- Email: [email protected]
An analysis of the intranuclear cascade evaporation model with in-medium nucleon-nucleon cross sections
28 July 1994 PHYSICS LETTERS B Physics Letters B 333 (1994) 22-26
ELSEVIER
An analysis of the intranuclear cascade evaporation model with in-medium nucleon-nucleon cross sections E. Suetomi 1, N. Kishida, H. Kadotani CRC Research Institute, Inc., 1-3-D16, Nakase, Miharaa-ku, Chiba 261-01, Japan Received 14 April 1994; revised manuscript received 2 June 1994 Editor: C. Mahaux
Abstract An analysis of the intranuclear cascade evaporation (INCE) model has been performed taking the presence of the mean field in nuclear matter into account. In-medium nucleon-nucleon (NN) cross sections were incorporated into an INCE code. Application of the in-medium NN cross sections resulted in significant reduction of differences between experimental differential neutron production cross sections and those of the INCE calculation using the free space NN cross sections.
1. Introduction For past ten years, a number of double differential neutron production cross sections have been measured for intermediate energy protons 100 to 800 MeV [ 1-5]. These cross sections are particularly important in several areas, e.g., accelerator shielding, space radiation effect, medical application, transmutation of transuranic wastes by spallation reaction, and other application areas. The intranuclear cascade evaporation (INCE) model [6,7] has been extensively used in predictions and analysis of those cross sections. Amian et al. [3,4] have measured the cross sections for medium-energy protons at 800 MeV and 597 MeV. Overall agreement between the experimental cross sections and those of the INCE model was fairly good. However some differences still remain in emitted neutron energies between a few MeV and a few tens of MeV.
1 E-mail address: [email protected].
In INCE calculation, the following cross sections are needed: the elastic and inelastic nucleon-nucleon ( N N ) scattering cross sections, the pion-nucleon scattering cross sections and the charge-exchange cross sections. Particularly the N N cross sections are important for incident nucleon below 1 GeV because in this energy range the elastic N N cross sections are dominant. Free space N N cross sections are ordinarily used in usual INCE codes, such as NMTC [ 8 ] and HETC [9]. But the in-medium N N cross sections have to be employed because of existence of nuclear mean field. Tsukada and Nakahara [ 10] have proposed to use a prolonged nucleon mean free path (mfp) within a nucleus to reduce the discrepancy between I N C E calculation and experimental data. They used the mfp that was multiplied by a constant independent of the nucleon energy. Li, Machleidt and Zhuo [ 11 ] have calculated the nucleon mfp in the normal nuclear matter. They showed that the ratios of mfp in free space to mfp in the nuclear matter vary with nucleon energies. Recently Li and Machleidt [ 12,13 ] have derived the in-medium elastic N N cross sections using a mi-
0370-2693/94/$07.00 (~) 1994 Elsevier Science B.V. All rights reserved SSDI 0 3 7 0 - 2 6 9 3 ( 9 4 ) 0 0 7 4 7 - U
E. Suetomi et al. / Physics Letters B 333 (1994) 22-26
croscopic nuclear matter model in energy range 50 through 300 MeV. They found that the in-medium total N N cross sections and the in-medium np-scattering angular distributions are very different from those of free space. This suggests that the in-medium N N scattering cross sections must be used in the INCE calculation. In this letter, we investigate the effects that the use of the in-medium N N cross sections cause to the differential neutron production cross sections.
