Pairing effects in Sn isotopes

Abstract

An extensive study of pairing effects in the Sn isotopes is carried out. The pairing Hamiltonian is treated by the chain-calculation method which provides practically exact solutions while involving less computational work than a complete-basis diagonalization. The coupling strength is fixed by reproducing the energy of the 9\ state in Sn, while the single-particle energies have been determined by an analysis of the experimental low-energy spectra of the odd-A isotopes. A detailed comparison of the calculated results with experimental data evidences the importance of neutron pairing correlations in the 50-82 shell. The results of this paper complement those of our previous study of the N"82 isotones. It turns out that the role of pairing correlations is similar to a large extent in both cases.

Monopole-optimized effective interaction for tin isotopes

“…Shell-model occupancies N j /(2j + 1) for the ground states of even tin isotopes 112−124 Sn calculated in this work in comparison with experimental data [77,78] and those calculated in Ref. [31]. j…”

A generalized seniority approach to the prediction of spectroscopic factors in odd-mass Sn isotopes

“…It may be noted that the adopted data sets for (d,p) stripping reactions in these isotopes have not changed much since the previous evaluations during 1980-90s. Our generalized seniority calculated results are in line with the previous interpretations of pairing correlations in the Sn isotopes by Andreozzi et al [35], where they have shown the dominance of h 11/2 , d 3/2 and s 1/2 orbits above N = 64. Table 1 compares the spectroscopic factors obtained from our generalized seniority results and the previous results of Andreozzi et al [35].…”

“…Our generalized seniority calculated results are in line with the previous interpretations of pairing correlations in the Sn isotopes by Andreozzi et al [35], where they have shown the dominance of h 11/2 , d 3/2 and s 1/2 orbits above N = 64. Table 1 compares the spectroscopic factors obtained from our generalized seniority results and the previous results of Andreozzi et al [35]. Besides, preliminary experimental data from a Ph.D. thesis [36] have been shown for comparison in Table 1 and Fig.…”

“…The principle experimental data have been taken from nuclear data sheets [28][29][30][31][32][33][34] for comparison. GS denotes the generalized seniority results, which have also been compared to the previous studies by using a pairing Hamiltonian approach [35]. The last column presents the preliminary experimental data taken from the thesis [36], where the quoted uncertainties are purely statistical.…”

Exact solution of the nuclear pairing problem

“…The model space here consists of five single-particle levels h 11/2 , d 3/2 , s 1/2 , g 7/2 , and d 5/2 , which can accommodate up to 32 neutrons. We will be interested in the evolution of neutron separation and correlation energies along the chain of the isotpes rather than in the specific spectra which were studied earlier with a number of approximate methods, for example [31], and can be considered in the future with our exact approach. The pairing matrix elements were obtained from the G-matrix derived from the recent CD-Bonn [32] nucleon-nucleon interaction with 132 Sn as a closed shell, where theQ-box method includes all non-folded diagrams up to the third order in the interaction and sums up the folded diagrams to infinite order [33].…”