Johnson and Soper's method of including deuteron break-up for the calculation of stripping cross sections

Abstract

The equations of Johnson and Soper (JS) are re-derived by utilizing an expansion of the deuteron-nucleus wave function in terms of the continuum eigenstates of the neutron-proton Hamiltonian, and are generalized so as to allow for break-up states in which the relative neutronproton angular momenta h ̵ l are different from zero. Apart from the ab initio neglect of the break-up energies, the approximation required to establish these equations are found to be acceptable. A numerical application for the case of 21.6 MeV (d, p) reactions on 40 Ca shows that the l = 2 breakup continuum has a small effect on the Δl = 3 and Δl = 1 stripping cross sections. A sum rule, expressing the generalized JS potentials in terms of potentials which depend on the individual break-up momenta, is established. Numerical application to the 21.6 MeV d- 40 Ca example shows that the l = 0 break-up spectrum contains break-up energies at least as large as 10 MeV, and that the 1 = 2 spectrum requires inclusion of break-up energies up to about 40 MeV. It is concluded that the neglect of break-up energies in the derivation of the JS equations requires further investigation.