Calculation of quadrupole deformation parameter ($\beta$) from reduced transition probability $B(E2)\uparrow$ for ($0^+_1\to 2^+_1$) transition at (even-even) $^{62-68}$Zn isotopes

TL;DR

This study uses shell-model calculations to determine quadrupole deformation parameters from B(E2) values in zinc isotopes, successfully matching experimental data and predicting new energy levels and transition probabilities.

Contribution

It provides a comprehensive shell-model analysis of $^{62-68}$Zn isotopes, including new predictions of energy levels and transition probabilities not previously experimentally known.

Findings

Calculated energy levels and B(E2) values agree with experimental data.

Predicted new energy levels and transition probabilities.

Confirmed and assigned angular momentum and parity for unknown states.

Abstract

In this work the excited energy levels, reduced transition probabilities, $B(E2)\uparrow$, intrinsic quadrupole moments and deformation parameters have been calculated for $^{62-68}$Zn isotopes with neutrons (N=32,34,36 and 38 ). Nushellx code has been applied for all energy states of (fp-shell) nuclei. Shell-model calculations for the zinc isotopes have been carried out with active particles distributed in the lp$_{3/2}$, 0f$_{5/2}$ and lp$_{1/2}$ orbits outside doubly-magic closed "56Ni"core nucleus. By using (f5p) model space and (f5pvh) interaction, the theoretical results have been obtained and compared with the available experimental results. The excited energies values, electric transition probability B(E2), intrinsic quadrupole moment (Q$_0$) and deformation parameters ($\beta_2$) have been appeared at complete agreement with the experimental values. As well as, the energy levels have been confirmed and determined for the angular momentum and parity of experimental values which have not been well established and determined experimentally. On the other hand, it has been predicted some of the new energy levels and electric transition probabilities for the $^{62-68}$Zn isotopes under this study which were previously unknown in experimental information.