An evaluation of thermal neutron capture on the stable tungsten isotopes is presented, with preliminary results for the compound systems 183;184;185;187W. The evaluation procedure compares the g-ray cross-section data collected at the Budapest reactor, with Monte Carlo simulations of g-ray emission following the thermal neutron-capture process. The statistical-decay code DICEBOX was used for the Monte Carlo simulations. The evaluation yields new gamma rays in 185W and the confirmation of spins in 187W, raising the number of levels below which the level schemes are considered complete, thus increasing the number of levels that can be used in neutron data libraries

Belgya, T.

Firestone, R.

Hurst, A. M.

Revay, Z. S.

Sleaford, B.

Summers, N. C.

Hurst, Aaron

Summers, Neil

Sleaford, Brad

Firestone, Richard B

Revay, Z.S.

UNT Digital Library

International Conference on Nuclear Data for Science and Technology 2010GAMMA SPECTRUM FROM NEUTRON CAPTURE ONTUNGSTEN ISOTOPESA. M. HURST∗1,2, N. C. SUMMERS1, B. W. SLEAFORD1, and R. B. FIRESTONE21Lawrence Livermore National Laboratory, Livermore, California 94551, USA2Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA∗Corresponding author. E-mail : AMHurst@lbl.govReceivedAccepted for PublicationAn evaluation of thermal neutron capture on the stable tungsten isotopes is presented, with preliminary results for thecompound systems183,184,185,187W. The evaluation procedure compares theγ-ray cross-section data collected at the Budapestreactor, with Monte Carlo simulations ofγ-ray emission following the thermal neutron-capture process. The statistical-decaycodeDICEBOX was used for the Monte Carlo simulations. The evaluation yields newγ rays in185W and the confirmationof spins in187W, raising the number of levels below which the level schemes are considered complete, thus increasing thenumber of levels that can be used in neutron data libraries.KEYWORDS : 183,184,185,187W, γ-ray cross sections, neutron capture, EGAF, DICEBOX, level density, photon strength function1. INTRODUCTIONImproved neutron-captureγ-ray spectra are needed in avariety non-proliferation programs, e.g. in neutron-transportcodes for applications in the interest of national security.Building upon known decay schemes and improving theγ-ray spectrum in the neutron data libraries will provide theextensive data essential for modeling and identification ofspecial nuclear materials (actinides) and associated mate-rials (e.g. structural materials). In this paper, we describeimprovements to the known decay schemes of the tungstenisotopes from neutron capture onto all but the least abundantof the stable tungsten isotopes,180W (natural abundance:0.12 %). The neutron-captureγ-ray decay data for the com-pound systems183,184,185,187W from theEvaluated Gamma-ray Activation File (EGAF) [1], has been evaluated bycomparing with simulated populations to previously ob-served levels in these isotopes based on statistical-modelcalculations using the Monte Carlo codeDICEBOX [2].These evaluations provide improved databases ofγ spec-tra, improved level schemes with clarification of nuclearstructure issues such as tentative/unknown spin-parity (Jπ)assignments, and will ultimately be used to provide newmeasurements of the total radiative thermal neutron-capturecross sections (e.g. see Ref. [3]). Furthermore, the resultsof these evaluations will provide input to the EvaluatedNuclear Data File (ENDF), a nuclear reaction database thatis used by the Monte Carlo Neutron Transport (MCNP)codes.2. THE EGAF PROJECTThis work uses experimental neutron-captureγ-raycross sectionσγ data from the EGAF database [1] tocompare with simulation (see Sec. 3.). Precise values ofthermalσγ have previously been measured with guidedneutron beams (thermal flux∼ 2 × 106 s−1cm−2) at the 10-MW Budapest reactor for all elemental targets withZ =1− 83, 90, and 92, except for He and Pm, in addition to theradioactive targets99Tc and129I [4,5]. Details of a typicalexperimental setup are described in Ref. [3]. Internal crosssections were calibrated using stoichiometric compoundscontaining elements with well-known cross sections, e.g. H,N, Cl, and S, in addition to homogeneous mixtures, such asH2O and HCl, and activation products with well-knownγrays, e.g.19F, 28Al, 100Tc, and235U.3. DICEBOXThe Monte Carlo statistical-decay code,DICEBOX [2],has been used to model the thermal neutron-captureγcascade by calculating the intensities of transitions feedingthe low-lying states. The code generates level-scheme sim-ulations (termednuclear realizations) following the thermalneutron-capture process according to the choice of inputtatistical-model level density and photon strength func-tions, and