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A semiclassical second-order differential equation for the inhomogeneous local gap $\Delta(r)$ is derived from a strict second-order $\hbar$ expansion of the anomalous pairing tensor and compared with a similar equation given by Simonucci et al. The second-order normal density matrix is given as well. Several extra gradient terms are revealed. Second-order expressions at finite temperature are given for the first time. The corresponding Ginzburg-Landau equation is presented and it is shown that, compared to the equation of Baranov and Petrov, an extra second-order gradient term is present. Applications to the pairing gap in cold atoms in a harmonic trap are presented., Comment: 12 pages, 4 figures. To be submitted to the EPJ A Topical Collection devoted to the legacy of Peter Schuck

The equation of motion for the two-fermion two-time correlation function in the pairing channel is considered at finite temperature. Within the Matsubara formalism, the Dyson-type Bethe-Salpeter equation (Dyson-BSE) with the frequency-dependent interaction kernel is obtained. Similarly to the case of zero temperature, it is decomposed into the static and dynamical components, where the former is given by the contraction of the bare interaction with the two-fermion density and the latter is represented by the double contraction of the four-fermion two-time correlation function, or propagator, with two interaction matrix elements. The dynamical kernel with the four-body propagator, being formally exact, requires approximations to avoid generating prohibitively complicated hierarchy of equations. We focus on the approximation where the dynamical interaction kernel is truncated on the level of two-body correlation functions, neglecting the irreducible three-body and higher-rank correlations. Such a truncation leads to the dynamical kernel with the coupling between correlated fermionic pairs, which can be interpreted as emergent bosonic quasibound states, or phonons, of normal and superfluid nature. The latter ones are, thus, the mediators of the dynamical superfluid pairing. In this framework, we obtained the closed system of equations for the fermionic particle-hole and particle-particle propagators. This allows us to study the temperature dependence of the pairing gap beyond the Bardeen-Cooper-Schrieffer approximation, that is implemented for medium-heavy nuclear systems. The cases of 68Ni and 44,46Ca are discussed in detail., Comment: Article: 11 pages, 5 figures

Starting from a general many-body fermionic Hamiltonian, we derive the equations of motion (EOM) for nucleonic propagators in a superfluid system. The resulting EOM is of the Dyson type formulated in the basis of Bogoliubov's quasiparticles. As the leading contributions to the dynamical kernel of this EOM in strongly-coupled regimes contain phonon degrees of freedom in various channels, an efficient method of calculating phonon's characteristics is required to successfully model these kernels. The traditional quasiparticle random phase approximation (QRPA) solvers are typically used for this purpose in nuclear structure calculations, however, they become very prohibitive in non-spherical geometries. In this work, by linking the notion of the quasiparticle-phonon vertex to the variation of the Bogoliubov's Hamiltonian, we show that the recently developed finite-amplitude method (FAM) can be efficiently employed to compute the vertices within the FAM-QRPA. To illustrate the validity of the method, calculations based on the relativistic density-dependent point-coupling Lagrangian are performed for the single-nucleon states in heavy and medium-mass nuclei with axial deformations. The cases of $^{38}$Si and $^{250}$Cf are presented and discussed., Comment: Article: 11 pages, 6 figures

A new method for calculating the symmetry-projected energy of coupled-cluster singles and doubles (CCSD) wave function through the Monte Carlo method is proposed. We present benchmark calculations in considering the three-level Lipkin model which is a simple and minimal model with two phases: spherical and deformed ones. It is demonstrated that this new method gives good ground state energy and low-lying spectra., Comment: 6 pages, 4 figures, submitted to PRC

In the previous paper I \cite{bhagwat20} 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 work using the Gogny D1S force within the ETF scheme. The parametrized ETF potentials and densities of paper I 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., Comment: 17 pages, 8 Figures and 2 Tables

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., Comment: 14 pages, 5 Figures, 2 Tables

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., Comment: 6 pages, 1 figure

