- Email: [email protected]
Cross Section Calculations of Deuteron-induced Reactions Using the Extended CCONE Code
Available online at www.sciencedirect.com
Nuclear Data Sheets 118 (2014) 305–307 www.elsevier.com/locate/nds
Cross Section Calculations of Deuteron-induced Reactions Using the Extended CCONE Code S. Nakayama,1, ∗ S. Araki,1 Y. Watanabe,1 O. Iwamoto,2 T. Ye,3 and K. Ogata4 1 2
Department of Advanced Energy Engineering Science, Kyushu University, Fukuoka 816-8580, Japan Nuclear Science and Engineering Directorate, Japan Atomic Energy Agency, Ibaraki 319-1195, Japan 3 Institute of Applied Physics and Computational Mathematics, Beijing 100094, China 4 Research Center for Nuclear Physics (RCNP), Osaka University, Osaka 567-0047, Japan We have extended the CCONE code to make it possible to calculate cross sections for deuteroninduced reactions. Elastic breakup and stripping reactions to continuum are calculated using another codes based on the Continuum-Discretized Coupled-Channels theory (CDCC) and the Glauber model, respectively, and the calculated results are inputted to the CCONE code as direct reaction components. Statistical decay from compound nuclei formed by nucleon stripping and deuteron absorption is calculated with the exciton and Hauser-Feshbach models implemented in the original CCONE code. The extended CCONE code is applied to analyses of deuteron-induced reactions on 27 Al and 58 Ni. CDCC calculations for deuteron elastic scattering show good agreement with the experimental data at incident energies of several tens of MeV. The calculated double-differential (d, xp) cross sections reproduce the measured ones at forward angles for incident energies of 56 and 100 MeV fairly well. I.
INTRODUCTION
In recent years, accelerator-driven neutron sources using deuteron-induced reactions on light nuclei (7 Li, 9 Be, 12 C, etc.) have been proposed for various neutron beam applications such as irradiation testing of fusion reactor materials, boron neutron capture therapy (BNCT), and production of radioisotopes for medical use. For development and detailed design of such accelerator-driven neutron sources, comprehensive nuclear data of deuteroninduced reactions are indispensable as fundamental data. Currently, available deuteron nuclear data can be found in TENDL [1], which has been developed by compiling the output of the TALYS code [2]. However, the present TALYS code cannot describe elastic breakup and stripping processes adequately as mentioned later in Sec. III. Thus, new comprehensive nuclear data of deuteron-induced reactions over wide ranges of target mass number and incident energy are required to estimate neutron yields and induced radioactivity accurately in the engineering design of accelerator-driven neutron sources. Experimental data of deuteron-induced reactions are not necessarily enough. In particular, double-differential cross sections (DDXs) for (d, xn) reactions indispensable for engineering design of neutron sources are missing over
∗
Corresponding author: [email protected]
http://dx.doi.org/10.1016/j.nds.2014.04.065 0090-3752/2014 Published by Elsevier B.V.
wide ranges of target mass number and incident energy. In such the case, theoretical model calculation plays an important role in nuclear data evaluation. In the present work, we have extended the CCONE code [3] used in the production of JENDL-4.0 [4] so as to make it possible to calculate the cross sections for deuteron-induced reactions, and applied it to calculations of DDXs for (d, xp) reactions measured systematically for 27 Al and 58 Ni at several incident energies [5, 6].
II.
CALCULATION METHOD
In the extended CCONE code, the cross sections for elastic breakup and stripping reactions to continuum are calculated using another codes based on the ContinuumDiscretized Coupled-Channels theory (CDCC) [7] and the Glauber model, respectively. The details of the calculation method are described in our preceding work [8]. In the CDCC and the Glauber model, the nucleon optical model potentials (OMPs) of target nucleus are necessary as input data. In the present work, we use Koning and Delaroche OMPs [9] at half the incident deuteron energy both for proton and neutron. In our previous work [8], the phenomenological movingsource (MS) model was used to estimate statistical decay components, i.e., preequilibrium and evaporation components. The MS model has low predictive power because it needs some parameters determined by fit-
Cross Section Calculations . . .