2. INCE cross
calculation
with
the in-medium
sections
1.0 + 0.1667El°Sp 3 1.0 + 9.704pl. 2 ,
I
I
I
',,,
10(
I
I
I
I
I
...... Bertini - -
g ,-
In-medium o np
(Li and Machleidt)
8(
0 o
60 £ 0
40
I-
20 i
(1)
O'np(E, p ) = [31.5 + 0 . 0 9 2 a b s ( 2 0 . 2 - E ° 5 3 ) 2"9 ]
1.0 + 0.0034E]'5]p 2 1.0 + 21.55p 1"34 '
'll
,,
0
trpp (E, p) = [23.5 + 0.00256( 18.2 - E°'5) 4"°]
×
I
NN
Li and Machleidt [ 12,13 ] proposed a parametrization for the in-medium total N N cross sections as a function of the incident nucleon energy up to 300 MeV and density of nuclear matter up to 2p0 (through this work we use the saturation density of normal nuclear matter p0 = 0.18 f m - 3 ) . The expression for the inmedium total p p and np cross sections are as follows:
×
120
23
(2)
where o'NN, E, and p are in the units of mb, MeV, and fm -3, respectively. It should be noted that whether there is some redundancy in using the cross sections of Refs. [ 12] and [ 13 ] in the I N C E code which then applies an additional Pauli correction. The Pauli correction on the G-matrix in Refs. [ 12] and [ 13] operates only on the intermediate virtual N N scattering process; off the energy shell. On the other hand, the Pauli correction in the INCE calculation imposes only on the real N N scattering process; on the energy shell. Thus these two corrections have no overlaps at all. Fig. 1 shows the total np cross sections as a function of nucleon energy in the laboratory system. The solid line indicates the in-medium total np cross sections from Eq. (2) for the normal nuclear matter. The dashed line indicates the free space total np cross sections by Bertini
5 /0
i
r loo
I
i
260
i
I
250
300
Nucleon Energy (MeV) Fig. l. In-medium total np cross sections for the normal nuclear matter as described by Eq. (2) (solid line) and free space total np cross sections [14] (dashed line) in the energy range 50-300 MeV.
[ 14], which are incorporated into a nucleon-meson transport code NMTC. Fig. 1 also shows that the inmedium total np cross sections decrease substantially in comparison with those of free space. We incorporated the in-medium total N N cross sections calculated with Eqs. (1) and (2) into N M T C / J A E R I [ 15] up to 300 MeV. N M T C / J A E R I is a modified version of NMTC. Li and Machleidt calculated the in-medium N N cross sections only below 300 MeV. Cassing et al. [ 16] have shown that in-medium N N cross sections are close to those of free space at about 400 MeV. Hence we adopted the free space N N cross sections above 400 MeV. The N N cross sections between 300 MeV and 400 MeV were obtained by the linear interpolation. The original N M T C / J A E R I assumes that the angular distributions for p p scattering are isotropic in the center-of-mass system for proton energies up to 500 MeV [ 14,15 ]. Since the in-medium p p angular distributions showed the same tendency, we employed the isotropic p p angular distributions up to 500 MeV. In contrast with the free space np angular distributions, those of the in-medium are more isotropic [ 12]. We therefore incorporated the isotropic np angular distributions into NMTC/JAERI. N M T C / J A E R I adopts the mass formula by Cameron [ 17] and the mass table compiled by Wapstra [ 18 ]. However both formula and table fail to reproduce mass excess data far from
24
E. Suetomi et al. /Physics Letters B 333 (1994) 22-26
10-T
3
Neutron Energy (MeV)
Neutron Energy (MeV)
Fig. 2. Calculated differential neutron production cross sections of the aluminum target are compared with the experimental data for SOO-MeVprotons. The solid lines correspond to the fly
statistical errors of the calculated values: (a) the free space NN cross sections 01s show the experimental data by Amian et al. [ 31.
Neutron Energy (MeV)
Neutron Energy (MeV)
Fig. 3. Same as in fig. 2, for the lead target.
the stability line. In this work the mass formula by Tachibana et al. [ 191 and the mass table revised by Wapstra et al. [20] were utilized. To study the effect of the mean field in nuclear matter, we calculated the double differential neutron production cross sections for 597-MeV and 800-MeV protons. The target materials for these calculations were aluminum and lead. Figs. 2 and 3 show the NMTC/JAERI calculations compared with the experi-
mental data by Amian et al. [ 31 for 800-MeV protons. The NMTC/JAERI calculations with the free space NN cross sections are shown in Figs. 2a and 3a. Figs. 2b and 3b show the NMTUJAERI calculations with the in-medium NN cross sections. Some differences are seen between the results obtained with the free space NN cross sections and the experimental data at energies between a few MeV and a few tens of MeV. On the other hand, the results calculated with the in-
25
E. Suetomi et aL / Physics Letters B 333 (1994) 22-26
104
........
