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20-Ca- 43 NRG EVAL-OCT04 A.J. Koning
NRG-2004 DIST-JAN09 20090105
----JEFF-311 Material 2034 REVISION 1
-----Incident neutron data
------ENDF-6 Format
*************************** JEFF-3.1.1 *************************
** **
** Original data taken from: JEFF-3.1 **
** **
******************************************************************
***************************** JEFF-3.1 *************************
** **
** Original data taken from: New evaluation **
** **
******************************************************************
NRG-2004: n + Ca-43
Author: A.J. Koning, NRG Petten
************** G E N E R A L I N F O R M A T I O N *************
This evaluated data file is based primarily on a theoretical
analysis with the nuclear model code TALYS [kon04], version 0.56.
The nuclear model parameters of TALYS have been adjusted to
reproduce the existing experimental data. The resulting data file
provides a complete representation of nuclear data needed for
transport, damage, heating, radioactivity, and shielding
applications over the incident neutron energy range from
1.0E-11 to 200 MeV.
This file is part of a larger collection of isotopic evaluations,
all created by running TALYS with input parameters that do not or
slightly deviate from the default values. The mutual quality of
these isotopic evaluations is thus relatively consistent.
The same set of nuclear models is used and, equally important,
the same ENDF-6 formatting procedures for each isotope. We have
intended to make this evaluation complete in its description of
reaction channels, and use a compact method to store the data.
For certain reactions and energy ranges TALYS may not be used.
This is the case when TALYS is not appropriate, such as for the
description of resonances, or when the directly available
experimental data is of better quality, as for e.g. low-energy
total cross sections. In these cases, we have adopted the best
possible data from an existing library, or directly from unfiled
experimental data. All transport data for particles, photons and
residual nuclides are filed using a combination of MF1,2,3,4 and
MF6. This includes cross sections, angular distributions,
double-differential spectra, discrete and continuum photon
production cross sections, and residual production (activation)
cross sections. Moreover, isomeric production data are stored in
MF8 and MF10. This evaluation can thus be used as both transport
and activation library. The data file has been created
automatically using the ENDF-6 format generator TEFAL.
##### ORIGIN
Data < 200 MeV : New evaluation NRG Petten
Resonance parameters (MF2/MT151): JENDL-3.3 for E < 40 keV
All other data : Produced with TALYS code
*************************** T H E O R Y **************************
TALYS is a computer code system for the prediction and analysis
of nuclear reactions. TALYS simulates reactions that involve
neutrons, gamma-rays, protons, deuterons, tritons, helions and
alpha-particles, in the 1 keV - 200 MeV energy range and for
target nuclides of mass 12 and heavier. This is achieved by
implementing a suite of nuclear reaction models into a single
code system. It enables to evaluate nuclear reactions from
the unresolved resonance region up to intermediate energies. This
evaluation is based on a theoretical analysis that utilizes the
optical model, compound nucleus statistical theory, direct
reactions and pre-equilibrium processes, in combination with
databases and models for nuclear structure. For Ca-43, the
following output of TALYS is stored in this data file:
- Total, elastic and non-elastic cross sections
- Elastic scattering angular distributions
- Inelastic cross sections to discrete states
- Inelastic scattering angular distributions to discrete states
- Exclusive channel cross sections, e.g. (n,g), (n,2n), (n,np),..
- Exclusive channel energy spectra
- Exclusive channel double-differential spectra
- Exclusive gamma production for discrete states and continuum
- Isomeric and ground state cross sections
- Residual production cross sections
- Total particle cross sections, e.g. (n,xn), (n,xp),..
- Total particle energy spectra
- Total particle double-differential spectra
Here follows a short description of the used nuclear models:
##### OPTICAL MODEL
All optical model calculations are performed by ECIS-97 [ray94],
in TALYS used as a subroutine. The default optical model
potentials (OMP) used are the local and global parameterizations
of Koning and Delaroche [kon03]. These are phenomenological OMPs
for neutrons and protons which in principle are valid over the
1 keV - 200 MeV energy range, though the low energy boundary of
validity may differ from nucleus to nucleus (e.g. for the total
cross sections, experimental data are included directly in the
file for energies below that boundary). Solving the Schroedinger
equation with this OMP yields the total cross section, the
shape-elastic cross section, the shape-elastic angular
distribution, the wave functions for the direct reaction cross
sections (see below), the transmission coefficients for the
compound nucleus model (see below) and the reaction cross
sections for the pre-equilibrium model (see below).
For neutrons and protons, the used parameterization is given in
Eq. (7) of [kon03].