NUCLEAR DATA SHEETS
ting the experimental data. Instead of the MS model, therefore, we calculate the cross sections for statistical decay from compound nuclei formed by nucleon stripping and deuteron absorption using the method based on the exciton and Hauser-Feshbach models implemented in the original CCONE code. For OMPs necessary in the CCONE calculation, we use Koning and Delaroche OMPs for proton and neutron, and An and Cai OMPs [10] for deuteron. Default values in the original CCONE code are used for the other physical parameters such as level density parameters. The DDXs of (d, xp) reactions are expressed by the incoherent summation of three components:
d2σ/dE/dΩ [mb/MeV/sr]
103
S. Nakayama et al.
Exp. data Ein = 100 MeV θ = 6 deg.
102
58
Ni (d,xp)
Statistical decay n-Stripping Ein = 56 MeV Breakup Total θ = 9.5 deg. TALYS
101
100
-1
10
d2 σ(d ,xp) d2 σBU d2 σST R d2 σSD = + + , dEdΩ dEdΩ dEdΩ dEdΩ
(1)
10
6
10
5
10
4
27
Al, 11.2 MeV (x104)
27
Al, 63 MeV (x102)
dσ/dΩ [mb/sr]
58
-1
Ni, 12 MeV (x10 )
101 100 10
58
58
60
Ni(d, xp)
(2)
where Rd , Rp , and Rn denote the formation fractions of three different compound nuclei, which are calcuCCON E lated with the Glauber model, and d2 σ(d,xp) /dEdΩ, 2 CCON E 2 CCON E d σ(p,xp) /dEdΩ, d σ(n,xp) /dEdΩ are the DDXs of (d, xp), (p, xp), and (n, xp) reactions calculated with the original CCONE code, respectively. In the calculation of (p, xp) and (n, xp) components in Eq. (2), we assume that the incident energies of proton and neutron are half the deuteron incident energy. Strictly speaking, this assumption is not correct because either neutron or proton absorbed in stripping reactions has a certain energy distribution. We use this assumption for reduction of computation time since our preliminary calculation showed that there is not so much difference between the calculation results of this approximate case and those of the case where energy distribution is considered exactly.
Exp.data CDCC d-OMP
2
20 40 proton Energy [MeV]
CCON E d2 σ(d,xp) d2 σSD =Rd dEdΩ dEdΩ CCON E CCON E d2 σ(p,xp) d2 σ(n,xp) + Rn , + Rp dEdΩ dEdΩ
103 10
100 0
following way:
8
107
20 40 60 80 proton Energy [MeV]
FIG. 2. Calculated and experimental DDXs for reaction at 56 and 100 MeV.
where d2 σBU /dEdΩ, d2 σST R /dEdΩ, and d2 σSD /dEdΩ correspond to DDXs for elastic breakup reaction, neutron stripping reaction, and statistical decay, respectively. DDXs for elastic breakup and neutron stripping reactions are directly calculated with the CDCC method and the Glauber model, respectively. In the case of deuteron-induced reactions, three types of compound nuclei are formed by absorption of either a neutron in the incident deuteron or a proton in it or the deuteron itself. Therefore, DDXs for the statistical decay from these three compound nuclei are calculated in the
10
0
Ni, 27.5 MeV (x10-2)
-1 58
-3
Ni, 56 MeV (x10 )
III.
10-2 10
-3
10
-4
10
-5
10
-6
First of all, we demonstrate the applicability of CDCC calculations to two target nuclei, 27 Al and 58 Ni. Fig. 1 shows comparisons between calculated and experimental differential cross sections for deuteron elastic scattering. Solid lines in the figure are the results of the CDCC calculation with Koning and Delaroche OMPs, and dashed lines are the results of the optical model calculation with An and Cai deuteron OMPs. Experimental data are taken from several references [11–16]. For both target
58
Ni, 79 MeV (x10-6)
0
10
20
30 θC.M. [deg.]
40
50
RESULTS AND DISCUSSION
60
FIG. 1. Calculated and experimental differential cross sections of deuteron elastic scattering from 27 Al or 58 Ni.
306
Cross Section Calculations . . .
