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22-Ti- 50 IRK EVAL-JAN04 Vienna:S.Tagesen, H.Vonach
DIST-JAN09 20090105
----JEFF-311 MATERIAL 2237
-----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 **
** Data includes covariance data from IRK Vienna **
******************************************************************
****************** Program LINEAR (VERSION 2002-1) ***************
For All Data Greater than 1.0000E-10 barns in Absolute Value
MT 1 and 102 Linearized for FIXUP (Within .10 per-cent)
****************** Program FIXUP (Version 2002-1) ****************
Reconstruction of missing cross sections: MF3/ MT2,MT3 and MT4
************** G E N E R A L I N F O R M A T I O N *************
This evaluation is part of a series of new evaluations for all
stable Ti isotopes especially designed to give the best possible
description of the natural element for neutron and gamma trans-
port calculations. The evaluation consists of a new evaluation
for file 3 and files 33 for all MT numbers for the fast neutron
energy range 0.2 - 20 MeV which is combined with the ENDF/B-VI
cross sections for MT1 and MT102 for natural Titanium for the
description of the resonance range (1.e-5 eV - 200 keV)
and file 4 and file 6 data (energy and angular distributions for
emitted particles and photons) from nuclear model calculations
with the new code TALYS (Kon 04). Details about these calculati-
ons are given in the next section of this file.
The new files 3 and 33 were derived in the following way:
Cross sections fron nuclear model calculations and their esti-
mated covariances (see table 1) are used as prior information
which is successively improved by adding experimental data (see
table 2) and by applying Bayes theorem to obtain the posterior
information. For this purpose the code GLUCS (Hetrick 80,
Tagesen 94, Tagesen 03) was used. Results of the TALYS calculation
were used for most of the reactions (see table 1). There are,
however, a few exceptions for the following reasons: For the
(n,g), (n,t) and (n,3He) reactions we used cross sections from
the European Activation File EAF, as these generally give a
better description of these cross sections. For the total cross
sections we use the TALYS calculation with a so called uninfor-
mative prior (very large uncertainties) so that the result is an
evaluation completely based on experimental data. Because much
better data for the total cross section of natural Ti are
available than for the individual isotopes, total cross sections
for Ti-nat have been used for all our Ti-evaluation. Thus the
evaluations for all Ti-isotopes contain the same evaluated total
cross section (Ti-nat) resulting in a very accurate total cross
section for the natural element derived by summing the isotopic
evaluations.
Table 1: Choice of basic cross sections and priors for the
GLUCS evaluation of 50-Ti
Reaction Cross section Covariance
total TALYS uninformative
n,2n TALYS own estimate
n,na TALYS own estimate
n,np TALYS own estimate
n,n1 TALYS own estimate
n,n2 TALYS own estimate
n,n3 TALYS own estimate
n,n4-20 TALYS own estimate
n,n cont TALYS own estimate
n,g EAF own estimate
n,p JENDL3.3 own estimate
n,d TALYS own estimate
n,t EAF own estimate
n,3He EAF own estimate
n,a JENDL3.3 own estimate
Table 2: Experimental data used in the GLUCS evaluation for
cross sections and covariances
Total (MT1):Foster 71, Barnard 74, Smith 78, Bratenahl 58,
Coon 52, Peterson 60, Conner 58, St. Pierre 59,
Carlson 67, Abfalterer 01, Cabe 73, Polycroniades 94
n,g (MT102): Dudey 69, Rigaud 74, Schwerer 74B, Vuletin 74
Zaikin 67
n,p (MT103): Pai 66, Qaim 76, Schwerer 76A, Pepelnik 85B,
Ikeda 88, Kobayashi 91, Molla 92, Ribanski 83, Viennot 91,
Fessler 00
n,a (MT107): Pepelnik 85A, Ikeda 88, Qaim 92, Subasi 96,
Ribanski 83, Grallert 93, Yuan 92, Qaim 91
n,49-Sc prod (MT28+104): Qaim 76
(n,p) and (n,d) cross sections were taken from JENDL3.3
because of the somewhat better agreement of these
calculations with the experimental data base.
In this way evaluated cross sections and covariances were
obtained for the 15 basic reactions in a group structure
of 36 neutron energy groups.
The covariances obtained in this way are directly used as
corresponding files 33 in the new evaluation. For the cross
sections (file 3) data a more detailed description is needed in
two respects. Cross section fluctuations within the relatively
large groups of the GLUCS evaluation have to be included, wherever
sufficiently well known and a number of our basic cross sections,
e.g., (n,n 4-20) have to be subdivided into their components n,n4
... n,n20 according to the calculated cross section ratios from
TALYS. This is documented in the section "file information", the
last section of this file 1. A more detailed description of this
new evaluation of cross sections and covariances for Ti is given
in (Tagesen 04).
*************************** T H E O R Y **************************
TALYS (Kon 04)is a computer code system for the prediction and
analysis of nuclear reactions. TALYS simulates reactions that in-
volve 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 Ti-46, 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
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 Ti-50, DWBA was used to compute the direct
cross sections to several low-lying discrete levels:
Level Energy Spin/Parity Deformation length delta_l
1 1.553780 2.0+ 0.340
2 2.674910 4.0+ 0.400
12 4.409990 3.0- 0.660
+ a few additional states with small deformation parameters.
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.
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 isotropic distribution for photons was adopted.
