10.2.1. Acknowledgements

Development and testing of ORIGEN data resources, libraries, and methods have been sponsored by many organizations including the US Nuclear Regulatory Commission (NRC), the US Department of Energy (DOE), and nuclear power and research institutions.

10.2.2. Version Information

Following is a description of the data resources available for use with ORIGEN in different SCALE versions. Methodologies and algorithms used in applying the data are described in the ORIGEN chapter.

10.2.2.1. Version 6.3 (2021)

Data lead(s): A. Holcomb and W. Wieselquist

Nuclear data in ORIGEN has had minor updates for SCALE 6.3. The old ENDF/B-VII.0 libraries have been removed. There are new libraries for 302-groups (for fast-spectrum systems) and 1597-groups as an very fine group option for any spectrum. Data for recoverable energy per capture for Gd-155 and Gd-157 has been updated from 5 MeV to 8.5360 and 7.9370 MeV, respectively.

10.2.2.2. Version 6.2 (2016)

Data lead(s): I. C. Gauld, D. Wiarda, M. Pigni, and W. Wieselquist

Nuclear data in ORIGEN are unchanged from SCALE 6.1.3 except for the modification of independent fission yields for thermal fission of ²³⁵U and ²⁴¹Pu and fast fission of ²³⁸U to provide greater compatibility between the direct and cumulative fission yields when using the updated decay data from ENDF/B-VII.1. Additionally, ORIGEN no longer has its own independent source of nuclide mass and abundance data and now relies on the SCALE Standard Composition library so that there is consistency in this data across SCALE. D. Mueller and W. Wieselquist are acknowledged for testing of the new yield data. W. Wieselquist and S. Hart are acknowledged for the revision of this chapter.

10.2.2.3. Version 6.1.3 (2011)

Data lead (s): I. C. Gauld and D. Wiarda

SCALE 6.1 represented a complete revision and update of the nuclear data available in ORIGEN. The following is a summary from the SCALE 6.1 manual.

The ORIGEN data libraries include nuclear decay data, neutron reaction cross sections, neutron induced fission product yields, delayed gamma-ray emission data, and neutron emission data. The nuclear decay data libraries have been updated based on ENDF/B-VII evaluations and expanded to include 903 activation products and structural materials, 174 actinides, and 1149 fission products. The cross section libraries have been revised using evaluations from the JEFF-3.0/A neutron activation file, containing data for 774 target nuclides, more than 12,000 neutron-induced reactions, and more than 20 different reaction types below 20 MeV. The JEFF-3.0/A activation file is processed into several multigroup cross section libraries, from 44 groups to 238 groups, that can be used to determine the neutron reaction transition rates in ORIGEN. Energy-dependent ENDF/B-VII fission product yields are provided for 30 fissionable actinides. Photon yield data libraries have been updated based on the most recent ENSDF nuclear structure evaluations processed using the NuDat program. The photon libraries contain discrete photon line energy and intensity data for decay gamma and x-rays emission for 982 radionuclides, prompt and equilibrium continuum fission product spectra from spontaneous fission, $\left( \alpha,n \right)$ reactions in oxide fuel, and bremsstrahlung from decay beta (negatron and positron) particles slowing down in either UO₂ fuel or water matrix. Methods and data libraries used to calculate the neutron yields and energy spectra for spontaneous fission, $\left( \alpha,n \right)$ reactions in any matrix, and delayed neutron emission are adopted from the SOURCES code. The libraries used by ORIGEN can be coupled directly with detailed and problem-dependent physics calculations to obtain self-shielded problem-dependent cross sections based on the most recent evaluations of ENDF/B-VII. In addition, the library formats allow multiple sets of cross section data to be stored on a library to represent the changes in cross sections during irradiation.

10.2.3. Introduction

ORIGEN data resources include nuclear decay data, multigroup neutron reaction cross sections, neutron-induced fission product yields, and decay emission data for photons, neutrons, alpha particles and beta particles. The available resources are summarized in Table 10.2.1 and described in greater detail in the subsequent sections. The “Unit” column shows the corresponding unit number for use with FIDO input systems (e.g. with COUPLE).

