Nuclear Photodisintegration in the1sShell: A Perturbative Approach to the Dipole Sum Rules

The integrated and bremsstrahlung-weighted $E1\mathrm{}$ photoabsorption cross sections, ${\sigma }_{\mathrm{int}}$ and ${\sigma }_{\mathrm{b}}$, have been calculated for the lightest nuclei, ${\mathrm{H}}^2$, ${\mathrm{H}}^3$, ${\mathrm{He}}^3$, and ${\mathrm{He}}^4$, within the framework of a second-order perturbation procedure. For the purpose of comparison, two Gaussian nucleon-nucleon potentials were employed: one containing a repulsive core and central attractive and tensor components, the other only central attractive and tensor components. The results for ${\sigma }_{\mathrm{int}}$ indicate that while reasonable over-all agreement with experiment may be achieved with either potential, the component contributions differ widely because of the admixture of the repulsive core. Furthermore, the results for ${\sigma }_{\mathrm{b}}$ for the deuteron seem to indicate a deficiency in the present choice of oscillator basis functions when applied to the loosely bound system. Considerable improvement for ${\sigma }_{\mathrm{b}}$ is noted for ${\mathrm{H}}^3$, ${\mathrm{He}}^3$, and ${\mathrm{He}}^4$, where the nuclei are more tightly bound and less extended structures. It is found by analyzing exact and approximate third-order contributions to both the deuteron binding energy and integrated cross section that the use of a wave function containing parameters determined by minimization of the perturbation expansion through second order is probably not acceptable, at least for this nucleus. This is further substantiated by comparison with the binding-energy results obtained from an exact numerical solution of the coupled $S$ and $D$ radial differential equations.