NASATechnicalPaper3350August1993SemiempiricalFragmentationModels onGalacticCosmicRayTransportCalculationsWith Hydrogen TargetJudy L.Shinn,John W.Wilson,andFrancisF.Badavi

NASATechnicalPaper33501993SemiempiricalFragmentationModels onGalacticCosmicRayTransportCalculationsWith Hydrogen TargetJudy L.ShinnandJohn W.WilsonLangleyResearchCenterHampton,VirginiaFrancis F.BadaviChristopher NewportUniversityNewportNews,Virginia

AbstractNuclear fragmentat ioncrosssections ofSilberberg and Tsao thatar e more accurate for a hydrogen target have been implemented inthe databaseto replacethose ofRudstam foragalactic cosmicraytr ansportcode(HZETRN).Samplecalculations havebeenmadeforthetr ansportedgalacticcosmicray uxthroughaliquidhydrogenshieldatsolar minimumcondition to determine theeffectofsuch a change.The transportedflux basedon the Silberberg-Tsao semiempiricalfor-malism contains fewerhigh- LET(linearenergy transfer) componentsbut morelow-LETcomponents than theresultsbasedonRudstam'sfor-malism; and this disparity deepensas theshieldthicknessincreases.Acomparisonof theresults obtained fromusingbothenergy-dependentandenergy-independent crosssectionsofSilberberg andTsaoindicatesthat the energy-independent assumption resultsinan underestimationof high-LET flux above 100 keV/?m by approximately40 percentfora15-g/cm2thicknessof liquid hydrogen. Similar resultswere ob-taine dinaprevious study(NASATP-3243)whenbothenergy-dependentandenergy-independentcross sections ofRudstamwere considered.Nonetheless, the presentstudy found that anenergy-independentcal-culation would bebestaccomplished byusingRudstam's crosssectionsas done inthe past forvarious engineeringapplications.Intro ductionEstimates ofgalactic cosmicrayexposure andthe requiredshieldingforastronautsduring theirin terplanetary missionrely onradiation transportco des thataccurately describe the interactionsandpropagation of theseradiation fieldsthroughoutthebulkmedium(ref. 1). HZETRN(ref. 2),whichisa state-of-the-art galacticcosmic raytransport codede veloped atthe LangleyResearch Center,containsdetailed descriptions of physical processessuch asenergy loss, nuclearabsorption, and fragmentationcross sectionsof projectileions. However,theun-certainties ofnuclear fragmentation crosssectionsexisting inthe coderemain fairly largebecause ofthe lack ofreliable experimental data(ref.3). Thiscondition is especiallytrue forcollisions ofheavyions onheavyionsfor which theresultsofNUCFRG(ref.4), based onasemiempiricalabrasion-ablationmodel,are usedasinputstoHZETRN.(Note that animpro vedversion of aheavyionfragmentationmo delwill b eavailableforuse asinputsintheimmediatefuture.) Forcollisions ofheavyions onprotons,Rudstam'ssemiempirical parameterization (ref. 5)has beenusedin theexistingHZETRN.Rudstamand Metropolis etal. (refs.5and 6,resp ectively) were the pioneers whosystematizedhigh-energycrosssectionmeasurementsintoause-ful analyticalrelationship describing nuclear reac-tions. Theseanalytical relationships havebeen re-vised andimproved bymany newresearchersasnewcross-section databecome available.Themost com-prehensiv eset ofsemiempirical estimatesof crosssections for a hydrogentarget is perhaps due toSilb erberg and Tsao(refs. 7and8),and tothe mostrecen twork of Webber,Kish, and Schrier(ref. 9).In thepresent study, the formulationofSilberbergandTsao forahydrogentargetwillreplace thatofRudstam in HZETRN, and theeffectofsuch a re-placemen t will beexaminedforestimatesofgalacticcosmicray exposureusingliquidhydrogenasashield.TransportMethodsAs