Table 10.2.1 Available resources in ORIGEN
Description	Alias	Unit	Category	Location in SCALE data directory
ENDF/B-VII.1 decay data	decay	27	Decay	origen_data/origen.rev03.decay.data
ENDF/B-VII.0-based fission yield data	yields	17	Yield	origen_data/origen.rev05.yields.data
JEFF-3.0/A - 56g	n56	75	Reaction	origen.rev01.jeff56g
JEFF-3.0/A - 200g	n200	78	Reaction	origen.rev03.jeff200g
JEFF-3.0/A - 252g	n252	74	Reaction	origen.rev01.jeff252g
JEFF-3.0/A - 302g	n302		Reaction	origen.rev00.jeff302g
JEFF-3.0/A - 1597g	n1597		Reaction	origen.rev00.jeff1597g
Energy per fission and capture			Energy	n/a
Master photon (x-ray and gamma) emission data			Emission	origen_data/origen.rev04.mpkkxgam.data
Spontaneous fission and $\left(\alpha,n \right)$ reaction gamma rays			Emission	origen_data/origen.rev00.mpsfangm.data
Bremsstrahlung from beta particles slowing down in water			Emission	origen_data/origen.rev00.mpbrh2om.data
Bremsstrahlung from positrons slowing down in water			Emission	origen_data/origen.rev00.mpbrh2op.data
Bremsstrahlung from beta particles slowing down in UO₂			Emission	origen_data/origen.rev00.mpbruo2m.data igen_data/or
Bremsstrahlung from positrons			Emission	origen_data/origen.rev00.mpbruo2p.data
Neutron source emission and alpha decay data			Emission	origen_data/origen.rev01.alphdec.data rigen_data/o
Alpha particle stopping cross section expansion coeffcients			Emission	origen_data/origen.rev00.stcoeff.data
Target $\left( \alpha,n\right)$ product excited level branching data			Emission	origen_data/origen.rev00.alphyld.data
Target $\left(\alpha,n \right)$ cross section data			Emission	origen_data/origen.rev00.alphaxs.data
Beta source emission data			Emission	origen_data/origen.rev00.ensdf95beta.data

10.2.4. Decay Resource

The nuclear data stored on the decay resource is based on ENDF/B-VII.1 evaluations [Origen-Data-ResourcesCHO+11], including half-lives, decay modes and branching fractions, and recoverable energy per disintegration. Decay modes include beta ($\beta^-$), positron ($\beta^+$) and electron capture (EC), isomeric transition (IT), alpha ($\alpha$), spontaneous fission (SF), delayed neutron ($\beta^-\,n$) emission, neutron emission (n), double beta decay $\left( \beta^- \beta^- \right)$, and decay by beta and alpha emission ($\beta^- \alpha$). The decay resource also includes radiotoxicity factors based on the radioactivity concentration guides (RCGs) for air and water as defined in Part 10, Title 20, of the Code of Federal Regulations (10CFR20) [Origen-Data-Resources10c]. RCGs specify the maximum permissible concentrations of an isotope in soluble and insoluble forms for both ingestion and inhalation and for occupational and unrestricted exposure. The radiotoxicity is calculated as the dilution volume of a nuclide for cases of direct ingestion or inhalation. The values are defined to be the smaller (i.e., more toxic) of the values for soluble and insoluble forms of the isotope. The maximum permissible RCGs for air and water are the public exposure limits for adult ingestion and inhalation dose coefficients of ICRP Publication 72 [Origen-Data-ResourcesInternationalCoRPICRP77]. External exposure dose coefficients for noble gases were obtained from the Environmental Protection Agency (EPA) Federal Guidance Report 12 [Origen-Data-ResourcesUEPAEPA93]. Recoverable energy includes the delayed energy from all electron-related radiations (e.g., $\beta^-$, $\beta^+$, Auger electrons), all gamma rays, x-rays, annihilation radiations, and the average energy of all heavy charged particles and delayed neutrons. The average alpha energy includes the energy of the recoil nucleus. A part of the recoverable energy per decay not included in the ENDF/B-VII.1 values is the additional contribution from spontaneous fission. This energy was calculated as the product of the spontaneous fission branching fraction and recoverable energy per fission using a value of 200 MeV per fission and then added to the ENDF/B-VII.1 recoverable Q energy. A value of 12.56 MeV gamma energy per fission was used in computing the fraction of recoverable spontaneous fission energy from gamma rays. External Bremsstrahlung radiation is not included in the Q-value since the Bremsstrahlung spectrum depends on electron interactions with the medium that contains the decay nuclide. The energy from capture gamma rays accompanying $\left( \alpha,n \right)$ reactions is not included either since it also depends on the medium.

Appendix A describes the decay resource file format. It is important to note that the decay resource not only defines fundamental decay data, but also the complete ORIGEN nuclide set, including the “duplicates” of nuclides across sublibraries. For example, a version of ¹⁵⁵Gd is contained in both the light nuclide/activation product and fission product sublibraries. Appendix D includes the full list of the nuclides on the ORIGEN decay library “end7dec” created by COUPLE based on the current decay resource, including duplicates. Appendix E contains a list of the fundamental decay data only, without duplicates. To consider a different set of nuclides in an ORIGEN calculation, the current process is to alter the decay resource and then regenerate the “end7dec” decay library with COUPLE. By default, all subsequent libraries created from COUPLE using problem-dependent reaction transitions are based on the “end7dec” decay library and will therefore include the modified nuclide set.