is further constrained by theγ-ray transitionprobabilities along with known nuclear structure proper-ties of the investigated isotope in the Evaluated NuclearStructure Data File (ENSDF) database [6]. TheDICEBOXA. M. HURST et al., Gamma spectrum from neutron capture on tungsten isotopescode also uses internal conversion coefficient data fromBand Raman (BrIcc) [7]. In the following calculations, Acritical energy, Ecrit, is defined as the energy level, belowwhich, all information in the decay scheme is unique andcomplete. The code then takes all energy-level andγ-raybranching information beneathEcrit from experimental data.The known level scheme is taken from RIPL-3 [8] (Refer-ence Input Parameter Library) withEcrit taken as the energyof the level which is the minimum ofNC (the number oflevels for which the spins and parities are unique) andNmax(the maximum number of levels for which the level schemeis complete). The level scheme is then supplemented withthe new information from EGAF. Supplemental feeding tothese measured discrete lines from the quasi continuum (i.e.aboveEcrit) is simulated byDICEBOX. All levels andγ raysin the quasi continuum are randomly generated dependingon the input level density and photon strength functionmodels selected. In this work 2× 104 capture stateγ-ray decay cascades were randomly generated per nuclearrealization using the Monte Carlo method. Measured crosssections of primary transitions (i.e. a transition depopulatingthe capture state) to levels belowEcrit were used in each nu-clear realization. Good statistical variation in the simulatedlevel feedings was achieved by averaging over five separatenuclear realizations.Along with the adopted experimental level scheme be-low Ecrit and the capture-state spin composition,J, whereJ = 1/2+ for capture onto even-even targets, andJ =Jgs(target)±1/2 for capture onto odd-A and odd-odd targets,the population of the low-lying levels is largely influencedthrough the choice of level-density and photon strengthfunction models for the different transition types. In thefollowing simulations (Sec. 4.) the back-shifted Fermi gasmodel [9,10] with von Egidy parameterization [11] wasadopted.DICEBOX only considers photon strength functions forelectric dipole (E1), magnetic dipole (M1), and electricquadrapole (E2) transition types. Of these transitions,E1are by far dominant, followed byM1, while E2 are consid-erably less significant. A form of the generalized Lorentzianmodel has been used to describe the shape of the giantelectric dipole resonance (GDR) in the present calculations.The parameterization sets for theE1 GDRs for thetungsten isotopes were extracted from experimental datacompiled in the RIPL-2 [12] database. For theM1 GDRphoton strength function, a compound model accountingfor scissors-type and spin-flip type excitation modes wasadopted, with the resonance-shape parameterization esti-mated from a previous study of the170,171,172Yb isotopes[13]. Finally, a giant electric quadrapole photon strengthfunction model describing both isoscalar and isovectorvibrational modes was adopted for theE2 transitions [14].4. RESULTSThe results of the calculations simulating the thermal-captureγ cascade using theDICEBOX code are presentedin this section. Modeling of the thermal-neutron captureprocess onto the four most abundant of the naturally-occurring tungsten isotopes,182W (26.5 %),183W (14.3 %),184W (30.6 %), and186W (28.4 %), has been used to evaluatethe knownγ spectrum and make improvements to the decayschemes in the corresponding(A+1)W compound systems.With the exception of the184W compound system, all othercompounds are formed from neutron capture onto an even-even target, accordingly the capture state isJπ = 1/2+ forthese systems.The results of the simulated populations are shown incomparison to the experimental depopulations in the fol-lowing population-depopulation plots presented in log-logspace. Uncertainties along the horizontal axis (experimen-tal depopulation) correspond to experimental errors, whilethose on the vertical axis (simulated population) are due toPorter-Thomas [15] fluctuations in generating the differentnuclear realizations. If the level scheme of the isotope iscomplete and unique up to the definedEcrit, and the decayis purely statistical (i.e. no collective eff cts), then all datapoints should fall on the slope ofy = x. Scatter around thisline provides a measure of the quality and completeness ofboth simulation and experimental data. In the correspondingdecay schemes (shown only for185W and187W), the widthof the arrow illustrates the relative intensity of the transition:the black part of the arrow represents theγ decay andthe white part internal