40-Zr- 93 JAEA EVAL-SEP09 A.Ichihara, K.Shibata, S.Kunieda+
DIST-MAY10 20100209
----JENDL-4.0 MATERIAL 4034
-----INCIDENT NEUTRON DATA
------ENDF-6 FORMAT
History
09-08 The data above the resolved resonance region were evaluated
by A.Ichihara.
09-09 Compiled by A.Ichihara.
MF= 1 General information
MT=451 Descriptive data and directory
MF= 2 Resonance parameters
Resolved resonance parameters were taken from JENDL-3.3/1/.
MT=151 Resolved and unresolved resonance parameters
Resolved resonance region (MLBW formula) : below 1.7 keV
Resonance parameters were newly evaluated as follows:
Resonance energies, neutron widths and radiation widths were
mainly taken from the measurement of Macklin/2/ up to 6.1 keV.
Neutron widths not measured were determined from capture area
data, and total and radiation widths of Macklin et al./3/
Average radiation widths were deduced to be 0.145 eV for
s-wave resonances, and 0.250 eV for p-wave resonances. Total
spin J of some resonances was tentatively estimated with a
random number method. Neutron orbital angular momentum L of
some resonances was estimated with a method of Bollinger and
Thomas/4/. Scattering radius was based on the systematics of
measured values for neighboring nuclides. A negative
resonance was added so as to reproduce the thermal capture
cross section given by Mughabghab et al./5/
Unresolved resonance parameters were adopted from JENDL-2.
The neutron strength functions, S0, S1 and S2 were calculated
with optical model code CASTHY/6/. The observed level spacing
was determined to reproduce the capture cross section
calculated with CASTHY. The effective scattering radius was
obtained from fitting to the calculated total cross section at
100 keV.
Typical values of the parameters at 70 keV:
S0 = 0.370e-4, S1 = 5.480e-4, S2 = 0.360e-4, Sg = 5.31e-4,
Gg = 0.200 eV, R = 6.734 fm.
Unresolved resonance region : 1.7 keV - 500 keV
The unresolved resonance parameters were recalculated using
the ASREP code/7/.
The parameters should be used only for self-shielding
calculation.
Thermal cross sections and resonance integrals at 300 K
----------------------------------------------------------
0.0253 eV res. integ. (*)
(barns) (barns)
----------------------------------------------------------
Total 7.9241E+00
Elastic 5.6846E+00
n,gamma 2.2395E+00 1.8197E+01
----------------------------------------------------------
(*) Integrated from 0.5 eV to 10 MeV.
MF= 3 Neutron cross sections
MT= 1 Total cross section
The cross sections were taken from JENDL-3.3/1/ for neutron
energies below 50 keV.
The cross sections were calculated with the POD code/8/
for neutron energies larger than 50 keV.
MT= 2 Elastic scattering cross section
Calculated as (total - sum of partial cross sections).
MT= 3 Non-elastic cross section
Sum of partial cross sections.
MT= 4,51-91 (n,n') cross section
Calculated with POD code /8/.
MT= 16 (n,2n) cross section
Calculated with POD code /8/.
MT= 17 (n,3n) cross section
Calculated with POD code /8/.
MT= 22 (n,na) cross section
Calculated with POD code /8/.
MT= 28 (n,np) cross section
Calculated with POD code /8/.
MT= 32 (n,nd) cross section
Calculated with POD code /8/.
MT=102 Capture cross section
The cross sections were taken from JENDL-3.3/1/ for neutron
energies below 50 keV.
The cross sections were calculated with the POD code/8/
for neutron energies larger than 50 keV.
MT=103 (n,p) cross section
Calculated with POD code /8/.
MT=104 (n,d) cross section
Calculated with POD code /8/.
MT=105 (n,t) cross section
Calculated with POD code /8/.
MT=106 (n,He3) cross section
Calculated with POD code /8/.
MT=107 (n,a) cross section
Calculated with POD code /8/.
MT=203 (n,xp) cross section
Calculated with POD code /8/.
MT=204 (n,xd) cross section
Calculated with POD code /8/.
MT=205 (n,xt) cross section
Calculated with POD code /8/.