. . . . . . . .
I
.
.
.
.
.
.
.
.
I
.
.
.
.
.
.
.
.
Pb(p,xn) Ep=8OOMeV
...... 1 t
eg
~ 10-2" ~ ~ ~ 2 0
degaS=
lOO
i
0~ 10.4
150 d e g ' ~ ~
!
lO-,
..................
..!
101
102
10 3
o
, ooeo . 10 °
Neutron Energy(MeV)
I
10~ =~.==R~.,~
I
I
pbilp ixn)
.
.
i
==ll
.,I
101
. . . . . . . .
I
10 2 v
,
10 3
Neutron Energy(MeV)
Fig. 4. Same as in Fig. 2(b), for 597-MeV protons. The open symbols show the experimental data by Amian et al. [4].
. . . . .
3
°°
i
10 °
10
.
.
.
.
Ep=597MeVt
Fig. 6. Dependence on np-scattering angular distributions in the INCE calculation. The solid lines correspond to the :Eltr statistical errors of the calculations using the angular distributions of the free space NN scattering and the in-medium total NN cross sections. The open symbols show the experimental data by Amian et al. [31. sections were incorporated into N M T C / J A E R I . The I N C E calculation reproduces the experimental data as well as Fig. 3b, This indicates that the in-medium total N N cross sections play a more important role than the angular distributions for the N N scattering.
~ lO -2
o o 10.4
10 0
3. C o n c l u s i o n
150 de
101 102 Neutron Energy(MeV)
103
Fig. 5. Same as in Fig. 4, for the lead target. m e d i u m N N cross sections show good agreement at angles o f 30, 60, and 120 ° . G o o d agreement was also obtained between the experiments for 597-MeV protons [4] and the calculations with the in-medium N N cross sections (cf. Figs. 4 and 5). Fig. 6 demonstrates the weak dependence on np-scattering angular distributions in the I N C E calculation. In this case the inm e d i u m total N N cross sections with anisotropic angular distributions o f the free space differential cross
The I N C E calculations have been performed for the differential neutron production cross sections from thin targets of aluminum and lead induced by 597M e V and 800-MeV protons. To assess the effect due to presence o f the mean field, we incorporated the inmedium N N cross sections into N M T C / J A E R I . Comparison o f the I N C E calculations with the experimental data showed that application o f the inmedium N N cross sections reduce the differences between the calculations using the free space N N cross sections and experimental data. The dependence on the angular distributions of N N scattering is also studied. It is found that the angular dependence is moderate. We therefore conclude that the in-medium total N N cross sections play an important role in the I N C E calculation.
26
E. Suetomi et al./Physics Letters B 333 (1994) 22-26
Although the inelastic N N scattering reaction occurs for energy above 400 MeV, we used the free space N N inelastic cross sections in this work. The effect of the in-medium inelastic cross sections is under investigation.
Acknowledgments One of the authors (E.S.) would like to thank Dr. G.Q. Li for providing the in-medium N N cross section data to us. We are indebted to Dr. M.M. Meier for supplying the experimental data of differential neutron production cross sections.
References [ 1 ] S. Cierjacks, Y. Hino, E Raupp, L. Buth, D. Filges, E Cloth and T.W. Armstrong, Phys. Rev. C 36 (1987) 1976. [2] M.M. Meier, D.A. Clark, C.A. Goulding, J.B. McCleUand, G.L. Morgan, C.E. Moss and W.B. Amian, Nucl. Sci. Eng. 102 (1989) 310. [3] W.B. Amian, R.C. Byrd, C.A. Goulding, M.M. Meier, G.L. Morgan, C.E. Moss and D.A. Clark, Nucl. Sci. Eng. 112 (1992) 78. [4] W.B. Amian, R.C. Byrd, D.A. Clark, C.A. Goulding, M.M. Meier, G.L. Morgan and C.E. Moss, Nucl. Sci. Eng. 115 (1993) 1.