energeticions traverse through bulkmat-ter, theyloseenergythroughtheir interaction withatomic electrons alongtheir trajectories. On occa-sion, theyinteractviolentlywithnucleiofthematterandthusproduceion fragmentsor secondarynucle-ons movingin theforwarddirectionandlow-energyfragmentsof thestrucktargetnucleus. The transportproblemfortheshort-rangetargetfragmentscan beeasily solved in closed formintermsofcollision den-sit y(ref.10)and treatedseparately. Hence,thepro jectile-ionfragmentor secondarynucleontrans-portis theremainingproblemof interest. Intheprevious work(ref. 10), theprojectile-ionfragmentsandsecondary nucleons weretreated asifall wentstraigh t ahead (ref. 11). Thestraight-aheadapprox-imation is found to bequite accurate forthenearlyisotropiccosmicrayfluence(ref.10).1

Because ofthelongrangeofthecoulombforce and the largepercentageof the material volumebeingo ccupiedby electrons,theelectroninteractions can, toagood approximation, betreated asacontinuousslo wing-downprocess overanyfinite pathlength. Althoughthe energylostby anion oversomefixedpathlength fluctuates about a meanvalue,thisfluctuationamountsto nomore thanafew percent (refs.12{15)and isofno importanceinthe study of space radiation.In thefollowing,acontinuousslowing-downtheorywillbeassumed, andtherelevantquantityisthe averagelossperunitofpathlength.With thestraight-ahead approximationandthetargetsecondaryfragmentsneglected(refs.10and11),thetransportequationmay bewritten as<=@@x??j @@ES(E)+oej(E)>=OEj(x;E)=XkZ1Efjk(E;E0)OEk(x;E0)dE0(1)whereOEj(x;E) is thefluxofionsoftypejwithatomicmassAjandchargeZjatxmovingalongthex-axisatenergyE(inunitsofMeV/amu),oejisthe correspondingmacroscopic nuclearabsorptioncrosssection,S(E)isthe stopping power (continuousslowing-downapproximation)ofthe protons,f jk(E;E0) is adifferentialenergycrosssection forproductionofionjincollisionbyionk, and?jisthe rangescaling parameterthat is definedas?j =Z2jAj(2)Thesolutiontoequation(1)isfoundtobe subjectto theboundaryconditionatx= (that is,OEj(0;E));whichisthe incidentbeamspectrum.By transforming the heavy iontransport equationtoan integral alongthecharacteristic curveof thatparticular ion(ref.10)andusing the perturbationtheory (ref. 16),the solutionto equation (1) is givenasastepping procedure withstepsizehinthex-direction(ref. 17). Thus,j (x+h;r)ssexp???j(r;h)?j(x;r+?jh)+XkZh0Z1rexp???j(r;z)??k(r0;h?z)?fjk(r+?jz;r0)?k?x;r0+?k(h?z)?dr0dz(3)wherej(x;rj)=S(E)OEj(x;E)rjisthe residualrangeofionjgiven byr j(E)=ZE0dE0Sj(E0)andthe exponentialisthe integrating factor with? j(r;t)=Zt0oej(r+?jt0)dt0Currently, weassume forZj >1andk>jthatfjk(r;r0)=fjk(r0)ffi(r?r0)(4)2

Using equati on(4), equation(3)now becomesj (x+h;r)ssexp [??j(r;h)]j(x;r+?jh)+XkZh0dzexp[??j(r;z)??k(r0;h?z)]oejk(r0)?k[x;r0+?k(h?z)] (5)wit hr0=r+?jz. Equation(5) is fu rtherapproximatedasj(x+h;r)ssexp[??j(r;h)]j(x;r+?jh)+XkZh0dzexp[??j(r;z)??k(r;h?z)]oejk(r)k[x;r+?jz+?k(h?z)]ssexp[?oej(r)h]j(x;r+?jh)+Xkoejk(r)(exp[?oej(r)h]?exp[?oek(r)h]oek(r)?oej(r))k(x;r+?jh)+O[(?k??j)h](6)Equation(6)isthe stepping formalismwith energy-dependent crosssectionsfork>4He. Thecorrespondingsteppingformalism fornucleonshasbeendiscussedin detailinreferences8{19. These stepping formalisms arethen used to march the solutionfrom thesurface boundarytothedesired shieldthickness.Nucl earFragmentation DataBaseE ven thoughtheaccuracy of the experimentaldatamay improve forspeci ficreactions, a reason-able means of representing datain computationalpro ceduresfor cosmicraytransport