MT=206 (n,xHe3) cross section
Calculated with POD code /8/.
MT=207 (n,xa) cross section
Calculated with POD code /8/.
MF= 4 Angular distributions of emitted neutrons
MT= 2 Elastic scattering
The angular distributions were taken from JENDL-3.3/1/
for neutron energies below 50 keV.
The angular distributions were calculated with the POD
code /8/ for neutron energies larger than 50 keV.
MF= 6 Energy-angle distributions of emitted particles
MT= 16 (n,2n) reaction
Neutron spectra calculated with POD/8/.
MT= 17 (n,3n) reaction
Neutron spectra calculated with POD/8/.
MT= 22 (n,na) reaction
Neutron spectra calculated with POD/8/.
MT= 28 (n,np) reaction
Neutron spectra calculated with POD/8/.
MT= 32 (n,nd) reaction
Neutron spectra calculated with POD/8/.
MT= 51 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 52 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 53 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 54 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 55 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 56 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 57 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 58 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 59 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 60 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 61 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 62 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 63 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 64 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 65 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 66 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 67 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 68 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 69 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 70 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 71 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 72 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 73 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 74 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 75 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 76 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 77 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 78 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 79 (n,n') reaction
Neutron angular distributions calculated with POD/8/.
MT= 91 (n,n') reaction
Neutron spectra calculated with POD/8/.
MT= 203 (n,xp) reaction
Proton spectra calculated with POD/8/.
MT= 204 (n,xd) reaction
Deuteron spectra calculated with POD/8/.
MT= 205 (n,xt) reaction
Triton spectra calculated with POD/8/.
MT= 206 (n,xHe3) reaction
He3 spectra calculated with POD/8/.
MT= 207 (n,xa) reaction
Alpha spectra calculated with POD/8/.
MF=12 Gamma-ray multiplicities
MT= 3 Non-elastic gamma emission
Calculated with POD code /8/.
MF=14 Gamma-ray angular distributions
MT= 3 Non-elastic gamma emission
Assumed to be isotropic.
MF=15 Gamma-ray spectra
MT= 3 Non-elastic gamma emission
Calculated with POD code /8/.
***************************************************************
* Nuclear Model Calculations with POD Code /8/ *
***************************************************************
1. Theoretical models
The POD code is based on the spherical optical model, the
distorted-wave Born approximation (DWBA), one-component exciton
preequilibrium model, and the Hauser-Feshbach-Moldauer statis-
tical model. With the preequilibrim model, semi-empirical
pickup and knockout process can be taken into account for
composite-particle emission. The gamma-ray emission from the
compound nucleus can be calculated within the framework of the
exciton model. The code is capable of reading in particle
transmission coefficients calculated by separate spherical or
coupled-channel optical model code.
2. Optical model parameters
Neutrons:
Koning and Delaroche /9/
Protons:
Koning and Delaroche /9/
Deuterons:
Lohr and Haeberli /10/
Tritons:
Becchetti and Greenlees /11/
He-3:
Becchetti and Greenlees /11/
Alphas:
Lemos /12/ potentials modified by Arthur and Young /13/
The radius parameters r_V = r_I = 1.44 fm were used in the
calculation.
3. Level scheme of Zr- 93
Nuclear discrete levels were obtained from RIPL-2/14/.
Contribution of the direct process was calculated by DWBA
for the levels marked with '*'.
------------------------------------------------
No. Ex(MeV) J PI DWBA
------------------------------------------------
0 0.00000 5/2 +
1 0.26688 3/2 +
2 0.94714 1/2 + * (l=2, beta=0.06)
3 1.01800 1/2 + * (l=2, beta=0.06)
4 1.16860 1/2 + * (l=2, beta=0.06)
5 1.22200 1/2 + * (l=2, beta=0.06)
6 1.42541 3/2 +
7 1.45045 3/2 +
8 1.46300 7/2 +
9 1.47015 5/2 +
10 1.59800 7/2 +
11 1.64200 3/2 +
12 1.73500 3/2 +
13 1.90956 1/2 +
14 1.91856 1/2 -
15 2.02500 9/2 - * (l=3, beta=0.17)
16 2.04000 7/2 +
17 2.04700 3/2 +
18 2.07500 7/2 -
19 2.07800 7/2 +
20 2.09469 1/2 +
21 2.18462 1/2 +
22 2.27600 7/2 -
23 2.30200 7/2 -
24 2.36300 9/2 -
25 2.39100 1/2 +
26 2.45765 3/2 -
27 2.47384 3/2 +
28 2.53140 5/2 +
29 2.54800 5/2 +
------------------------------------------------
Levels above 2.55800 MeV are assumed to be continuous.
