Related papers: New Discrete Basis for Nuclear Structure Studies
Compared with the traditional spherical harmonics, the spherical needlets are a new generation of spherical wavelets that possess several attractive properties. Their double localization in both spatial and frequency domains empowers them…
In this review, a new method is proposed based on Cantor's theory of Cardinality to analyze the experimental data on unstable nuclear systems which includes fundamental particles and their flavours, $\beta$-decay including spin and parity,…
Background: The isotropic harmonic oscillator supplemented by a strong spin-orbit interaction has been the cornerstone of nuclear structure since its inception more than seven decades ago. In this paper we introduce---or rather…
Weakly bound and unbound three-body nuclei are studied by using the pseudostate method within the hyperspherical formalism. After introducing the theoretical framework, the method is applied first to the $\boldsymbol{^9}$Be nucleus, showing…
The hyperspherical harmonic basis is used to describe bound states in an $A$--body system. The approach presented here is based on the representation of the potential energy in terms of hyperspherical harmonic functions. Using this…
The scattering of a weakly bound three-body system by a target is discussed. A transformed harmonic oscillator basis is used to provide an appropriate discrete and finite basis for treating the continuum part of the spectrum of the…
The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…
The discrete variable representation (DVR) basis is nearly optimal for numerically representing wave functions in nuclear physics: Suitable problems enjoy exponential convergence, yet the Hamiltonian remains sparse. We show that one can…
We investigate the stability and softness of nuclei against quadrupole, octupole, and hexadecapole deformation. By applying the spherical Skyrme-force Hartree-Fock Bardeen-Cooper-Schrieffer quasi-particle random phase approximation, we…
I review arguments demonstrating how the concept of "particle" numbers arises in the form of equidistant energy eigenvalues of coupled harmonic oscillators representing free fields. Their quantum numbers (numbers of nodes of the wave…
We investigate the use of the sinc collocation and harmonic oscillator bases for solving a two-particle system bound by a Gaussian potential described by the radial Schr\"odinger equation. We analyze the properties of the bound state wave…
The collective structure of atomic nuclei intermediate between spherical and quadrupole deformed structure presents challenges to theoretical understanding. However, models have recently been proposed in terms of potentials which are soft…
The rotating nuclei represent one of most interesting subjects for theoretical and experimental studies. They open a new dimension of nuclear landscape, namely, spin direction. Contrary to the majority of nuclear systems, their properties…
The scattering of a weakly bound (halo) projectile nucleus by a heavy target nucleus is investigated. A new approach, called the Uncorrelated Scattering Approximation, is proposed. The main approximation involved is to neglect the…
We explore the impact of optimizations of the single-particle basis on the convergence behavior and robustness of ab initio no-core shell model calculations. Our focus is on novel basis sets defined by the natural orbitals of a correlated…
In this article, we present a space-frequency theory for spherical harmonics based on the spectral decomposition of a particular space-frequency operator. The presented theory is closely linked to the theory of ultraspherical polynomials on…
Ab initio calculations face the challenge of describing a complex multiscale quantum many-body system. The nuclear wave function has both strong short-range correlations and long-range contributions. Natural orbitals provide a means of…
Investigation into the properties and structure of unstable nuclei far from stability remains a key avenue of research in modern nuclear physics. These efforts are motivated by the continual observation of unexpected structure phenomena in…
The spatial dispersion of the single-nucleon wave functions is analyzed using the self-consistent mean-field framework based on nuclear energy density functionals, and with the harmonic oscillator approximation for the nuclear potential. It…
We present calculations of ground state properties of spherical, doubly closed-shell nuclei from $^{16}$O to $^{208}$Pb employing the techniques of many-body perturbation theory using a separable density dependent monopole interaction. The…