NUCLEAR DATA SHEETS
tial to choose theoretical models to describe adequately both the breakup and stripping processes characteristic of deuteron-induced reactions. The extended CCONE code is also applied to calculate the DDXs for 27 Al(d, xp) reaction at two incident energies of 56 and 100 MeV. The results are shown in Fig. 3. The calculation reproduces the experimental data as well as that for 58 Ni. As shown in Figs. 2 and 3, the present calculation fails to reproduce several peaks observed in the high emission energy region, although fairly good agreement between the calculation and the measurement is obtained in the continuum region of (d, xp) spectra. These peaks correspond to the transition to bound states in the residual nucleus via neutron stripping. Since the Glauber model cannot treat this transition properly, a conventional distorted wave Born approximation (DWBA) approach with spectroscopic factor for each bound state will be necessary to describe such the stripping reaction. We plan to perform DWBA calculations because the transition to bound states become relatively important as the incident energy decreases.
nuclei, the CDCC calculation reproduces the experimental data at forward angles over a wide range of incident energy as well as the optical model calculation.
d2σ/dE/dΩ [mb/MeV/sr]
103
Statistical decay n-Stripping Breakup Total TALYS
Exp. data Ein = 100 MeV θ = 6 deg.
102
27
Al (d,xp)
Ein = 56 MeV θ = 9.5 deg.
101
100
10-1
0
20 40 60 80 proton Energy [MeV]
100 0
FIG. 3. Same as in Fig. 2 but for
20 40 proton Energy [MeV] 27
S. Nakayama et al.
60
Al(d, xp) reaction.
Next, we use the extended CCONE code to calculate the DDXs of (d, xp) reactions and investigate the ranges of incident energy and target mass number to which the code is applicable. Fig. 2 shows comparisons between the calculated and experimental DDXs for 58 Ni(d, xp) reaction at 56 and 100 MeV. At both incident energies, the present calculation reproduces both the shape and magnitude of the experimental (d, xp) spectra at forward angles better than TALYS calculation. Especially, a distinct difference between both calculations is seen in the broad peak around half the deuteron incident energy. The characteristic peak is formed by proton emission via elastic breakup and neutron stripping processes. These components are calculated with the Kalbach empirical formula in TALYS code, while they are calculated using physics-based CDCC and Glauber models in the present work. This indicates that it is essen-
The extended CCONE code was applied to deuteroninduced reactions on 27 Al and 58 Ni. CDCC calculations for deuteron elastic scattering show good agreement with the experimental data. The calculated double-differential (d, xp) cross sections reproduce the experimental ones at forward angles for incident energies of 56 and 100 MeV better than those with the TALYS code. Further comparisons with available experimental data including activation cross sections over wide ranges of incident energy and target mass number will be necessary to confirm the applicability of the present calculation method to deuteron nuclear data evaluation.
[1] A.J. Koning and D. Rochman, Nucl. Data Sheets 113, 2841 (2012). [2] A.J. Koning, S. Hilaire and M.C. Duijvestijn, Proceedings of the International Conference on Nuclear Data for Science and Technology, Nice, France, editors O. Bersillon, F. Gunsing, E. Bauge, R. Jacqmin, and S. Leray, EDP Sciences, 211 (2008). [3] O. Iwamoto, J. Nucl. Sci. Technol. 44, 687 (2007). [4] K. Shibata, O. Iwamoto, T. Nakagawa et al., J. Nucl. Sci. Technol. 48, 1 (2011). [5] D. Ridikas, W. Mittig, H. Savajols et al., Phys. Rev. C 63, 014610 (2000). [6] N. Matsuoka, M. Kondo, H. Sakaguchi et al., Nucl. Phys. A 345, 1 (1980). [7] M. Yahiro, K. Ogata, T. Matsumoto and K. Minomo, Prog. Theor. Exp. Phys. 2012, 01A206 (2012), and
references therein. [8] T. Ye, S. Hashimoto, Y. Watanabe et al., Phys. Rev. C 84, 054606 (2011). [9] A.J. Koning and J.P. Delaroche, Nucl. Phys. A 713, 231 (2003). [10] H. An and C. Cai, Phys. Rev. C 73, 054605 (2006). [11] M. Takeda, J. Phys. Soc. Jpn. 15, 557 (1960). [12] E.G. Auld, D.G. Crabb, L. Bird et al., Nucl. Phys. A 101, 65 (1967). [13] L.L. Lee, Jr. and J.P. Schiffer, Phys. Rev. 134, B765 (1964). [14] S. Mayo and J.E. Testoni, Nucl. Phys. 36, 615 (1962). [15] K. Hatanaka, K. Imai, S. Kobayashi et al., Nucl. Phys. A 340, 93 (1980). [16] E.J. Stephenson, J.C. Collins, C.C. Foster et al., Phys. Rev. C 28, 134 (1983).
IV.
