abstract

Neutron-induced reactions on \(^{60}\)Ni were examined to study nuclear reaction mechanisms and provide a comparison with nuclear models. The analysis is based entirely on previously published experimental data, from charged-particle detection at Peking University to \(\gamma \)-ray spectroscopy at the Los Alamos Neutron Science Center/Weapons Neutron Research (LANSCE/WNR) facility. Charged-particle detection provides direct insight into \(\alpha \)-particle cross sections at lower energies, while the \(\gamma \)-ray measurements allow for a reliable determination of total cross sections for residual even–even isotopes at higher energy ranges. Experimental cross sections for the \(^{60}\)Ni\((n, X)^{54,55,56,57}\)Fe reactions were collected from the Experimental Nuclear Reaction Data (EXFOR) database and compared with the newest Evaluated Nuclear Data Files (ENDF): JENDL-5, ENDF/B-VIII.1, TENDL-2023, and theoretical predictions from TALYS 2.0 extended to intermediate energies \(\sim 240\) MeV. TALYS 2.0 successfully reproduces the shape of the energy dependence of the total cross section for selected \(\alpha \)-emission channels within the theoretical uncertainty band, except for the \(^{60}\)Ni\((n, 4n2p)^{55}\)Fe channel, while the multi-nucleon emission channels at high incident-neutron energies are also in good agreement with the TALYS 2.0 predictions above \(\sim 180\) MeV.

abstract

We argue that modular classes of \(Q\)-manifolds provide an efficient method for addressing the existence of supersymmetric Berezin volumes in the supergeometric representation theory of the \(\mathcal {N}=2\) \(d=1\) supertranslation algebra. We establish a cohomological coherence criterion for the existence of a Berezin volume that is invariant under both of the supercharges.

abstract

We develop a unified microcanonical formulation for \(N\) noninteracting particles with an arbitrary number \(p\) of equally spaced local energy levels, \(0,\varepsilon ,2\varepsilon ,\dots ,(p-1)\varepsilon \). The exact microcanonical multiplicity is expressed as a coefficient of a local generating function, providing a finite-\(N\) representation that can also be systematically analyzed in the thermodynamic limit. By converting this coefficient extraction into a contour integral and applying saddle-point analysis, we obtain analytical expressions for the entropy per particle \(s(u,p)\) and the inverse temperature \(\beta (u,p)\), where \(u=E/(N\varepsilon )\in \left [ 0,p-1\right ] \). The main result is a single arbitrary-\(p\) solution that contains the two-level and three-level systems as special cases and connects them continuously to the unbounded limit \(p\rightarrow \infty \). For every finite \(p\), the upper spectral bound produces an entropy maximum at \(u_\mathrm {c}=(p-1)/2\), where the inverse temperature vanishes and the positive-temperature branch changes into a negative-temperature branch. As \(p \) increases, this characteristic energy is displaced toward higher values, and in the limit \(p\rightarrow \infty \) the upper bound is removed, the finite-energy entropy maximum disappears, and only positive temperatures remain. The formulation therefore provides an analytically controlled description of the crossover between bounded- and unbounded-spectrum thermodynamics. Beyond the present model, the method supplies an exact microcanonical template for discrete additive systems whose local spectra can be encoded by generating functions, including finite-level quantum and spin systems.