To calculate the transmission coefficients and reaction cross
sections for deuterons, tritons, helions and alpha particles, we
use OMPs that are directly derived from our nucleon potentials
using Watanabe's folding approach [mad88].
##### DIRECT REACTIONS
The built-in ECIS-97 is used for coupled-channels or DWBA
calculations for rotational or vibrational (or a combination of
these) nuclides. For Ca-43, DWBA was used to compute the direct
cross sections to several low-lying discrete levels of the
even-even core Ca-42. The weak-coupling model was then used
to spread the collective strength over the odd levels of Ca-43.
In addition, a macroscopic, phenomenological model to describe
giant resonances in the inelastic channel is used. For each
multipolarity an energy weighted sum rule applies and a DWBA
calculation with ECIS-97 is performed for each giant resonance
state. The cross section is then spread over the continuum with a
Gaussian distribution.
##### COMPOUND NUCLEUS
For binary compound nucleus reactions we use the model of
Moldauer [mol80], i.e. the Hauser-Feshbach model [hau52]
corrected for width fluctuations. The transmission coefficients
have been generated with the aforementioned OMPs and the full
j,l-dependence of the transmission coefficients in the
Hauser-Feshbach model is used. For each nucleus that can be
reached through a binary reaction, several discrete levels and a
continuum described by level densities are included
simultaneously as competing channels.
The compound nucleus angular distributions are calculated with
the Blatt-Biedenharn formalism [bla52], leading to compound
nucleus Legendre coefficients that are added to their direct
counterparts. For multiple compound emission, i.e. emitted
particles after the binary emission, we use the Hauser-Feshbach
model. Again, for each residual nucleus several discrete states
are included as well as a continuum described by level densities.
Multiple compound emission is continued until all reaction
channels are closed and the population distribution of all
residual nuclides is depleted, through gamma decay, until they
end up in the ground state or in an isomer.
For the level density, we take the composite formula proposed by
Gilbert and Cameron [gil65], consisting of a constant temperature
law at low energies and a Fermi gas expression at high energies.
For the level density parameter a we use the energy dependent
expression proposed by Ignatyuk [ign75] to take into account the
damping of shell effects at high excitation energy. We have
obtained the parameters for the Ignatyuk formula from a
simultaneous fit to all experimental D_0 values as present in the
RIPL library. If necessary, we adjust individual parameters to
obtain a better fit to experiment.
Gamma-ray transmission coefficients are generated with the
Kopecky-Uhl generalized Lorentzian for strength
functions [kop90], with giant dipole resonance parameters taken
from the RIPL library [rip98], and normalized with experimental
radiative widths [gar84].
##### PRE-EQUILIBRIUM REACTIONS
For pre-equilibrium reactions, which become important for
incident energies above about 10 MeV, we use the two-component
exciton model [kon04b], in which the neutron or proton types of
particles and holes are followed throughout the reaction. For
energies above 20 MeV, multiple pre-equilibrium emission up to
any order of particle emission was included in the calculations.
A parameterization for the squared matrix element is used that is
valid for the whole energy range of this evaluation.
For deuterons, tritons, helions and alpha-particles, an extra
contribution was added from the pick/up and knock-out reaction
model by Kalbach [kal01].
For photons, the model of Akkermans and Gruppelaar [akk85] was
applied, to simulate the direct and semi-direct capture
processes.
The angular distribution systematics by Kalbach [kal88] were used
to describe the angular distributions for all continuum
particles. An isotopic distribution for photons was adopted.
****** C O M P A R I S O N W I T H E X P E R I M E N T *****
This evaluation was performed simultaneously with other adjacent
isotopes, both for incident neutrons and protons. This enables,
when compared with a single-isotope effort, to put stronger
constraints on the produced calculated data, i.e. a globally
good comparison between TALYS and experimental data is requested
for all isotopes at the same time, while nucleus-specific input
(default or adjusted) parameters are consistently used for all
isotopes. Also, experimental data that is not available for the
isotope under study may be present, and tested, for adjacent
nuclides or for other projectiles. If these can be successfully
described by the models, a similar performance can be expected
for the present data file.
A few level density parameters for residual nuclides have been
adjusted to enforce agreement with the experimental data. The
changes in the level density parameters, a, were all kept within
10% of their default values.
##### TOTAL AND REACTION CROSS SECTIONS AND ELASTIC SCATTERING
The spherical OMP was tested against experimental data for total
cross sections and elastic scattering angular distributions.
