Complex potential model for low-energy neutron scattering
The optical model for low-energy neutron scattering is treated explicitly by means of a new form of complex potential which permits an exact solution of the S-wave Schrödinger equation. This potential is everywhere continuously differentiable and its imaginary part consists of both a volume and a surface absorption term which is in close agreement with recent theoretical calculations of the spatial distribution of the imaginary potential. Closed-form expressions are obtained for the logarithmic derivative of the wave function, and hence for the S-wave strength function and scattering length, from which their dependence on all potential parameters can be studied explicitly. In particular, it is shown that concentrating the absorption in the nuclear surface can serve as a remedy for a well-known discrepancy, by lowering the minima of the strength function to more realistic values. © 1961.