The status of different extensions of the Random Phase Approximation (RPA) is reviewed. The general framework is given within the Equation of Motion Method and the equivalent Green's function approach for the so-called Self-Consistent RPA (SCRPA). The role of the Pauli principle is analyzed. A comparison among various approaches to include Pauli correlations, in particular, renormalized RPA (r-RPA), is performed. The thermodynamic properties of nuclear matter are studied with several cluster approximations for the self-energy of the single-particle Dyson equation. More particle RPA's are shortly discussed with a particular attention to the alpha-particle condensate. Results obtained concerning the Three-level Lipkin, Hubbard and Picket Fence Models, respectively, are outlined. Extended second RPA (ESRPA) is presented.

Mixing single and triple fermions an exact killing operator of the Coupled Cluster Doubles (CCD) wave function with good symmetry was found in \cite{Tohy13}. Using these operators with the equation of motion (EOM) method the so-called self-consistent odd particle number random phase approximation (odd-RPA) was set up. Together with the stationarity condition of the two body density matrix it is shown that the killing conditions allow to reduce the order of correlation functions contained in the matrix elements of the odd-RPA equations to a fully self consistent equation for the single particle occupation numbers. Excellent results for the latter and the ground state energies are obtained in an exactly solvable model from weak to strong couplings., Comment: 9 pages, 3 figures

Average, global pairing behaviours of electronic devices, like films, wires, and grains are studied with semiclassical methods, as Weyl and Thomas-Fermi approximations, in the ultrasmall, i.e., quantal regime, which exhibits strong quantum fluctuations and shell effects. This is the case also for superfluid nuclei. Results, mostly analytic, are elaborated for average size dependences, ready for easy use also in other circumstances. Comparisons with experimental results are given where possible.

As is well known, the single level seniority model of pairing has been solved exactly since long using angular momentum algebra. It is shown that it can also be solved using the Dyson equation of standard many-body theory. The formalism shows some interesting many-body aspects.

The two-fermion two-point correlation function in the pairing channel is discussed in the equation of motion framework. Starting from the bare two-fermion interaction, we derive the equation of motion for the two-fermion pair propagator in a strongly-correlated medium. The resulting equation is of the Dyson type with the kernel having a static and a one frequency dependent components and, thus, can be regarded as Dyson Bethe-Salpeter equation (Dyson-BSE). The many-body hierarchy generated by the dynamical interaction kernel is truncated on the level of two-body correlation functions, thus neglecting the explicit three-body and higher-rank correlations. The truncation is performed via a cluster expansion of the intermediate three-particle-one-hole correlation function irreducible in the particle-particle channel, that leads to the coupling between single fermions and emergent collective modes of excitation. The latter couplings are, thus, derived in terms of the exact mapping of the in-medium two-fermion correlation functions onto the domain of bosonic quasibound states (phonons) without introducing new parameters. The approach is applied to calculations of the pairing gaps in medium-mass nuclear systems, that include calcium, nickel and tin isotopic chains., Comment: Article: 14 pages, 8 figures

When the density of a nuclear system is decreased, homogeneous states undergo the so-called Mott transition towards clusterised states, e.g. alpha clustering, both in nuclei and in nuclear matter. Here we investigate such a quantum phase transition (QPT) by using microscopic energy density functional (EDF) calculations both with the relativistic and the Gogny approaches on the diluted $^{16}$O 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. Complementary approaches are used in order to understand this QPT. A study of spatial localisation properties as a function of the density allows to derive a value of the Mott density in agreement with the one obtained by fully microscopic calculations in $^{16}$O and in nuclear matter. Moreover a study of the spontaneous symmetry breaking of the rotational group in $^{16}$O, down to the discrete tetrahedral one, provides further insight on the features displayed by the single-particle spectrum obtained within the EDF approach.The content of the tetrahedrally deformed A-nucleon product state in terms of spherical particle-hole configurations is investigated. Finally a study of quartet condensation and the corresponding macroscopic QPT is undertaken in infinite matter., Comment: 13 pages, 13 figures

