeeRef.[12]fordetails. Allcoalescednucleonsareremovedfromthedistributions
ofnucleonssothatatomicandmassnumbersareconserved.
Condensationprobabilityγ Resultsshowsignificantimprovementintheproduction
j
ofheavyclustersacrosstheenergyrange. However,toomany
The condensation probability, γ , represents the proba- alphaparticleswerelost(coalescedintoheavyclusters); so
j
bility that p excited nucleons (excitons) will condense to p (4He)wasincreasedtocompensate. SeeRefs.[14]and[15]
j c
fordetails.Thenewvaluesforp fortheextendedcoalescence
c
modelare:
p (d) = 90MeV/c;
c
p (t) = p (3He)=108MeV/c; (7)
c c
p (4He) = 130MeV/c;
c
p (LF) = 175MeV/c.
c
For300MeV<T <1000MeVtheyare:
p (d) = 150MeV/c;
c
p (t) = p (3He)=175MeV/c; (8)
c c
p (4He) = 205MeV/c;
c
p (LF) = 250MeV/c.
c
MCNP6IMPLEMENTATION
The culmination of this work is the implementation
of CEM with these heavy-cluster upgrades, which we call
CEM03.03F,intoMCNP6.
TheGENXSoptionallowsforvariouscrosssectionstobe
Fig. 1. Comparison of experimental data for 480 MeV p +
talliedinMCNP6. Previously,productioncrosssectionswere
natAg → 6Li at 60◦, measured by Green, et al. [18] (green
onlyavailableforfragmentsupto4He. Thus,anecessaryfirst
circles) to calculated results from CEM03.03F (blue solid
stepinimplementingtheimprovedCEM03.03FintoMCNP6
involvesextendingtheabilitytooutputproductioncrosssec- lines),MCNP6-Fwithnpreqtyp=66(reddashedlines),and
tionstoheavyclusters. ThisGENXSupgradeaccomplishes MCNP6withtheGENXSextensiononly(purpledash-dotted
thisandincludestheabilitytotallyandoutputdoubledifferen- lines).
tialcrosssections,angle-integratedorenergy-integratedcross
sections,aswellasthetotalproductioncrosssection,forany for 480 MeV p + natAg → 6Li at 60◦, compared to experi-
heavyionwithvalidZAID.FordetailsseeRef.[16]. mental data measured by Green, et al. [18]. MCNP6 with
CEM03.03Fwasimplementedintoaworkingversionof theGENXSextensiononlydoesnotcontainanyofthefour
MCNP6,whichwecallMCNP6-F.Twooftheupgradesare light-fragment upgrades discussed in this work. MCNP6-F
alwaysimplemented: theupgradedNASA-Kalbachinverse producessignificantlyimprovedresultsandmatchesthedata
crosssectionsinthepreequilibruimstage,andthenewenergy- reasonablywell.
dependentγ model. Theothertwoupgrades(extensionof Fig. 2 displays the results for 200 MeV p + 197Au →
j
preequilibrium emission to 28Mg, and the extension of the 7Be at 45◦, compared to experimental data by Machner, et
coalescence model to 7Be), both of which increase compu- al. [19]. This figure shows not only dramatically improved
tationtime,maybeturnedoffifdesired. Avariable,called heavy-clusterproductionbyMCNP6-Fathighenergies,but
npreqtyp,wascreatedtospecifythenumberofpreequilibrium alsoimprovedproductionatrelativelylowenergiesaroundthe
particles considered for emission. It is now the twelfth op- preequilibriumpeak. Webelievethisisduetotheheavytarget
tionontheLCAcardoftheMCNP6inputfile. Itsmaximum (gold)andthereforeanincreasedabilitytoproducetheselow-
(anddefault)valueis66,similartothenevtypevariableused energy heavy clusters from both the extended coalescence
for the evaporation stage. See Ref. [17] for a list of the 66 modelandtheextendedpreequilibriummodel.
particles considered in the preequilibrium stage. In the old Across the reactions we tested we found that the new
model,6preequilibriumparticleswereconsidered,andthere- MCNP6-F,ingeneral,givesimprovedresultscomparedtothe
foreavalueofnpreqtyp=6turnsoffboththepreequilibrium unmodifiedMCNP6,mostespeciallyforheavy-clusterspectra.
andcoalescenceextensions. Theextendedcoalescencemodel FurtherdetailsandmoreresultscanbefoundinRef.[17].
is implemented for values of npreqtyp>6. MCNP6-F also The goal of producing energetic light fragments in
includestheGENXSextension. MCNP6 has been accomplished by implementing several
BasictestingandverificationofMCNP6-Fhasbeencom- heavy-clusterupgradesasoutlinedinthispaper.
pletedwiththeresultsbeingpresentedbelow.Inaddition,MPI
testinghasbeencompleted. Uponfurthertesting,weantici- ACKNOWLEDGMENTS
patetheseheavy-ionupgradesandtheGENXSextensionwill
WearegratefultoDrs. ChristopherWernerandAvneet
beincludedinthenextreleaseofMCNP6.
Sood of Los Alamos National Laboratory for encouraging
discussionsandsupport.
Results
ThisstudywascarriedoutundertheauspicesoftheNa-
Double differential cross section spectra for several re- tionalNuclearSecurityAdministrationoftheU.S.Department
actions are plotted in this section. Fig. 1 shows the results ofEnergyatLosAlamosNationalLaboratoryunderContract
uationofNuclearReactionCross-SectionsandFragment
YieldsinCarbonBeamsUsingtheSHIELD-HITMonte
CarloCode.ComparisonwithExperiments,”Physicsin
Medicine&Biology,57,4369(2012).
