# Shape evolution of Zr nuclei and roles of tensor force

## TL;DR

This study uses axial Hartree-Fock calculations with a semi-realistic interaction to explore the shape evolution of Zr nuclei, highlighting the significant role of tensor forces in nuclear deformation and magicity.

## Contribution

It demonstrates the importance of tensor-force effects in accurately predicting shape transitions and magic numbers in Zr isotopes, improving upon previous mean-field models.

## Key findings

- Reproduces deformation at N≈40, previously difficult to model.
- Predicts shape changes at specific neutron numbers, including spherical, prolate, oblate, and return to spherical.
- Shows tensor forces are crucial for understanding magicity and shape evolution in Zr nuclei.

## Abstract

Shape evolution of Zr nuclei are investigated by the axial Hartree-Fock (HF) calculations using the semi-realistic interaction M3Y-P6, with focusing on roles of the tensor force. Deformation at $N\approx 40$ is reproduced, which has not been easy to describe within the self-consistent mean-field calculations. The spherical shape is obtained in $46\leq N\leq 56$, and the prolate deformation is predicted in $58\leq N\leq 72$, while the shape switches to oblate at $N=74$. The sphericity returns at $N=80$ and $82$. The deformation in $60\lesssim N\lesssim 70$ resolves the discrepancy in the previous magic-number prediction based on the spherical mean-field calculations [Prog. Theor. Exp. Phys. \textbf{2014}, 033D02]. It is found that the deformation at $N\approx 40$ takes place owing to the tensor force with a good balance. The tensor-force effects significantly depend on the configurations, and are pointed out to be conspicuous when the unique-parity orbit (e.g. $n0h_{11/2}$) is present near the Fermi energy, delaying deformation. These effects are crucial for the magicity at $N=56$ and for the predicted shape change at $N=74$ and $80$.