No-Core MCSM calculation for $^{10}$Be and $^{12}$Be low-lying spectra

TL;DR

This paper applies a no-core Monte Carlo Shell Model with realistic potentials to study low-lying states of $^{10}$Be and $^{12}$Be, achieving good agreement with experimental data and discussing effects of center-of-mass motion removal.

Contribution

It introduces a no-core MCSM approach with realistic interactions for $^{10}$Be and $^{12}$Be, providing detailed insights into their low-lying spectra and deformation properties.

Findings

Good agreement of excitation energies with experimental data.

Significant effects of center-of-mass removal on certain states.

Indication that larger model spaces are needed for $^{12}$Be.

Abstract

The low-lying excited states of $^{10}$Be and $^{12}$Be are investigated within a no-core Monte Carlo Shell Model (MCSM) framework employing a realistic potential obtained via the Unitary Correlation Operator Method. The excitation energies of the 2$^+_1$ and 2$^+_2$ states and the B(E2;$\,2^+_{1,2}\rightarrow$ 0$^+_{g.s.}$) for $^{10}$Be in the MCSM with a standard treatment of spurious center-of-mass motion show good agreement with experimental data. Some properties of low-lying states of $^{10}$Be are studied in terms of quadrupole moments, E2 transitions and single-particle occupation numbers. The E2 transition probability of $^{10}$C, the mirror nucleus of $^{10}$Be, is also presented with a good agreement to experiment. The triaxial deformation of $^{10}$Be and $^{10}$C is discussed in terms of the B(E2) values. The removal of the spurious center-of-mass motion affects differently on various states: for instance, negligible effects on the 2$^+_1$ and 2$^+_2$ levels of $^{10}$Be, while significant and favorable shift for the 1$^-_1$ level. It is suggested that the description of $^{12}$Be needs a larger model space as well as some other higher excited states of $^{10}$Be, as an indicator that these are dominated by intruder configurations.