calculationisstillachallenge. For HZETRNandotherradia-tiontransport codesdevelopedatLangley(refs. 18and 20),a pointrepresentation of thedata isavoidedb ecause largemultidimensionalarrays will eventu-ally rivalcomputer storage. Instead,various semi-empirical methodssuitableforcertain target or frag-men t groups areputtogetheringeneratingthedatabase. These semiempirical methods,whichare builton availableexperimentaldata and sometheoreticalbasedescribingapproximately thesystematicvaria-tionofreactioncross sections,offer thepossibilityof implementinganyadditionalnecessarycorrectionfactorsoradjusting someexistingparameters.Whena nucleusiscollidedbyhigh-energy nucle-ons, someindividualnuclear constituentsare ejectedb ydirectknockout (ref. 21). Theremaining nuclearstructure isleftin anexcited statewhichseeks anequilibrium minimum-energyconfigurationthroughparticle emission (ref. 5). Thisstate is thebasis ofRudstam 'sformulation forthesystematicsof spal-lation productsproduced in suchcollisions. In hisformalism, the distributionofresultantisotopesthatare relatedtothe statisticalnatureofthe evaporationpro cess(ref. 22)isassumedtobe Gaussiancenteredatthenuclear stability line,andthetotal changein nuclear massandthe dependenceon theincidentpro jectileenergy aretreatedempirically. FollowingRudstam'swork, SilberbergandTsao (refs.7and8)lateraddedmore correctivefactors to theformalismas more experimental databecame available.Inad-dition,they added a scaling factor thatrelatesthefragmentationcrosssectionproduced ona hydrogentarget tothaton theheaviertarget.Samplesoffragmentation crosssectionoejkusedasinputs to HZETRN areshown asafunctionofprojectile-ionchargeZkandfragment-ion chargeZj infigures1and2fora liquid hydrogentargetandinfigures3and4fora water target atvariousen-ergies ofthe projectiles. Figures 1and3reflecttheresultsproduced byusing Rudstam's formalism forthe fragmentswithZj>2,whereasfigures2and4reflectthose by usingtheSilberberg-Tsao formal-ism. For nucleonandhelium fragments, the crosssections wereobtained fromtheresultsof Bertiniet al. (refs.23and24). (Notethat thecross sectionsho wnin thefigures has beenreduced,forconve-nience,by afactorof10 fornucleon fragmentsandafactorof4forhelium fragments.)Becausethe scal-ing factor inthe formalismof Silberberg and Tsaodo esnotgiveadequate resultsfor a target heavierthan hydrogen (ref. 25), the semiempirical abrasion-ablationmodel (ref.4)isusedin obtainingthe cross3

sections contributedbytheoxygenions in thewatertarget .F or all thecrosssections shownin figures 1{4at three separatepro jectileenergies(150,600,and2400MeV/amu),the peakofthefragments spectra(at constantZk) isgenerally higher aspredictedbyRudstam thanthatpredicted bySilberbergandTsao. Conversely,thespread fromthepeak tothe fragments withlowerZislower for Rudstam,whereas the zig-zag shape overeven and oddZ charges ismorepronouncedfor Silberberg andTsao.A tenergiesbelow150MeV/amu,some results(notsho wn)givenbyRudstam'sformalism areerroneous ;th us,forthe transportcalculationspresented herein,the valuesofcrosssectionat150MeV/amu havebeenextrap olated tobelow150MeV for projectileionswithZ>20, as has beendonein reference 17.Re sultsBy using Rudstam's formalism, severalstudiesweremadeinthepastthatinvolvedgalacticcosmicray (GCR)transport calculationsthroughashieldthatcontained hydrogenatoms, such aswater(tis-sue equivalent)(refs. 26and 27) orliquid hydrogen(ref. 28). Inthesecalculations, the crosssectionsw ereassumedtobe energy independentandset equalto theasymptoticvaluesat