7. S.MASHNIKandL.KERBY,“MCNP6Fragmentation
of Light Nuclei at Intermediate Energies,” Nuclear In-
strumentsandMethodsinPhysicsResearchA,764,59
(2014),arXiv:1404.7820.
8. K.GUDIMA,G.OSOSKOV,andV.TONEEV,“Model
forPre-EquilibriumDecayofExcitedNuclei,”Yadernaya
Fizika,21(1975),[SovietJournalofNuclearPhysics21
(1975)139-143].
9. S.MASHNIKandV.TONEEV,“MODEX–theProgram
forCalculationoftheEnergySpectraofParticlesEmitted
intheReactionsofPre-EquilibriumandEquilibriumStat-
sticalDecays,”JINRCommunication,P4-8417(1974).
10. I.DOSTROVSKY,Z.FRAENKEL,andG.FRIEDLAN-
DER,“MonteCarloCalculationsofNuclearEvaporation
Processes. III. Applications to Low-Energy Reactions,”
PhysicalReview,116,683(1959).
11. R. TRIPATHI, F. CUCINOTTA, and J. WILSON, “Ac-
Fig. 2. Comparison of experimental data for 200 MeV p + curate Universal Parameterization of Absorption Cross
197Au→7Beat45◦,measuredbyMachner,etal.[19](green Sections,”NuclearInstrumentsandMethodsinPhysics
circles) to calculations from CEM03.03F (blue solid lines), ResearchB,117,347(1996).
MCNP6-Fwithnpreqtyp=66(reddashedlines),MCNP6-F 12. L.KERBYandS.MASHNIK,“TotalReactionCrossSec-
withnpreqtyp=6(greendash-dottedlines),andMCNP6with tionsinCEMandMCNP6atIntermediateEnergies,”Nu-
clearInstrumentsandMethodsB,356-357,135(2015).
theGENXSextensiononly(purpledottedlines).
13. L.KERBY,“AnEnergy-DependentNumericalModelfor
No. DE-AC52-06NA25396. theCondensationProbability,γj,”LANLReport,LA-UR-
Thisworkwassupportedinpart(forL.M.K)bytheM. 15-26648(2015).
HildredBlewettFellowshipoftheAmericanPhysicalSociety, 14. K.GUDIMA,S.MASHNIK,andL.KERBY,“Fragmen-
www.aps.org. tation of Light Nuclei at Intermediate Energies Simu-
lated with MCNP6,” LANL Report, LA-UR-15-27417,
REFERENCES presented at the Fifth International Conference on Nu-
clearFragmentationFromBasicResearchtoApplications
1. T.GOORLEY,etal.,“InitialMCNP6ReleaseOverview, (NUFRA2015),4–11October2015,Kemer(Antalya),
MCNP6version0.1,”NuclearTechnology,180,298–315 Turkey(2015).
(2012). 15. L. KERBY and S. MASHNIK, “Production of Heavy
2. K.GUDIMA,S.MASHNIK,andV.TONEEV,“Cascade- ClusterswithanExpandedCoalescenceModelinCEM,”
ExcitonModelofNuclearReactions,”NuclearPhysicsA, TransactionsoftheAmericanNuclearSociety,112,577
401,329–361(1983). (2015).
3. S. MASHNIK, K. GUDIMA, R. PRAEL, A. SIERK, 16. L. KERBY, S. MASHNIK, and J. BULL, “MCNP6
M. BAZNAT, and N. MOKHOV, “CEM03.03 and GENXSOptionExpansiontoIncludeFragmentSpectra
LAQGSM03.03EventGeneratorsfortheMCNP6,MC- ofHeavyIons,”LANLReport,LA-UR-15-27858(2015),
NPX,andMARS15TransportCodes,”JointICTP-IAEA summary accepted for presentation at PHYSOR 2016,
AdvancedWorkshoponModelCodesforSpallationRe- SunValley,Idaho,USA,May1-5,2016.
actions. Trieste, Italy (February 2008), LANL Report 17. L. KERBY, S. MASHNIK, K. GUDIMA, A. SIERK,
LA-UR-08-2931,arXiv:0812.1820. J.BULL,andM.JAMES,“ProductionofEnergeticHeavy
4. K. GUDIMA, S. MASHNIK, and A. SIERK, ClustersinCEMandMCNP6,”LANLReport,LA-UR-
“User Manual for the code LAQGSM,” (2001), 15-29524(2015).
LANL Report LA-UR-01-6804; http://lib- 18. R. GREEN, R. KORTELING, and K. JACKSON, “In-
www.lanl.gov/lapubs/00818645.pdf. clusiveProductionofIsotopicallyResolvedLiThrough
5. I.PSHENICHNOV,A.BOTVINA,I.MISHUSTIN,and MgFragmentsby480MeVp+AgReactions,”Physical
W.GRAINER,“NuclearFragmentationReactionsinEx- ReviewC,29,1806–1824(1984).
tendedMediaStudiedwithGEANT4Toolkit,”Nuclear 19. H. MACHNER, et al., “Isotopic production cross sec-
InstrumentsandMethodsinPhysicsResearchB,268,604 tionsinproton-nucleuscollisionsat200MeV,”Physical
(2010). ReviewC,73,044606(2006).
6. M.HULTQVIST,M.LAZZERONI,A.BOTVINA,I.GU-
DOWSKA,N.SOBOLEVSKY,andA.BRAHME,“Eval-