[Paper Review] Particle-Hole Multiplets Near Closed Shells

A. Covello, L. Coraggio+2 more|ArXiv.org|Dec 13, 2002

Nuclear physics research studies3 citations

TL;DR

This paper presents a shell-model study of particle-hole multiplets in odd-odd nuclei near doubly magic 132Sn and 100Sn using a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential. The calculations reproduce experimental energy levels with high accuracy, confirming the predictive power of realistic shell-model interactions in regions far from stability and supporting future experimental efforts with radioactive beams.

ABSTRACT

We report here on a shell-model study of nuclei close to doubly magic 132Sn and 100Sn focusing attention on particle-hole multiplets. In our study we make use of realistic effective interactions derived from the CD-Bonn nucleon-nucleon potential. We present results for the four nuclei 132Sb, 130Sb, 102In and 98Ag. Comparison shows that the calculated results are in very good agreement with the experimental data available for these nuclei far from stability. This supports confidence in the predictions of our calculations which may stimulate, and be helpful to, future experiments.

Motivation & Objective

• To investigate particle-hole multiplets in nuclei near doubly magic 132Sn and 100Sn as probes of the neutron-proton effective interaction.
• To test the predictive power of realistic shell-model interactions derived from modern nucleon-nucleon potentials in regions far from stability.
• To provide reliable spectroscopic predictions for unstable nuclei near 132Sn and 100Sn to guide future radioactive beam experiments.
• To extend the study of particle-hole multiplet patterns—previously observed in 208Bi—to the 132Sn and 100Sn regions using a modern theoretical framework.

Proposed method

• Employed a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential using a new many-body approach instead of the traditional G-matrix method.
• Defined a model space centered on 132Sn and 100Sn cores, including valence orbits in the 50–82 and 28–50 shells for protons and neutrons.
• Used experimental single-particle energies from 133Sb and 131Sn for 132Sb and 130Sb, and theoretical values from prior studies for 102In and 98Ag where experimental data were unavailable.
• Solved the shell-model Hamiltonian in a truncated model space using the projected effective interaction, with no adjustable parameters.
• Calculated energy levels and wave functions for particle-hole configurations such as πg7/2 νh−111/2 and πg9/2−1 νd5/2.
• Compared calculated energy levels with experimental data to validate the interaction and model space.

Experimental results

Research questions

• RQ1 How accurately can realistic shell-model calculations describe particle-hole multiplets in nuclei near 132Sn and 100Sn?
• RQ2 Do the energy level patterns of particle-hole multiplets in 132Sb and 102In resemble those observed in 208Bi, particularly the J=0 and J=max states being highest in energy?
• RQ3 Can the effective interaction derived from the CD-Bonn NN potential reproduce experimental spectra in these doubly closed-shell regions without adjustable parameters?
• RQ4 What is the structure of the wave functions in the low-lying states of these odd-odd nuclei, particularly the role of core excitations and configuration mixing?

Key findings

• The calculated energy levels for the πg7/2 νh−111/2 multiplet in 132Sb show excellent agreement with experiment, with the 8− state at 92 keV above the 4+ ground state, matching the experimental observation.
• The calculated multiplets in 130Sb, 102In, and 98Ag exhibit the same characteristic pattern as in 208Bi: the states with minimum and maximum J have the highest excitation energy, while the (jπ+ jν − 1) state is the lowest-lying.
• The largest discrepancy between theory and experiment is 130 keV, observed for the 5+ state in 98Ag, indicating overall high accuracy in reproducing experimental spectra.
• The wave functions of the low-lying states are dominated by the primary particle-hole configurations, with significant mixing from other configurations—especially in the 7+ state of 102In, where non-primary configurations contribute up to 50%.
• The results confirm the validity of the Brennan-Bernstein coupling rule, as the (jπ+ jν − 1) state is consistently the lowest in energy across all multiplets studied.
• The study demonstrates that realistic shell-model calculations using a CD-Bonn-based effective interaction can quantitatively describe spectroscopic properties in doubly closed-shell regions far from stability, with no adjustable parameters.