highenergy. Recently,impro vementswere madeto HZETRNby removingthe energy-independent assumption;andtheeffectsofsuch changesto the existingresults wereexam-ined intermsofLETspectrathatshowedasubstan-tial enhancement ofhigh-LET components(ref.17).Inthepresent study, Rudstam's formalism was re-placed bythat of SilberbergandTsao,andthe effectof thatreplacement wasthen examinedbycomparingthe GCRexposurelevelsbehindtheliquid hydrogenshield atthesolarminimum conditiongivenbytheCREMEmodelofreference29.Thehigh-LET radiationcomponents areusuallydegradedto lower LETcomponents asaresultofn uclear interactionsbetweenprojectile andtargetn uclei,andsuch processesbecome moresignificantastheparticles penetratefarther intotheshieldmedium.This degradationisillustratedinfigure5inwhichthe annualdifferentialdoseanddoseequiv-alent areplottedasafunctionof LET(orL) for2{, 5{,and15{g/cm2thicknessesoftheshield.Thespikesseeninthe figures correspond tothe zero slopeof stoppingpower(dS=dE=0)at minimumioniza-tion(ref.30) ofeachion,withprotons startingatthelo westLETfollowedby increasingZfor theincreas-ingL. Because the LETcoordinateisplottedonalogarithmscale,the differential doseL dN=dLiscon-vertedtoL2dN=dL(whereN=ROEdE) sothattheareaunderthecurve is linearlyproportionaltothetotaldose.Similarly,thedifferentialdoseequivalentisplotted asQL2dN=dL, where thequalityQisafunctionofL. Themagnificationindose equivalentat thehigh-LET region isaresult ofthe ICRP 60quality factor(ref.31).Thedifferencesbetween the spectrafor thefrag-men tation cross sectionbyRudstam'sformalism(fig.1) and those bySilberberg andTsao (fig. 2)as discussed earlierare reflectedin thecalculatedLET sp ectrafor the transportedflux throughtheliquid hydrogenshield. Infigure6(a), theratioofthe LETspectra forthedifferentialfluxcalculatedbyusingSilberberg and Tsaorelative tothatby us-ing Rudstamisdisplayed forthethreethicknessesoftheshield.The Silberberg-Tsao model producesmore lowerZfragments and fewer higherZfrag-ments,andtherefore morelowerLET componentsand fewer higher LETcomponents accordingtothespikesidentifiedforeachionin figure5. As a re-sult, theratio(fig.6(a)) ishigherat LETvaluesnearthe 100-MeV/cm region andlowerathighervaluesofLET. Thesedeviationsfromunitybecome morepro-nounced astheshield thicknessincreases. A similarcomparisonofintegralfluxLETspectraisshowninfigure 6(b)inwhich theratio atthe lowestLETis al-most identicalto unity; this indicates thatthe totalflux doesnotchange appreciablybecauseofdiffer-ences in thefragmentationmodel.Inthepreviousstudy(ref. 17), the removalofthe energy-independent assumptionwasimportantintherisk assessment ofGCR exposure. Usingthe liquid hydrogenshieldasan example,the LETcomp onents above100keV/?m(or 1000MeV/cm),whichcould contribute some biological-riskordersofmagnitude higher than thelowercomponents,wereshownto increaseby 40percent ata 15-g/cm2thic knessbecauseoftheremoval of the assumption.This conclusionwasbasedontheuseofRudstam'sformalism.Similar results wereobtainedinfigure7withthedata basegiven bySilberbergandTsao.Notein figure5thattheregionnear10000keV/?mwasnot ascriticalbecause ofthe diminishingfluxinthisregion.Acomparisonismadewith thetransport calcu-lations usingthe energy-dependent Silberberg-Tsaodatabaseandtheenergy-independent data basefromRudstam to serveasareferencefor theearlierGCRexposurestudies madewith the olddata baseandthe assumptionofan energy-independent crosssec-tion whichistakento bethe asymptoticvalue at2 GeV/amu. The ratioofthetwocalculations inLET spectra,for bothdifferentialandintegralfluxshowninfigures8(a)and8(b), respectively,displays4

