Shell Model in the Continuum—Application to the Four-Nucleon System

The continuum shell model is applied to the study of the elastic scattering of protons from ${\mathrm{He}}^3$ as well as to the photodisintegration of ${\mathrm{He}}^4$. A semiquantitative fit is obtained for the scattering phases and the photoabsorption cross section using a model Hamiltonian consisting of a real, local potential and a finiterange effective interaction. Two approximations for the total wave function of the system are studied, and it is found that the photoabsorption cross section is sensitive to the approximation used, while the calculated scattering phases are fairly independent of the details of the wave function. A method for improving the convergence of the Born series is proposed and is found to be useful in this calculation.