[5] S. Stamer, W. Scobel, W.B. Amian, R.C. Byrd, R.C. Haight, J.L. Ullmann, R.W. Bauer, M. Blann, B.A. Pohl, L Bisplinghoff and R. Bonetti, Phys. Rev. C 47 (1993) 1647. [6] N. Metropolis, R. Bivins, M. Storm, A. Turkevich, J.M. Miller and G. Friedlander, Phys. Rev. 110 (1958) 185. [7] H.W. Bertini, Phys. Rev. 188 (1969) 1711. [8] W.A. Coleman and T.W. Armstrong, Nucl. Sci. Eng. 43 (1971) 353. [9] T.W. Armstrong and K.C. Chandler, Nucl. Sci. Eng. 49 (1972) 110. [10] K. Tsukada and Y. Nakahara, Atomkemenergie.Kemtechnik 44 (1984) 186. [ 11] G.Q. Li, R. Machleidt and Y.Z. Zhuo, Phys. Rev. C 48 (1993) 1062. [12] G.Q. Li and R. Machleidt, Phys. Rev. C 48 (1993) 1702. [13] G.Q. Li and R. Machleidt, Phys. Rev. C 49 (1994) 566. [14] H.W. Bertini, ORNL-3383 Oak Ridge National Laboratory (1963), unpublished. [ 15] Y. Nakahara and T. Tsutsui, Nuclear Program Abstracts, Vol. 2 (NEA Data Bank, Nuclear Energy Agency, 1993) p. 1010, unpublished. [16] W. Cassing, V. Metag, U. Mosel and K. Niita, Phys. Rep. 188 (1990) 363. [17] A.G.W. Cameron, Can. J. Phys. 35 (1957) 1021. [18] A.H. Wapstra, Physica 21 (1955) 367. [19] T. Taehibana, M. Uno, M. Yamada and S. Yamada, Atomic Data and Nuclear Data Tables 39 (1988) 251. [20] A.H. Wapstra, G. Audi and R. Hoekstra, Atomic Data and Nuclear Data Tables 39 (1988) 281.
ELSEVIER
An analysis of the intranuclear cascade evaporation model with in-medium nucleon-nucleon cross sections E. Suetomi 1, N. Kishida, H. Kadotani CRC Research Institute, Inc., 1-3-D16, Nakase, Miharaa-ku, Chiba 261-01, Japan Received 14 April 1994; revised manuscript received 2 June 1994 Editor: C. Mahaux
Abstract An analysis of the intranuclear cascade evaporation (INCE) model has been performed taking the presence of the mean field in nuclear matter into account. In-medium nucleon-nucleon (NN) cross sections were incorporated into an INCE code. Application of the in-medium NN cross sections resulted in significant reduction of differences between experimental differential neutron production cross sections and those of the INCE calculation using the free space NN cross sections.
1. Introduction For past ten years, a number of double differential neutron production cross sections have been measured for intermediate energy protons 100 to 800 MeV [ 1-5]. These cross sections are particularly important in several areas, e.g., accelerator shielding, space radiation effect, medical application, transmutation of transuranic wastes by spallation reaction, and other application areas. The intranuclear cascade evaporation (INCE) model [6,7] has been extensively used in predictions and analysis of those cross sections. Amian et al. [3,4] have measured the cross sections for medium-energy protons at 800 MeV and 597 MeV. Overall agreement between the experimental cross sections and those of the INCE model was fairly good. However some differences still remain in emitted neutron energies between a few MeV and a few tens of MeV.