***************** 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
Only the scattering radius from ENDF/B-VI is given
##### MF3: REACTION CROSS SECTIONS
- MT1 : Total cross section
Below 0.2 MeV:
Cross sections calculated from resonance
parameters for Ti-nat from ENDF/B-VI
0.2 - 20 MeV:
Results of the GLUCS evaluation (group cross sections) with
superimposed fine structure:
Fluctuations in the total cross section (A. Trkov):
The basic evaluation was done for average cross sections
over broad energy intervals above 200 keV, but experimental
data indicate considerable structure, which was found to be
well reproduced by the data in the ENDF/B-VI Rel.8 file for
the same element.
A smooth, piecewise linear function was constructed, which
preserved the broad bin average cross sections from the
ENDF/B-VI Rel.8 data. The modulating function, defined as the
ratio of the fluctuating total cross section with the smooth
function was calculated. Using the same method, a similar
smooth function was defined for the new evaluation.
Multiplying this smooth function with the modulating function
gives the final total cross section, which retains the shape
of the ENDF/B-VI Rel.8 data, but reproduces the broad bin
average values of the new evaluation.
- MT16 : (n,2n) cross section TALYS
- MT22 : (n,na) cross section TALYS
- MT28 : (n,np) cross section GLUCS
- MT51 : (n,n'1) cross section for 1st excited state TALYS
- MT52 : (n,n'2) cross section for 2nd excited state TALYS
- MT53 : (n,n'3) cross section for 3rd excited state TALYS
- MT54-70 : (n,n'4)-(n,n'20) cross sections from GLUCS evaluation
of MT854 (n,n'4-20) by dividing this cross section
into its partials MT 54 - 70 according to the cross
section ratio from the TALYS calculation
- MT91 : (n,n') continuum cross section TALYS
- MT102 : (n,gamma) cross section: 0.2 - 20 MeV GLUCS
below 0.2 MeV: ENDF/B-VI for Ti-nat
- MT103 : (n,p) cross section GLUCS
- MT104 : (n,d) cross section GLUCS
- MT105 : (n,t) cross section EAF
- MT106 : (n,3He) cross section EAF
- MT107 : (n,a) cross section GLUCS
- MT600-610 and 649: (n,p) cross section for 0th-10th excited
state and (n,p) continuum cross section
from evaluation result for MT103 by dividing this
cross section into its partitials (n,p0),...,(n,p10)
and (n,p-cont) according to the cross sections
from the TALYS calculations.
- MT650-655 and 699: (n,d) cross section for 0th-5th excited
state and (n,d) continuum cross section
from evaluation result for MT104 by dividing this
cross section into its partitials (n,d0),...,(n,d5)
and (n,d-cont) according to the cross sections
from the TALYS calculations.
- MT700-705 and 749: (n,t) cross section for 0th-5th excited
state and (n,t) continuum cross section
from evaluation result for MT105 by dividing this
cross section into its partitials (n,t0),...,(n,t5)
and (n,t-cont) according to the cross sections
from the TALYS calculations.
- MT750-755 and 799: (n,3He) cross section for 0th-5th excited
state and (n,3He) continuum cross section
from evaluation result for MT106 by dividing this
cross section into its partitials (n,3He0),...,
(n,3He5) and (n,3He-cont) according to the cross
sections from the TALYS calculations.
- MT800-810 and 849: (n,a) cross section for 0th-10th excited
state and (n,a) continuum cross section
from evaluation result for MT107 by dividing this
cross section into its partitials (n,a0),...,(n,a10)
and (n,a-cont) according to the cross sections
from the TALYS calculations.
##### 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
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.
##### 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.
- 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:
-----
- MT22 : (n,na) energy-angle distr. and photon production
- MT28 : (n,np) energy-angle distr. and photon production
- MT91 : (n,n') continuum energy-angle distr. and phot. prod.
- MT102 : (n,gamma) photon production
- MT111 : (n,2p) 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.
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
##### MF33: COVARIANCE DATA FOR REACTION CROSS SECTIONS
Covariance data for
- MT1
- MT2 = derived Covarance matrix given as NC subsection
- MT3 = derived Covarance matrix given as NC subsection
- MT4 = derived Covarance matrix given as NC subsection
- MT16
- MT22
- MT28
- MT51
- MT52
- MT53
- MT54-70 lumped to MT854
- MT91
- MT102
- MT103
- MT104
- MT105
- MT106
- MT107
- MT111
- MT854 = lumped covariance matrix for MT54-70
all NI-subsections taken directly from the results of our GLUCS
calculations.
*********************** R E F E R E N C E S **********************
[akk85] J.M. Akkermans and H. Gruppelaar, Phys. Lett. 157B, 95
(1985).
[bla52] J.M. Blatt and L.C. Biedenharn, Rev. Mod. Phys. 52, 725
(1952).
[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).
[Hetrick 80] D.M. Hetrick and C.Y. Fu, GLUCS: A Generalized Least-
Squares Program for Updating Cross Section Evaluations
with Correlated Data Sets, Report ORNL/TM-7341 (1980)
[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).
[ray94] J. Raynal, Notes on ECIS94, CEA Saclay Report
No. CEA-N-2772, 1994.
[rip98] Handbook for calculations of nuclear reaction data:
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(1998).
[Tagesen 94] S. Tagesen and D.M. Hetrick, Proc. Int. Conf. on
Nuclear Data for Science and Technology, Gatlinburg,
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[Tagesen 03] S. Tagesen, H. Vonach and G. Winkler,
EFF-DOC 878 (2003)
[Tagesen 04] S. Tagesen, H. Vonach and A. Wallner, JEFF/DOC-1002
(2004)
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