4. Level density parameters
Energy-dependent parameters of Mengoni-Nakajima /15/ were used
---------------------------------------------------
Nuclei a* Pair T E0 Ematch Elv_max
1/MeV MeV MeV MeV MeV MeV
---------------------------------------------------
Zr- 94 12.185 2.475 0.769 0.465 8.300 2.908
Zr- 93 12.414 1.244 0.757 -0.394 6.540 2.548
Zr- 92 11.704 2.502 0.852 0.517 8.693 3.058
Zr- 91 11.890 1.258 0.822 0.031 6.329 2.395
Y - 93 11.549 1.244 0.710 0.014 5.795 2.070
Y - 92 11.929 0.000 0.493 0.199 1.501 2.900
Y - 91 11.338 1.258 0.772 0.115 5.977 2.689
Sr- 91 12.543 1.258 0.625 0.591 4.649 4.249
Sr- 90 11.748 2.530 0.778 1.141 7.584 3.627
Sr- 89 10.953 1.272 0.720 1.044 4.474 4.050
---------------------------------------------------
5. Gamma-ray strength functions
M1, E2: Standard Lorentzian (SLO)
E1 : Standard Lorentzian (SLO) /16/
The position and width parameters in the E1
radiation were taken from the tabulation of
Dietrich and Berman/17/.
6. Preequilibrium process
Preequilibrium is on for n, p, d, t, He-3, and alpha.
The single particle state density parameters were
7.990, 7.742, 7.612, 7.202, 7.390, 6.958, 7.877 MeV^(-1)
for Zr-94, Zr-93, Y-93, Sr-90, Y-92, Y-91, and Sr-91.
Effects of the particle pickup (and knockout for alpha) were
estimated using the semi-empirical formulas by Kalbach/18/.
These components were multiplied by a factor of two and
added to the statistical model calculation.
Preequilibrium capture is on (the parameters were obtained
from /17/).
References
1) K.Shibata et al., J. Nucl. Sci. Technol. 39, 1125 (2002).
2) R.L.Macklin et al., Nucl. Sci. Eng. 92, 525 (1986).
3) R.L.Macklin, Astrophys. Space Sci. 115, 71 (1985).
4) L.M.Bollinger, G.E.Thomas, Phys. Rev. 171, 1293 (1968).
5) S.F.Mughabghab et al., "Neutron Cross Sections, Vol. I,
Part A", Academic Press (1981).
6) S.Igarasi, J. Nucl. Sci. Technol. 12, 67 (1975).
7) Y.Kikuchi et al., JAERI-Data/Code 99-025 (1999)
[in Japanese].
8) A.Ichihara et al., JAEA-Data/Code 2007-012 (2007).
9) A.J.Koning, J.P.Delaroche, Nucl. Phys. A713, 231 (2003).
10) J.M.Lohr, W.Haeberli, Nucl. Phys. A232, 381 (1974).
11) F.D.Becchetti,Jr., G.W.Greenlees, "Polarization
Phenomena in Nuclear Reactions," p.682, The University
of Wisconsin Press (1971).
12) O.F.Lemos, Orsay Report, Series A, No.136 (1972).
13) E.D.Arthur, P.G.Young, LA-8626-MS (1980).
14) T.Belgya et al., IAEA-TECDOC-1506 (2006).
15) A.Mengoni, Y.Nakajima, J. Nucl. Sci. Technol. 31, 151
(1994).
16) M.Brink, Ph.D thesis, Oxford University, 1955.
17) S.S.Dietrich, B.L.Berman, Atom. Data Nucl. Data Tables,
38, 199 (1988).
18) C.Kalbach, Z. Phys. A283, 401 (1977).