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Register a new userStudy of the transition from pairing vibrational to pairing rotational regimes between magic numbers N=50 and N=82, with two-nucleon transfer
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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.
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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.
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.
We discuss the binding mechanism of 11Li based on an extended three-body model of Li+n+n. In the model, we take into account the pairing correlation of p-shell neutrons in 9Li, in addition to that of valence neutrons outside the 9Li nucleus, and solve the coupled-channel two- and three-body problems of 10Li and 11Li, respectively. The results show that degrees of freedom of the pairing correlation in 9Li play an important role in the structure of 10Li and 11Li. In 10Li, the pairing correlation in 9Li produces a so-called pairing-blocking effect due to the presence of valence neutron, which degenerates s- and p-wave neutron orbits energetically. In 11Li, on the other hand, the pairing-blocking effect is surpassed by the core-n interaction due to two degrees of freedom of two valence neutrons surrounding 9Li, and as a result, the ground state is dominated by the p-shell closed configuration and does not show a spatial extension with a large r.m.s. radius. These results indicate that the pairing correlation is realized differently in odd- and even-neutron systems of 10Li and 11Li. We further improve the tail part of the 9Li-n interaction, which works well to reproduce the observed large r.m.s. radius in 11Li.
The pairing correlation energy for two-nucleon configurations with the spin-parity and isospin of $J^pi=0^+$, $T$=1 and $J^pi=1^+$, $T$=0 are calculated with $T$=1 and $T$=0 pairing interactions, respectively. To this end, we consider the $(1f2p)$ shell model space, including single-particle angular momenta of $l=3$ and $l=1$. It is pointed out that a two-body matrix element of the spin-triplet $T$=0 pairing is weakened substantially for the $1f$ orbits, even though the pairing strength is much larger than that for the spin-singlet $T$=1 pairing interaction. In contrast, the spin-triplet pairing correlations overcome the spin-singlet pairing correlations for the $2p$ configuration, for which the spin-orbit splitting is smaller than that for the $1f$ configurations, if the strength for the T=0 pairing is larger than that for the T=1 pairing by 50% or more. Using the Hartree-Fock wave functions, it is also pointed out that the mismatch of proton and neutron radial wave functions is at most a few % level, even if the Fermi energies are largely different in the proton and neutron mean-field potentials. These results imply that the configuration with $J^pi=0^+$, $T$=1 is likely in the ground state of odd-odd $pf$ shell nuclei even under the influence of the strong spin-triplet $T$=0 pairing, except at the middle of the $pf$ shell, in which the odd proton and neutron may occupy the $2p$ orbits. These results are consistent with the observed spin-parity $J^{pi}=0^+$ for all odd-odd $pf$ shell nuclei except for $^{58}_{29}$Cu, which has $J^{pi}=1^+$.
We present a new analysis of the pairing vibrations around 56Ni, with emphasis on odd-odd nuclei. This analysis of the experimental excitation energies is based on the subtraction of average properties that include the full symmetry energy together with volume, surface and Coulomb terms. The results clearly indicate a collective behavior of the isovector pairing vibrations and do not support any appreciable collectivity in the isoscalar channel.
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