Nuclear lattice effective field theory as a testing ground for $\alpha$-cluster structures in ${}^{24}\mathrm{Mg}$

Abstract

The framework of nuclear lattice effective field theory (NLEFT) is applied to ${}^{24}\mathrm{Mg}$, with the perspective of obtaining a model-independent density map of the geometry of a sample of excited states of the nucleus. The Hamiltonian incorporates Wigner SU(4)-symmetric nuclear forces as well as the Coulomb interaction. The coupling constants of the spin-isospin symmetric nucleon-nucleon potentials have been adjusted in order to reproduce the experimental ground-state (g.s.) energy of ${}^{24}\mathrm{Mg}$ as well as the experimental Tjon ratio between the binding energies of ${}^3\mathrm{H}$ and ${}^4\mathrm{He}$. The ensuing parameter set turns out to be capable of capturing the experimental trend of the binding energy per nucleon, reproducing simultaneously within 1% deviation the measured values for ${}^{18}\mathrm{F}$, ${}^{22}\mathrm{Na}$, ${}^{26}\mathrm{Al}$, ${}^{28}\mathrm{Si}$, ${}^{30}\mathrm{P}$ and ${}^{32}\mathrm{S}$. Considerations based on the convergence rate of Euclidean-time extrapolations for the two lowest energy eigenvalues highlight the dual nature of the $0_1^{+}$ and $2_1^{+}$ states, of hybrid mean-field and $\alpha$-cluster type. For the latter, triaxial $\alpha$-cluster configurations seem to be favoured over the axially-symmetric ones, whereas oblate superdeformation might characterize a rotational band at $20$ MeV excitation energy.

Comments: 11 pages, 1 table, 2 figures, proceedings of the CLUSTER'26 Conference, 8-12 June 2026, Institute of Physics (Islington, London, UK)