Influence of the hexadecapole deformation on the two neutrino double-$\text{be}ta$ decay

Abstract

The two neutrino double beta $({\beta }^{-}{\beta }^{-}{)}_{2\nu }$ decay of ${}^{94,96}$Zr, ${}^{98,100}$Mo, ${}^{104}$Ru, ${}^{110}$Pd, ${}^{128,130}$Te and ${}^{150}$Nd nuclei for the $0^{+}\to 0^{+}$ transition is studied in the PHFB model in conjunction with the pairing plus quadrupole-quadrupole plus hexadecapole-hexadecapole effective two-body interaction and the effect of the latter is investigated on the calculation of nuclear transition matrix elements $M_{2\nu }$. The reliability of the intrinsic wave functions of parent and daughter nuclei involved in the $({\beta }^{-}{\beta }^{-}{)}_{2\nu }$ decay of above mentioned nuclei is established by obtaining an overall agreement between a number of theoretically calculated spectroscopic properties, namely the yrast spectra, reduced $B(E2$:$0^{+}\to 2^{+})$ transition probabilities, static quadrupole moments $Q(2^{+})$ and $g$-factors $g(2^{+})$ and the available experimental data. The effect of deformation on $M_{2\nu }$ is also investigated to inveterate its inverse relation with nuclear deformation.

Comments: 12 pages