CONCLUSIONS
Acknowledgements: This work was supported by JSPS KAKENHI Grant Number 22560820.
307
Nuclear Data Sheets 118 (2014) 305–307 www.elsevier.com/locate/nds
Cross Section Calculations of Deuteron-induced Reactions Using the Extended CCONE Code S. Nakayama,1, ∗ S. Araki,1 Y. Watanabe,1 O. Iwamoto,2 T. Ye,3 and K. Ogata4 1 2
Department of Advanced Energy Engineering Science, Kyushu University, Fukuoka 816-8580, Japan Nuclear Science and Engineering Directorate, Japan Atomic Energy Agency, Ibaraki 319-1195, Japan 3 Institute of Applied Physics and Computational Mathematics, Beijing 100094, China 4 Research Center for Nuclear Physics (RCNP), Osaka University, Osaka 567-0047, Japan We have extended the CCONE code to make it possible to calculate cross sections for deuteroninduced reactions. Elastic breakup and stripping reactions to continuum are calculated using another codes based on the Continuum-Discretized Coupled-Channels theory (CDCC) and the Glauber model, respectively, and the calculated results are inputted to the CCONE code as direct reaction components. Statistical decay from compound nuclei formed by nucleon stripping and deuteron absorption is calculated with the exciton and Hauser-Feshbach models implemented in the original CCONE code. The extended CCONE code is applied to analyses of deuteron-induced reactions on 27 Al and 58 Ni. CDCC calculations for deuteron elastic scattering show good agreement with the experimental data at incident energies of several tens of MeV. The calculated double-differential (d, xp) cross sections reproduce the measured ones at forward angles for incident energies of 56 and 100 MeV fairly well. I.
INTRODUCTION
In recent years, accelerator-driven neutron sources using deuteron-induced reactions on light nuclei (7 Li, 9 Be, 12 C, etc.) have been proposed for various neutron beam applications such as irradiation testing of fusion reactor materials, boron neutron capture therapy (BNCT), and production of radioisotopes for medical use. For development and detailed design of such accelerator-driven neutron sources, comprehensive nuclear data of deuteroninduced reactions are indispensable as fundamental data. Currently, available deuteron nuclear data can be found in TENDL [1], which has been developed by compiling the output of the TALYS code [2]. However, the present TALYS code cannot describe elastic breakup and stripping processes adequately as mentioned later in Sec. III. Thus, new comprehensive nuclear data of deuteron-induced reactions over wide ranges of target mass number and incident energy are required to estimate neutron yields and induced radioactivity accurately in the engineering design of accelerator-driven neutron sources. Experimental data of deuteron-induced reactions are not necessarily enough. In particular, double-differential cross sections (DDXs) for (d, xn) reactions indispensable for engineering design of neutron sources are missing over
∗
Corresponding author: [email protected]
http://dx.doi.org/10.1016/j.nds.2014.04.065 0090-3752/2014 Published by Elsevier B.V.
wide ranges of target mass number and incident energy. In such the case, theoretical model calculation plays an important role in nuclear data evaluation. In the present work, we have extended the CCONE code [3] used in the production of JENDL-4.0 [4] so as to make it possible to calculate the cross sections for deuteron-induced reactions, and applied it to calculations of DDXs for (d, xp) reactions measured systematically for 27 Al and 58 Ni at several incident energies [5, 6].
II.
CALCULATION METHOD
In the extended CCONE code, the cross sections for elastic breakup and stripping reactions to continuum are calculated using another codes based on the ContinuumDiscretized Coupled-Channels theory (CDCC) [7] and the Glauber model, respectively. The details of the calculation method are described in our preceding work [8]. In the CDCC and the Glauber model, the nucleon optical model potentials (OMPs) of target nucleus are necessary as input data. In the present work, we use Koning and Delaroche OMPs [9] at half the incident deuteron energy both for proton and neutron. In our previous work [8], the phenomenological movingsource (MS) model was used to estimate statistical decay components, i.e., preequilibrium and evaporation components. The MS model has low predictive power because it needs some parameters determined by fit-
Cross Section Calculations . . .