We present a microscopic calculation of $\alpha$-cluster formation in heavy nuclei $^{104}$Te ($\alpha$+$^{100}$Sn), $^{212}$Po ($\alpha$+$^{208}$Pb) and their neighbors $^{102}$Sn, $^{102}$Te, $^{210}$Pb and $^{210}$Po by using the quartetting wave function approach. Improving the local density approximation, the shell structure of the core nucleus is considered, and the center-of-mass (c.o.m.) effective potential for the quartet is obtained self-consistently from the shell model wavefunctions. The $\alpha$-cluster formation and decay probabilities are obtained by solving the bound-state of the c.o.m. motion of the quartet and the scattering state of the formed $\alpha$-cluster in the Gurvitz approach. Striking shell effects on the $\alpha$-cluster formation probabilities are analyzed for magic numbers 50, 82 and 126. The computed $\alpha$-decay half-lives of these special nuclei are compared with the newest experimental data., Comment: 16 pages, 4 figures

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 RPA (SCRPA) 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 the 1D Hubbard model give very good results., Comment: 12 pages, 27 figures, to be published in PRC. arXiv admin note: substantial text overlap with arXiv:1905.04672

Non-perturbative aspects of the quantum many-body problem are revisited, discussed and advanced in the equation of motion framework. We compare the approach to the two-fermion response function truncated on the two-body level by the cluster expansion of the dynamical interaction kernel to the approach known as time blocking approximation. Such a comparison leads to an extended many-body theory with non-perturbative treatment of high-order configurations. The present implementation of the advanced theory introduces a new class of solutions for the response functions, which include explicitly beyond-mean-field correlations between up to six fermions. The novel approach, which includes configurations with two quasiparticles coupled to two phonons (2q$\otimes$2phonon), is discussed in detail for the particle-hole nuclear response and applied to medium-mass nuclei. The proposed developments are implemented numerically on the basis of the relativistic effective meson-nucleon Lagrangian and compared to the models confined by two-fermion and four-fermion configurations, which are considered as state-of-the-art for the response theory in nuclear structure calculations. The results obtained for the dipole response of $^{42,48}$Ca and $^{68}$Ni nuclei in comparison to available experimental data show that the higher configurations are necessary for a successful description of both gross and fine details of the spectra in both high-energy and low-energy sectors., Comment: Article: 28 pages, 19 figures

We present some recent developments on the nuclear many-body problem, such as the treatment of high-order correlations and finite temperature in the description of in-medium two-nucleon propagators. In this work we discuss two-time propagators of the particle-hole type, which describe the response of finite nuclei to external probes without nucleon transfer. The general theory is formulated in terms of the equation of motion method for these propagators with the only input from the bare nucleon-nucleon interaction. The numerical implementation was performed on the basis of the effective mason-nucleon Lagrangian in order to study the energy-dependent kernels of different complexity. The finite-temperature extension of the theory with $ph\otimes phonon$ configurations is applied to a study of the multipole response of medium-mass nuclei., Comment: 4 pages, 5 figures: Contribution to the Proceedings of The IV International Conference on Nuclear Structure and Dynamics NSD2019

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., Comment: 5 pages; v2: minor revision (pairing gaps from 5-point formula and improved figures)

We present a number conserving particle-hole RPA theory for collective excitations in the transition from normal to superfluid nuclei. The method derives from an RPA theory developed long ago in quantum chemistry using antisymmetric geminal powers, or equivalently number projected HFB states, as reference states. We show within a minimal model of pairing plus monopole interactions that the number conserving particle-hole RPA excitations evolve smoothly across the superfluid phase transition close to the exact results, contrary to particle-hole RPA in the normal phase and quasiparticle RPA in the superfluid phase that require a change of basis at the broken symmetry point. The new formalism can be applied in a straightforward manner to study particle-hole excitations on top of a number projected HFB state., Comment: Under revision in PLB