conversion; primary transitions arethose from the capture state (the highest level, not plotted toscale on the energy axis) represented by blue arrows. Newinformation is highlighted in red on the decay schemes.Fig. 1. Simulated population versus experimental depopulationfor the compound systems183W (left) and184W (right)4.1 182W(n,γ)183WDecay data extracted from the RIPL-3 database suggests10 known levels above the ground state, indicating a valueEcrit = 475.4 keV for 183W. No further information wasavailable in the EGAF database to allowEcrit to be raised.The RIPL-3 and EGAF data compare well beneathEcrit.The next highest level at 487 keV with a tentative (13/2+)assignment, is not seen in the EGAF database, due to itshigh spin. Three primaries have been observed feeding2A. M. HURST et al., Gamma spectrum from neutron capture on tungsten isotopeslevels belowEcrit: a 6190.6-keVE1 transition to the 1/2−ground state, a 6144.2-keVE1 transition to the 3/2− 46.5-keV level, and a 5981.8-keVE1 transition to the 3/2−208.8-keV level. The calculation shown in Fig. 1(left) usesσγ information from the EGAF database;σγ data fromRIPL-3 does not produce a statistically-significant differentresult. The deviation of the data from the line is not clear,although, it could point to poor knowledge of the measuredγ-ray intensities for some low-energy transitions deexcit-ing low-lying states. This is currently being investigated.Additionally, an unreported 9/2− (308.9 keV)→ 5/2−(291.7 keV)E2 transition has beenimplantedinto the levelscheme since this would follow a likely rotational sequence.However, the addition/removal of this transition makes nostatistical difference to the overall result.4.2 183W(n,γ)184WLike 183W, the number of known levels cannot beextended beyond that in RIPL-3. The next level aboveEcritat 1283.6 keV is tentatively reported as a (1−, 2−) state.However, since a corresponding level has not been reportedin EGAF it is not possible to extendEcrit higher in anattempt to establish the configuration of the 1283.6-keVlevel. Since the target nucleus,183W, is odd-A and has a1/2−gs, the capture state at 7.4117 MeV in184W can haveeither a 0− or 1− configuration. The present calculation inFig. 1(right) assumes 100 % capture in the 1− state. Allσγ data has been taken from the RIPL-3 file. It should benoted that the RIPL-3 file contains a transition from the3− state at 1221.3 keV to the ground state which has notbeen reported in the EGAF file. Figure 1(right) shows thatthe only data point deviating significantly from the line isthe excited 0+ state. Various combinations of capture-statefractions are currently being investigated along withσγ datafrom the EGAF database to test the effect on the overallresult. The calculation also includes seven primaries feedingstates below Ecrit: 7412.0-keVE1 to the 0+ ground state,7299.7-keVE1 to the 2+ state at 111.2 keV, 6507.2-keVE1to the 2+ state at 903.3 keV, 6408.9-keVE1 to the 0+ stateat 1002.5 keV, 6289.9-keVE1 to the 2+ state at 1121.4 keV,6281.5-keVM1 to the 2− state at 1130.0 keV, and 6190.6-keV M1 to the 3− state at 1221.3 keV.4.3 184W(n,γ)185WThe number of levels belowEcrit has been increasedfrom 8, in RIPL-3, to 10, based on 2 new levels with corre-spondingγ-decays in the EGAF data. Figure 2(a) shows thenew decay scheme for185W that has been used to producethe optimal population-depopulation results of Fig. 2(b).The next highest state aboveEcrit, 384 keV (13/2+), dueto its high spin, contains noγ-decay information in EGAF.Using DICEBOX, it has been possible to confirm the, pre-viously tentative, 9/2− assignment for the 301.1-keV state,while the postulated tentative (7/2−) assignment from RIPL-3 for the 332.1-keV state has been changed to a 9/2− state onthe basis of population-depopulation arguments. Addition-ally, the energies for both of these states is more accuratelymeasured in EGAF. The RIPL-3 entries for these states were3/21/25/23/27/25/211/27/29/29/213/29/2246642937017410818816412295132241024317715070562351272662391581441/2+S(n) = 5.7537 MeV0.0023.5465.9193.36173.71187.89197.44243.39384.00390.49Ex [keV]Ecrit332.12301.105753.655729.205658.60RIPL EcritW185392661442723515610−/ −(RIPL J  )(7/2−)(9/2−)π(      )(b)(a)Fig. 2. 185W: (a) decay scheme; (b) simulated population versusexperimental depopulation.reported as 302 keV (9/2−) and 334 keV (7/2−), with noγ-decay information from either state. Four newγ transitionshave been reported deexciting the 332.1-keV state and twonew transitions deexciting the 301.1-keV state in EGAF.Furthermore, three newγ rays deexciting the lower levels at243.4 keV, 197.4 keV, and 93.4 keV, have also been reportedin EGAF. However, a new transition reported in EGAF from187.9-keV 5/2− → 173.7-keV 7/2− has not been included inthe calculation. This very low-energy transition has been re-ported with a seemingly unrealistic cross section; the largestbranch by almost a factor of four. Inclusion of this transitioncauses the data to deviate significantly from the line inFig. 