NUCLEAR DATA SHEETS
ting the experimental data. Instead of the MS model, therefore, we calculate the cross sections for statistical decay from compound nuclei formed by nucleon stripping and deuteron absorption using the method based on the exciton and Hauser-Feshbach models implemented in the original CCONE code. For OMPs necessary in the CCONE calculation, we use Koning and Delaroche OMPs for proton and neutron, and An and Cai OMPs [10] for deuteron. Default values in the original CCONE code are used for the other physical parameters such as level density parameters. The DDXs of (d, xp) reactions are expressed by the incoherent summation of three components:
d2σ/dE/dΩ [mb/MeV/sr]
103
S. Nakayama et al.
Exp. data Ein = 100 MeV θ = 6 deg.
102
58
Ni (d,xp)
Statistical decay n-Stripping Ein = 56 MeV Breakup Total θ = 9.5 deg. TALYS
101
100
-1
10
d2 σ(d ,xp) d2 σBU d2 σST R d2 σSD = + + , dEdΩ dEdΩ dEdΩ dEdΩ
(1)
10
6
10
5
10
4
27
Al, 11.2 MeV (x104)
27
Al, 63 MeV (x102)
dσ/dΩ [mb/sr]
58
-1
Ni, 12 MeV (x10 )
101 100 10
58
58
60
Ni(d, xp)
(2)
where Rd , Rp , and Rn denote the formation fractions of three different compound nuclei, which are calcuCCON E lated with the Glauber model, and d2 σ(d,xp) /dEdΩ, 2 CCON E 2 CCON E d σ(p,xp) /dEdΩ, d σ(n,xp) /dEdΩ are the DDXs of (d, xp), (p, xp), and (n, xp) reactions calculated with the original CCONE code, respectively. In the calculation of (p, xp) and (n, xp) components in Eq. (2), we assume that the incident energies of proton and neutron are half the deuteron incident energy. Strictly speaking, this assumption is not correct because either neutron or proton absorbed in stripping reactions has a certain energy distribution. We use this assumption for reduction of computation time since our preliminary calculation showed that there is not so much difference between the calculation results of this approximate case and those of the case where energy distribution is considered exactly.
Exp.data CDCC d-OMP
2
20 40 proton Energy [MeV]
CCON E d2 σ(d,xp) d2 σSD =Rd dEdΩ dEdΩ CCON E CCON E d2 σ(p,xp) d2 σ(n,xp) + Rn , + Rp dEdΩ dEdΩ
103 10
100 0
following way:
8
107
20 40 60 80 proton Energy [MeV]
FIG. 2. Calculated and experimental DDXs for reaction at 56 and 100 MeV.
where d2 σBU /dEdΩ, d2 σST R /dEdΩ, and d2 σSD /dEdΩ correspond to DDXs for elastic breakup reaction, neutron stripping reaction, and statistical decay, respectively. DDXs for elastic breakup and neutron stripping reactions are directly calculated with the CDCC method and the Glauber model, respectively. In the case of deuteron-induced reactions, three types of compound nuclei are formed by absorption of either a neutron in the incident deuteron or a proton in it or the deuteron itself. Therefore, DDXs for the statistical decay from these three compound nuclei are calculated in the
10
0
Ni, 27.5 MeV (x10-2)
-1 58
-3
Ni, 56 MeV (x10 )
III.
10-2 10
-3
10
-4
10
-5
10
-6
First of all, we demonstrate the applicability of CDCC calculations to two target nuclei, 27 Al and 58 Ni. Fig. 1 shows comparisons between calculated and experimental differential cross sections for deuteron elastic scattering. Solid lines in the figure are the results of the CDCC calculation with Koning and Delaroche OMPs, and dashed lines are the results of the optical model calculation with An and Cai deuteron OMPs. Experimental data are taken from several references [11–16]. For both target
58
Ni, 79 MeV (x10-6)
0
10
20
30 θC.M. [deg.]
40
50
RESULTS AND DISCUSSION
60
FIG. 1. Calculated and experimental differential cross sections of deuteron elastic scattering from 27 Al or 58 Ni.
306
Cross Section Calculations . . .