1 E-mail address: [email protected].
In INCE calculation, the following cross sections are needed: the elastic and inelastic nucleon-nucleon ( N N ) scattering cross sections, the pion-nucleon scattering cross sections and the charge-exchange cross sections. Particularly the N N cross sections are important for incident nucleon below 1 GeV because in this energy range the elastic N N cross sections are dominant. Free space N N cross sections are ordinarily used in usual INCE codes, such as NMTC [ 8 ] and HETC [9]. But the in-medium N N cross sections have to be employed because of existence of nuclear mean field. Tsukada and Nakahara [ 10] have proposed to use a prolonged nucleon mean free path (mfp) within a nucleus to reduce the discrepancy between I N C E calculation and experimental data. They used the mfp that was multiplied by a constant independent of the nucleon energy. Li, Machleidt and Zhuo [ 11 ] have calculated the nucleon mfp in the normal nuclear matter. They showed that the ratios of mfp in free space to mfp in the nuclear matter vary with nucleon energies. Recently Li and Machleidt [ 12,13 ] have derived the in-medium elastic N N cross sections using a mi-
0370-2693/94/$07.00 (~) 1994 Elsevier Science B.V. All rights reserved SSDI 0 3 7 0 - 2 6 9 3 ( 9 4 ) 0 0 7 4 7 - U
E. Suetomi et al. / Physics Letters B 333 (1994) 22-26
croscopic nuclear matter model in energy range 50 through 300 MeV. They found that the in-medium total N N cross sections and the in-medium np-scattering angular distributions are very different from those of free space. This suggests that the in-medium N N scattering cross sections must be used in the INCE calculation. In this letter, we investigate the effects that the use of the in-medium N N cross sections cause to the differential neutron production cross sections.
2. INCE cross
calculation
with
the in-medium
sections
1.0 + 0.1667El°Sp 3 1.0 + 9.704pl. 2 ,
I
I
I
',,,
10(
I
I
I
I
I
...... Bertini - -
g ,-
In-medium o np
(Li and Machleidt)
8(
0 o
60 £ 0
40
I-
20 i
(1)
O'np(E, p ) = [31.5 + 0 . 0 9 2 a b s ( 2 0 . 2 - E ° 5 3 ) 2"9 ]
1.0 + 0.0034E]'5]p 2 1.0 + 21.55p 1"34 '
'll
,,
0
trpp (E, p) = [23.5 + 0.00256( 18.2 - E°'5) 4"°]
×
I
NN
Li and Machleidt [ 12,13 ] proposed a parametrization for the in-medium total N N cross sections as a function of the incident nucleon energy up to 300 MeV and density of nuclear matter up to 2p0 (through this work we use the saturation density of normal nuclear matter p0 = 0.18 f m - 3 ) . The expression for the inmedium total p p and np cross sections are as follows:
×
120
23
(2)
where o'NN, E, and p are in the units of mb, MeV, and fm -3, respectively. It should be noted that whether there is some redundancy in using the cross sections of Refs. [ 12] and [ 13 ] in the I N C E code which then applies an additional Pauli correction. The Pauli correction on the G-matrix in Refs. [ 12] and [ 13] operates only on the intermediate virtual N N scattering process; off the energy shell. On the other hand, the Pauli correction in the INCE calculation imposes only on the real N N scattering process; on the energy shell. Thus these two corrections have no overlaps at all. Fig. 1 shows the total np cross sections as a function of nucleon energy in the laboratory system. The solid line indicates the in-medium total np cross sections from Eq. (2) for the normal nuclear matter. The dashed line indicates the free space total np cross sections by Bertini
5 /0
i
r loo
I
i
260
i
I
250
300
Nucleon Energy (MeV) Fig. l. In-medium total np cross sections for the normal nuclear matter as described by Eq. (2) (solid line) and free space total np cross sections [14] (dashed line) in the energy range 50-300 MeV.