10.2.5. Neutron Reaction Resource

The neutron cross sections defining the nuclear reaction transmutation rates use a comprehensive collection of nuclear data evaluations compiled from the JEFF-3.0/A neutron activation files [Origen-Data-ResourcesSKFK03]. The JEFF-3.0/A files contain continuous energy neutron data for 774 target nuclei, including ground and metastable excited states, and 12,617 neutron-induced reactions below 20 MeV. The JEFF-3.0/A cross section data are developed directly from the European Activation File (EAF-2003) [Origen-Data-ResourcesFKS02] formatted as standard ENDF-6 format data. JEFF-3.0/A cross sections are stored using File 3, multiplicities on File 10, and isomeric branching to different metastable levels using File 9. The evaluations include many reactions that may be important for modeling fast fission and other high-energy systems. Neutron reactions are available for 23 reaction types, including $\left(n,n' \right)$, $\left(n,2n \right)$, $\left(n,3n \right)$, $\left(n,f \right)$, $\left(n,n' \alpha \right)$, $\left(n,2n\alpha\right)$, $\left(n,3n\alpha \right)$, $\left(n,n'p \right)$, $\left(n,n2\alpha \right)$, $\left(n,n'd \right)$, $\left(n,n't \right)$, $\left(n,n'{}^3 He \right)$, $\left(n,4n \right)$, $\left(n,2np \right)$, $\left(n,\gamma \right)$, $\left(n,p \right)$, $\left(n,d \right)$, $\left(n,t \right)$, $\left(n,{}^3\ He \right)$, $\left(n,\alpha \right)$, $\left(n,2\alpha \right)$, $\left(n,2p \right)$, and $\left(n,p\alpha \right)$.

The JEFF-3.0/A evaluations also include extensive compilations of energy-dependent branching fractions that define neutron reaction transitions to ground and metastable energy states. Energy-dependent branching is fully implemented in the ORIGEN cross section libraries. Implementation of the JEFF-3.0/A cross sections as ORIGEN multigroup data was accomplished by processing and collapsing the JEFF-3.0/A pointwise cross sections into a standard multigroup AMPX format using ENDF data-processing modules of the AMPX [Origen-Data-ResourcesDG02] cross section processing code system. The collapse is performed using a thermal Maxwellian-1/E-fission-1/E weighting spectrum (see Fig. 10.2.1) to provide infinite dilution multigroup cross sections.

Fig. 10.2.1 Pointwise flux spectrum used to generate collapsed cross section libraries.

Neutron reactions with transitions to multiple states of the daughter product are represented using separate cross sections to the ground and metastable states. A special reaction identifier (MT’) is defined for this implementation of metastable transitions as

(10.2.1)\[\text{MT}' = \text{MT}*10000 + 100*\text{LP} + \text{LT}\]

where MT is the reaction identifier, LP is the product metastable state, and LT is the target metastable state. Using the ¹⁸⁷W(n,3n)¹⁸⁵W cross section (MT=17) as an example, the reaction identifier 170000 defines the partial cross section to the ground state of ¹⁸⁵W, and 170100 defines the cross section to metastable ^185mW.

Cross section data from the JEFF-3.0/A neutron activation file are first converted to point-wise cross section data, are Doppler broadened to 900K, and then they are collapsed to different group structures. The following group strucures are available in SCALE:

238-group neutron (thermal applications),

252-group neutron (thermal applications),

56-group neutron (thermal applications),

200-group neutron (fast applications and shielding),

47-group neutron (applications using the BUGLE shielding transport library),

49-group neutron (collapsed version of 238 groups),

44-group neutron (collapsed version of 238 groups), and

999-group neutron (multipurpose).

Several minor modifications were made to the JEFF-3.0/A data:

The ²³⁹Np radiative neutron capture cross section was replaced with data from ENDF/B-VII.0. Neutron capture using JEFF-3.0/A cross sections was significantly larger than ENDF/B-VII.0 due to differences in the resonance cross section region. Although experimental resonance parameters are not available for ²³⁹Np, comparisons of ²⁴⁰Pu production during irradiation [Origen-Data-ResourcesGum54] obtained using the two evaluations showed that better agreement with the experiment was obtained using the ENDF/B-VII.0 evaluation.

The ${}^{241} Am (n,\gamma)$ branching fraction to the ²⁴²Am ground and metastable states was replaced by the evaluation from ENDF/B-VII.0 to yield better agreement with the results of destructive radiochemical assay measurements of irradiated fuels. The branching fraction of ²⁴¹Am to ^242mAm for thermal neutron capture changed from 8.2% in JEFF-3.0/A to 10.0% in ENDF/B-VII.0.

The cross section library header record information and a complete list of nuclides in JEFF-3.0/A libraries developed for ORIGEN are provided in Appendix E.

Because JEFF-3.0/A-based libraries are formatted as standard AMPX working libraries, they can be accessed and/or manipulated using standard AMPX utility modules in SCALE. For example, multigroup cross sections may be listed using the PALEALE module. Additionally, the data may be visualized using the Fulcrum user interface. Cross section plots of the 238-group JEFF-3.0/A library are illustrated in Fig. 10.2.2 for $(n,\gamma)$, $(n,\alpha)$, (n,2n), and (n,3n) cross sections to the ground and metastable states.

Before the cross sections in ORIGEN can be used, they must be collapsed with a user-defined multigroup flux to a one-group cross section and added to the ORIGEN binary library (see the COUPLE input description).