2(b). Further investigation of this transition is requiredto determine the validity of the measured value. EGAFσγdata were used for all states in these calculations. It shouldbe noted, however, that for two very low-energy transitions,the reported cross sections were reduced by factors of 10and 100, respectively, for the 93.4-keV 3/2− → 23.5-keV1/2− and 243.4-keV 7/2− → 187.9-keV 5/2− transitions.Again, cross sections for such low-energy transitions are3A. M. HURST et al., Gamma spectrum from neutron capture on tungsten isotopesdifficult to measure experimentally and soDICEBOX beenused to obtain fits that show better agreement betweenexperimental depopulations and simulated populations. Thecalculations also incorporate three primaries to low-lyingstates belowEcrit: 5753.7-keVE1 to the 3/2− ground state,5730.2-keVE1 to the 1/2− state at 23.5 keV, and 5660.3-keV E1 to the 3/2− state at 93.4 keV.4.4 186W(n,γ)187W3/25/21/27/23/5/29/27/211/27714620112420512759303226157102 98W18777.360.00145.73204.83201.43329.00350.543/2−5/2−1/2−3/2−5/2−(9/2−)7/2−303.217/2−RIPL EcritEcritEx [keV]S(n) = 5.4664 MeV5466.75320.65261.71/2+364.229/2−(7/2−)(7/2−)(3/2−)(RIPL J  )π(b)(a)Fig. 3. 187W: (a) decay scheme; (b) simulated population versusexperimental depopulation.New information in the EGAF database has increasedthe number of unique levels by 3, from the RIPL-3 value.It has also been possible to confirm the previous 7/2−assignment for the state at 201.4 keV usingDICEBOX.This new information is highlighted in Fig. 3(a). The nexthighest level aboveEcrit at 329 keV with a tentative (9/2−)configuration, due to its high spin, is not seen in EGAF. Thecorresponding calculations for this decay scheme, shownin Fig. 3(b), were executed using branching ratios fromthe EGAF database. It should be noted, however, that theRIPL-3 database reveals an extra branch from 5/2− 303.2-keV level to the 3/2− 204.8-keV level. The branching ratiosin RIPL-3 database also differ significantly to those inEGAF. Optimal results were obtained using informationfrom EGAF exclusively. The calculation also includes threeprimary transitions from the 5.4664-MeV capture state:5466.7-keVE1 to the 3/2− ground state, 5320.6-keVE1to the 1/2− level at 145.7 keV, and 5261.7-keVE1 to the3/2− level at 204.8 keV.ACKNOWLEDGMENTSThis work was performed under the auspices of theU. S. Department of Energy by Lawrence Livermore Na-tional Laboratory under Contract DE-AC52-07NA27344,and by the University of California, supported by the Direc-tor, Office of Science, Office of Basic Energy Sciences, ofthe U. S. Department of Energy at Lawrence Berkeley Na-tional Laboratory under Contract DE-AC02-05CH11231.REFERENCES[1] R. B. Firestoneet al., Database of Prompt Gamma Raysfrom Slow Neutron Capture for Elemental Analysis, IAEASTI/PUB/1263, 251 pp (2007).[2] F. Becvar, Nucl. Instrum. Methods A417, 434 (1998).[3] M. Krticka et al., Phys. Rev. C77, 054615 (2008).[4] T. Belgya et al., Proceedings of the 9th InternationalSymposium on Capture Gamma-Ray Spectroscopy and Re-lated Topics, Budapest, Hungary, Oct. 8-12, edited byG. Molná, T. Belgya, Zs. Ŕevay (Springer-Verlag, Bu-dapest/Berlin/Heidelberg, 1997), P: 826.[5] Zs. Révay et al., Handbook of Prompt Gamma Activa-tion Analysis with Neutron Beams, edited by G. L. Molńar(Kluwer, Boston, 2004).[6] Evaluated Nuclear Structure Data File, an electronicdatabase of evaluated experimental nuclearstructure data maintained by the National NuclearData Center, Brookhaven National Laboratory,http://www.nndc.bnl.gov/ensdf/.[7] T. Kibédiet al., Nucl. Intsrum. Methods A589, 202 (2008).[8] R. Capoteet al., ”RIPL - Reference Input Parameter Libraryfor Calculation of Nuclear Reactions and Nuclear DataEvaluations”, Nuclear Data Sheets 110 (2009) 3107.[9] T. D. Newton, Can. J. Phys.34, 804 (1956).[10] A. Gilbert and A. G. W. Cameron, Can. J. Phys.43, 1446(1965).[11] T. von Egidy and D. Bucurescu, Phys. Rev. C72, 044311(2005).[12] T. Belgya et al., Reference Input Parameter Library,Handbook for calculations of nuclear reaction data,RIPL-2, IAEA-TECDOC-1506 (IAEA, Vienna, 2006),http://www-nds.iaea.org/ripl2/.[13] U. Agvaanluvsanet al., Phys. Rev. C70, 054611 (2004).[14] M. Krti čka, Doctoral Thesis,Photon Strength Functionsin Rare-Earth Nuclei Studied from Slow Neutron Capture,Charles University, Prague (2002).[15] C. E. Porter and R. G. Thomas, Phys. Rev.104, 483 (1956).4