NUCLEAR DATA SHEETS
tial to choose theoretical models to describe adequately both the breakup and stripping processes characteristic of deuteron-induced reactions. The extended CCONE code is also applied to calculate the DDXs for 27 Al(d, xp) reaction at two incident energies of 56 and 100 MeV. The results are shown in Fig. 3. The calculation reproduces the experimental data as well as that for 58 Ni. As shown in Figs. 2 and 3, the present calculation fails to reproduce several peaks observed in the high emission energy region, although fairly good agreement between the calculation and the measurement is obtained in the continuum region of (d, xp) spectra. These peaks correspond to the transition to bound states in the residual nucleus via neutron stripping. Since the Glauber model cannot treat this transition properly, a conventional distorted wave Born approximation (DWBA) approach with spectroscopic factor for each bound state will be necessary to describe such the stripping reaction. We plan to perform DWBA calculations because the transition to bound states become relatively important as the incident energy decreases.
nuclei, the CDCC calculation reproduces the experimental data at forward angles over a wide range of incident energy as well as the optical model calculation.
d2σ/dE/dΩ [mb/MeV/sr]
103
Statistical decay n-Stripping Breakup Total TALYS
Exp. data Ein = 100 MeV θ = 6 deg.
102
27
Al (d,xp)
Ein = 56 MeV θ = 9.5 deg.
101
100
10-1
0
20 40 60 80 proton Energy [MeV]
100 0
FIG. 3. Same as in Fig. 2 but for
20 40 proton Energy [MeV] 27
S. Nakayama et al.
60
Al(d, xp) reaction.
Next, we use the extended CCONE code to calculate the DDXs of (d, xp) reactions and investigate the ranges of incident energy and target mass number to which the code is applicable. Fig. 2 shows comparisons between the calculated and experimental DDXs for 58 Ni(d, xp) reaction at 56 and 100 MeV. At both incident energies, the present calculation reproduces both the shape and magnitude of the experimental (d, xp) spectra at forward angles better than TALYS calculation. Especially, a distinct difference between both calculations is seen in the broad peak around half the deuteron incident energy. The characteristic peak is formed by proton emission via elastic breakup and neutron stripping processes. These components are calculated with the Kalbach empirical formula in TALYS code, while they are calculated using physics-based CDCC and Glauber models in the present work. This indicates that it is essen-
The extended CCONE code was applied to deuteroninduced reactions on 27 Al and 58 Ni. CDCC calculations for deuteron elastic scattering show good agreement with the experimental data. The calculated double-differential (d, xp) cross sections reproduce the experimental ones at forward angles for incident energies of 56 and 100 MeV better than those with the TALYS code. Further comparisons with available experimental data including activation cross sections over wide ranges of incident energy and target mass number will be necessary to confirm the applicability of the present calculation method to deuteron nuclear data evaluation.
[1] A.J. Koning and D. Rochman, Nucl. Data Sheets 113, 2841 (2012). [2] A.J. Koning, S. Hilaire and M.C. Duijvestijn, Proceedings of the International Conference on Nuclear Data for Science and Technology, Nice, France, editors O. Bersillon, F. Gunsing, E. Bauge, R. Jacqmin, and S. Leray, EDP Sciences, 211 (2008). [3] O. Iwamoto, J. Nucl. Sci. Technol. 44, 687 (2007). [4] K. Shibata, O. Iwamoto, T. Nakagawa et al., J. Nucl. Sci. Technol. 48, 1 (2011). [5] D. Ridikas, W. Mittig, H. Savajols et al., Phys. Rev. C 63, 014610 (2000). [6] N. Matsuoka, M. Kondo, H. Sakaguchi et al., Nucl. Phys. A 345, 1 (1980). [7] M. Yahiro, K. Ogata, T. Matsumoto and K. Minomo, Prog. Theor. Exp. Phys. 2012, 01A206 (2012), and
references therein. [8] T. Ye, S. Hashimoto, Y. Watanabe et al., Phys. Rev. C 84, 054606 (2011). [9] A.J. Koning and J.P. Delaroche, Nucl. Phys. A 713, 231 (2003). [10] H. An and C. Cai, Phys. Rev. C 73, 054605 (2006). [11] M. Takeda, J. Phys. Soc. Jpn. 15, 557 (1960). [12] E.G. Auld, D.G. Crabb, L. Bird et al., Nucl. Phys. A 101, 65 (1967). [13] L.L. Lee, Jr. and J.P. Schiffer, Phys. Rev. 134, B765 (1964). [14] S. Mayo and J.E. Testoni, Nucl. Phys. 36, 615 (1962). [15] K. Hatanaka, K. Imai, S. Kobayashi et al., Nucl. Phys. A 340, 93 (1980). [16] E.J. Stephenson, J.C. Collins, C.C. Foster et al., Phys. Rev. C 28, 134 (1983).
IV.
CONCLUSIONS
Acknowledgements: This work was supported by JSPS KAKENHI Grant Number 22560820.
307