Fig. 10.2.2 238-group JEFF-3.0/A cross sections for ¹⁸⁷W.

10.2.6. Fission Yield Resource

The fission-yield resource contains the energy-dependent direct yields of each fission product for 30 fissionable actinides, including ^227,228,232Th, ²³¹Pa, ^232–238U, ^238-242Pu, ^241,242m,243Am, ^237,238Np, ^242-246,248Cm, ^249,252Cf, and ²⁵⁴Es. Independent (direct) fission product yields are stored as atom percent per fission, and except for ²³⁵U(thermal), ²³⁸U(fast), and ²⁴¹Pu(thermal), they are obtained from ENDF/B-VII.0 [Origen-Data-ResourcesCOH+06] File 8 and MT=454.

Revised independent fission product yields for ²³⁵U(thermal), ²³⁸U(fast), and ²⁴¹Pu(thermal) were adopted to address inconsistencies between the direct and cumulative fission yields in ENDF/B-VII.0 caused by the use of updated nuclear decay schemes in the decay sublibrary [Origen-Data-ResourcesFWP15, Origen-Data-ResourcesPFG15]. Namely, recent changes in the decay data, particularly the delayed neutron branching fractions, result in calculated fission product concentrations that do not agree with the cumulative fission yields in the ENDF/B-VII.0 library. These issues were particularly evident for the three cited isotopes because their fissioning systems result in a preferential formation of fragments that are sensitive to the changes in the decay data. For example, a study on ²³⁹Pu(thermal) showed negligible differences between cumulative yields calculated (using the recent decay data sublibrary) and the cumulative yields in ENDF/B-VII.0. Energy-dependent product yields are available for thermal, fast, and high-energy incident neutron energies. For fast fission, the value of the energy of incident neutron was modified from the value of 500 keV tabulated in ENDF/B-VII.0 to more accurately represent the relationship between the energy distribution of the neutrons causing fission and the and the fission neutron spectrum energy. For this implementation of the yield data, the effective incident neutron energy for fast fission was adjusted from 500 keV to 2.0 MeV to better reflect the average fission energy of most nuclides. The neutron energies for thermal fission (0.0253 eV) and high energy fission (14 MeV) are unchanged.

The fission product yields also include cumulative ternary yields from the JEF-2.2 fission yield library [Origen-Data-ResourcesNuclearEAgency00] for ³H and ⁴He. The nuclide ³He was also added to the fission product library since it is a decay product of tritium.

Note that inclusion of fission yields for each actinide in an ORIGEN library can be controlled by the user through COUPLE. Actinides not assigned with explicit yields do not produce fission products during fission.

Table 10.2.2 Fissionable isotopes having explicit fission yields
Nuclide	Neutron-induced fission energies 1
²²⁷Th	Thermal
²²⁹Th	Thermal
²³²Th		Fast	High energy
²³¹Pa		Fast
²³²U	Thermal
²³³U	Thermal
²³⁴U		Fast	High energy
²³⁵U	Thermal	Fast	High energy
²³⁶U		Fast	High energy
²³⁷U		Fast
²³⁸U		Fast	High energy
²³⁷Np	Thermal	Fast	High energy
²³⁸Np		Fast
²³⁸Pu		Fast
²³⁹Pu	Thermal	Fast	High energy
²⁴⁰Pu	Thermal	Fast	High energy
²⁴¹Pu	Thermal	Fast
²⁴²Pu	Thermal	Fast	High energy
²⁴¹Am	Thermal	Fast	High energy
^242mAm	Thermal
²⁴³Am		Fast
²⁴²Cm		Fast
²⁴³Cm	Thermal	Fast
²⁴⁴Cm		Fast
²⁴⁵Cm	Thermal
²⁴⁶Cm		Fast
²⁴⁸Cm		Fast
²⁴⁹Cf	Thermal
²⁵¹Cf	Thermal
²⁵⁴Es	Thermal

1: Neutron energy causing fission

10.2.7. Energy Resource

The energy resource is a set of data defined internally to ORIGEN to compute the total power during irradiation if the flux is known, or the total flux if the power is known. The data include the energy contributed by fission and capture. The recoverable energy values taken primarily from ENDF/B evaluations are listed in Table 10.2.3 and Table 10.2.4. The recoverable energy for fission and neutron capture for nuclides not listed in the tables are assumed to be 200 MeV and 5.0 MeV, respectively.