almostan oscillatory behavior overa widerangeofL ET. Thus,some ofthedifferencesareprobablycan-celled out.One arrivesattheinterestingobserva-tionthat anenergy-independentcalculation usingthe Rudstamcross sectionsyieldsresults similar tothose ofanenergy-dependent calculation usingtheSilb erberg-Tsaovalues.ConcludingRemarksNuclear fragmentationcrosssections ofSilber-b ergand Tsaothat are moreaccurate forahy-drogen target havebeen placedin thedata basefor calculationsofgalactic cosmicray (GCR)trans-p ort. Whencompared withtheolddata baseofRudstam, theSilberberg-Tsaomodelproduces fewerhigher chargefragments but morelower charge frag-men ts.Samplecalculations of GCRtransport witha liquid hydrogenshieldreflect suchdifferences ofcross sectionsinthat thetransported fluxbased onthe Silberberg-Tsaomodelcontainsfewer high-LET(linear energytransfer) componentsbutmore lowerLET components. This disparity deepens astheshield thicknessincreases.WhentheSilberberg-Tsaocross sections areassumed tobe energy indepen-den tin the database, the comparativeresults in-dicate an underestimationoftheLET componentsa bove 100 ke V/?m byapproximately40percent fora15-g/cm2thicknessofliquidhydrogencaused bytheassumption. Moreover,thepresentstudyfoundthatanenergy-independentcalculationwouldbebest ac-complished byusingRudstam's crosssections asdonein thepast.NASALangleyResearchCenterHampton, VA23681-0001June8,1993References1.Wilson,John W.; Townsend,Lawrence W.; Schimmer-ling, Walter;Khandelwal,GovindS.; Khan,Ferdous;Nealy,JohnE.;Cucinotta,FrancisA.;Simonsen, Lisa C.;Shinn, JudyL.;and Norbury,John W.:Tra nsportMethodsandInteractions forSpaceRadiations.NASARP-1257,1991.2.Wilson,John W.;Chun,Sang Y.; Badavi, ForoozF.;T ownsend,LawrenceW.; andLamkin, Stanley L.:H ZETRN:A Heavy Ion-Nucleon Transport Code forSp aceRadiations.NASATP-3146,1991.3.Townsend, LawrenceW.; Cucinotta, Francis A.; andWilson, JohnW.: HZEReactionsandData-BaseDe-velopment. Paper presentedatNATOAdvancedStudyInstituteon BiologicalEffects and Physicsof SolarandGalactic Cosmic Radiation(Amer?c~aode Pera,Portugal),Oct.12{23,1991.4.Wilson,John W.; Townsend, LawrenceW.;andBadavi,F.F.:A SemiempiricalNuclearFragmentationModel.Nucl. Instrum.&MethodsPhys.Res., vol. B18,no. 3,F eb.1987,pp. 225{231.5.Rudstam, G.: Systematics of Spallation Yields.Zeitschrift furNaturforschung,vol.21a,no.7,July1966,pp. 1027{1041.6.Metropolis, N.; Bivins,R.; Storm,M.; Turkevich,An thony;Miller,J. M.;andFriedlander,G.:MonteCarloCalculationsonIntranuclearCascades.I. Low-EnergyStudies.Phys. Review, secondser.,vol. 110,no.1,Apr.1, 1958,pp.185{203.7.Silberberg, R.;andTsao,C. H.: PartialCross-SectionsinHigh-Energy Nuclear Reactions, and AstrophysicalApplications. I. TargetsWithZ<=28.Astrophys.J.Suppl.Ser., no.220(I), vol. 25,1973, pp. 315{333.8. Silberberg, R.;Tsao,C.H.;andShapiro,M. M.: Semi-empirical CrossSections, andApplicationstoNuclearInteractions of Cosmic Rays.Sp allationNuclear Reac-tions and Their Applications, B. S. P. ShenandM. Merker,eds., D.Reidel Publ. Co., c.1976,pp. 49{81.9.Webber,W.R.; Kish,J.C.;andSchrier, D.A.: Formulafor CalculatingPartial Cross Sections forNuclearRe-actions of NucleiWith E? >200MeV/Nucleon in Hy-drogenTargets.Phys. Review C, vol. 41, no. 2,Feb.1990, pp.566{571.10. Wilson,JohnW.:AnalysisoftheTheoryofHigh-EnergyIonTransport.NASATND-8381, 1977.11. Wilson, JohnW.:HeavyIonTransport inthe StraightA headApproximation.NASATP-2178,1983.12. Janni, JosephF.: ProtonRange-EnergyTables, 1keV{10 GeV|EnergyLoss,Range,Path Length,Time-of-Flight, Straggling, MultipleScattering,andNuclearInteractionProbability. Part1.For63 Compounds.At .Data& Nucl.DataTables, vol. 27,nos.2/3, Mar./May1982, pp.147{339.13. Janni, JosephF.: ProtonRange-EnergyTables, 1keV{10 GeV|EnergyLoss,Range,Path Length,Time-of-Flight, Straggling, MultipleScattering,andNuclearInteractionProbability. Part2. For Elements1<=Z<=92.At. Data & Nucl. DataTables, vol. 27, nos. 4/5,July/Sept.1982, pp.341{529.14. Schimmerling,Walter;Rapkin, Marwin; Wong,Mervyn;and Howard, Jerry: The Propagation of RelativisticHea vyIonsin MultielementBeam Lines.Me d. Phys.,vol.13, no.2,Mar./Apr.1986,pp.217{228.15. Alsmiller,R. G.,Jr.;Barish, J.;andScott,W. W.: TheEffects ofMultipleCoulomb ScatteringandRangeStrag-glinginShieldingAgainstSolar-FlareProtons.Nucl. Sci.&Eng., vol. 35,no.3,Mar. 1969,pp.405{406.16. Wilson,JohnW.;and Lamkin, StanleyL.:PerturbationTheoryforCharged-ParticleTransp ortinOneDimension.Nucl. Sci. & Eng., vol. 57, no. 4, Aug. 1975,pp. 292{299.5

17. Shinn,JudyL.; John, Sarah; Tripathi,Ram K.;Wi lson, JohnW.;Townsend,LawrenceW.;andNorbury,JohnW.:Fully Energy-Dependent HZET RN(A GalacticCo smic-Ray TransportCode).NASATP-3243,1992.18. Wilson, John W.; Townsend, LawrenceW.; Nealy,John E.;Chun,Sang Y.;Hong,B.S.;Buck, WarrenW.;Lamkin, S.L.;Ganapol,BarryD.;Khan,Ferdous;andCucinotta,FrancisA.:BRYNTRN: A BaryonTransportModel. NASATP-2887,1989.19. Shinn,Judy L.;Wilson,JohnW.;Weyland,Mark;andCucinotta,Francis A.:Impr ovements in ComputationalAccuracy of BRYNTRN (ABaryonTransportCode).NASATP-3093,1991.20. Wilson,JohnW.;Lamkin,StanleyL.;Farhat, Hamidul-lah; Ganapol,BarryD.; and Townsend, LawrenceW.:AHier archy ofTransportApproximationsforHighEnergyHeavy(HZE)Ions.NASATM-4118, 1989.21. Serber,R.:NuclearReactions atHigh Energies.Phys.R eview, vol. 72,no.11, Dec.1,1947, pp.1114{1115.22. Dostrovsky,I.; Rabinowitz,P.;andBivins, R.: MonteCarlo Calculations of High-Energy NuclearInteractions.I.Systematics ofNuclear Evaporation.Phys. Review,vol.111,no. 6,Sept. 15,1958, pp.1659{1676.23. Bertini, HugoW.;Guthrie, MiriamP.; and Culkowski,Arline H.:NonelasticInteractionsof Nucleonsandss-MesonsWith ComplexNuclei atEnergies Below 3Ge V. CRNL-TM-3148,U.S.AtomicEnergyCommission,Mar.28,1972.24.MECC-7IntranuclearCascadeCode,500-MeVProtonson 0-16. I4CAnalysisCodes(Programmedfor H.W.Bertini ).AvailablefromRadiationShielding InformationCen ter, Oak RidgeNational Lab.,1968.25. Wilson, JohnW.;Townsend,Lawrence W.; andKhan,F erdous:Evaluation of HighlyIonizingComponentsinHigh-EnergyNucleonRadiation Fields.He althPhys.,vol.57,no. 5,Nov.1989,pp. 717{724.26. Shinn,Judy L.;Wilson,John W.; and Nealy, JohnE.:R eliability ofEquivalentSphereModelinBlood-FormingOrganDose Estimation. NASA TM-4178,1990.27. Cucinotta, FrancisA.;Atwell, William; Weyland,Mark;Hardy, AlvaC.;Wilson,John W.;Townsend,La wrenceW.;Shinn, JudyL.; and Katz, Robert:R adi-ation Risk Predictionsfor SpaceStationFreedomOrbits.NASATP-3098,1991.28. Townsend, Lawrence W.; Nealy, John E.; Wilson,John W.; and Simonsen, LisaC.:Estimates ofGalac-tic Cosmic Ray ShieldingRequirementsDuring SolarMinimum. NASA TM-4167,1990.29. Adams, James H., Jr.:Cosmic Ray Effectson Micro-ele ctronics,Part IV. NRLMemo. Rep.5901 (Revised),NavalResearchLab., Dec.31, 1987.30. Wilson,JohnW.; and Badavi,Francis F.:A StudyoftheGenerationof Linear EnergyTransferSpectraforSpaceRadiations. NASA TM-4410,1992.31.1990Recommendationsof theInternational Commissionon RadiologicalProtection. ICRP Publ. 60, PergamonPress Inc.,c.1991.6