[ 14], which are incorporated into a nucleon-meson transport code NMTC. Fig. 1 also shows that the inmedium total np cross sections decrease substantially in comparison with those of free space. We incorporated the in-medium total N N cross sections calculated with Eqs. (1) and (2) into N M T C / J A E R I [ 15] up to 300 MeV. N M T C / J A E R I is a modified version of NMTC. Li and Machleidt calculated the in-medium N N cross sections only below 300 MeV. Cassing et al. [ 16] have shown that in-medium N N cross sections are close to those of free space at about 400 MeV. Hence we adopted the free space N N cross sections above 400 MeV. The N N cross sections between 300 MeV and 400 MeV were obtained by the linear interpolation. The original N M T C / J A E R I assumes that the angular distributions for p p scattering are isotropic in the center-of-mass system for proton energies up to 500 MeV [ 14,15 ]. Since the in-medium p p angular distributions showed the same tendency, we employed the isotropic p p angular distributions up to 500 MeV. In contrast with the free space np angular distributions, those of the in-medium are more isotropic [ 12]. We therefore incorporated the isotropic np angular distributions into NMTC/JAERI. N M T C / J A E R I adopts the mass formula by Cameron [ 17] and the mass table compiled by Wapstra [ 18 ]. However both formula and table fail to reproduce mass excess data far from
24
E. Suetomi et al. /Physics Letters B 333 (1994) 22-26
10-T
3
Neutron Energy (MeV)
Neutron Energy (MeV)
Fig. 2. Calculated differential neutron production cross sections of the aluminum target are compared with the experimental data for SOO-MeVprotons. The solid lines correspond to the fly
statistical errors of the calculated values: (a) the free space NN cross sections 01s show the experimental data by Amian et al. [ 31.
Neutron Energy (MeV)
Neutron Energy (MeV)
Fig. 3. Same as in fig. 2, for the lead target.
the stability line. In this work the mass formula by Tachibana et al. [ 191 and the mass table revised by Wapstra et al. [20] were utilized. To study the effect of the mean field in nuclear matter, we calculated the double differential neutron production cross sections for 597-MeV and 800-MeV protons. The target materials for these calculations were aluminum and lead. Figs. 2 and 3 show the NMTC/JAERI calculations compared with the experi-
mental data by Amian et al. [ 31 for 800-MeV protons. The NMTC/JAERI calculations with the free space NN cross sections are shown in Figs. 2a and 3a. Figs. 2b and 3b show the NMTUJAERI calculations with the in-medium NN cross sections. Some differences are seen between the results obtained with the free space NN cross sections and the experimental data at energies between a few MeV and a few tens of MeV. On the other hand, the results calculated with the in-
25
E. Suetomi et aL / Physics Letters B 333 (1994) 22-26
104
........
. . . . . . . .
I
.
.
.
.
.
.
.
.
I
.
.
.
.
.
.
.
.
Pb(p,xn) Ep=8OOMeV
...... 1 t
eg
~ 10-2" ~ ~ ~ 2 0
degaS=
lOO
i
0~ 10.4
150 d e g ' ~ ~
!
lO-,
..................
..!
101
102
10 3
o
, ooeo . 10 °
Neutron Energy(MeV)
I
10~ =~.==R~.,~
I
I
pbilp ixn)
.
.
i
==ll
.,I
101
. . . . . . . .
I
10 2 v
,
10 3
Neutron Energy(MeV)
Fig. 4. Same as in Fig. 2(b), for 597-MeV protons. The open symbols show the experimental data by Amian et al. [4].
. . . . .
3
°°
i
10 °
10
.
.
.
.
Ep=597MeVt
Fig. 6. Dependence on np-scattering angular distributions in the INCE calculation. The solid lines correspond to the :Eltr statistical errors of the calculations using the angular distributions of the free space NN scattering and the in-medium total NN cross sections. The open symbols show the experimental data by Amian et al. [31. sections were incorporated into N M T C / J A E R I . The I N C E calculation reproduces the experimental data as well as Fig. 3b, This indicates that the in-medium total N N cross sections play a more important role than the angular distributions for the N N scattering.