Table 10.2.3 Recoverable energy (MeV) values for actinides
Nuclide	Fission	Capture
²³⁰Th	190.00	5.010
²³²Th	189.21	4.786
²³³Th	190.00	6.080
²³¹Pa	190.00	5.660
²³³Pa	189.10	5.197
²³²U	200.00	5.930
²³³U	191.29	6.841
²³⁴U	190.30	5.297
²³⁵U	194.02	6.545
²³⁶U	192.80	5.124
²³⁸U	198.12	4.804
²³⁷Np	195.10	5.490
²³⁹Np	200.00	4.970
²³⁸Pu	197.80	5.550
²³⁹Pu	200.05	6.533
²⁴⁰Pu	199.79	5.241
²⁴¹Pu	202.22	6.301
²⁴²Pu	200.62	5.071
²⁴³Pu	200.00	6.020
²⁴¹Am	202.30	5.529
^242mAm	202.29	6.426
²⁴³Am	202.10	5.363
²⁴⁴Cm	200.00	6.451
²⁴⁵Cm	200.00	6.110

Table 10.2.4 Recoverable energy (MeV) values for activation and fission products
Nuclide	Capture
¹H	2.225
¹⁰B	2.790
¹⁶O	4.143
⁵⁶Fe	7.600
⁵⁸Ni	9.020
⁹⁰Zr	7.203
⁹¹Zr	8.635
⁹²Zr	6.758
⁹⁶Zr	5.571
⁹⁵Mo	9.154
⁹⁵Tc	7.710
¹⁰¹Ru	9.216
¹⁰³Rh	6.999
¹⁰⁵Rh	7.094
¹⁰⁹Ag	6.825
¹³¹Xe	8.936
¹³⁵Xe	7.880
¹³³Cs	6.704
¹³⁴Cs	6.550
¹⁴³Nd	7.817
¹⁴⁵Nd	7.565
¹⁴⁷Pm	5.900
¹⁴⁸Pm	7.266
^148mPm	7.266
¹⁴⁷Sm	8.140
¹⁴⁹Sm	7.982
¹⁵⁰Sm	5.596
¹⁵¹Sm	8.258
¹⁵²Sm	5.867
¹⁵³Eu	6.444
¹⁵⁴Eu	8.167
¹⁵⁵Eu	6.490

10.2.8. Emission Resources

The two main groups for emission resources are the photon (gamma) resource, which includes beta particle emission data, and the neutron resource, which includes alpha emission data.

10.2.8.1. Gamma Emission

The resources for gamma emission are stored as separate files (see Table 10.2.5) containing the photon data associated with different modes of decay or photon production. The photon data sets include decay gamma and x-ray line-energy data, gamma rays accompanying spontaneous fission, gamma rays accompanying $\left( \alpha,n \right)$ reactions in oxide fuels, and Bremsstrahlung spectra from decay electrons/positrons slowing down in UO₂ and water. The photon energy spectra can be generated in any energy group structure for all activation products, actinides, and fission product nuclides with photon yield data.

Table 10.2.5 Photon data files
File name	Description
MPDKXGAM	x-ray and gamma emissions line data
MPSFANGM	spontaneous fission and $\left( \alpha,n \right)$ reactions
MPBRH2OM	bremsstrahlung from beta particles slowing down in water
MPBRH2OP	bremsstrahlung from positrons slowing down in water
MPBRUO2M	bremsstrahlung from beta particles slowing down in UO₂
MPBRUO2P	bremsstrahlung from positrons slowing down in UO₂

All photon data sets are constructed with the same format (see Appendix C). The majority of the photon emissions are discrete energy lines. Photon continuum data, used to represent Bremstrahlung and some other gamma-ray emission spectra, are stored at discrete energies and approximately expanded to a continuum, as needed. Gamma and x-ray yields are directly from ENDF/B-VII.1 decay files containing spectral data for decay transitions of 1,132 nuclides. A separate file contains emission spectra for gamma rays accompanying spontaneous fission and for gamma rays accompanying $\left( \alpha, n \right)$ reactions in oxide fuels [Origen-Data-ResourcesCHG79]. The spontaneous fission spectra combine prompt and equilibrium fission product gamma-ray components. The prompt spectrum is similar to that of ²³⁵U, and the delayed fission product gamma intensity at equilibrium is about 0.75 of that from the prompt fission gamma rays. Based on measured prompt fission gamma spectra from ²³⁵U, spontaneous fission spectra are computed from the following approximation:

(10.2.2)\[\begin{split}N\left(E \right) \cong \begin{cases} 11.5 & 0.1 \leq\ E \leq 0.6\ MeV \\ 35.4 e^{-1.78 E} & 0.6 \leq E < 1.5\ MeV \\ 12.6 e^{-1.09 E} & 1.5 \leq E \leq 10.5\ MeV \\ 0 & \text{otherwise.} \end{cases}\end{split}\]

where

N(E) = number of photons per unit energy per fission (photons/MeV per fission) at energy E, where E is the photon energy (MeV).

For medical and industrial spontaneous fission source applications, a more accurate simulation of the source may be desirable. Work has been performed on ²⁵²Cf source modeling to explicity represent the fission product generation from fission and the delayed gamma emission. In this application, the equilibrium spontaneous fission gamma spectrum was replaced with an evaluation of the ²⁵²Cf prompt gamma spectrum, and the delayed fission product gamma rays was modeled explicitly in ORIGEN by generating the time-dependent fission products using ²⁵²Cf spontaneous fission product yields from ENDF/B-VII.0 [Origen-Data-ResourcesIGW11]. This was performed by adding decay transitions to the ORIGEN library from the actinides to the fission products. The spectrum of gamma rays accompanying $\left( \alpha,n \right)$ reactions is based on reaction data for alpha interactions on ¹⁸O and from studies for ²³⁸PuO₂ systems. The spectrum is computed from the approximation:

(10.2.3)\[N\left( E \right) \cong 2.13 \cdot 10^{-8}\ e^{- 1.38E}\]

where

N(E) = number of photons per unit energy per alpha decay (photons/MeV per disintegration) at energy E (MeV).

