Investigation of entanglement in $N = Z$ nuclei within no-core shell model

TL;DR

This study investigates the entanglement structure of $^{20}$Ne and $^{22}$Na nuclei using the No-Core Shell Model, analyzing how entanglement entropy relates to nuclear states, interactions, and electromagnetic transition strengths.

Contribution

It introduces the use of single-orbital entanglement entropy within NCSM to analyze nuclear structure and guides optimal frequency selection for improved electromagnetic transition calculations.

Findings

Entanglement entropy increases with Nmax and decreases with frequency.

Optimal frequencies enhance electromagnetic transition strengths.

N3LO interaction better predicts certain B(E2) transitions.

Abstract

In this work, we explore the entanglement structure of two $N = Z$ nuclei, $^{20}$Ne and $^{22}$Na using single-orbital entanglement entropy within the No-Core Shell Model (NCSM) framework for two realistic interactions, INOY and N$^3$LO. We begin with the determination of the optimal frequencies based on the variation of ground-state (g.s.) binding energy with NCSM parameters, $N_{max}$ and $\hbar \Omega$, followed by an analysis of the total single-orbital entanglement entropy, $S_{tot}$, for the g.s. of $^{20}$Ne and $^{22}$Na. Our results show that $S_{tot}$ increases with $N_{max}$ and decreases with $\hbar \Omega$ after reaching a maximum. We use $S_{tot}$ to guide the selection of an additional set of optimal frequencies that can enhance electromagnetic transition strengths. We also calculate the low-energy spectra and $S_{tot}$ for four low-lying states of $^{20}$Ne and six low-lying states of $^{22}$Na. Finally, we calculate a few $E2$ and one $M1$ transition strengths, finding that N$^3$LO provides better results for $B(E2; 5^+_1 \to 3^+_1$) and INOY performs well for the $B(M1; 0_1^+ \to 1_1^+)$ transition in the $^{22}$Na nucleus while considering the first set of optimal frequencies. We also observe that the second set of optimal frequencies enhances electromagnetic transition strengths, particularly for the states with large and comparable $S_{tot}$. Also, for both nuclei, the $S_{tot}$ for INOY and N$^3$LO are close while considering the second set of optimal frequencies, suggesting that the calculated $S_{tot}$ are more dependent on $\hbar \Omega$ than the interactions employed for the same model space defined by the $N_{max}$ parameter.