92-U -234 JAEA+ EVAL-JAN10 O.Iwamoto, T.Nakagawa, et al.
DIST-JUL13 20130624
----JENDL-4.0u2 MATERIAL 9225
-----INCIDENT NEUTRON DATA
------ENDF-6 FORMAT
Update File Distribution
Sep.14,2012 JENDL-4.0u1
History
05-12 Fission cross section was evaluated with GMA code.
06-06 Resonance parameters were modified.
07-05 Calculated with CCONE code.
07-11 Resonance parameters were revised.
Data were compiled as JENDL/AC-2008/1/.
09-03 Negative resonance, (1,452) and (1,455) were revised.
09-08 (MF1,MT458) was evaluated.
10-01 Data of prompt gamma rays due to fission were given.
10-02 Covariance data were given.
12-02 For MF1/MT458, E_nu and E_R were corrected. As a result,
the Q-vaues (= E_R) were modified for MF3/MT18,19,20,21,38.
Re-compiled by K. Shibata.
13-06 (MF2,MT151) LFW was corrected.
(MF32,MT151) LFW and RP were corrected.
MF=1 General Information
MT=451 Descriptive data and dictionary
MT=452 Number of neutrons per fission
Sum of MT=455 and 456.
MT=455 Delayed neutrons per fission
Determined from nu-d of the following three nuclides and
partial fission cross sections calculated with CCONE code/2/.
U -235 = 0.01053
U -234 = 0.0067
U -233 = 0.004998
The data for U-235 and U233is average of systematics
by Tuttle/3/, Benedetti et al./4/ and Waldo et al./5/
For U-234, determined from experimental data of
Borzakov et al./6/, Conant et al./7/ and Keepin
et al./8/.
Six group decay constants were adopted from Brady and
England/9/.
MT=456 Prompt neutrons per fission
(same as JENDL-3.3)
Based on the experimental data by Mather et al./10/ Nu-p of
Cf-252 spontaneous fission was assumed to be 3.756.
MT=458 Components of energy release due to fission
Total energy and prompt energy were calculated from mass
balance using JENDL-4 fission yields data and mass excess
evaluation. Mass excess values were from Audi's 2009
evaluation/11/. Delayed energy values were calculated from
the energy release for infinite irradiation using JENDL FP
Decay Data File 2000 and JENDL-4 yields data. For delayed
neutron energy, as the JENDL FP Decay Data File 2000/12/ does
not include average neutron energy values, the average values
were calculated using the formula shown in the report by
T.R. England/13/. The fractions of prompt energy were
calculated using the fractions of Sher's evaluation/14/ when
they were provided. When the fractions were not given by Sher,
averaged fractions were used.
MF= 2 Resonance parameters
MT=151
Resolved resonance parameters (MLBW: 1.0-5 eV - 1.5 keV)
Dridi/15/ analyzed the capture cross section measured at
n_TOF with SAMMY code, and obtained the neutron and capture
widths of resonances up to 1.5 keV. Their parameters were
adopted in the present file. Since cross sections calculated
with MLBW formula were almost the same as those with RM
formula, MLBW formula was adopted.
Fission widths were calculated from the neutron and capture
widths of Dridi et al. and fission areas calculated from the
resonance parameters of James et al./16/ For new
resonances measured by Dridi, fission width was not given.
The fission width of 5.17-eV resonance was determined so as
to reproduce the fission cross section measured by Heyse et
al./17/
A negative resonance was assumed at -0.97 eV by Dridi/15/.
Its parameters were adjusted to the thermal cross sections.
Scattering radius of 9.6 fm was adopted, which was in good
agreement with CCONE calculation.
The thermal cross sections to be reproduced:
Fission = 0.064 +- 0.014 b
Wagemans et al./18/
Capture = 100.2 +- 1.0 b
Pomerance/19/, Lounsbury et al./20/, Cabell et al./21/
Bringer et al./22/
Unresolved resonance parameters (1.5 keV - 80 keV)
Parameters were determined with ASREP code/23/ so as to
reproduce cross sections in this energy region.
The parameters are used only for self-shielding calculations.
Thermal cross sections and resonance integrals (at 300K)
-------------------------------------------------------
0.0253 eV reson. integ.(*)
(barns) (barns)
-------------------------------------------------------
total 118.18
elastic 17.82
fission 0.0670 5.20
capture 100.29 610
-------------------------------------------------------
(*) In the energy range from 0.5 eV to 10 MeV.
MF= 3 Neutron cross sections
Cross sections above the resolved resonance region except for
the elastic scattering (MT=2) and fission cross sections (MT=18,
19, 20, 21, 38) were calculated with CCONE code/2/.
