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

Abstract

The continuum shell model is applied to the study of the elastic scattering of protons from He 3 as well as to the photodisintegration of 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.

A coupled-channels treatment of the positive-parity resonances in4He

“…This procedure is shown to be indispensable, in order to avoid the appearance of spurious resonances in the region of excitation energies of interest. The parameters of the calculations have been essentially fixed in earlier studies [7,29] on negativeparity states. The only quantities that had to be specified here were the one-body potentials U, corresponding to the s-and d-waves.…”

“…These can be broadly classified into three categories: (i) the R-matrix approach [1][2][3][4][5]; (ii) the resonating group method [6], which has been extensively applied to interpret the scattering of nucleons by the mass-3 system; and finally, (iii) the shell model in the continuum approach [7,8]. A systematic study of the negativeparity resonances by using the coupled-channels method based on the lp-i h model in the continuum [9] has shown that this formalism is quite successful in handling the nuclear structure and continuum aspects in a consistent and straightforward manner.…”