Validity of Gaussian spin distribution and spin-cutoff parameter for nuclear level and particle–hole state densities

Determine whether the angular-momentum (spin) dependence of both the phenomenological nuclear level density and the particle–hole state density follows a Gaussian distribution characterized by the spin-cutoff parameter σ² (the square of the dispersion).

Background

The paper addresses the angular-momentum dependence of nuclear level density (NLD) and particle–hole state density, which underpin compound-nucleus Hauser–Feshbach and preequilibrium emission models. A Gaussian spin distribution with dispersion σ² (the spin-cutoff parameter) has been widely assumed since the Bethe Fermi-gas framework and Ericson’s relation linking σ² to the nuclear moment of inertia and temperature, but pairing and collective effects suggest possible deviations.

Motivated by recent isomeric cross-section measurements in deuteron-induced reactions on molybdenum that challenge standard assumptions, the authors show that enforcing different effective moments of inertia requires significant and often unrealistic changes in other NLD parameters. This emphasizes the need to resolve the fundamental question of the correct spin distribution and the spin-cutoff parameter governing NLD and particle–hole densities.

References

In fact, both densities are most important for basic research as well as various applications from nuclear technology to medical praxis. However, their Gaussian spin dependence, with the square of dispersion known as the spin-cutoff parameter o2, is yet an open question.

— Long-standing problem: The nuclear level density angular-momentum dependence and isomeric data assessment  (2604.01648 - Avrigeanu et al., 2 Apr 2026) in Section I. Introduction, p. 023001-1