Novel Shape Evolution in Sn Isotopes from Magic Numbers 50 to 82

A novel shape evolution in the Sn isotopes by the state-of-the-art application of the Monte Carlo shell model calculations is presented in a unified way for the ^{100-138}Sn isotopes. A large model space consisting of eight single-particle orbits for protons and neutrons is taken with the fixed Hamiltonian and effective charges, where protons in the 1g_{9/2} orbital are fully activated. While the significant increase of the B(E2;0_{1}^{+}→2_{1}^{+}) value, seen around ^{110}Sn as a function of neutron number (N), has remained a major puzzle over decades, it is explained as a consequence of the shape evolution driven by proton excitations from the 1g_{9/2} orbital. A second-order quantum phase transition is found around N=66, connecting the phase of such deformed shapes to the spherical pairing phase. The shape and shell evolutions are thus described, covering topics from the Gamow-Teller decay of ^{100}Sn to the enhanced double magicity of ^{132}Sn.