The photon yields in this data set are continuum spectra represented by discrete lines with an energy width of 500 keV and range from 250 keV to 10.25 MeV.

Two photon data sets contain bremsstrahlung spectra from decay electrons and positrons slowing down in a UO₂ fuel matrix. The yields are in the form of continuum spectra represented in the data sets as discrete lines using up to 70 quasi-logarithmic spaced energy points over the energy range between 0 and 13.5 MeV. Two libraries contain bremsstrahlung spectra from decay electrons and positrons slowing down in water. Bremsstrahlung spectra were calculated using a computer program developed by Dillman et al. [Origen-Data-ResourcesDSF73] using beta spectra derived from Evaluated Nuclear Structure Data Files (ENSDF) decay data with a computer program written by Gove and Martin [Origen-Data-ResourcesGM71].

10.2.8.2. Neutron Emission

There are four neutron emission resources used by ORIGEN to calculate the neutron intensities and spectra: (1) neutron decay data, (2) an alpha-particle stopping power, (3) a target $\left( \alpha,n \right)$ cross section, and (4) a target $\left( \alpha,n \right)$ product level branching. All of the neutron data are stored in a text format with names and descriptions given in Table 10.2.6. The neutron decay data contain basic decay information for decay processes that lead to direct and indirect emission of neutrons, including spontaneous fission branching fractions, alpha decay branching fractions, delayed neutron branching fractions, alpha-particle decay energies, Watt fission spectrum parameters, and delayed neutron spectra. The stopping cross sections, $\left( \alpha,n \right)$ target cross sections, and product-level branching data are used in calculating the neutron yield and spectra from $\left( \alpha,n \right)$ reactions.

The neutron data were obtained directly from the updated SOURCES-4B code package. The sources of the neutron data are described by Shores [Origen-Data-ResourcesSho00]. An update was made to correct an error in the ²⁵⁰Cf spontaneous fission neutron branching fraction in the neutron source decay data distributed with the SOURCES code. The ²⁵⁰Cf branching fraction was incorrectly assigned the value from ²⁵²Cf of $3.092 \cdot 10^{-2}$. A corrected value of $7.700 \cdot 10^{-4}$ from ENDF/B-VII.1 is used.

Table 10.2.6 Neutron source data libraries
File name	Description
ALPHDEC	Neutron source decay data
STCOEFF	Stopping cross section expansion coefficients
ALPHYLD	Target $\left( \alpha,n \right)$ product level branching
ALPHAXS	Target $\left( \alpha,n \right)$ cross section

The neutron source decay contains spontaneous fission data for the 49 actinides listed in Table 10.2.7. These data include the spontaneous fission branching fraction, the number of neutrons per fission ($nu$), and the watt spectrum parameters for spontaneous fission. The spontaneous fission neutron energy spectrum is approximated using spectral parameters A and B, such that

(10.2.4)\[N\left( E \right) \cong \text{C\ }e^{ - \frac{E}{A}}\sinh \sqrt{\text{BE}}\]

where E is the neutron energy and C is a normalization constant.

Table 10.2.7 Nuclides with spontaneous fission data and spectral parameters
²³⁰Th	²³⁹U	²⁴⁰Pu	²⁴⁴Am	²⁵⁰Cm
²³²Th	²³⁶Np	²⁴¹Pu	^244mAm	²⁴⁹Bk
²³¹Pa	^236mNp	²⁴²Pu	²⁴⁰Cm	²⁴⁸Cf
²³²U	²³⁷Np	²⁴³Pu	²⁴¹Cm	²⁵⁰Cf
²³³U	²³⁸Np	²⁴⁴Pu	²⁴²Cm	²⁵²Cf
²³⁴U	²³⁹Np	²⁴⁰Am	²⁴³Cm	²⁵⁴Cf
²³⁵U	²³⁶Pu	²⁴¹Am	²⁴⁴Cm	²⁵³Es
²³⁶U	²³⁷Pu	²⁴²Am	²⁴⁵Cm	^254mEs
²³⁷U	²³⁸Pu	^242mAm	²⁴⁶Cm	²⁵⁵Es
²³⁸U	²³⁹Pu	²⁴³Am	²⁴⁸Cm

Delayed neutron branching fractions and neutron spectra for 105 fission products are listed in Table 10.2.8. The delayed neutron spectra are tabulated in discrete 10 keV bins from 50 keV to about 2 MeV.

