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Observing the effects of numbers of valence nucleons on $0_{g s}^{+} \to 2_{1}^{+}$ transitions in deformed nuclei by comparing proton and neutron transition matrix elements

P. D. Cottle ¹, L. A. Riley ², A. Gade ^3,4, K. W. Kemper ¹, and M. Spieker¹

¹Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
²Department of Physics and Astronomy, Ursinus College, Collegeville, Pennsylvania 19426, USA
³Facility for Rare Isotope Beams, Michigan State University, East Lansing, Michigan 48824, USA
⁴Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA

Phys. Rev. C 114, 034301 – Published 1 September, 2026

DOI: https://doi.org/10.1103/q4ws-71zc

Abstract

We examined the ratios of neutron and proton transition matrix elements, $M_{n} / M_{p}$ , for the $0_{g s}^{+} \to 2_{1}^{+}$ transitions in 48 even-even stable nuclei with $N > 20$ for which electromagnetic matrix elements were compiled by Pritychenko et al. and for which high-quality inelastic proton-scattering data were available. Several deformed rare-earth nuclei have $(M_{n} / M_{p}) / (N / Z)$ values significantly below 1.0, which is not consistent with a simple liquid-drop picture. However, this phenomenon can be explained using a schematic picture in which $M_{p}$ reaches a maximum at proton midshell ( $Z = 66$ ) and $M_{n}$ reaches its maximum at neutron midshell ( $N = 104$ ). Several midmass vibrational nuclei have $M_{n} / M_{p}$ values significantly below $N / Z$ , which is not consistent with the expectation that $M_{n} / M_{p} = N / Z$ in such nuclei. A shell-model investigation of these observations might yield insights about this behavior.

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References (34)

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Observing the effects of numbers of valence nucleons on $0_{g s}^{+} \to 2_{1}^{+}$ transitions in deformed nuclei by comparing proton and neutron transition matrix elements

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Observing the effects of numbers of valence nucleons on 0gs+→21+ transitions in deformed nuclei by comparing proton and neutron transition matrix elements

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Observing the effects of numbers of valence nucleons on $0_{g s}^{+} \to 2_{1}^{+}$ transitions in deformed nuclei by comparing proton and neutron transition matrix elements