We study the average and global pairing behaviours of electronic devices, like films, wires, and grains using semiclassical methods, such as Weyl and Thomas–Fermi approximations, in the ultrasmall, i.e., quantal regime, which exhibits strong quantum fluctuations and shell effects. We discuss how these results, mostly analytic, are elaborated for average size dependencies, in order to be used in other circumstances when the fully quantal calculation become computationally too expensive. We also compare the results with latest experimental one where possible.

The fine structure of the scissors mode is investigated within the time dependent Hartree-Fock-Bogoliubov (TDHFB) approach. The solution of TDHFB equations by the Wigner function moments (WFM) method predicts a splitting of the scissors mode into three intermingled branches. Together with the conventional scissors mode two new modes arise due to spin degrees of freedom. They generate significant M1 strength below the conventional energy range. The results of calculations of scissors resonances in rare earths and actinides by WFM and quasiparticle-phonon nuclear model methods are compared with experimental data. A remarkable coherence of both methods together with experimental data is observed.

Analytic average mean-field potentials of the Fermi-function (Woods-Saxon) type for the whole nuclear chart with space-dependent effective mass are deduced from the D1S Gogny force. Those ready-for-use potentials are advertised as an alternative to other existing phenomenological mean-field potentials.

In the previous paper [Bhagwat, Centelles, Vi\~nas, and Schuck, Phys. Rev. C 103, 024320 (2021)] we have shown that self-consistent extended Thomas-Fermi (ETF) potentials and densities associated with a given finite-range interaction can be parametrized by generalized Fermi distributions. As a next step, a comprehensive calculation of ground-state properties of a large number of spherical and deformed even-even nuclei is carried out in the present paper using the Gogny D1S force within the ETF scheme. The parametrized ETF potentials and densities of the previous paper are used to calculate the smooth part of the energy and the shell corrections within the Wigner-Kirkwood semiclassical averaging scheme. It is shown that the shell corrections thus obtained, along with a simple liquid drop prescription, yield a good description of ground-state masses and potential-energy surfaces for nuclei spanning the entire periodic table.

The formal implications of a quartet coherent-state ansatz for proton-neutron pairing are analyzed. Its nonlinear annihilation operators, which generalize the BCS linear quasiparticle operators, are computed in the quartetting case. Their structure is found to generate nontrivial relationships between the many-body correlation functions. The intrinsic structure of the quartet coherent state is detailed as it hints to the precise correspondence between the quartetting picture and the symmetry restored pair condensate picture for the proton-neutron pairing correlations.

When the density of a nuclear system is decreased, homogeneous states undergo the so-called Mott transition towards clusterized states, e.g., a clustering, both in nuclei and in nuclear matter. Here we investigate such a quantum phase transition (QPT) by using microscopic energy density functional calculations with with the relativistic and the Gogny approaches on the diluted O-16 nucleus. The evolution of the corresponding single-particle spectrum under dilution is studied, and a Mott-like transition is predicted at about 1/3 of the saturation density. A complementary study of quartet condensation and the corresponding macroscopic QPT is undertaken in infinite matter.

A comparison of pairing properties in cuprates and nuclear matter is briefly discussed. Quartet (alpha-particle) condensation is a very important aspect of nuclear physics. The physics of the Hoyle state in 12 C will be outlined and its crucial role for the existence of life on earth explained.

Recently, Allmond and Wood [Phys. Lett. B 767, 226 (2017)] were able to extract the three moments of inertia $I_k$ of a dozen of superfluid triaxial nuclei from experimental data. The observed dependence of the $I_k$ on the deformation parameters is rather smooth. Here we show that these moments of inertia can be surprisingly well explained by a semiclassical cranked Hartree-Fock-Bogoliubov (HFB) calculation in which the velocity field is a simple superposition of rigid and irrotational flows.

Coupled equations for even and odd particle number correlation functions are set up via the equation of motion method. For the even particle number case this leads to self-consistent random-phase approximation equations already known from the literature. From the equations of the odd particle number case the single-particle occupation probabilities are obtained in a self-consistent way. This is the essential new procedure of this work. Both even and odd particle number cases are based on the same correlated vacuum and, thus, are coupled equations. Applications to the Lipkin model and to the one-dimensional Hubbard model give very good results.

Stimulated by the still puzzling competition between spin-singlet and spin-triplet pairing in nuclei, the 3SD1 neutron-proton pairing is investigated in the framework of BCS theory of nuclear matter. The medium polarization effects are included in the single particle spectrum and also in the pairing interaction starting from the G-matrix, calculated in the Brueckner-Hartree-Fock approximation. The vertex corrections due to spin and isospin collective excitations of the medium are determined from the Bethe-Salpeter equation in the RPA limit, taking into account the tensor correlations. It is found that the self-energy corrections confine the superfluid state to very low-density, while remarkably quenching the magnitude of the energy gap, while the induced interaction has an attractive effect. The interplay between spin-singlet and spin-triplet pairing is discussed in nuclear matter as well as in finite nuclei.