A Dyson Bethe-Salpeter equation (Dyson-BSE) for fermion pairs is presented whose kernel has a static and a one frequency dependent contribution, analogous to the self energy of the single particle Dyson equation with the (static) mean field term and the energy dependent correlation term. The static part of the Dyson-BSE is the self-consistent mean field for the vibrations. At the same time, for the correlated single particle self-energy a full particle-vibration coupling (PVC) scattering equation is established where the vibration is the same as obtained from the Dyson-BSE. Both equations, single particle Dyson equation and Dyson-BSE, are coupled through self-consistency. Numerical results for Lipkin and 1D Hubbard chain are very promising., Comment: Article in memoriam of P.F. Bortignon

The first $3^-$ and $4^-$ states of $^{12}$C are studied in the present container model, in which the shift parameter is introduced to break the parity symmetry for projecting out the negative-parity states. Taking the limit as the shift parameter approaches zero and by variational calculations for one-deformed size parameter, the local energy minima are obtained for the $3^-$ and $4^-$ states. It is found that the obtained single THSR (Tohsaki-Horiuchi-Schuck-R\"{o}pke) wave functions for $3^-$ and $4^-$ states are 96% and 92% equivalent to the corresponding GCM wave functions, respectively. The calculated intrinsic densities further show that these negative-parity states of three clusters, different with the traditional understanding of rigid triangle structure, are found to have nonlocalized clustering structure in the two-dimensional container picture., Comment: 7 pages, 5 figures

The time-dependent density-matrix theory (TDDM) where the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for reduced density matrices is truncated by approximating a three-body density matrix with one-body and two-body density matrices is applied to the Lipkin model. It is shown that in the large $N$ limit the ground state in TDDM approaches the exact solution. Various truncation schemes for the three-body density matrix are also tested for an extended three-level Lipkin model., Comment: 11 pages, 17 figures

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 QPNM methods are compared with experimental data. A remarkable coherence of both methods together with experimental data is observed., Comment: 24 pages, 11 figures

A formally exact Bethe-Salpeter-like equation for the linear-response function is introduced with a kernel which depends only on the one frequency of the applied field. This is in contrast with the standard Bethe-Salpeter equation (BSE) which involves multiple-frequency integrals over the kernel and response functions. From the one-frequency kernel, known approximations are straightforwardly recovered. However, the present formalism lends itself to more powerful approximations. This is demonstrated with the exact analytical solution of the Hubbard molecule. Similarities and differences of the $GW$+BSE approach with the self-consistent random-phase approximation (RPA) is also discussed.

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., Comment: Contribution to EuNPC2018-conference

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

In order to study the nucleon-nucleon pairing effects in clustering nuclei, we formulate a superposed Tohsaki-Horiuchi-Schuck-Roepke (THSR) wave function, which includes both molecular-orbit and pairing configurations explicitly. With this new wave function, we investigate the abnormal deuteron-like pn-pairing effect in 10B with T=0 and S=1 (isoscalar) by comparing with isovector NN pairs (T=1, S=1) in 10Be and 10C. Energies are calculated for the ground states of 10Be, 10B and 10C nuclei, and the 1+ excited state of 10B. These energies are essentially improved comparing with studies using previous version of THSR wave function. Further more, overlaps between the total wave function and the pairing component indicate that the NN pairing effect is more visible in 10B than in 10Be and 10C. By analyzing the energies and the overlaps between wave function components, we observe two different mechanisms enhancing the formation of deuteron-like pairs in 10B. We also discuss the pairing effect by showing average distances between components in each nucleus and density distributions of valance nucleons.

