Abstract. In the present work we calculate the allowed β − -decay half-lives of nuclei with Z = 20 − 30 and N ≤ 50 systematically under the framework of the nuclear shell model. A recent study shows that some nuclei in this region belong to the island of inversion. We perform calculation for f p shell nuclei using KB3G effective interaction. In the case of Ni, Cu, and Zn, we used JUN45 effective interaction. Theoretical results of Q values, half-lives, excitation energies, logf t values, and branching fractions are discussed and compared with the experimental data. In the Ni region, we also compared our calculated results with recent experimental data [Z. Y. Xu et al., Phys. Rev. Lett. 113, 032505, 2014]. Present results agree with the experimental data of half-lives in comparison to QRPA. Nuclear β − -decay half-lives for f p and f pg shell nuclei 2
IntroductionThe neutron density becomes very diffused and the single-particle spectrum shows the similarity of the harmonic-oscillator as we approach towards the neutron-drip line [1,2]. We can see this effect at N = 40 shell gap. Recently intruder configurations are found in the neutron rich nuclei around this shell gap [3,4,5,6,7]. Thus the nuclear structure study of these nuclei in this region is very important [8,9,10].Sorlin et al. Using RIBF facility at RIKEN, the half-lives of twenty neutron-rich nuclei with Z = 27 − 30 are reported in ref. [14]. In that work, sizable magicity was reported for both the proton number Z = 28 and the neutron number N = 50 in 78 Ni. A sudden shortening of half-lives of the nickel isotopes beyond N = 50 were observed in this work, although this effect is not found in the Cu-Ge-Ga chains. The half-lives results from LISE2000 spectrometer at GANIL for 71 Co and 73 Co are reported in ref.[15]. The half-lives of 77,78 Ni were measured for the first time by Hosmer et al. [16], at NSCL, MSU. Recently the beta decay half-lives of 38 very neutron-rich Kr to Tc isotopes are measured at RIKEN [17].Despite the progress in the experimental side, we need theoretical estimates for half-lives of neutron rich nuclei, especially those belonging to the island of inversion. These calculations are based on allowed GT-transitions. Many theoretical calculations from the quasiparticle random phase approximation (QRPA) based on the HartreeFock Bogoliubov theory [18] or other global models [19,20,21] are available in the literature. These calculations underestimate the correlation among nucleons which predict GT-strength at low-energies. Recently, shell model calculations for the β − -decays of Z = 9 − 13 nuclei are reported by Li and Ren [22]. The motivation of the present work is to study β − -decay properties of Z = 20 − 30 nuclei using the nuclear shell model. This paper is organized as follows. In section 2, we present the formulas for the calculation of β − decay half-lives. Shell model spaces, effective interactions and the quenching factors adopted in our calculations are reported in section 3. In section 4, we present theoretical results along w...