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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. 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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. 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