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., Comment: 9 pages, 4 figures, 34 conferences

This report adresses topics and questions of common interest in the fields of ultra-cold gases and nuclear physics in the context of the BCS-BEC crossover. The BCS-BEC crossover has recently been realized experimentally, and essentially in all of its aspects, with ultra-cold Fermi gases. This realization, in turn, has raised the interest of the nuclear physics community in the crossover problem, since it represents an unprecedented tool to test fundamental and unanswered questions of nuclear many-body theory. Here, we focus on the several aspects of the BCS-BEC crossover, which are of broad joint interest to both ultra-cold Fermi gases and nuclear matter, and which will likely help to solve in the future some open problems in nuclear physics (concerning, for instance, neutron stars). Similarities and differences occurring in ultra-cold Fermi gases and nuclear matter will then be emphasized, not only about the relative phenomenologies but also about the theoretical approaches to be used in the two contexts. After an introduction to present the key concepts of the BCS-BEC crossover, this report discusses the mean-field treatment of the superfluid phase, both for homogeneous and inhomogeneous systems, as well as for symmetric (spin- or isospin-balanced) and asymmetric (spin- or isospin-imbalanced) matter. Pairing fluctuations in the normal phase are then considered, with their manifestations in thermodynamic and dynamic quantities. The last two Sections provide a more specialized discussion of the BCS-BEC crossover in ultra-cold Fermi gases and nuclear matter, respectively. The separate discussion in the two contexts aims at cross communicating to both communities topics and aspects which, albeit arising in one of the two fields, share a strong common interest., Comment: 91 pages, 51 figures

Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schr\"odinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of the GW approximation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods., Comment: 23 pages, 9 figures, 11 tables

In order to study the correlation between clusters and nucleons in light nuclei, we formulate a new superposed THSR wave function which describes both spatial large spreading and cluster-correlated dynamics of valence nucleons. By using the new THSR wave function, the binding energy of 9B is essentially improved comparing with our previous studies. We calculate the excited states of 9B and obtain the energy spectrum of 9B which is consistent with the experimental results, including prediction of the 1/2+ excited state of 9B which is not fixed yet experimentally. We study the proton dynamics in 9B and find that the cluster-proton correlation plays an essential role for the proton dynamics in the ground state of 9B. Further more, we discuss the density distribution of the valence proton with special attention to its tail structure. Finally, the resonance nature of excited states of 9B is illustrated by comparing root-mean-square radii between the ground and excited states., Comment: 16 pages, 8 figures

We discuss some special aspects of the nuclear many-body problem related to isospin transfer. The major quantity of interest is the in-medium propagator of a particle-hole configuration of the proton-neutron character, which determines the nuclear response to isospin transferring external fields. One of the most studied excitation modes is the Gamow-Teller resonance (GTR), which can, therefore, be used as a sensitive test for the theoretical approaches. Its low-energy part, which is responsible for the beta decay half-lives, is especially convenient for this. Models benchmarked against the GTR can be used to predict other, more exotic, excitations studied at nuclear rare isotope beam facilities and in astrophysics. As far as the precision is concerned, the major problem in such an analysis is to disentangle the effects related to the underlying interaction and those caused by the many-body correlations. Therefore, approaches (i) based on fundamental concepts for the nucleon-nucleon interaction which (ii) include complex many-body dynamics are the preferred ones. We discuss progress and obstacles on the way to such approaches., Comment: 9 pages, 5 figures, Contribution to the Proceedings of the 6th International Conference on New Frontiers in Physics (ICNFP2017)

A truncation scheme of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for reduced density matrices, where a three-body density matrix is approximated by two-body density matrices, is improved to take into account a normalization effect. The truncation scheme is tested for the Lipkin model. It is shown that the obtained results are in good agreement with the exact solutions., Comment: 4 pages, 6 figures

Quartetting ($\alpha$-like clustering) occurs in low density matter ($\le 0.03$ fm$^{-3}$) which exists, e.g., at the surface of nuclei. It is of interest for the $\alpha$ preformation to calculate the $\alpha$ decay of heavy nuclei such as $^{212}$Po, but also in light nuclei (e.g., $^{20}$Ne) which shows strong signatures of quartetting. We analyze the intrinsic structure of the $\alpha$-like cluster and the center of mass motion of the quartet, in particular the role of Pauli blocking. The Thomas-Fermi model for the (daughter) core nucleus is improved introducing quasiparticle nucleon states. Calculations performed for harmonic oscillator basis states show that the effective potential for the quartet center of mass motion remains nearly constant within the core nucleus. The relation to the THSR (Tohsaki-Horiuchi-Schuck-R\"opke) approach is discussed., Comment: 26 pages, 9 figures

