Mitsuji Kawai

Study of Deuteron Stripping Reaction by Coupled Channel Theory. II Properties of Interaction Kernel and Method of Numerical Solution

The purpose of the present series of papers is to study the deuteron stripping reaction in terms of the method of coupled channels in order to investigate the theoretical back ground of distorted wave Born approximation (DWBA) for the nuclear rearrangement collision which has been studied only inadequately compared with the nuclear inelastic scattering, in contrast to the great success of DWBA in the actual analysis of the experiment.

Effects of channel non-orthogonality in (d, p) reactions

Abstract Coupled channel calculations for (d, p) reactions were performed in which a strong coupling between the d and p channels was assumed. Reactions investigated were 16O(d, p) 17O(2s) and 40Ca(d, p) 41Ca(2p) at Ed =10.5 MeV and the related (d, d) and (p, p) scattering processes. The nonorthogonality of the d- and p-channels were taken into account. The results of these calculations are presented and are compared with the coupled channel calculations neglecting the channel nonorthogonality and also compared with the DWBA and optical model calculations.

The (p-d-t) process in strong (p, t) transitions

Abstract The (p-d-t) process in 48 Ca(p, t) 48 Ca(p, t) 46 Ca(0 + , g.s.; 2 + , 1.34 MeV) and 116 Sn(p, t) 114 Sn(0 + , g.s.) at 20 MeV was investigated. The calculations showed that the two-step process is important in all the transitions investigated, and is enhanced in the Sn transition by the pairing correlations in the BCS ground states.

NUCLEAR THREE-BODY FORCES

Abstract The three-body nuclear potential is calculated assuming that: (1) three pions are exchanged among three nucleons; (2) the static pion theory is valid without pion-pion interactions. The obtained expressions are very complicated, so that numerical calculations are carried out only in the case of the triton forming an equilateral triangle. The result is compared with the previously calculated three-body potential due to two-pion exchange. It is found that the latter is predominant if the length of a side is more than 0.8 h m πc .

A two-step process in the 210Pb(p, d)209Pb reaction

Abstract The 210 Pb(p, d) 209 Pb reaction leading to the single particle states of 209 Pb have been analyzed. In the weak transitions to the li 11/2 , 3d 5/2 , 4s 1/2 , 2g 7/2 and 3d 3/2 single particle states the contribution of the two-step process p→t→d was found to be of the same order of magnitude as the direct pick-up process. The calculated cross sections taking both the direct pick-up and the two-step processes into account agree well with the experimental ones. Two step processes via inelastic scattering were found to be small.

The Spin-Flip Scattering of High Energy Protons by Light Nuclei

The spin-flip inelastic scattering of high energy protons is investigated for the 15.1 Mev excitation of C12 ancl the 9.2 Mev excitation of N14. The electromagnetic interaction is found to be far too weak to account for the observed cross sections. The spin-flip cross sections clue to the (rr1 ·<r2) (-r1 part of the nuclear interaction are calculated by means of the impulse approximation. In the case of C12 the cross section can l1e calculated without referring to any special nuclear model from theft-value of the fl-clccay of B12 or N 12 to the ground state of C12. The result agrees very well with the experimental cross section showing the validity of the assumptions involved in the calculation. It is also shown that the spin-flip scattering is the only process which shows the angular distribution with maximum at Oo leaving the residual nucleus in a discrete low-lying excited state. The nuclear matrix element of the transition estimated conversely from the observed cross section may be used as a datum: for the relevant nuclear states. In particular the separate contributions of the spin and the orbital angular momenta to the M1 r-transition between the relevant states can be estimated and are found to be of the ratio 1 to 0.3 both for C12 and NI4. Discussions arc given on the approximations used in the calculations as well as on the nuclear states relevant to the excitations.

An Analysis of Some Neutron Transfer Reactions Using Microscopic Form Factors

Form factors of one-neutron transfer reactions were calculated by the method developed by the authors for the transition between the two-neutron (or -neutron-hole) states of 180, SSNi, 210Pb, UN and 2ospb and the single-neutron (or -neutron-hole) states of the neighbouring nuclei using the known shell-model wave functions and corresponding two-body interactions. For strong transitions the calculated form factor F is close to that given by the separation energy method FsE, while for weak transitions they are considerably different. The shape of F is intermediate between FsE and FEFB given by the effective binding energy method. Strong correlation was found between the relative importance of the two-body interaction in F and the energy shift of the two-particle (or -hole) level from the zeroth-order shell-model energy. The angular distribution calculated either by DWBA or by adiabatic theory of Johnson and Soper (AD) was quite insensitive to the shape of the form factor inside the nucleus, although magnitude was sometimes different by a factor of 4 depending on whether F or FsE was used. For 180(p,d) 170 and the weak transitions in 210Pb(p,d)209Pb, no satisfactory agreement was obtained by either AD or DWBA. It is suggested that two-step mechanisms may be important in these processes.

A numerical study of the validity of DWBA for (d, p) reactions

Abstract The S -matrix of (d, p)-reactions was calculated by (a) Coulobm wave Born approximation (CWBA), (b) DWBA and (c) coupled channels method (CC): The angular momentum space can be divided into three regions according as (I) CWBA = DWBA = CC, (II) CWBA ≠ DWBA = CC and (III) CWBA ≠ DWBA ≠ CC.