Consult [kon03] for the complete experimental database and for a
comparison of calculations and measurements over the whole energy
range for natural Ca.
##### OTHER PARTIAL CROSS SECTIONS
- (n,gamma):
The calculated capture cross section is renormalized, by
overruling the default renormalization to the s-wave strength
function, to the available experimental data, all taken from the
EXFOR database. A normalization factor of 0.80 was used. The
pre-equilibrium gamma cross section was adjusted to the data by
multiplying the calculated result by a factor of 3.0.
- (n,p):
Many experimental (n,p) cross sections are available from EXFOR.
These have been used as validation for our TALYS calculation.
##### PARTICLE SPECTRA
For Ca-43, an adjustment of the default matrix element
parameterization of [kon04b] for pre-equilibrium reactions of a
factor of 0.7 was needed, to describe the aforementioned cross
sections and emission spectra for nuclides in this mass range.
For high-energy neutron and charged particle spectra, the average
quality is also determined by the pre-equilibrium model and its
global parameterization. No high-energy experiments are
available, though neutron induced reaction spectra between 28 and
63 MeV on Al [ben02], Si [ben02b] and Fe [sly03] have enabled us
to better constrain the results, through the aforementioned
matrix element, for particle yields and double-differential
spectra for all ejectiles up to alpha particles.
***************** F I L E I N F O R M A T I O N ****************
##### MF1: GENERAL INFORMATION
- MT451 : Descriptive data and directory
This text and the full directory of used MF/MT sections.
##### MF2: RESONANCE PARAMETERS
- MT151 : Resonance parameters
Resolved parameters for MLBW formula were adopted from JENDL-3.3.
They are given in the energy region from 1.0e-5 eV to 40 keV.
Parameters were taken from the recommended data of BNL [mug81]
and the data for a negative resonance were added so as to
reproduce the recommended thermal cross sections for capture and
scattering [mug81]. The scattering radius was assumed to be
3.6 fermi. Calculated 2200 m/sec cross sections and resonance
integrals are as follows:
2200 m/s cross section(b) res. integral(b)
elastic 4.160
capture 11.66 5.798
total 15.82
##### MF3: REACTION CROSS SECTIONS
Unless stated otherwise, all the data present in the following
MT-sections have been calculated with TALYS. If the maximal cross
section in an excitation function over the whole energy range
does not exceed 1.e-9 b, the MT-number is not included at all.
Cross sections lower than 1.e-20 b are assumed to have no
physical meaning and are set to zero.
- MT1 : Total cross section
Above 40 keV, calculations from the spherical OMP [kon03] were
used.
- MT2 : Elastic scattering cross section
Obtained by subtracting the non-elastic cross section from the
total cross section. Below 40 keV, resonance parameters are
used.
- MT3 : Non-elastic cross section
Calculated with the optical model over the whole energy range.
Below 40 keV, resonance parameters are used.
- MT4 : Total inelastic cross section
Sum of MT=51-91.
- MT5 : (n,anything) cross section
For energies below 20 MeV, MT5 contains the lumped (n,gamma x)
cross section, where x may represent neutron, proton, deuteron,
triton, Helium-3 or alpha. Using the relative yields of MF6/MT5,
the (n,gamma n), (n,gamma p), ..., (n,gamma alpha) can be
recovered. These cross sections are relatively small. However,
addition of these cross sections, which can not be stored in any
other MT-number, ensures that the partial cross sections add up
to the non-elastic cross section. Above 20 MeV, MT5 contains the
total non-elastic cross section, with which the information of
MF6/MT5 can be combined to obtain particle production cross
sections and (double-)differential cross sections.
- MT16 : (n,2n) cross section
- MT17 : (n,3n) cross section
- MT22 : (n,na) cross section
- MT24 : (n,2na) cross section
- MT28 : (n,np) cross section
- MT32 : (n,nd) cross section
- MT41 : (n,2np) cross section
- MT51-70 : (n,n') cross section for 1st-20th excited state
- MT91 : (n,n') continuum cross section
- MT102 : (n,gamma) cross section
Below 40 keV, resonance parameters are used.
- MT103 : (n,p) cross section
- MT104 : (n,d) cross section
- MT105 : (n,t) cross section
- MT106 : (n,h) cross section
- MT107 : (n,a) cross section
- MT108 : (n,2a) cross section
- MT111 : (n,2p) cross section
- MT112 : (n,pa) cross section
- MT600-610: (n,p) cross section for 0th-10th excited state
Obtained by mapping continuum (n,p) cross section from
pre-equilibrium and compound model on discrete states.
