Two-Nucleon Problem When the Potential Is Nonlocal but Separable. I

TLDR

The two‑nucleon problem is studied using a nonlocal separable potential of the form \((p|V|p')=-(\lambda/M)g(p)g(p')\). Exact solutions for bound and continuum states are obtained, allowing the interaction to be prescribed independently for each angular momentum; an example with \(g(p)=(p^2+\beta^2)^{-1}\) is compared to low‑energy neutron‑proton data, and deuteron photodisintegration is also analyzed. This flexibility renders scattering analysis straightforward and unambiguous.

Abstract

The two-nucleon problem is considered in terms of an interaction of the form $(\mathrm{p}|V|{\mathrm{p}}^{\ensuremath{'}})=\ensuremath{-}(\frac{\ensuremath{\lambda}}{M})g(p)g({p}^{\ensuremath{'}})$. In this case we can find exact solutions both for bound states and for continuum states, and prescribe arbitrarily and independently the interaction effective in states of different angular momenta. This important feature makes the analysis of scattering straightforward and unambiguous. An example for $g(p)={({p}^{2}+{\ensuremath{\beta}}^{2})}^{\ensuremath{-}1}$ is presented and compared with the low-energy neutron-proton data. The photodisintegration of the deuteron in our model is also discussed.