The nonlocalized clustering approach is generalized to 8-11Be isotopes with isospin dependent spin-orbit potential. A new form of the Tohsaki-Horiuchi-Schuck-R\"opke (THSR) wave function is introduced to provide a correct description for the {\sigma}-binding neutron in 11Be. Systematic calculations for 8-11Be isotopes are performed and results fit well with experimental values. The low energy spectrum of 11Be is also obtained, especially the correct spin-parity 1/2+ is reproduced for the intruder ground state. The exotic neutron halo structure of 11Be is studied by calculations of root-mean-square radii and density distribution. We obtain a large spatial distribution for the last valence neutron of 11Be, which fits the phenomenological extracted value from experimental data. The spectroscopic factor is also calculated and discussed for the 1/2+ ground state of 11Be., Comment: 14 pages, 5 figures

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., Comment: 15 pages, 8 figures

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., Comment: 11 pages, 6 figures, 1 table, discussion added, accepted for publication in Phys. Rev. C

The present understanding of the structure of the Hoyle state in 12C is reviewed. Most of the theoretical approaches to the Hoyle state are shortly summarized. The corresponding results are analyzed with respect to whether they give evidence to the alpha particle condensation structure of the Hoyle state (and other Hoyle-like states in heavier self-conjugate nuclei) or not., Comment: Colloquium article

In this article we review the present status of alpha clustering in nuclear systems. First of all, an important aspect is condensation in nuclear matter. Second, the alpha container model, recently been proposed by Tohsaki-Horiuchi-Schuck-Roepke (THSR), will be outlined and the ensuing condensate aspect of the Hoyle state at 7.65 MeV in 12C will be investigated in some detail. After 15 years since the proposal of the alpha condensation concept a critical assessment of this idea will be given. Alpha gas states in other nuclei like 16O and 13C will be considered. The THSR wave function can also describe configurations of one alpha particle on top of a doubly magic core. The cases of 20Ne and 212Po will be investigated., Comment: review article

The coupled dynamics of low lying modes and various giant resonances are studied with the help of the Wigner Function Moments method generalized to take into account spin degrees of freedom and 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., Comment: arXiv admin note: substantial text overlap with arXiv:1502.05546, arXiv:1301.2513

The Barcelona-Catania-Paris-Madrid (BCPM) 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 and, in addition, the description of Giant Quadrupole Resonance energies is greatly improved., Comment: 8 pages, 5 figures

The Bogoliubov-Born-Green-Kirkwood-Yvon or Time-Dependent Density Matrix (TDDM) hierarchy of equations for higher density matrices is truncated at the three body level in approximating the three body correlation function by a quadratic form of two body ones, closing the equations in this way. The procedure is discussed in detail and it is shown in non-trivial model cases that the approximate inclusion of three body correlation functions is very important to obtain precise results. A small amplitude approximation of this time dependent nonlinear equation for the two body correlation function is performed (STDDM*-b) and it is shown that the one body sector of this generalised non-linear second RPA equation is equivalent to the Self-Consistent RPA (SCRPA) approach which had been derived previously by different techniques. It is discussed in which way SCRPA also contains the three body correlations. TDDM and SCRPA are tested versus exactly solvable model cases., Comment: 27 pages, 14 figures

The influence of the core polarization on the effective nuclear interaction of asymmetric nuclear matter is calculated in the framework of the induced interaction theory. The strong isospin dependence of the density and spin density fluctuations is studied along with the interplay between the neutron and proton core polarizations. Moving from symmetric nuclear matter to pure neutron matter the crossover of the induced interaction from attractive to repulsive in the spin singlet state is determined as a function of the isospin imbalance.The density range in which it occurs is also determined. For the spin triplet state the induced interaction turns out to be always repulsive. The implications of the results for the neutron star superfluid phases are shortly discussed., Comment: 6 pages, 4 figures

