Study of Deuteron Stripping Reaction by Coupled Channel Theory. III

Abstract

The method of coupled channels (CC) for the (d, p) reaction described by the authors [Prog. Theor. Phys. 41 (1969), 391 and 43 (1970), 347] was applied to the calculation of ¹⁶O(d, p)¹⁷O(2s), ¹²C(d, p)¹³C(1p), ⁴⁰Ca(d, p)⁴¹Ca(2p) and (1f) and the related (d, d) and (p, p) processes. Detailed numerical studies were made under the assumption that the deuteron and proton channels were coupled by the interaction kernel with the Gaussian-type n-p interaction, V_np. The non-orthogonality term in the kernel was neglected. Comparison was made with the results of DWBA and CWBA (Coulomb wave Born approximation) with the same V_np and using the same distorting potentials as in CC. The same potentials were used in the optical model (OPT) calculation of the elastic cross sections which were also compared with the results of CC. Appreciable effect of CC was seen in the elastic as well as (d, p) cross sections. In the latter CC reduces the cross section at the backward angles. The effect of CC was analysed in terms of the S-matrix elements in the partial wave representation. For the (d, p) matrix elements, S^(L)_{pl, dL}, the angular momentum space, (L, l) was found to be divided into three fairly distinct regions: (1) the CWBA region with l > l₀ and L > L₀ where CWBA = DWBA = CC, (2) the DWBA region with l > l₀, L ≤L₀ where CWBA ≠ DWBA = CC and (3) the internal region with l ≤l₀ where CWBA ≠ DWBA ≠ CC. The numbers l₀ and L₀ correspond to the maximum angular momenta at which the distortion of the proton and deuteron partial waves, respectively, becomes appreciable which is indicated by the first appreciable deviation of the absolute value of the elastic S-matrix element from 1, say less than 0.8. For the elastic S-matrix elements CC reduces the absolute value in most cases of (p, p), as one would intuitively expect, but not always so for (d, d). A detailed study of the effect of CC as a function of the coupling strength, D, was also made. In the internal region the effect of CC was found to be appreciable if D is larger than ∼1/3 of the realistic value, D₀. At D = D₀, even the addition of the next order term of the DWB series to DWBA or OPT was found to be inadequate the internal region. It was found that zero-range approximation is useful in semi-quantitative investigation of CC.