Shell evolution of N=20 nuclei and Gamow-Teller strengths of 30,32,34^{30,32,34}Mg by the deformed QRPA

Gamow-Teller (GT) strength distributions of Mg isotopes are investigated within a framework of the deformed quasi-particle random phase approximation(DQRPA). We found that the N=20 shell closure in $^{28 \sim 34}$Mg was broken by the prolate shape deformation originating from the {\it fp}-intruder states. The shell closure breaking gives rise to a shift of low-lying GT excited states into high-lying states. Discussions regarding the shell evolution trend of single particle states around N=20 nuclei are also presented with the comparison to other approaches.Comment: 5 pages, 5 figures. arXiv admin note: text overlap with arXiv:1206.2156. text overlap with arXiv:1206.215

Neutrino reactions on 138^{138}La and 180^{180}Ta via charged and neutral currents by the Quasi-particle Random Phase Approximation (QRPA)

Cosmological origins of the two heaviest odd-odd nuclei, $^{138}$La and $^{180}$Ta, are believed to be closely related to the neutrino-process. We investigate in detail neutrino-induced reactions on the nuclei. Charged current (CC) reactions, $^{138}$Ba$(\nu_e, e^{-}) ^{138}$La and $^{180}$Hf$(\nu_e, e^{-}) ^{180}$Ta, are calculated by the standard Quasi-particle Random Phase Approximation (QRPA) with neutron-proton pairing as well as neutron-neutron, proton-proton pairing correlations. For neutral current (NC) reactions, $^{139}$La$(\nu \nu^{'}) ^{139}${La}$^*$ and $^{181}$Ta$(\nu, \nu^{'}) ^{181}$Ta$^*$, we generate ground and excited states of odd-even target nuclei, $^{139}$La and $^{181}$Ta, by operating one quasi-particle to even-even nuclei, $^{138}$Ba and $^{180}$Hf, which are assumed as the BCS ground state. Numerical results for CC reactions are shown to be consistent with recent semi-empirical data deduced from the Gamow-Teller strength distributions measured in the ($^{3}$He, t) reaction. Results for NC reactions are estimated to be smaller by a factor about 4 $\sim$ 5 rather than those by CC reactions. Finally, cross sections weighted by the incident neutrino flux in the core collapsing supernova are presented for further applications to the network calculations for relevant nuclear abundances

Origin of 21+2_1^+ Excitation Energy Dependence on Valence Nucleon Numbers

It has been shown recently that a simple formula in terms of the valence nucleon numbers and the mass number can describe the essential trends of excitation energies of the first $2^+$ states in even-even nuclei. By evaluating the first order energy shift due to the zero-range residual interaction, we find that the factor which reflects the effective particle number participating in the interaction from the Fermi orbit governs the main dependence of the first $2^+$ excitation energy on the valence nucleon numbers.Comment: 9 pages, 5 figure

Residual Tensor Force Effects on the Gamow-Teller states in Magic Nuclei, 48Ca, 90Zr, 132Sn, and 208Pb

We investigate the tensor force (TF) effect %in the residual interaction on the Gamow-Teller (GT) transitions in four magic nuclei, $^{48}$Ca, $^{90}$Zr, $^{132}$Sn and $^{208}$Pb. The TF is taken into account by using the Br\"uckner $G$-matrix theory with the charge-dependent (CD) Bonn potential as the residual interaction of charge-exchange quasiparticle random phase approximation (QRPA). We found that particle-particle ($p-p$) tensor interaction does not affect the GT transitions because of the closed shell nature in the nuclei, but repulsive particle-hole ($p-h$) residual interaction for the $p-h$ configuration of spin-orbit partners dominates the high-lying giant GT states for all of the nuclei. It is also shown that appreciable GT strengths are shifted to lower energy region by the attractive $p-h$ TF for the same $j_\pi=j_\nu$ configuration, and produce the low-lying GT peak about 2.5 MeV in $^{48}$Ca. Simultaneously, in $^{90}$Zr and $^{132}$Sn, the low-energy strength appears as a lower energy shoulder near the main GT peak. On the other hand, the shift of the low-lying GT state is not seen clearly for $^{208}$Pb because of the strong spin-orbit splitting of high $j$ orbits, which dominates the GT strength

Universal Expression for the Lowest Excitation Energy of Natural Parity Even Multipole States

We present a new expression for the energy of the lowest collective states in even-even nuclei throughout the entire periodic table. Our empirical formula is extremely valid and holds universally for all of the natural parity even multipole states. This formula depends only on the mass number and the valence nucleon numbers with six parameters. These parameters are determined easily and unambiguously from the data for each multipole state. We discuss the validity of our empirical formula by comparing our results with those of other studies and also by estimating the average and the dispersion of the logarithmic errors of the calculated excitation energies with respect to the measured ones.Comment: 10 pages, 5 figure