MT= 1 Total cross section
The cross section was calculated with CC OMP of Soukhovitskii
et al./24/
MT=2 Elastic scattering cross section
Calculated as total - non-elstic scattering cross sections
MT=18 Fission cross section (Above 1.5 keV)
Above 1.5 keV, the following experimental data were analyzed
with the GMA code/25/:
Authors Energy range Data points Reference
James+ 1.40keV - 8.86MeV 2845 /16/
Behrens+ 0.105 - 18.90 MeV 147 /26/(*1)
Meadows 0.600 - 9.91 MeV 56 /27/(*1)
Goverdovskiy+ 16.0 MeV 1 /28/(*1)
Kanda+ 0.490 - 6.97 MeV 30 /29/(*1)
Goverdovskiy+ 4.91 - 10.4 MeV 33 /30/(*1)
Goverdovskiy+ 0.210 - 0.997 MeV 22 /31/(*1)
Meadows 14.7 MeV 1 /32/(*1)
Fursov+ 0.130 - 7.40 MeV 71 /33/(*1)
(*1) Relative to U-235 fission. Data were converted to
cross sections using JENDL-3.3 data.
The results of GMA were used to determine the parameters in
the CCONE calculation.
MT=19, 20, 21, 38 Multi-chance fission cross sections
Calculated with CCONE code, and renormalized to the total
fission cross section (MT=18).
MF= 4 Angular distributions of secondary neutrons
MT=2 Elastic scattering
Calculated with CCONE code.
MT=18 Fission
Isotropic distributions in the laboratory system were assumed.
MF= 5 Energy distributions of secondary neutrons
MT=18 Prompt fission neutrons
Calculated with CCONE code.
MT=455 Delayed neutrons
Taken from Brady and England /9/.
MF= 6 Energy-angle distributions
Calculated with CCONE code.
Distributions from fission (MT=18) are not included.
MF=12 Photon production multiplicities
MT=18 Fission
Calculated from the total energy released by the prompt
gamma-rays due to fission given in MF=1/MT=458 and the
average energy of gamma-rays.
MF=14 Photon angular distributions
MT=18 Fission
Isotoropic distributions were assumed.
MF=15 Continuous photon energy spectra
MT=18 Fission
Experimental data measured by Verbinski et al./34/ for
U-235 thermal fission were adopted.
MF=31 Covariances of average number of neutrons per fission
MT=452 Number of neutrons per fission
Combination of covariances for MT=455 and MT=456.
MT=455
Error of 15% was assumed.
MT=456
Covariance of obtained by fitting a stlight line to
data points with errors of 2% at 1 MeV and 5% at 10 MeV.
MF=32 Covariances of resonance parameters
Format of LCOMP=0 was adopted. Errors of neutron and
capture widths were adopted from Ref./35/ Those of fission
widths were assumed to be the same as relative error of
fission widths given by James et al./16/
Further errors of 10% were added to the total, elastic
scattering, fission and capture cross sections in the
resonance region.
MF=33 Covariances of neutron cross sections
Covariances were given to all the cross sections by using
KALMAN code/36/ and the covariances of model parameters
used in the theoretical calculations.
For the following cross sections, covariances were determined
by different methods.
MT=18 Fission cross section
Above 1.5 keV, evaluated with GMA code/25/. Variances
obtained by GMA were multiplied by a factor of 1.5.
MT=102 Capture cross section
Above 1.5 keV, Covariance matrix was obtained with CCONE and
KALMAN codes/36/.
MF=34 Covariances for Angular Distributions
MT=2 Elastic scattering
Covariances were given only to P1 components.
MF=35 Covariances for Energy Distributions
MT=18 Fission spectra
Estimated with CCONE and KALMAN codes.
*****************************************************************
Calculation with CCONE code
*****************************************************************
Models and parameters used in the CCONE/2/ calculation
1) Coupled channel optical model
Levels in the rotational band were included. Optical model
potential and coupled levels are shown in Table 1.
2) Two-component exciton model/37/
* Global parametrization of Koning-Duijvestijn/38/
was used.
* Gamma emission channel/39/ was added to simulate direct
and semi-direct capture reaction.
3) Hauser-Feshbach statistical model
* Moldauer width fluctuation correction/40/ was included.
* Neutron, gamma and fission decay channel were included.
* Transmission coefficients of neutrons were taken from
coupled channel calculation in Table 1.
* The level scheme of the target is shown in Table 2.
* Level density formula of constant temperature and Fermi-gas
model were used with shell energy correction and collective
enhancement factor. Parameters are shown in Table 3.
* Fission channel:
Double humped fission barriers were assumed.
