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Quantum stability criterion for α-clustering: A generalized harmonic oscillator approach with pairing and spin-orbit interactions

Mohamed Douici1, Rima Mebrek2, and Rachid Fermous1,*

  • 1Laboratoire de Valorisation des Substances Naturelles (LVSN), Khemis Miliana University, Route de Theniet El Had, 44225 Khemis Miliana, Algeria
  • 2Quantum Electronics Laboratory, Faculty of Physics, USTHB, B. P. 32 El-Alia Bab-Ezzouar, 16111 Algiers, Algeria

  • *Contact author: r.fermous@univ-dbkm.dz
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Phys. Rev. C 114, 014317 – Published 15 July, 2026

DOI: https://doi.org/10.1103/9z34-b378

Abstract

We present a theoretical framework for understanding α-clustering in even-even self-conjugate (N=Z) nuclei through a deformed harmonic oscillator approach that incorporates schematic nuclear interactions. The work introduces three enhancements to conventional single-particle gap analyses: (1) a generalized four-nucleon stability criterion ΔEclus(4)=min(4ΔE,−Epair+2ΔE,−2Epair) that accounts for the correlated nature of alpha clusters, (2) the incorporation of a schematic spin-orbit interaction ΔESO=−κℏω0[l·s] that breaks degeneracies, and (3) a BCS-inspired pairing correction Epair=(−Δ02/G)exp[−1/(Gρ(EF))] that modifies cluster stability near the Fermi surface. Using this framework we compute cluster stability maps for a complete set of self-conjugate nuclei from He4 to Ge64, documenting the evolution of α-cluster correlations across the nuclear chart. The results indicate that while the overall magnitude of cluster stability decreases with increasing mass number due to growing level density, localized regions of enhanced stability persist at specific deformations that correspond to experimentally observed cluster configurations. The spin-orbit interaction selectively suppresses certain configurations while preserving the most robust ones, offering a possible explanation as to why some harmonic oscillator predictions are not observed experimentally. Pairing effects become increasingly important in heavier systems (A>40), sometimes enhancing stability at large deformations through superfluid-type correlations. This systematic study provides a qualitative bridge between simple harmonic oscillator insights and realistic mean-field predictions, offering a useful exploratory framework for interpreting cluster structures in self-conjugate nuclei.

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Phys. Rev. C 114, 014317– Published 15 July, 2026
  • Received 12 March 2026
  • Revised 26 April 2026
  • Accepted 8 June 2026
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