The Self-Consistent RPA (SCRPA) approach is elaborated for cases with a continuously broken symmetry, this being the main focus of the present article. Correlations beyond standard RPA are summed up correcting for the quasi-boson approximation in standard RPA. Desirable properties of standard RPA such as fullfillment of energy weighted sum rule and appearance of Goldstone (zero) modes are kept. We show theoretically and, for a model case, numerically that, indeed, SCRPA maintains all properties of standard RPA for practically all situations of spontaneously broken symmetries. A simpler approximate form of SCRPA, the so-called renormalised RPA, also has these properties. The SCRPA equations are first outlined as an eigenvalue problem, but it is also shown how an equivalent many body Green's function approach can be formulated., Comment: 13 pages, 8 figures

We extend the new concept of nonlocalized clustering to the nucleus 10Be with proton number Z=4 and neutron number N=6 (N=Z+2). The Tohsaki-Horiuchi-Schuck-R\"opke (THSR) wave function is formulated for the description of different structures of 10Be. Physical properties such as energy spectrum and root-mean-square radii are calculated for the first two 0+ states and corresponding rotational bands. With only one single THSR wave function, the calculated results show good agreement with other models and experimental values. We apply, for the first time, the THSR wave function on the chain orbit ({\sigma}-orbit) structure in the 0^+_2 state of 10Be. The ring orbit ({\pi}-orbit) and {\sigma}-orbit structures are further illustrated by calculating the density distribution of the valence neutrons. We also investigate the dynamics of ff-clusters and the correlations of two valence neutrons in 10Be., Comment: 18 pages, 7 figures

A microscopic calculation of $\alpha$-cluster preformation probability and $\alpha$ decay width in the typical $\alpha$ emitter $^{212}$Po is presented. Results are obtained by improving a recent approach to describe $\alpha$ preformation in $^{212}$Po [Phys. Rev. C 90, 034304 (2014)] implementing four-nucleon correlations (quartetting). Using the actually measured density distribution of the $^{208}$ Pb core, the calculated alpha decay width of $^{212}$Po agrees fairly well with the measured one., Comment: 7 pages, 5 figures, 1 table, submitted to Phys. Rev. C

Using the $\hbar$-expansion of the Green's function of the Hartree-Fock-Bogoliubov equation, we extend the second-order Thomas-Fermi approximation to generalized superfluid Fermi systems by including the density-dependent effective mass and the spin-orbit potential. We first implement and examine the full correction terms over different energy intervals of the quasiparticle spectra in calculations of finite nuclei. Final applications of this generalized Thomas-Fermi method are intended for various inhomogeneous superfluid Fermi systems., Comment: 8 pages, 10 figures, PRC

Nuclear scissors modes are considered in the frame of Wigner function moments method generalized to take into account spin degrees of freedom and pair correlations simultaneously. 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 in rare earth nuclei., Comment: arXiv admin note: text overlap with arXiv:1301.2513

An extension of the time-dependent Hartree-Fock-Bogoliubov theory (ETDHFB) which includes higher-order effects such as screening of the pairing correlation is proposed. ETDHFB is applied to a fermion system trapped in a harmonic potential to test its feasability by comparison with the exact solution. With the use of perturbative expressions for the pairing tensor and the two-body density matrix derived from ETDHFB, the screening effect is investigated for atomic fermion systems and isotopes of tin nuclei. It is found that the screening effect on the pairing correlation is not significant., Comment: 12 pages, 9 figures

Within the context of Hartree-Fock-Bogoliubov theory, we study the behavior of superfluid Fermi systems when they pass from a small to a large container. Such systems can be now realized thanks to recent progress in experimental techniques. It will allow to better understand pairing properties at overflow and in general in rapidly varying external potentials.