- MT649 : (n,p) continuum cross section
- MT650-655: (n,d) cross section for 0th-5th excited state
Obtained by mapping continuum (n,d) cross section from
pre-equilibrium and compound model on discrete states.
- MT699 : (n,d) continuum cross section
- MT700-705: (n,t) cross section for 0th-5th excited state
Obtained by mapping continuum (n,t) cross section from
pre-equilibrium and compound model on discrete states.
- MT749 : (n,t) continuum cross section
- MT750-755: (n,h) cross section for 0th-5th excited state
Obtained by mapping continuum (n,h) cross section from
pre-equilibrium and compound model on discrete states.
- MT799 : (n,h) continuum cross section
- MT800-810: (n,a) cross section for 0th-10th excited state
Obtained by mapping continuum (n,a) cross section from
pre-equilibrium and compound model on discrete states.
- MT849 : (n,a) continuum cross section
##### MF4: ANGULAR DISTRIBUTIONS OF SECONDARY PARTICLES
The versatility of MF6 for the storage of almost any secondary
distribution entails that we only use MF4 for the neutron elastic
scattering distribution. All data are generated with TALYS.
- MT2 : Elastic angular distribution
The flag LTT=3 is used to indicate a switch at 20 MeV from a
Legendre representation to a tabulated representation. For
incident energies below 20 MeV, the Legendre coefficients are
given on a sufficiently precise energy grid. They are a sum of
calculated Legendre coefficients for compound nucleus and
shape-elastic scattering. For incident energies above 20 MeV,
relative angular distributions are tabulated on an angular grid.
##### MF6: PRODUCT ENERGY-ANGLE DISTRIBUTIONS
In MF6 we store all secondary energy, angle, and energy-angle
distributions, as well as all residual and discrete + continuum
photon production cross sections. We thus do not use MF12-15 for
the photon production that accompanies each reaction. All data
are generated with TALYS.
- MT5 : (n,anything) yields and energy-angle distributions
For energies below 20 MeV, MT5 contains the relative yields of
the (n,gamma x) reaction, where x may represent neutron, proton,
deuteron, triton, Helium-3 or alpha. Using the (n,gamma x) cross
section of MF3/MT3, the (n,gamma p), ..., (n,gamma alpha) cross
section can be recovered. For energies above 20 MeV, MT5 contains
the production yields of particles and residual products. It also
contains the secondary energy-angle distributions for all
particles and photons. First, the yields for neutrons are given
for the whole energy range. Next, on a secondary energy grid the
relative emission spectra are given together with the parameters
for the Kalbach systematics for angular distributions. Inelastic
scattering cross sections for discrete states have been broadened
and added to the continuum spectra. This procedure is repeated
for protons, deuterons, tritons, Helium-3, alpha particles and
photons. Finally, the residual production yields are given per
final product. All these yields and relative distributions can
be multiplied with the cross sections given in MF3/MT5 to get
the production cross sections and (double-)differential cross
sections.
- MT16 : (n,2n) energy-angle distr. and photon production
First, for each type of outgoing particle, the (trivial) integer
particle yields are given. Next, on a sufficiently dense incident
energy grid the secondary energy-angle distributions are
specified by means of the relative emission spectra and the
parameters for the Kalbach systematics for angular distributions.
Next, the photon yield is tabulated as a function of incident
energy. For each incident energy, the photon production is given
for all discrete gamma lines present in the final nucleus. A
continuum photon distribution is added to this. We assume
isotropy for all produced gamma rays.
For the following MT-numbers, the same procedure as for MT16 is
followed:
-----
- MT17 : (n,3n) energy-angle distr. and photon production
- MT22 : (n,na) energy-angle distr. and photon production
- MT24 : (n,2na) energy-angle distr. and photon production
- MT28 : (n,np) energy-angle distr. and photon production
- MT32 : (n,nd) energy-angle distr. and photon production
- MT41 : (n,2np) energy-angle distr. and photon production
- MT91 : (n,n') continuum energy-angle distr. and phot. prod.
- MT102 : (n,gamma) photon production
- MT108 : (n,2a) energy-angle distr. and photon production
- MT111 : (n,2p) energy-angle distr. and photon production
- MT112 : (n,pa) energy-angle distr. and photon production
- MT649 : (n,p) continuum energy-angle distr. and photon prod.
- MT699 : (n,d) continuum energy-angle distr. and photon prod.
- MT749 : (n,t) continuum energy-angle distr. and photon prod.
- MT799 : (n,h) continuum energy-angle distr. and photon prod.