Gamma Spectrum from Neutron Capture on Tungsten Isotopes

LLNL-PROC-434051Gamma Spectrum from NeutronCapture on Tungsten IsotopesA. M. Hurst, N. C. Summers, B. Sleaford, R.Firestone, T. Belgya, Z. S. RevayJune 3, 2010International Conference on Nuclear Data for Science andTechnology 2010Jeju Island, South KoreaApril 26, 2010 through April 30, 2010Disclaimer  This document was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor Lawrence Livermore National Security, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes.  International Conference on Nuclear Data for Science and Technology 2010GAMMA SPECTRUM FROM NEUTRON CAPTURE ONTUNGSTEN ISOTOPESA. M. HURST∗1,2, N. C. SUMMERS1, B. W. SLEAFORD1, R. B. FIRESTONE2, T. BELGYA3, and Z. S. REVAY31Lawrence Livermore National Laboratory, Livermore, California 94551, USA2Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA3Institute of Isotope and Surface Chemistry, H-1525, Budapest, Hungary∗Corresponding author. E-mail : AMHurst@lbl.govReceivedAccepted for PublicationAn evaluation of thermal neutron capture on the stable tungste i otopes is presented, with preliminary results for thecompound systems183,184,185,187W. The evaluation procedure compares theγ-ray cross-section data collected at the Budapestreactor, with Monte Carlo simulations ofγ-ray emission following the thermal neutron-capture process. The statistical-decaycodeDICEBOX was used for the Monte Carlo simulations. The evaluation yields newγ rays in185W and the confirmationof spins in187W, raising the number of levels below which the level schemesar considered complete, thus increasing thenumber of levels that can be used in neutron data libraries.KEYWORDS : 183,184,185,187W, γ-ray cross sections, neutron capture, EGAF, DICEBOX, level density, photon strength function1. INTRODUCTIONImproved neutron-captureγ-ray spectra are needed in avariety non-proliferation programs, e.g. in neutron-transportcodes for applications in the interest of national security.Building upon known decay schemes and improving theγ-ray spectrum in the neutron data libraries will provide theextensive data essential for modeling and identification ofspecial nuclear materials (actinides) and associated mate-rials (e.g. structural materials). In this paper, we describeimprovements to the known decay schemes of the tungstenisotopes from neutron capture onto all but the least abundantof the stable tungsten isotopes,180W (natural abundance:0.12 %). The neutron-captureγ-ray decay data for the com-pound systems183,184,185,187W from theEvaluated Gamma-ray Activation File (EGAF) [1], has been evaluated bycomparing with simulated populations to previously ob-served levels in these isotopes based on statistical-modelcalculations using the Monte Carlo codeDICEBOX [2].These evaluations provide improved databases ofγ spec-tra, improved level schemes with clarification of nuclearstructure issues such as tentative/unknown spin-parity (Jπ)assignments, and will ultimately be used to provide newmeasurements of the total radiative thermal neutron-capturecross sections (e.g. see Ref. [3]). Furthermore, the resultsof these evaluations will provide input to the EvaluatedNuclear Data File (ENDF), a nuclear reaction database thatis used by the Monte Carlo Neutron Transport (MCNP)codes.2. THE EGAF PROJECTThis work uses experimental neutron-captureγ-raycross sectionσγ data from the EGAF database [1] tocompare with simulation (see Sec. 3.). Precise values ofthermalσγ have previously been measured with guidedneutron beams (thermal flux∼ 2 × 106 s−1cm−2) at the 10-MW Budapest reactor for all elemental targets withZ =1− 83, 90, and 92, except for He and Pm, in addition to theradioactive targets99Tc and129I [4,5]. Details of a typicalexperimental setup are described in Ref. [3]. Internal crosssections were calibrated using stoichiometric compoundscontaining elements with well-known cross sections, e.g. H,N, Cl, and S, in addition to homogeneous mixtures, such asH2O and HCl, and activation products with well-knownγrays, e.g.19F, 28Al, 100Tc, and235U.3. DICEBOXThe Monte Carlo statistical-decay code,DICEBOX [2],has been used to model the thermal neutron-captureγcascade by calculating the intensities of transitions feedingthe low-lying states. The code generates level-scheme sim-ulations (termednuclear realizations) following the thermalneutron-capture process according to the choice of inputstatistical-model level density and photon strength func-ions, and is