Self-consistent calculations of the strength function and radiative neutron capture cross section for stable and unstable tin isotopes

Abstract

The $E1$ strength function for 15 stable and unstable Sn even-even isotopes from $A=100$ to $A=176$ are calculated using a self-consistent microscopic theory which, in addition to the standard (quasiparticle) random-phase approximation [(Q)RPA] approach, takes into account phonon coupling and the single-particle continuum (by means of the discretization procedure) with a cutoff of 100 MeV. Our analysis shows two distinct regions for which the integral characteristics of both the giant and pygmy resonances behave rather differently. For neutron-rich nuclei, starting from $^{132}\mathrm{Sn}$, we obtain a giant $E1$ resonance which significantly deviates from the widely used systematics extrapolated from experimental data in the $\ensuremath{\beta}$-stability valley. We show that the inclusion of phonon coupling is necessary for a proper description of the low-energy pygmy resonances and the corresponding transition densities for $A<132$ nuclei, while in the $A>132$ region the influence of phonon coupling is significantly smaller. The radiative neutron capture cross sections leading to the stable $^{124}\mathrm{Sn}$ and unstable $^{132}\mathrm{Sn}$ and $^{150}\mathrm{Sn}$ nuclei are calculated with both the (Q)RPA and the beyond-(Q)RPA strength functions and shown to be sensitive to both the predicted low-lying strength and the phonon-coupling contribution. The comparison with the widely used phenomenological generalized Lorentzian approach shows considerable differences both for the strength function and the radiative neutron capture cross section. In particular, for the neutron-rich $^{150}\mathrm{Sn}$, the reaction cross section is found to be increased by a factor greater than 20. We conclude that the present approach may provide a complete and coherent description of the $\ensuremath{\gamma}$-ray-strength function for astrophysics applications. In particular, such calculations are highly recommended for a reliable estimate of the electromagnetic properties of exotic nuclei.