- MT849 : (n,a) continuum energy-angle distr. and photon prod.
-----
- MT51 : (n,n') angular distribution and photon production
for first excited state
The angular distribution for inelastic scattering to the first
inelastic state is given with Legendre coefficients up to 20 MeV.
Next, the exclusive yields for all the discrete gamma rays that
originate from this particular level are given.
For the following MT-numbers, the same procedure as for MT51 is
followed:
-----
- MT52-70 : (n,n') angular distribution and photon production
for 2nd-20th excited state
- MT600-610: (n,p) angular distribution and photon production
for 0th-10th excited state
- MT650-655: (n,d) angular distribution and photon production
for 0th-5th excited state
- MT700-705: (n,t) angular distribution and photon production
for 0th-5th excited state
- MT750-755: (n,h) angular distribution and photon production
for 0th-5th excited state
- MT800-810: (n,a) angular distribution and photon production
for 0th-10th excited state
-----
***** F I L E C H E C K I N G A N D P R O C E S S I N G ****
This file has been checked successfully by the BNL checking
codes CHECKR-6.12, FIZCON-6.12 and PSYCHE-6.12 [dun01] and has
been processed successfully into an MCNP library by the
processing code NJOY99.81 [mac00].
*********************** R E F E R E N C E S **********************
[akk85] J.M. Akkermans and H. Gruppelaar, Phys. Lett. 157B, 95
(1985).
[ben02] S. Benck, I. Slypen, J.-P. Meulders, V. Corcalciuc, and
M.B. Chadwick, Nucl. Sci. Eng. 140, 86 (2002).
[ben02b] S. Benck, I. Slypen, J.-P. Meulders, and V. Corcalciuc,
Nucl. Sci. Eng. 141, 1 (2002).
[ber03] O. Bersillon, Bruyeres-le-Chatel, private communication.
[bla52] J.M. Blatt and L.C. Biedenharn, Rev. Mod. Phys. 52, 725
(1952).
[dun01] C. Dunford, ENDF Utility Codes Release 6.12, (2001).
[gar84] D.G. Gardner, in Neutron Radiative Capture, OECD/NEA
Series on Neutron Physics and Nuclear Data in Science and
Technology, eds. A. Michaudon et al., p. 62 (1984).
[gil65] A. Gilbert and A.G.W. Cameron, Can. J. Phys. 43, 1446
(1965).
[hau52] W. Hauser and H. Feshbach, Phys. Rev. 87, 366 (1952).
[ign75] A.V. Ignatyuk, G.N. Smirenkin, and A.S. Tishin, Sov. J.
Nucl. Phys. 21, no. 3, 255 (1975).
[kal88] C. Kalbach, Phys. Rev. C37, 2350 (1988).
[kal01] C. Kalbach, PRECO-2000: Exciton model pre-equilibrium
code with direct reactions, Duke University 2001,
www.nndc.bnl.gov/nndcscr/model-codes/preco-2000/.
[kon03] A.J. Koning and J.P. Delaroche, Nucl. Phys. A713, 231
(2003).
[kon04] A.J. Koning, S. Hilaire and M.C. Duijvestijn, unpublished
(2004).
[kon04b] A.J. Koning and M.C. Duijvestijn, to be published
(2004).
[kop90] J. Kopecky and M. Uhl, Phys. Rev. C42, 1941 (1990).
[mac00] R.E. Macfarlane, NJOY99 - Code system for producing
pointwise and multigroup neutron and photon cross
sections from ENDF/B Data, RSIC PSR-480 (2000).
[mad88] D.G. Madland, in Proceedings of a Specialists' Meeting on
Preequilibrium Reactions, Semmering, Austria,
February 10-12 1988, (OECD, Paris 1988), p. 103.
[mol80] P.A. Moldauer, Nucl. Phys. A344, 185 (1980).
[mug81] S.F. Mughabghab, M. Divadeenam, and. N.E. Holden,
Neutron Cross Sections, Vol. I, Neutron Resonance
Parameters and Thermal Cross Sections (Academic Press,
1981).
[ray94] J. Raynal, Notes on ECIS94, CEA Saclay Report
No. CEA-N-2772, 1994.
[rip98] Handbook for calculations of nuclear reaction data:
Reference Input Parameter Library, IAEA-TECDOC-1034
(1998).
[sly03] I. Slypen, N. Nica, A.J. Koning, E. Raeymackers,
S. Benck, J.P. Meulders, and V. Corcalciuc,
Journ. Phys. G, November 2003 (2003).
************************* C O N T E N T S ************************
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