Fission barrier penetrabilities were calculated with
Hill-Wheler formula/41/. Fission barrier parameters were
shown in Table 4. Transition state model was used and
continuum levels are assumed above the saddles. The level
density parameters for inner and outer saddles are shown in
Tables 5 and 6, respectively.
* Gamma-ray strength function of Kopecky et al/42/,/43/
was used. The prameters are shown in Table 7.
------------------------------------------------------------------
Tables
------------------------------------------------------------------
Table 1. Coupled channel calculation
--------------------------------------------------
* rigid rotor model was applied
* coupled levels = 0,1,2,3,4 (see Table 2)
* optical potential parameters /24/
Volume:
V_0 = 49.97 MeV
lambda_HF = 0.01004 1/MeV
C_viso = 15.9 MeV
A_v = 12.04 MeV
B_v = 81.36 MeV
E_a = 385 MeV
r_v = 1.2568 fm
a_v = 0.633 fm
Surface:
W_0 = 17.2 MeV
B_s = 11.19 MeV
C_s = 0.01361 1/MeV
C_wiso = 23.5 MeV
r_s = 1.1803 fm
a_s = 0.601 fm
Spin-orbit:
V_so = 5.75 MeV
lambda_so = 0.005 1/MeV
W_so = -3.1 MeV
B_so = 160 MeV
r_so = 1.1214 fm
a_so = 0.59 fm
Coulomb:
C_coul = 1.3
r_c = 1.2452 fm
a_c = 0.545 fm
Deformation:
beta_2 = 0.213
beta_4 = 0.066
beta_6 = 0.0015
* Calculated strength function
S0= 0.94e-4 S1= 2.42e-4 R'= 9.58 fm (En=1 keV)
--------------------------------------------------
Table 2. Level Scheme of U-234
-------------------
No. Ex(MeV) J PI
-------------------
0 0.00000 0 + *
1 0.04350 2 + *
2 0.14335 4 + *
3 0.29607 6 + *
4 0.49704 8 + *
5 0.74120 10 +
6 0.78629 1 -
7 0.80988 0 +
8 0.84930 3 -
9 0.85170 2 +
10 0.92674 2 +
11 0.94785 4 +
12 0.96260 5 -
13 0.96860 3 +
14 0.98945 2 -
15 1.02370 4 +
16 1.02380 12 +
17 1.02383 3 -
18 1.04453 0 +
19 1.06930 4 -
20 1.08530 2 +
21 1.09090 5 +
22 1.09590 6 +
23 1.12527 7 -
24 1.12668 2 +
25 1.12760 5 -
26 1.15000 3 +
27 1.16520 3 +
28 1.17210 6 +
29 1.17420 1 +
30 1.19473 6 -
-------------------
*) Coupled levels in CC calculation
Table 3. Level density parameters
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
U-235 18.5328 0.7828 2.6265 0.3874 -0.9246 3.1046
U-234 18.4650 1.5689 2.5578 0.3902 -0.1511 3.9087
U-233 18.3972 0.7861 2.4694 0.3819 -0.8199 2.9895
U-232 18.3293 1.5757 2.6095 0.3887 -0.1141 3.8805
U-231 18.2614 0.7895 2.6793 0.4123 -1.1756 3.4264
--------------------------------------------------------
Table 4. Fission barrier parameters
----------------------------------------
Nuclide V_A hw_A V_B hw_B
MeV MeV MeV MeV
----------------------------------------
U-235 5.790 0.600 5.600 0.320
U-234 6.220 1.040 5.000 0.600
U-233 5.970 0.800 5.400 0.520
U-232 5.800 1.040 5.100 0.600
U-231 6.000 0.800 5.600 0.520
----------------------------------------
Table 5. Level density above inner saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
U-235 20.3497 0.9133 2.6000 0.3445 -1.7123 3.1133
U-234 20.2753 1.8304 2.6000 0.3306 -0.5810 3.8304
U-233 18.0364 0.9172 2.6000 0.3977 -2.2218 3.5172
U-232 20.1263 1.8383 2.6000 0.3319 -0.5731 3.8383
U-231 20.0518 0.9211 2.6000 0.3325 -1.4903 2.9211
--------------------------------------------------------
Table 6. Level density above outer saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
U-235 20.8948 0.9133 0.1000 0.3865 -1.0315 3.2133
U-234 20.2753 1.8304 0.0600 0.4009 -0.2030 4.2304
U-233 16.2328 0.9172 0.0200 0.5015 -1.6781 3.9172
U-232 20.1263 1.8383 -0.0200 0.3745 0.1401 3.8383
U-231 20.0518 0.9211 -0.0600 0.3758 -0.7765 2.9211
--------------------------------------------------------
Table 7. Gamma-ray strength function for U-235
--------------------------------------------------------
K0 = 1.501 E0 = 4.500 (MeV)
* E1: ER = 10.90 (MeV) EG = 2.50 (MeV) SIG = 300.00 (mb)
ER = 13.80 (MeV) EG = 4.70 (MeV) SIG = 450.00 (mb)
* M1: ER = 6.64 (MeV) EG = 4.00 (MeV) SIG = 2.68 (mb)
* E2: ER = 10.21 (MeV) EG = 3.29 (MeV) SIG = 6.52 (mb)
--------------------------------------------------------
References
1) O.Iwamoto et al.: J. Nucl. Sci. Technol., 46, 510 (2009).
