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

State Complexity of Regular Tree Languages for Tree Matching

We study the state complexity of regular tree languages for tree matching problem. Given a tree t and a set of pattern trees L, we can decide whether or not there exists a subtree occurrence of trees in L from the tree t by considering the new language L′ which accepts all trees containing trees in L as subtrees. We consider the case when we are given a set of pattern trees as a regular tree language and investigate the state complexity. Based on the sequential and parallel tree concatenation, we define three types of tree languages for deciding the existence of different types of subtree occurrences. We also study the deterministic top-down state complexity of path-closed languages for the same problem.</jats:p