further constrained by theγ-ray transitionprobabilities along with known nuclear structure proper-ties of the investigated isotope in the Evaluated NuclearA. M. HURST et al., Gamma spectrum from neutron capture on tungsten isotopesStructure Data File (ENSDF) database [6]. TheDICEBOXcode also uses internal conversion coefficient data fromBand Raman (BrIcc) [7]. In the following calculations, Acritical energy, Ecrit, is defined as the energy level, belowwhich, all information in the decay scheme is unique andcomplete. The code then takes all energy-level andγ-raybranching information beneathEcrit from experimental data.The known level scheme is taken from RIPL-3 [8] (Refer-ence Input Parameter Library) withEcrit taken as the energyof the level which is the minimum ofNC (the number oflevels for which the spins and parities are unique) andNmax(the maximum number of levels for which the level schemeis complete). The level scheme is then supplemented withthe new information from EGAF. Supplemental feeding tothese measured discrete lines from the quasi continuum (i.e.aboveEcrit) is simulated byDICEBOX. All levels andγ raysin the quasi continuum are randomly generated dependingon the input level density and photon strength functionmodels selected. In this work 2× 104 capture stateγ-ray decay cascades were randomly generated per nuclearrealization using the Monte Carlo method. Measured crosssections of primary transitions (i.e. a transition depopulatingthe capture state) to levels belowEcrit were used in each nu-clear realization. Good statistical variation in the simulatedlevel feedings was achieved by averaging over five separatenuclear realizations.Along with the adopted experimental level scheme be-low Ecrit and the capture-state spin composition,J, whereJ = 1/2+ for capture onto even-even targets, andJ =Jgs(target)±1/2 for capture onto odd-A and odd-odd targets,the population of the low-lying levels is largely influencedthrough the choice of level-density and photon strengthfunction models for the different transition types. In thefollowing simulations (Sec. 4.) the back-shifted Fermi gasmodel [9,10] with von Egidy parameterization [11] wasadopted.DICEBOX only considers photon strength functions forelectric dipole (E1), magnetic dipole (M1), and electricquadrupole (E2) transition types. Of these transitions,E1are by far dominant, followed byM1, while E2 are consid-erably less significant. A form of the generalized Lorentzianmodel has been used to describe the shape of the giantelectric dipole resonance (GDR) in the present calculations.The parameterization sets for theE1 GDRs for thetungsten isotopes were extracted from experimental datacompiled in the RIPL-2 [12] database. For theM1 GDRphoton strength function, a compound model accountingfor scissors-type and spin-flip type excitation modes wasadopted, with the resonance-shape parameterization esti-mated from a previous study of the170,171,172Yb isotopes[13]. Finally, a giant electric quadrupole photon strengthfunction model describing both isoscalar and isovectorvibrational modes was adopted for theE2 transitions [14].4. RESULTSThe results of the calculations simulating the thermal-captureγ cascade using theDICEBOX code are presentedin this section. Modeling of the thermal-neutron captureprocess onto the four most abundant of the naturally-occurring tungsten isotopes,182W (26.5 %),183W (14.3 %),184W (30.6 %), and186W (28.4 %), has been used to evaluatethe knownγ spectrum and make improvements to the decayschemes in the corresponding(A+1)W compound systems.With the exception of the184W compound system, all othercompounds are formed from neutron capture onto an even-even target, accordingly the capture state isJπ = 1/2+ forthese systems.The results of the simulated populations are shown incomparison to the experimental depopulations in the fol-lowing population-depopulation plots presented in log-lospace. Uncertainties along the horizontal axis (experimen-tal depopulation) correspond to experimental errors, whilethose on the vertical axis (simulated population) are due toPorter-Thomas [15] fluctuations in generating the differentnuclear realizations. If the level scheme of the isotope iscomplete and unique up to the definedEcrit, and the decayis purely statistical (i.e. no collective eff cts), then all datapoints should fall on the slope ofy = x. Scatter around thisline provides a measure of the quality and completeness ofboth simulation and experimental