We present a microscopic description of cluster emission processes within the Cluster--Hartree--Fock (CHF) self--consistent field (SCF) theory. The starting point is a Woods--Saxon (WS) mean field (MF) with spin--orbit and Coulomb terms. Pairing is treated through standard Bardeen--Cooper--Schrieffer (BCS) quasiparticles. The residual two--body interaction is given by a density--dependent Wigner force having a Gaussian shape with a center of mass (com) correction located in a region of low nuclear density slightly beyond the geometrical contact radius of a system comprised from a nucleus and a surface cluster. We show that such a description adequately reproduces the ground state (gs) shape of a spherical nucleus while the surface correction enhances the radial tail of single particle orbitals, thus allowing for an adequate description of the $\alpha$-decay width for unstable systems.

In the present work we explore the inclusive $\psi(2S)$ meson photoproduction from nuclei near the kinematic threshold within the collision model, based on the nuclear spectral function, for incoherent direct photon--nucleon charmonium creation processes. The model takes into account the final $\psi(2S)$ absorption, target nucleon binding and Fermi motion. We calculate the absolute and relative excitation functions for production of $\psi(2S)$ mesons on $^{12}$C and $^{184}$W target nuclei at near-threshold photon beam energies of 8.0--16.4 GeV, the absolute momentum differential cross sections for their production off these target nuclei at laboratory polar angles of 0$^{\circ}$--10$^{\circ}$, the momentum dependence of the ratio of these cross sections as well as the A-dependences of the ratios (transparency ratios) of the total cross cross sections for $\psi(2S)$ production at photon energy of 13 GeV within the different scenarios for the $\psi(2S)N$ absorption cross section. We also calculate the A-dependence of the ratio of $\psi(2S)$ and $J/\psi$ photoproduction transparency ratios at photon energies around of 11.5 GeV within the adopted scenarios for this cross section. We demonstrate that both the absolute and relative observables considered reveal a definite sensitivity to these scenarios. Therefore, the measurement of such observables in future experiments at the upgraded up to 22 GeV CEBAF facility in the near-threshold energy region might shed light both on the $\psi(2S)N$ absorption cross section and on its part associated with the nondiagonal process $\psi(2S)+N \to J/\psi+N$ at finite momenta, which are of crucial importance in understanding of charmonium production and suppression in high-energy nucleus--nucleus collisions in a search for the quark-gluon plasma.

The uniform electron gas (UEG) is a cornerstone of density-functional theory (DFT) and the foundation of the local-density approximation (LDA), one of the most successful approximations in DFT. In this work, we extend the concept of UEG by introducing excited-state UEGs, systems characterized by a gap at the Fermi surface created by the excitation of electrons near the Fermi level. We report closed-form expressions of the reduced kinetic and exchange energies of these excited-state UEGs as functions of the density and the gap. Additionally, we derive the leading term of the correlation energy in the high-density limit. By incorporating an additional variable representing the degree of excitation into the UEG paradigm, the present work introduces a new framework for constructing local and semi-local state-specific functionals for excited states.

We study neutrino induced charge current coherent pion production ($\nu_\mu\text{CC-Coh}\pi$) as a tool for constraining the neutrino flux at the Deep Underground Neutrino Experiment (DUNE). The neutrino energy and flavor in the process can be directly reconstructed from the outgoing particles, making it especially useful to specifically constrain the muon neutrino component of the total flux. The cross section of this process can be obtained using the Adler relation with the $\pi$-Ar elastic scattering cross section, taken either from external data or, as we explore, from a simultaneous measurement in the DUNE near detector. We develop a procedure that leverages $\nu_\mu\text{CC-Coh}\pi$ events to fit for the neutrino flux while simultaneously accounting for relevant effects in the cross section. We project that this method has the statistical power to constrain the uncertainty on the normalization of the flux at its peak to a few percent. This study demonstrates the potential utility of a $\nu_\mu\text{CC-Coh}\pi$ flux constraint, though further work will be needed to determine the range of validity and precision of the Adler relation upon which it relies, as well as to measure the $\pi$-Ar elastic scattering cross section to the requisite precision. We discuss the experimental and phenomenological developments necessary to unlock the $\nu_\mu\text{CC-Coh}\pi$ process as a "standard candle'' for neutrino experiments.