2) O.Iwamoto: J. Nucl. Sci. Technol., 44, 687 (2007).
3) R.J.Tuttle: INDC(NDS)-107/G+Special, p.29 (1979).
4) G.Benedetti et al.: Nucl. Sci. Eng., 80, 379 (1982).
5) R.Waldo et al.: Phys. Rev., C23, 1113 (1981).
6) S.B.Borzakov et al.: Phys. At. Nuclei, 61, 530 (2000).
7) J.F.Conant, P.F.Palmedo: Nucl. Sci. Eng., 44, 173 (1971).
8) G.R.Keepin et al.: Phys. Rev., 107, 1044 (1957).
9) M.C.Brady, T.R.England: Nucl. Sci. Eng., 103, 129(1989).
10) D.S.Mather et al.: Nucl. Phys., 66, 149 (1965).
11) G.Audi: Private communication (April 2009).
12) J.Katakura et al.: JAERI 1343 (2001).
13) T.R.England et al.: LA-11151-MS (1988).
14) R.Sher, C.Beck: EPRI NP-1771 (1981).
15) W.Dridi: Thesis to Universite d'Evry Val d'Essonne (2006).
16) G.D.James et al.: Phys. Rev., C15, 2083 (1977).
17) J.Heyse et al.: Nucl. Sci. Eng., 156, 211 (2007).
18) C.Wagemans et al.: Nucl. Sci. Eng., 141, 171 (2002).
19) H.Pomerance: ORNL-CF-51-12, p.151 (1951).
20) M.Lounsbury et al.: 1970 Helsinki, Vol.1, p.287 (1970).
21) M.Cabell, M.Wilkins: AERE-R-6761 (1971).
22) O.Bringer et al.: 2007 Nice (ND2007), p.619 (2007).
23) Y.Kikuchi et al.: JAERI-Data/Code 99-025 (1999) in Japanese.
24) E.Sh.Soukhovitskii et al.: Phys. Rev. C72, 024604 (2005).
25) W.P.Poenitz: BNL-NCS-51363, Vol.I, p.249 (1981).
S.Chiba, D.L.Smith: ANL/NDM-121 (1991).
26) J.W.Behrens, G.W.Carlson: Nucl. Sci. Eng., 63, 250 (1977).
27) J.W.Meadows: Nucl. Sci. Eng., 65, 171 (1978).
28) A.A.Goverdovskii et al.: Sov. Atomic Energy, 60, 494 (1986).
29) K.Kanda et al.: 1985 Santa Fe, Vil.1, p.569 (1985).
30) A.A.Goverdovskii et al.: Sov. Atomic Energy, 62, 238 (1987).
31) A.A.Goverdovskii et al.: Sov. Atomic Energy, 63, 568 (1987).
32) J.W.Meadows: Ann. Nucl. Energy, 15, 421 (1988)..
33) B.I.Fursov et al.: Sov. Atom. Energy, 71, 827 (1991).
34) V.V.Verbinski et al.: Phys. Rev., C7, 1173 (1973).
35) W.Dridi et al.: 2006 Vancouver (PHYSOR-2006), C032 (2006).
36) T.Kawano, K.Shibata, JAERI-Data/Code 97-037 (1997) in
Japanese.
37) C.Kalbach: Phys. Rev. C33, 818 (1986).
38) A.J.Koning, M.C.Duijvestijn: Nucl. Phys. A744, 15 (2004).
39) J.M.Akkermans, H.Gruppelaar: Phys. Lett. 157B, 95 (1985).
40) P.A.Moldauer: Nucl. Phys. A344, 185 (1980).
41) D.L.Hill, J.A.Wheeler: Phys. Rev. 89, 1102 (1953).
42) J.Kopecky, M.Uhl: Phys. Rev. C41, 1941 (1990).
43) J.Kopecky, M.Uhl, R.E.Chrien: Phys. Rev. C47, 312 (1990).