data. In the correspondingdecay schemes (shown only for185W and187W), the widthof the arrow illustrates the relative intensity of the transition:the black part of the arrow represents theγ decay andthe white part internal conversion; primary transitions arethose from the capture state (the highest level, not plottedtoscale on the energy axis) represented by blue arrows. Newinformation is highlighted in red on the decay schemes.Fig. 1. Simulated population versus experimental depopulationfor the compound systems183W (left) and184W (right)4.1 182W(n,γ)183WDecay data extracted from the RIPL-3 database suggests10 known levels above the ground state, indicating a valueEcrit = 475.4 keV for 183W. No further information wasavailable in the EGAF database to allowEcrit to be raised.The RIPL-3 and EGAF data compare well beneathEcrit.The next highest level at 487 keV with a tentative (13/2+)assignment, is not seen in the EGAF database, due to itshigh spin. Three primaries have been observed feeding2A. M. HURST et al., Gamma spectrum from neutron capture on tungsten isotopeslevels belowEcrit: a 6190.6-keVE1 transition to the 1/2−ground state, a 6144.2-keVE1 transition to the 3/2− 46.5-keV level, and a 5981.8-keVE1 transition to the 3/2−208.8-keV level. The calculation shown in Fig. 1(left) usesσγ information from the EGAF database;σγ data fromRIPL-3 does not produce a statistically-significant differentresult. The deviation of the data from the line is not clear,although, it could point to poor knowledge of the measuredγ-ray intensities for some low-energy transitions deexcit-ing low-lying states. This is currently being investigated.Additionally, an unreported 9/2− (308.9 keV)→ 5/2−(291.7 keV)E2 transition has beenimplantedinto the levelscheme since this would follow a likely rotational sequence.However, the addition/removal of this transition makes nostatistical difference to the overall result.4.2 183W(n,γ)184WLike 183W, the number of known levels cannot beextended beyond that in RIPL-3. The next level aboveEcritat 1283.6 keV is tentatively reported as a (1−, 2−) state.However, since a corresponding level has not been reportedin EGAF it is not possible to extendEcrit higher in anattempt to establish the configuration of the 1283.6-keVlevel. Since the target nucleus,183W, is odd-A and has a1/2−gs, the capture state at 7.4117 MeV in184W can haveeither a 0− or 1− configuration. The present calculation inFig. 1(right) assumes 100 % capture in the 1− state. Allσγ data has been taken from the RIPL-3 file. It should benoted that the RIPL-3 file contains a transition from the3− state at 1221.3 keV to the ground state which has notbeen reported in the EGAF file. Figure 1(right) shows thatthe only data point deviating significantly from the line isthe excited 0+ state. Various combinations of capture-statefractions are currently being investigated along withσγ datafrom the EGAF database to test the effect on the overallresult. The calculation also includes seven primaries feedingstates below Ecrit: 7412.0-keVE1 to the 0+ ground state,7299.7-keVE1 to the 2+ state at 111.2 keV, 6507.2-keVE1to the 2+ state at 903.3 keV, 6408.9-keVE1 to the 0+ stateat 1002.5 keV, 6289.9-keVE1 to the 2+ state at 1121.4 keV,6281.5-keVM1 to the 2− state at 1130.0 keV, and 6190.6-keV M1 to the 3− state at 1221.3 keV.4.3 184W(n,γ)185WThe number of levels belowEcrit has been increasedfrom 8, in RIPL-3, to 10, based on 2 new levels with corre-spondingγ-decays in the EGAF data. Figure 2(a) shows thenew decay scheme for185W that has been used to producethe optimal population-depopulation results of Fig. 2(b).The next highest state aboveEcrit, 384 keV (13/2+), dueto its high spin, contains noγ-decay information in EGAF.Using DICEBOX, it has been possible to confirm the, pre-viously tentative, 9/2− assignment for the 301.1-keV state,while the postulated tentative (7/2−) assignment from RIPL-3 for the 332.1-keV state has been changed to a 9/2− state onthe basis of population-depopulation arguments. Addition-ally, the energies for both of these states is more accuratelymeasured in EGAF. The RIPL-3 entries for these states were3/21/25/23/27/25/211/27/29/29/213/29/2246642937017410818816412295132241024317715070562351272662391581441/2+S(n) = 5.7537 MeV0.0023.5465.9193.36173.71187.89197.44243.39384.00390.49Ex [keV]Ecrit332.12301.105753.655729.205658.60RIPL EcritW185392661442723515610−/ −(RIPL J  )(7/2−)(9/2−)π(      )(b)(a)Fig. 2. 