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Register a new userShell model analysis of the $ B(E2,2^+ rightarrow 0^+)$s in the A=70 T=1 triplet
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he $B(E2,2^+ rightarrow 0^+)$ transition strengths of the T=1 isobaric triplet $^{70}$Kr, $^{70}$Br, $^{70}$Se, recently measured at RIKEN/RIBF, are discussed in terms of state of the art large scale shell model calculations using the JUN45 and JUN45+LNPS plus Coulomb interactions. In this letter we argue that, depending on the effective charges used, the calculations are either in line with the experimental data within statistical uncertainties, or the anomaly happens in $^{70}$Br, rather than $^{70}$Kr. In the latter case, we suggest that it can be due to the presence of a hitherto undetected 1$^+$ T=0 state below the yrast 2$^+$ T=1 state. Our results do not support a shape change of $^{70}$Kr with respect to the other members of the isobaric multiplet.
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The $A=4$ nuclei, i.e., $^4$H, $^4$He and $^4$Li, establish an interesting isospin $T=1$ isobaric system. $^4$H and $^4$Li are unbound broad resonances, whereas $^4$He is deeply bound in its ground state but unbound in all its excited states. The present situation is that experiments so far have not given consistent data on the resonances. Few-body calculations have well studied the scatterings of the $4N$ systems. In the present work, we provide many-body calculations of the broad resonance structures, in an textit{ab initio} framework with modern realistic interactions. It occurs that, indeed, $^4$H, $^4$Li and excited $^4$He are broad resonances, which is in accordance with experimental observations. The calculations also show that the first $1^-$ excited state almost degenerates with the $2^-$ ground state in the pair of mirror isobars of $^4$H and $^4$Li, which may suggest that the experimental data on energy and width are the mixture of the ground state and the first excited state. The $T = 1$ isospin triplet formed with an excited state of $^4$He and ground states of $^4$H and $^4$Li is studied, focusing on the effect of isospin symmetry breaking.
The lightest Xenon isotopes are studied in the framework of the Interacting Shell Model (ISM). The valence space comprises all the orbits lying between the magic closures N=Z=50 and N=Z=82. The calculations produce collective deformed structures of triaxial nature that encompass nicely the known experimental data. Predictions are made for the (still unknown) N=Z nucleus 108-Xe. The results are interpreted in terms of the competition between the quadrupole correlations enhanced by the pseudo-SU(3) structure of the positive parity orbits and the pairing correlations brought in by the 0h11/2 orbit. We have studied as well the effect of the excitations from the 100-Sn core on our predictions. We show that the backbending in this region is due to the alignment of two particles in the 0h11/2 orbit. In the N=Z case, one neutron and one proton align to J=11 and T=0. In 110-Xe and 112-Xe the alignment begins in the J=10 T=1 channel and it is dominantly of neutron neutron type. Approaching the band termination the alignment of a neutron and a proton to J=11 and T=0 takes over. In a more academic mood, we have explored the role of the isovector and isoscalar pairing correlations on the structure on the yrast bands of 108-Xe and 110-Xe and examined the role of the isovector and isoscalar pairing condensates in these N~Z nuclei.
The role of discrete (or point-group) symmetries is discussed in the framework of the Cluster Shell Model which describes the splitting of single-particle levels in the deformed field of cluster potentials. We discuss the classification of the eigenstates for the cases of a triangular and tetrahedral configuration of alpha-particles in terms of the irreducible representations of the double point groups D(3h) and T(d), respectively, and show how the discrete symmetry of a given eigenstate can be determined. Finally, we derive the Coriolis coupling for each one of these geometrical configurations.
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 $J^{pi}=1^+$.
In this contribution, we present the cluster shell model which is analogous to the Nilsson model, but for cluster potentials. Special attention is paid to the consequences of the discrete symmetries of three alpha-particles in an equilateral triangle configuration. This configuration is characterized by a special structure of the rotational bands which can be used as a fingerprint of the underlying geometric configuration. The cluster shell model is applied to the nucleus 13C.
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