Figure4. Semiempirical, differential fragmentationcross sectionforwater targetasfunctionof projectile-ion chargeandfragment-ionchargeaccordingtoSil berberg-Tsao formalism forfragments heavier thanhelium. Crosssectionsshownfor nucleonandhelium fragmentshave beenreduced byfactorsof 10 and 4,resp ectively. (1cm2/gconvertsto29.9 barns.)1

REPORT DOCUMENTATIONPAGEFormApprovedOMB No. 0704-0188Publicreportingburdenforthiscollection of information is estimatedtoaverage 1hourperresponse,includingthetimeforreviewing instructions, searchingexisting data sources,gatheringandmaintainingthedataneeded,andcompletingandreviewingthe collectionofinformation.Send commentsregardingthisburdenestimate orany otherasp ectofthiscollectionofinformation, includingsuggestionsforreducingthisburden,toWashingtonHeadquartersServices,Directoratefor Information Operations andReports, 1215JeffersonDavis Highway, Suite1204, Arlington,VA 22202-4302,andtotheOffice of Management andBudget,Paperwork ReductionProject (0704-0188),Washington, DC20503.1.AGENCYUSEONLY(Leaveblank)2.REPORTDATE3.REPORTTYPEANDDATES COVEREDAu gust1993TechnicalPaper4.TITLE ANDSUBTITLESemiempirical Fragmentation Modelson GalacticCosmic RayT ransport CalculationsWithHydrogen Target6. AUTHOR(S)JudyL. Shinn,JohnW.Wilson, and FrancisF.Badavi7.PERFORMING ORGANIZATIONNAME(S)AND ADDRESS(ES)NASA LangleyResearchCenterHampton, VA23681-00019.SPONSORING/MONITORINGAGENCY NAME(S) ANDADDRESS(ES)National Aeronautics and SpaceAdministrationWashington, DC 20546-00015.FUNDING NUMBERSWU199-45-16-118.PERFORMING ORGANIZATIONREPORT NUMBERL-1722710. SPONSORING/MONITORINGAGENCY REPORTNUMBERNASATP-335011. SUPPLEMENTARY NOTESShinnandWilson:LangleyResearch Center,Hampton,VA; Badavi: ChristopherNewport University,Newp ortNews,VA.12a.DISTRIBUTION/AVAILABILITYSTATEMENT12b.DISTRIBUTION CODEUnclassified{UnlimitedSubject Category9313. ABSTRACT(Maximum 200 words)Nuclear fragmentationcross sections ofSilberberg andTsao that are moreaccuratefora hydrogentargetha vebeen implemented in thedata basetoreplace thoseofRudstam foragalactic cosmicray transportcode(H ZETRN). Samplecalculations havebeenmade forthetransportedgalacticcosmicray uxthrough a liquidh ydrogenshieldatsolarminimumconditiontodetermine theeffectofsuchachange.Thetransported flux basedon theSilberberg-Tsaosemiempirical formalismcontainsfewer high-LET(linear energy transfer)componentsbut morelow-LET componentsthantheresultsbasedonRudstam'sformalism;andthisdisparitydeepensasthe shield thicknessincreases. Acomparisonof theresults obtained fromusing bothenergy-dependentandenergy-independent crosssectionsofSilberbergandTsao indicatesthattheenergy-independentassumptionresultsinan underestimationofhigh-LET fluxabove100keV/?m byapproximately40percent fora15-g/cm2thicknessofliquidhydrogen.Similar results wereobtainedin apreviousstudy(NASA TP-3243)whenbothenergy-dep endentandenergy-independent crosssections of Rudstamwereconsidered.Nonetheless,thepresentstudy found thatanenergy-independentcalculation would bebestaccomplished byusing Rudstam's crosssections asdonein thepastforvariousengineering applications.14. SUBJECTTERMS15. NUMBEROF PAGESGalacticcosmicraytransport; Semiempiricalnuclear fragmentationmodel1616. PRICECODEA0317. SECURITY CLASSIFICATION18. SECURITYCLASSIFICATION19. SECURITY CLASSIFICATION20. LIMITATIONOF REPORTOF THIS PAGEOF ABSTRACTOF ABSTRACTUnclassifiedUnclassifiedNSN 7540-01-280-5500StandardForm298(Rev. 2-89)Prescribed byANSIStd. Z39-18298-102