Table 10.2.8 Nuclides with delayed neutron emission spectral data
⁷⁹Zn	⁸⁹Br	⁹⁷Y	¹²⁸In	⁴¹I
⁷⁹Ga	⁹⁰Br	^97mY	¹²⁹In	⁴²I
⁸⁰Ga	⁹¹Br	⁹⁸Y	^129mIn	⁴³I
⁸¹Ga	⁹²Br	^98mY	¹³⁰In	¹⁴¹Xe
⁸²Ga	⁹³Br	⁹⁹Y	¹³¹In	¹⁴²Xe
⁸³Ga	⁹²Kr	¹⁰⁰Y	¹³²In	¹⁴³Xe
⁸³Ge	⁹³Kr	¹⁰⁴Zr	¹³³Sn	¹⁴⁴Xe
⁸⁴Ge	⁹⁴Kr	¹⁰⁵Zr	¹³⁴Sn	¹⁴¹Cs
⁸⁵Ge	⁹⁵Kr	¹⁰³Nb	¹³⁵Sn	¹⁴²Cs
⁸⁶Ge	⁹²Rb	¹⁰⁴Nb	^134mSb	¹⁴³Cs
⁸⁴As	⁹³Rb	¹⁰⁵Nb	¹³⁵Sb	¹⁴⁴Cs
⁸⁵As	⁹⁴Rb	¹⁰⁶Nb	¹³⁶Sb	¹⁴⁵Cs
⁸⁶As	⁹⁵Rb	¹⁰⁹Mo	¹³⁷Sb	¹⁴⁶Cs
⁸⁷As	⁹⁶Rb	¹¹⁰Mo	¹³⁶Te	¹⁴⁷Cs
⁸⁷Se	⁹⁷Rb	¹⁰⁹Tc	¹³⁷Te	¹⁴⁷Ba
⁸⁸Se	⁹⁸Rb	¹¹⁰Tc	¹³⁸Te	¹⁴⁸Ba
⁸⁹Se	⁹⁹Rb	¹²²Ag	¹³⁹Te	¹⁴⁹Ba
⁹⁰Se	⁹⁷Sr	¹²³Ag	¹³⁷I	¹⁵⁰Ba
⁹¹Se	⁹⁸Sr	¹²⁸Cd	¹³⁸I	¹⁴⁷La
⁸⁷Br	⁹⁹Sr	¹²⁷In	¹³⁹I	¹⁴⁹La
⁸⁸Br	¹⁰⁰Sr	^127mIn	¹⁴⁰I	¹⁵⁰La

Neutron yields from alpha-particle interaction are available for 19 $\left( \alpha,n \right)$ target nuclides: ⁷Li, ⁹Be, ¹⁰B, ¹¹B, ¹³C, ¹⁴N, ¹⁷O, ¹⁸O, ¹⁹F, ²¹Ne, ²²Ne, ²³Na, ²⁵Mg, ²⁶Mg, ²⁷Al, ²⁹Si, ³⁰Si, ³¹P, and ³⁷Cl. The neutron decay data contain discrete alpha-particle energies and branching fractions for 89 actinides and 7 fission products listed in Table 10.2.9. The sources of the level branching fraction data and the $\left( \alpha,n \right)$ cross section data are listed in Table 10.2.10. The stopping cross sections and $\left( \alpha,n \right)$ target cross section and product level branching libraries are used in calculating the neutron yield and spectra from Ziegler [Origen-Data-ResourcesZie77] for all elements with Z < 93, and from Wilson [Origen-Data-ResourcesWPS+83] for all elements geq 93.

Table 10.2.9 Nuclides with $\alpha$-particle emission data for neutron yield calculations
¹⁴²Ce	²¹⁶Po	²²⁶Ac	²³⁷Np	²⁴⁵Cm
¹⁴⁴Nd	²¹⁸Po	²²⁷Ac	²³⁵Pu	²⁴⁶Cm
¹⁴⁶Sm	²¹⁵At	²²⁶Th	²³⁶Pu	²⁴⁷Cm
¹⁴⁷Sm	²¹⁷At	²²⁷Th	²³⁷Pu	²⁴⁸Cm
¹⁴⁸Sm	²¹⁸At	²²⁸Th	²³⁸Pu	²⁴⁹Bk
¹⁴⁹Sm	²¹⁹At	²²⁹Th	²³⁹Pu	²⁴⁸Cf
¹⁵²Gd	²¹⁷Rn	²³⁰Th	²⁴⁰Pu	²⁴⁹Cf
²¹⁰Pb	²¹⁸Rn	²³²Th	²⁴¹Pu	²⁵⁰Cf
²¹⁰Bi	²¹⁹Rn	²³⁰Pa	²⁴²Pu	²⁵¹Cf
²¹¹Bi	²²⁰Rn	²³¹Pa	²⁴⁴Pu	²⁵²Cf
²¹²Bi	²²²Rn	²³⁰U	²⁴⁰Am	²⁵³Cf
²¹³Bi	²²¹Fr	²³¹U	²⁴¹Am	²⁵⁴Cf
²¹⁴Bi	²²²Fr	²³²U	^242mAm	²⁵³Es
²¹⁰Po	²²³Fr	²³³U	²⁴³Am	²⁵⁴Es
²¹¹Po	²²²Ra	²³⁴U	²⁴⁰Cm	^254mEs
²¹²Po	²²³Ra	²³⁵U	²⁴¹Cm	²⁵⁵Es
²¹³Po	²²⁴Ra	²³⁶U	²⁴²Cm	²⁵⁴Fm
²¹⁴Po	²²⁶Ra	²³⁸U	²⁴³Cm	²⁵⁵Fm
²¹⁵Po	²²⁵Ac	²³⁵Np	²⁴⁴Cm	²⁵⁶Fm
				²⁵⁷Fm

