Related papers: Proxy-SU(3): A symmetry for heavy nuclei
A collective vector-boson model with broken SU(3) symmetry, in which the ground state band and the lowest $\gamma$ band belong to the same irreducible representation but are non-degenerate, is applied to several deformed even-even nuclei.…
Rotational $SU(3)$ algebraic symmetry continues to generate new results in the shell model (SM). Interestingly, it is possible to have multiple $SU(3)$ algebras for nucleons occupying an oscillator shell $\eta$. Several different aspects of…
It is shown that the SU(3) symmetry of the fermion dynamical symmetry model is essentially preserved even for highly nondegenerate spherical single-particle energies. The breaking of SU(3) symmetry by single-particle energy terms for either…
In the applications of proxy-SU(3) model in the context of determining $(\beta,\gamma)$ values for nuclei across the periodic table, for understanding the preponderance of triaxial shapes in nuclei with $Z \ge 30$, it is seen that one needs…
The quasi-degeneracy between the single-particle states $(n,\,l,\,j=l+1/2)$ and $(n-1,\,l+2,\,j=l+3/2)$ indicates a special and hidden symmetry in atomic nuclei---the so-called pseudospin symmetry (PSS)---which is an important concept in…
We examine nucleon-nucleon realistic interactions, based on their SU(3) decomposition to SU(3)-symmetric components. We find that many of these interaction components are negligible, which, in turn, allows us to identify a subset of…
The systematics of experimental energy differences between the levels of the ground state band and the gamma-1 band in even-even nuclei are studied as a function of the angular momentum L, demonstrating a decrease of the energy differences…
Quantum systems with SU($N$) symmetry are paradigmatic settings for quantum many-body physics. They have been studied for the insights they provide into complex materials and their ability to stabilize exotic ground states. Ultracold…
SO(10) supersymmetric grand unified theories [SUSY GUTs] provide a beautiful framework for physics beyond the standard model. Experimental measurements of the three gauge couplings are consistent with unification at a scale $M_G \sim 3…
We considered the characteristic features of SU(3) partial dynamical symmetry in the interacting boson model framework to demonstrate the relevance of this technique in the nuclear spectroscopy of Dy (A=160) nucleus. The predictions of…
The isospin-invariant interacting boson model IBM-3 is analyzed in situations where $SU_T(3)$ charge symmetry [or, equivalently, $U_L(6)$ $sd$ symmetry] is conserved. Analytic expressions for energies, electromagnetic transitions,…
Prolate to oblate shape transitions have been predicted in an analytic way in the framework of the Interacting Boson Model (IBM), determining O(6) as the symmetry at the critical point. Parameter-independent predictions for prolate to…
Supersymmetric (SUSY) grand unified theories (GUTs) appear to be best motivated for understanding strong, weak and electromagnetic interactions of nature. We briefly review emergence of new formulas for running fermion masses valid in…
We briefly review the issues of proton decay and fermion masses and mixings in minimal supersymmetric grand unified theories. We argue that minimal SU(5), although tightly constrained by proton decay data, is still not ruled out. However,…
We consider a novel approach to the nuclear shell model. The one-dimensional harmonic oscillator in a box is used to introduce the concept of an oblique-basis shell-model theory. By implementing the Lanczos method for diagonalization of…
Using a new approximate analytic parameter-free proxy-SU(3) scheme, we make predictions of shape observables for actinides and superheavy elements, namely beta and gamma deformation variables, and compare these with predictions by…
Applications of rotational $SU(3)$ symmetry in nuclei, using Elliott's $SU(3)$ or pseudo-$SU(3)$ or proxy-$SU(3)$ model, often need just the lowest or leading $SU(3)$ irreducible representation (irrep) $(\lambda_H, \mu_H)$. For nucleons in…
The concept of non-abelian horizontal symmetry $SU(3)_H$ can greatly help in understanding the fermion and sfermion flavour structures in supersymmetric grand unification. For the sake of demonstration the $SU(5)\times SU(3)_H$ model,…
Results of shell-model calculations for lower fp-shell nuclei show that SU(3) symmetry breaking in this region is driven by the single-particle spin-orbit splitting. However, even though states of the yrast band exhibit SU(3) symmetry…
Supersymmetry (SUSY) is a symmetry transforming bosons to fermions and vice versa. Indications of its existence have been extensively sought after in high-energy experiments. However, signatures of SUSY have yet to be detected. In this…