~ lO -2
o o 10.4
10 0
3. C o n c l u s i o n
150 de
101 102 Neutron Energy(MeV)
103
Fig. 5. Same as in Fig. 4, for the lead target. m e d i u m N N cross sections show good agreement at angles o f 30, 60, and 120 ° . G o o d agreement was also obtained between the experiments for 597-MeV protons [4] and the calculations with the in-medium N N cross sections (cf. Figs. 4 and 5). Fig. 6 demonstrates the weak dependence on np-scattering angular distributions in the I N C E calculation. In this case the inm e d i u m total N N cross sections with anisotropic angular distributions o f the free space differential cross
The I N C E calculations have been performed for the differential neutron production cross sections from thin targets of aluminum and lead induced by 597M e V and 800-MeV protons. To assess the effect due to presence o f the mean field, we incorporated the inmedium N N cross sections into N M T C / J A E R I . Comparison o f the I N C E calculations with the experimental data showed that application o f the inmedium N N cross sections reduce the differences between the calculations using the free space N N cross sections and experimental data. The dependence on the angular distributions of N N scattering is also studied. It is found that the angular dependence is moderate. We therefore conclude that the in-medium total N N cross sections play an important role in the I N C E calculation.
26
E. Suetomi et al./Physics Letters B 333 (1994) 22-26
Although the inelastic N N scattering reaction occurs for energy above 400 MeV, we used the free space N N inelastic cross sections in this work. The effect of the in-medium inelastic cross sections is under investigation.
Acknowledgments One of the authors (E.S.) would like to thank Dr. G.Q. Li for providing the in-medium N N cross section data to us. We are indebted to Dr. M.M. Meier for supplying the experimental data of differential neutron production cross sections.
References [ 1 ] S. Cierjacks, Y. Hino, E Raupp, L. Buth, D. Filges, E Cloth and T.W. Armstrong, Phys. Rev. C 36 (1987) 1976. [2] M.M. Meier, D.A. Clark, C.A. Goulding, J.B. McCleUand, G.L. Morgan, C.E. Moss and W.B. Amian, Nucl. Sci. Eng. 102 (1989) 310. [3] W.B. Amian, R.C. Byrd, C.A. Goulding, M.M. Meier, G.L. Morgan, C.E. Moss and D.A. Clark, Nucl. Sci. Eng. 112 (1992) 78. [4] W.B. Amian, R.C. Byrd, D.A. Clark, C.A. Goulding, M.M. Meier, G.L. Morgan and C.E. Moss, Nucl. Sci. Eng. 115 (1993) 1.
[5] S. Stamer, W. Scobel, W.B. Amian, R.C. Byrd, R.C. Haight, J.L. Ullmann, R.W. Bauer, M. Blann, B.A. Pohl, L Bisplinghoff and R. Bonetti, Phys. Rev. C 47 (1993) 1647. [6] N. Metropolis, R. Bivins, M. Storm, A. Turkevich, J.M. Miller and G. Friedlander, Phys. Rev. 110 (1958) 185. [7] H.W. Bertini, Phys. Rev. 188 (1969) 1711. [8] W.A. Coleman and T.W. Armstrong, Nucl. Sci. Eng. 43 (1971) 353. [9] T.W. Armstrong and K.C. Chandler, Nucl. Sci. Eng. 49 (1972) 110. [10] K. Tsukada and Y. Nakahara, Atomkemenergie.Kemtechnik 44 (1984) 186. [ 11] G.Q. Li, R. Machleidt and Y.Z. Zhuo, Phys. Rev. C 48 (1993) 1062. [12] G.Q. Li and R. Machleidt, Phys. Rev. C 48 (1993) 1702. [13] G.Q. Li and R. Machleidt, Phys. Rev. C 49 (1994) 566. [14] H.W. Bertini, ORNL-3383 Oak Ridge National Laboratory (1963), unpublished. [ 15] Y. Nakahara and T. Tsutsui, Nuclear Program Abstracts, Vol. 2 (NEA Data Bank, Nuclear Energy Agency, 1993) p. 1010, unpublished. [16] W. Cassing, V. Metag, U. Mosel and K. Niita, Phys. Rep. 188 (1990) 363. [17] A.G.W. Cameron, Can. J. Phys. 35 (1957) 1021. [18] A.H. Wapstra, Physica 21 (1955) 367. [19] T. Taehibana, M. Uno, M. Yamada and S. Yamada, Atomic Data and Nuclear Data Tables 39 (1988) 251. [20] A.H. Wapstra, G. Audi and R. Hoekstra, Atomic Data and Nuclear Data Tables 39 (1988) 281.