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Register a new userNovel shape evolution in Sn isotopes from magic numbers 50 to 82
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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 100-138Sn 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 1g9/2 orbital are fully activated. While the significant increase of the B(E2; 0+1 -> 2+1) value, seen around 110Sn 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 1g9/2 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 100Sn to the enhanced double magicity of 132Sn.
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Absolute values of two-particle transfer cross sections along the Sn-isotopic chain from closed shell to closed shell (100Sn,132Sn) are calculated taking properly into account nuclear correlations, as well as the successive, simultaneous and non-orthogonality contributions to the differential cross sections. The results are compared with systematic, homogeneous bombarding conditions (p, t) data. The observed agreement, almost within statistical errors and without free parameters, testify to the fact that theory is able to be quantitative in its predictions.
The shapes of neutron-rich exotic Ni isotopes are studied. Large-scale shell model calculations are performed by advanced Monte Carlo Shell Model (MCSM) for the $pf$-$g_{9/2}$-$d_{5/2}$ model space. Experimental energy levels are reproduced well by a single fixed Hamiltonian. Intrinsic shapes are analyzed for MCSM eigenstates. Intriguing interplays among spherical, oblate, prolate and gamma-unstable shapes are seen including shape fluctuations, $E$(5)-like situation, the magicity of doubly-magic $^{56,68,78}$Ni, and the coexistence of spherical and strongly deformed shapes. Regarding the last point, strong deformation and change of shell structure can take place simultaneously, being driven by the combination of the tensor force and changes of major configurations within the same nucleus.
We have performed microscopic distorted-wave Born approximation (DWBA) calculations of differential cross sections for the two reactions 136Sn(p,t)134Sn and 134Sn(t,p)136Sn, which are within reach of near-future experiments with radioactive ion beams. We have described the initial and final nuclear states in terms of the shell model, employing a realistic low-momentum two-body effective interaction derived from the CD-Bonn nucleon-nucleon potential that has already proved quite successful in describing the available low-energy energy spectrum of 134Sn. We discuss the main features of the predicted cross sections for the population of the low-lying yrast states in the two nuclei considered.
Rare isotope beams of neutron-deficient $^{106,108,110}$Sn nuclei from the fragmentation of $^{124}$Xe were employed in an intermediate-energy Coulomb excitation experiment yielding $B(E2, 0^+_1 to 2^+_1)$ transition strengths. The results indicate that these $B(E2,0^+_1 to 2^+_1)$ values are much larger than predicted by current state-of-the-art shell model calculations. This discrepancy can be explained if protons from within the Z = 50 shell are contributing to the structure of low-energy excited states in this region. Such contributions imply a breaking of the doubly-magic $^{100}$Sn core in the light Sn isotopes.
Influence of magic numbers on nuclear radii is investigated via the Hartree-Fock-Bogolyubov calculations and available experimental data. With the $ell s$ potential including additional density-dependence suggested from the chiral effective field theory, kinks are universally predicted at the $jj$-closed magic numbers and anti-kinks (textit{i.e.} inverted kinks) are newly predicted at the $ell s$-closed magic numbers, both in the charge radii and in the matter radii along the isotopic and isotonic chains where nuclei stay spherical. These results seem consistent with the kinks of the charge radii observed in Ca, Sn and Pb and the anti-kink in Ca. The kinks and the anti-kinks could be a peculiar indicator for magic numbers, discriminating $jj$-closure and $ell s$-closure.
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