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Shell model description of the $N=82$ isotonic chain with a new effective interaction

Y. X. Yu, Q. Y. Chen, Chong Qi, G. J. Fu

Abstract

In this work, we present a systematic study of low-lying states and electromagnetic properties of the semi-magic $N = 82$ isotonic chain with proton number $Z=51$-77, using the full configuration interaction shell model with a newly developed high-quality effective interaction. The calculations are performed in a large model space that includes all proton orbitals between $Z = 50$ and 82: $0g_{7/2}$, $1d_{5/2}$, $1d_{3/2}$, $2s_{1/2}$, and $0h_{11/2}$. The effective interaction is derived through the principal component analysis approach, starting from 160 two-body matrix elements and 5 single-particle energies and considering up to 30 degrees of freedom. Those are optimized by fitting to 204 available experimental energy levels. The resulting root-mean-square deviation is as low as 102 keV. The new interaction successfully reproduces the binding energies, low-lying spectra, electric quadrupole transition probabilities $B(E2)$, and magnetic dipole moments across both even-even and odd-mass isotones. The nuclear structure of low-lying states is analyzed in detail. Additionally, predictions are made for several more proton-rich nuclei beyond current experimental reach, including $^{155}\mathrm{Ta}$, $^{156}\mathrm{W}$, $^{157}\mathrm{Re}$, $^{158}\mathrm{Os}$, and $^{159}\mathrm{Ir}$.

Shell model description of the $N=82$ isotonic chain with a new effective interaction

Abstract

In this work, we present a systematic study of low-lying states and electromagnetic properties of the semi-magic isotonic chain with proton number -77, using the full configuration interaction shell model with a newly developed high-quality effective interaction. The calculations are performed in a large model space that includes all proton orbitals between and 82: , , , , and . The effective interaction is derived through the principal component analysis approach, starting from 160 two-body matrix elements and 5 single-particle energies and considering up to 30 degrees of freedom. Those are optimized by fitting to 204 available experimental energy levels. The resulting root-mean-square deviation is as low as 102 keV. The new interaction successfully reproduces the binding energies, low-lying spectra, electric quadrupole transition probabilities , and magnetic dipole moments across both even-even and odd-mass isotones. The nuclear structure of low-lying states is analyzed in detail. Additionally, predictions are made for several more proton-rich nuclei beyond current experimental reach, including , , , , and .

Paper Structure

This paper contains 10 sections, 26 equations, 10 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. Theoretical framework
  3. results and discussion
  4. Binding energies and separation energies
  5. Electromagnetic properties
  6. Low-lying structures of even-even nuclei
  7. Low-lying structures of odd-$A$ nuclei
  8. summary and outlook
  9. Tables of $B(E2)$ values and $g$-factors
  10. The mean-field single-particle energy derived from the monopole interaction

Figures (10)

  • Figure 1: (a) Difference between the shell model and reference values of the nuclear binding energy ($B_{\rm theo.} - B_{\rm ref.}$) for the $N=82$ isotones. The solid dots represents experimental values from the AME2020 database Wang_2021, while the open circles denote the Audi-Wapstra 2020 extrapolation (AW2020) Wang_2021. The dashed line in gray indicates the RMSD of 102 keV obtained for all 204 data points included in the fit (see the text). (b) One-proton and two-proton separation energies. The curves represent the shell model results in this work.
  • Figure 2: Comparison of $B(E2)$ values between experiment PhysRevC.104.014316A=135A=137A=139A=141A=143A=145A=147A=149A=151A=153A=134A=136A=138A=140A=142A=144A=146A=148A=150A=152A=154 and shell model, shown in a logarithmic scale. The dashed line denotes the line where calculated values equal experimental ones. Two transitions show noticeable deviations from this line (marked in red): A. $8_1^+ \to 6_1^+$ in $^{138}\textrm{Ba}$ and B. $8_1^+ \to 6_2^+$ in $^{138}\textrm{Ba}$. The data point for the $9/2_1^+ \to 7/2_1^+$ transition in $^{139}\textrm{La}$ falls outside the limits of this figure.
  • Figure 3: Same as Fig. \ref{['E2_log']}, but for the magnetic moment $\mu$ (in $\mu_{\rm N}$). The experimental values are taken from Refs. A=135A=137A=139A=141A=143A=145A=147A=134A=136A=138A=140A=142A=144A=146.
  • Figure 4: Low-lying spectra in the even-even isotones. The experimental values are taken from Refs. A=134A=136A=138A=140A=142A=144A=146A=148A=150A=152A=154. Only part of low-lying states are shown for simplicity.
  • Figure 5: Systematics of the yrast 2$^+$, 4$^+$, 6$^+$, 8$^+$ and 10$^+$ states in the even-even isotones (dots for experiment and solid curves for calculation). The figure also shows (as dashed curves) the calculated non-yrast 8$^+$ and 10$^+$ states in $^{136}\textrm{Xe}$-$^{142}\textrm{Nd}$, as well as the second 8$^+$ state in $^{144}\textrm{Sm}$, which are expected to be dominated by seniority-2 configurations (see discussion on $g$-factors in the main text).
  • ...and 5 more figures