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) randomphase 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 Sn, we obtain a giant E1 resonance which significantly deviates from the widely used systematics extrapolated from experimental data in the β-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 Sn and unstable 132 Sn and 150 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 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 γ -ray-strength function for astrophysics applications. In particular, such calculations are highly recommended for a reliable estimate of the electromagnetic properties of exotic nuclei.

Microscopic calculations of the characteristics of radiative nuclear reactions for double-magic nuclei

“…RPA + phonon coupling, can describe some observed structures of PDR in 132 Sn and partly 208 Pb only due to phonon coupling. For 132 Sn, we see the well-known structure at about 10 MeV (our approach gives a lower energy), usually called as pygmy-dipole resonance for the photoabsorption cross section, see the discussions in [9,14,15].…”

“…2 we show the PSFs for 132 Sn and 208 Pb calculated within our microscopic (ETFFS(TBA)), or simply TBA, and RPA methods with Skyrme forces SLy4. These PSFs have been recalculated from the theoretical photoabsorption cross sections taken from [9] ( 132 Sn) and [11] ( 208 Pb). The phenomenological EGLO PSFs are also shown.…”

“…In all the PSF calculations the smoothing parameter 200 keV has been used. See the details of the calculations in [9] and [10]. Quite recently, the fully self-consistent calculations of giant resonances [11] have been realized for double-magic nuclei within both RPA and TBA.…”

“…As a new feature in these calculations, the single-particle continuum was included, thus avoiding the artificial discretization usually implied in RPA and TBA. In our previous calculations for semimagic nuclei, see, for example, [9,10,12], a discretization procedure for the single-particle continuum was used (which gave the same results within CRPA for doublemagic nuclei [9]). As the self-consistent TBA calculations of photoabsorption or PSF are rather time-consuming, we have used the corresponding results for 132 Sn from Ref.…”

“…As the self-consistent TBA calculations of photoabsorption or PSF are rather time-consuming, we have used the corresponding results for 132 Sn from Ref. [9] and for 208 Pb from [11] obtained with the Skyrme forces SLy4 to calculate the above mentioned nuclear reaction characteristics.…”