Related papers: Quasi-SU(3) truncation scheme for even-even sd-she…
Shell model and interacting boson model spaces admit multiple $SU^{(\alpha)}(3)$ algebras generating the same rotational spectra but different $E2$ decay properties, depending on the phases ${\alpha}$ in the quadrupole generator. In the…
The recently-proposed effective shell-model interaction, the pairing-plus-multipole Hamiltonian with the monopole interaction obtained by empirical fits starting from the monopole-based universal force (PMMU), is systematically applied to…
We show that within the proxy-SU(3) scheme the wave functions of the normal parity orbitals in a given nuclear shell are affected very little as a result of the replacement of the abnormal parity orbitals by their 0[110] proxy-SU(3)…
The structure of A=3 low-energy scattering states is described using the hyperspherical harmonics method with realistic Hamiltonian models, consisting of two- and three-nucleon interactions. Both coordinate and momentum space two-nucleon…
In this work, $\mathcal{PT}$-symmetric Hamiltonians defined on quantum $sl(2, \mathbb R)$ algebras are presented. We study the spectrum of a family of non-Hermitian Hamiltonians written in terms of the generators of the non-standard…
Supersymmetry (SUSY) of Hamiltonian dictates double degeneracy between a pair of superpartners (SPs) transformed by supercharge, except at zero energy where modes remain unpaired in many cases. Here we explore a SUSY of complete isospectrum…
Rotational bands are commonplace in the spectra of atomic nuclei. Inspired by early descriptions of these bands by quadrupole deformations of a liquid drop, Elliott constructed a discrete nucleon representations of $\mathrm{SU}(3)$ from…
We present a symmetry-based approach for prolate-oblate and spherical-prolate-oblate shape coexistence, in the framework of the interacting boson model of nuclei. The proposed Hamiltonian conserves the SU(3) and $\overline{\rm SU(3)}$…
In this work we present $ab~initio$ shell-model calculations for electric quadrupole moments and magnetic dipole moments of $sd$ shell nuclei using valence-space Hamiltonians derived with two $ab~initio$ approaches: the in-medium similarity…
We present a method for the exact diagonalization of the $\mathrm{SU}(N)$ Heisenberg interaction Hamiltonian, using Young tableaux to work directly in each irreducible representation of the global $\mathrm{SU}(N)$ group. This generalized…
We study the Nonlinear (Polynomial, N-fold,...) Supersymmetry algebra in one-dimensional QM. Its structure is determined by the type of conjugation operation (Hermitian conjugation or transposition) and described with the help of the…
Even--even nuclei in the $A\sim100$ mass region are investigated within the framework of the interacting boson model-1 ({IBM-1}). The study includes energy spectra and electric quadrupole transition properties of zirconium, molybdenum,…
The proxy-SU(3) symmetry predicts, in a parameter-free way, based only on the Pauli principle and the short-range nature of the nucleon-nucleon interaction, non-vanishing values of the collective variable gamma almost everywhere across the…
The crystal symmetry of a material dictates the type of topological band structures it may host, and therefore symmetry is the guiding principle to find topological materials. Here we introduce an alternative guiding principle, which we…
We discuss the role of the broken symmetries in the connection of the shell, collective and cluster models. The cluster-shell competition is described in terms of cold quantum phases. Stable quasi-dynamical U(3) symmetry is found for…
Using a new approximate analytic parameter-free proxy-SU(3) scheme, simple predictions for the global feature of prolate dominance and for the locus of the prolate-oblate shape transition have been made and compared with empirical data.…
We show that a nearly perfect SU(3) symmetry emerges from an extended Projected Shell Model. Starting from a deformed potential we construct separate bases for neutron and proton collective rotational states by exact angular momentum…
The question of isospin-symmetry breaking in nuclei of the $sd$ shell is addressed. We propose a new global parameterization of the isospin-nonconserving (INC) shell-model Hamiltonian which accurately describes experimentally known isobaric…
Background: Ab initio many-body methods whose numerical cost scales polynomially with the number of particles have been developed over the past fifteen years to tackle closed-shell mid-mass nuclei. Open-shell nuclei have been further…
We present the results of the application of a nuclear potential consisting of two- and three-nucleon contact interactions in nuclear structure investigations. The nuclear Hamiltonian has been derived for a very low-energy regime within the…