185W: (a) decay scheme; (b) simulated population versusexperimental depopulation.reported as 302 keV (9/2−) and 334 keV (7/2−), with noγ-decay information from either state. Four newγ transitionshave been reported deexciting the 332.1-keV state and twonew transitions deexciting the 301.1-keV state in EGAF.Furthermore, three newγ rays deexciting the lower levels at243.4 keV, 197.4 keV, and 93.4 keV, have also been reportedin EGAF. However, a new transition reported in EGAF from187.9-keV 5/2− → 173.7-keV 7/2− has not been included inthe calculation. This very low-energy transition has been re-ported with a seemingly unrealistic cross section; the largestbranch by almost a factor of four. Inclusion of this transitioncauses the data to deviate significantly from the line inFig. 2(b). Further investigation of this transition is requiredto determine the validity of the measured value. EGAFσγdata were used for all states in these calculations. It shouldbe noted, however, that for two very low-energy transitions,the reported cross sections were reduced by factors of 10and 100, respectively, for the 93.4-keV 3/2− → 23.5-keV1/2− and 243.4-keV 7/2− → 187.9-keV 5/2− transitions.Again, cross sections for such low-energy transitions are3A. M. HURST et al., Gamma spectrum from neutron capture on tungsten isotopesdifficult to measure experimentally and soDICEBOX beenused to obtain fits that show better agreement betweenexperimental depopulations and simulated populations. Thecalculations also incorporate three primaries to low-lyingstates belowEcrit: 5753.7-keVE1 to the 3/2− ground state,5730.2-keVE1 to the 1/2− state at 23.5 keV, and 5660.3-keV E1 to the 3/2− state at 93.4 keV.4.4 186W(n,γ)187W3/25/21/27/23/5/29/27/211/27714620112420512759303226157102 98W18777.360.00145.73204.83201.43329.00350.543/2−5/2−1/2−3/2−5/2−(9/2−)7/2−303.217/2−RIPL EcritEcritEx [keV]S(n) = 5.4664 MeV5466.75320.65261.71/2+364.229/2−(7/2−)(7/2−)(3/2−)(RIPL J  )π(b)(a)Fig. 3. 187W: (a) decay scheme; (b) simulated population versusexperimental depopulation.New information in the EGAF database has increasedthe number of unique levels by 3, from the RIPL-3 value.It has also been possible to confirm the previous 7/2−assignment for the state at 201.4 keV usingDICEBOX.This new information is highlighted in Fig. 3(a). The nexthighest level aboveEcrit at 329 keV with a tentative (9/2−)configuration, due to its high spin, is not seen in EGAF. Thecorresponding calculations for this decay scheme, shownin Fig. 3(b), were executed using branching ratios fromthe EGAF database. It should be noted, however, that theRIPL-3 database reveals an extra branch from 5/2− 303.2-keV level to the 3/2− 204.8-keV level. The branching ratiosin RIPL-3 database also differ significantly to those inEGAF. Optimal results were obtained using informationfrom EGAF exclusively. The calculation also includes threeprimary transitions from the 5.4664-MeV capture state:5466.7-keVE1 to the 3/2− ground state, 5320.6-keVE1to the 1/2− level at 145.7 keV, and 5261.7-keVE1 to the3/2− level at 204.8 keV.ACKNOWLEDGMENTSThis work was performed under the auspices of theU. S. Department of Energy by Lawrence Livermore Na-tional Laboratory under Contract DE-AC52-07NA27344,and by the University of California, supported by the Direc-tor, Office of Science, Office of Basic Energy Sciences, ofthe U. S. Department of Energy at Lawrence Berkeley Na-tional Laboratory under Contract DE-AC02-05CH11231.REFERENCES[1] R. B. Firestoneet al., Database of Prompt Gamma Raysfrom Slow Neutron Capture for Elemental Analysis, IAEASTI/PUB/1263, 251 pp (2007).[2] F. Becvar, Nucl. Instrum. Methods A417, 434 (1998).[3] M. Krticka et al., Phys. Rev. C77, 054615 (2008).[4] T. Belgya et al., Proceedings of the 9th InternationalSymposium on Capture Gamma-Ray Spectroscopy and Re-lated Topics, Budapest, Hungary, Oct. 8-12, edited byG. Molná, T. Belgya, Zs. Ŕevay (Springer-Verlag, Bu-dapest/Berlin/Heidelberg, 1997), P: 826.[5] Zs. Révay et al., Handbook of Prompt Gamma Activa-tion Analysis with Neutron Beams, edited by G. L. Molńar(Kluwer, Boston, 2004).[6] Evaluated Nuclear Structure Data File, an electronicdatabase of evaluated experimental nuclearstructure data maintained by the National NuclearData Center, Brookhaven National Laboratory,http://www.nndc.bnl.gov/ensdf/.[7] T. Kibédiet al., Nucl. 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Gamma Spectrum from Neutron Capture on Tungsten Isotopes

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