Shell-model study of quadrupole collectivity in light tin isotopes

A realistic shell-model study is performed for neutron-deficient tin isotopes up to mass $A=108$. All shell-model ingredients, namely, two-body matrix elements, single-particle energies, and effective charges for electric quadrupole transition operators, have been calculated by way of the many-body perturbation theory, starting from a low-momentum interaction derived from the high-precision CD-Bonn free nucleon-nucleon potential. The focus has been on the enhanced quadrupole collectivity of these nuclei, which is testified by the observed large $B(E2;{0}_{1}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})\mathrm{s}$. Our results give evidence of the crucial role played by the $Z=50$ cross-shell excitations that need to be taken into account explicitly to obtain a satisfactory theoretical description of light tin isotopes. We find also that a relevant contribution comes from the calculated neutron effective charges, whose magnitudes exceed the standard empirical values. An original double-step procedure has been introduced to reduce effectively the model space in order to overcome the computational problem.

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