Table 10.2.10 Target $(\alpha,n)$ cross section and branching level isotopes and sources
Isotope	ZAID	Level branching fraction source data	Cross section data
⁷Li	30070	GNASH	Gibbons and Macklin [Origen-Data-ResourcesGM59]
⁹Be	40090	Geiger and Van der Zwain [Origen-Data-ResourcesGZ75]	Geiger and Van der Zwain [Origen-Data-ResourcesGZ75]
¹⁰B	50010	GNASH	Bair et al. [Origen-Data-ResourcesBC79]
¹¹B	50110	GNASH	Bair et al. [Origen-Data-ResourcesBC79]
¹³C	60130	GNASHa	Bair and Haas [Origen-Data-ResourcesBH73]
¹⁴N	70140	N/A	GNASH
¹⁷O	80170	Lessor and Schenter [Origen-Data-ResourcesLS71]	Perry and Wilson [Origen-Data-ResourcesPW81]
¹⁸O	80180	Lesser and Schenter [Origen-Data-ResourcesLS71]	Perry and Wilson [Origen-Data-ResourcesPW81]
¹⁹F	90190	Lesser and Schenter [Origen-Data-ResourcesLS71]	Balakrishnan et al. [Origen-Data-ResourcesMBM78]
²¹Ne	100210	N/A	GNASH
²²Ne	100220	N/A	GNASH
²³Na	110230	GNASH	GNASHa
²⁵Mg	120250	GNASH	GNASH
²⁶Mg	120260	GNASH	GNASH
²⁷Al	130270	GNASH	GNASHa
²⁹Si	140290	GNASH	GNASHa
³⁰Si	140300	GNASH	GNASHa
³¹P	150310	GNASH	GNASH
³⁷Cl	170370	GNASH	Woosley et. al. [Origen-Data-ResourcesWFHZ75]

2: GNASH-calculated data and measured data are available for these nuclides in the library. By default, the GNASH values are used. To use the measured data, the user must reverse the order of th GNASH and measured data in the library since the code uses the first set encountered in the library (GNASH set).

10.2.8.3. Beta Emission

Beta emission rates and energy spectra are calculated using an analytic expression for the kinetic energy of the emitted $\beta^-$ particles [Origen-Data-ResourcesGM71]:

(10.2.5)\[N\left( Z,W \right) = \frac{g^{2}}{{2\pi}^{3}} F\left( Z,W \right) \rho W \left( W_{0}- W \right)^{2}S_{n}\left( W \right) dW\]

where

$Z =$ atomic number of the daugher nucleus

$g =$ weak interaction coupling constant

$W =$ kinetic energy of beta particle (in $m_{e}c^{2}$ units)

$F\left( Z,W \right) =$ Fermi function

$W_{0} =$ endpoint beta energy

$\rho = \sqrt{W^{2} - 1}$ = electron momentum

$S_{n}\left( W \right) =$ spectral shape factor based on transition type

$n =$ classification of the transition type

Internal conversion electron emission is not considered.

The calculation requires nuclear data on the fraction of the beta transition to each exicited state of the daughter nucleus, the maximum endpoint energy of the transition (W0), and a classification of the beta transition (n) defined by the spin and parity change of the transition which defines the spectral shape factor. The transition classification uses n=0 for allowed and forbidden non-unique transitions, n=1 for first forbidden unique transitions, n=2 for second forbidden unique transitions, and n=3 for third forbidden unique transitions. These data are not stored in the decay data resource but are included in a separate beta decay resource used only for the beta calculation.

The beta decay data are stored in the formatted file origen.rev00.ensdf95beta.data. The data are derived from ENSDF as compiled in 1995. The file includes beta decay information for 715 beta decay nuclides and has 8486 beta transition branches.

10.2.8.4. Alpha Emission

Calculation of the alpha emission intensity and spectrum requires detailed information that is not available on the decay resource. The calculation requires the alpha particle energy and branching fraction for each transition branch. Unlike the beta spectrum, the alpha particles are emitted with discrete energies, and the source spectrum may be generated by straightforward binning into the user-defined group structure. Alpha particle emission data are also used in the $\left( \alpha,n \right)$ neutron source calculation. Therefore, the alpha emission spectra are calculated using the same alpha decay library in the neutron emission resource: origen.rev01.alphdec.data.

References

Origen-Data-Resources10c: Code of Federal Regulations, Title 10, Part 20.
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