With the Wigner Function Moments (WFM) method the scissors mode of the actinides and rare earth nuclei are investigated. The unexplained experimental fact that in $^{232}$Th a double hump structure is found finds a natural explanation within WFM. It is predicted that the lower peak corresponds to an isovector spin scissors mode whereas the higher lying states corresponds to the conventional isovector orbital scissors mode. The experimental situation is scrutinized in this respect concerning practically all results of $M1$ excitations.

This contribution gives a short review of recent theoretical advances in most topics of nuclear cluster physics concentrating, however, around α particle clustering. Along the route, the point of view will be critical mentioning not only progress but also failures and open problems.

The coupled dynamics of low-lying modes and various giant resonances are studied with the help of theWigner FunctionMomentsmethod generalized to take into account spin degrees of freedomand pair correlations simultaneously. The method is based on Time-Dependent Hartree–Fock–Bogoliubov equations. The model of the harmonic oscillator including spin–orbit potential plus quadrupole–quadrupole and spin–spin interactions is considered. New low-lying spin-dependent modes are analyzed. Special attention is paid to the scissors modes. A new source of nuclear magnetism, connected with counter-rotation of spins up and down around the symmetry axis (hidden angular momenta), is discovered. Its inclusion into the theory allows one to improve substantially the agreement with experimental data in the description of energies and transition probabilities of scissors modes.

The possibility that a four component Fermi gas with attractive interaction can form a quartet condensate at low density is pointed out. It is discussed that for quartets only the Bose-Einstein Condensatio (BEC) phase exists and that the analogue to the weak coupling long coherence BCS phase of pairing is absent. Precurser phenomena in finite nuclei are presented. For instance, the present understanding of the structure of the Hoyle state in 12 C being the gateway for Carbon production in the universe is reviewed. It is pointed out that a crucial test of any theory is the good reproduction of the experimental results for the inelastic form factor from ground to the Hoyle state. The performances of the so-called THSR wavwe function are outlined confirming the α particle condensation hypothesis proposed 15 years back in [1].

We present a microscopic calculation of alpha-cluster formation in heavy nuclei by using the quartetting wave function approach. The interaction of the quartet with the core nucleus is taken in local density approximation. The alpha-cluster formation is found to be particularly sensitive to the interplay of the mean field felt by the alpha-cluster and the Pauli blocking as a consequence of antisymmetrization. The striking feature of alpha-cluster formation probability across the major shell closures of 82 protons and 126 neutrons is reproduced. The shell (or subshell) effects on the alpha-cluster formation in superheavy nuclei are also analyzed.

We report on a new state of matter manifested by strongly correlated Fermi systems including various heavy fermion (HF) metals, two-dimensional quantum liquids such as \(^3\)He films, certain quasicrystals, and systems behaving as quantum spin liquids. Generically, these systems can be viewed as HF systems or HF compounds, in that they exhibit typical behavior of HF metals. At zero temperature, such systems can experience a so-called fermion condensation quantum phase transition (FCQPT). Combining analytical considerations with arguments based entirely on experimental grounds, we argue and demonstrate that the class of HF systems is characterized by universal scaling behavior of their thermodynamic, transport, and relaxation properties. That is, the quantum physics of different HF compounds is found to be universal, emerging irrespective of the individual details of their symmetries, interactions, and microscopic structure. This observed universal behavior reveals the existence of a new state of matter manifest in HF compounds. We propose a simple, realistic model to study the appearance of flat bands in two-dimensional ensembles of ultracold fermionic atoms, interacting with coherent resonant light. It is shown that signatures of these flat bands may be found in peculiarities in their thermodynamic and spectroscopic properties. We also show that the FCQPT, in generating flat bands and altering Fermi surface topology, is an essential progenitor of the exotic behavior of the overdoped high-temperature superconductors represented by \(\hbox {La}_{2-x}\hbox {Sr}_{x}x\hbox {CuO}_4\), whose superconductivity differs from that predicted by the classical Bardeen–Cooper–Schrieffer theory. The theoretical results presented are in good agreement with recent experimental observations, closing the colossal gap between these empirical findings and Bardeen–Cooper–Schrieffer-like theories.

The Barcelona-Catania-Paris-Madrid functional recently proposed to describe nuclear structure properties of finite nuclei is generalized as to include a realistic effective mass. The resulting functional is as good as the previous one in describing binding energies, radii, deformation properties, etc. In addition, the description of giant quadrupole resonance energies is greatly improved.

An effective alpha particle equation is derived for cases where an alpha particle is bound to a doubly magic nucleus. As an example, we consider Po-212 with the alpha on top of the Pb-208 core. The fully quantal solution of the problem is inspired by the THSR (Tohsaki-Horiuchi-Schuck-Ropke) wave function concept that has been successfully applied to light nuclei. Shell model calculations are improved by including four-particle (alpha-like) correlations that are of relevance when the matter density becomes low. In the region where the alpha-like cluster penetrates the core nucleus, the intrinsic bound state wave function transforms at a critical density into an unbound four-nucleon shell model state. We present a microscopic calculation of both alpha-cluster preformation probability and decay width in typical alpha-emitter Po-212. Using actually measured density distribution of the Pb-208 core, the calculated alpha decay width of Po-212 agrees fairly well with the measured one. Applications to other nuclei (Ne-20) are discussed.