Symmetry Limit Research Articles

Dynamical Symmetry and B(E2) Transitions of (_42^94)Mo by Utilizing (IBM-1)

Background:In this study, we utilize the IBM-1 model to theoretically investigate the structural characteristics of , with a specific emphasis on a nucleus consisting of 5 bosons. Employing the IBM-1, an innovative interacting boson model, we analyze the nuclear structure. Materials and Methods: In our theoretical exploration, we delved into the nuclear architecture of Molybdenum. Employing the Interacting Boson Model (IBM-1), we identified the pertinent Hamiltonian to scrutinize the isotope in this research endeavor. Results: Our investigation delved into the symmetry limit of the proposed nucleus, unveiling its stable nature within the SU(5) dynamical symmetry domain. To optimize alignment with observed energy states in experiments, we meticulously determined the parameters in the IBM-1 Hamiltonian equation. Furthermore, our research extends to the computation of B(E2) transitions, quadrupole moments, and energy levels across all bands for the examined nucleus. Conclusions: Our investigation reveals the stability of the nucleus in the isotope, showcasing the presence of SU(5) dynamical symmetry. These findings offer fresh perspectives by suggesting additional electric quadrupole moments.

Extremal functions for a fractional Morrey inequality: Symmetry properties and limit at infinity

In a series of articles, Hynd and Seuffert have studied extremal functions for the Morrey inequality. Building upon their work, we study the extremals of a Morrey-type inequality for fractional Sobolev spaces. We verify a few of the results in the spirit of Hynd and Seuffert concerning the symmetry of extremals and their limit at infinity.

Origin of regularity in different nuclei from the viewpoint of the effective quadrupole deformation and triaxiality

This paper presents a theoretical investigation of the possible relation between the regularity of nuclei and the quadrupole deformation of different levels (and also triaxiality). The present paper aims to uncover the underlying physical reasons for this regularity. To this aim, we calculated the effective quadrupole deformation of different levels using the interacting boson model. Also, different ratios between the quadrupole deformations of the energy levels in the ground, beta, and gamma bands are defined. The results for the energy levels confirm the correctness of labeling these states by the quantum numbers of U(5) and SU(3) dynamical symmetry limits (and also the extraction processes). Also, we observed a repetition pattern for these ratios for regular nuclei. Of course, the regularity and sameness of repetition patterns for the levels of the rotational bands are more than the levels of the ground band. For further study, we analyzed the effective quadrupole deformation values of different levels of regular nuclei using random matrix theory. The results show a strong statistical correlation for these quantities and confirm the observed repetition pattern. Also, the results of our studies showed that regular nuclei have triaxial properties.

Dynamical symmetry of (_42^102)Mo by utilizing (IBM-1)

The structure of ( ) was explored theoretically with IBM-1 in this work. The symmetry limit of the proposed nucleus was investigated. The considered nucleus was discovered to be deformed with O(6) dynamical symmetry area with gamma-ray softened nucleus. In addition, the B(E2) transition, quadrupole moment, and energy levels for all bands would be computed in this study. According to recent research, ( ) is unstable to gamma, and their transition behaviors are generally similar to symmetric (γ -soft) O(6) limits. When the current findings are compared to the experimental results, they show a high level of agreement.

Form factors of B(s) to light scalar mesons with the B -meson light-cone sum rules

In this work, the transition form factors of the semileptonic decays of B(s) to the light scalar mesons with masses close to 1.5 GeV such as K0*(1430),a0(1450), and f0(1500) are calculated in the framework of the light-cone sum rules. For this purpose, the two- and three-particle B-meson distribution amplitudes (DAs) are used. Note that it is possible to use the B-meson DAs for the Bs meson in the SU(3)F symmetry limit. The transition form factors are obtained in terms of the two-particle DAs up to twist-five accuracy, and the three-particle up to twist-six level. We apply two classes of the phenomenological models for the DAs of the B meson. The longitudinal lepton polarization asymmetries and branching fractions for the semileptonic decays of B(s) to the light scalar mesons are estimated with the help of these form factors. Published by the American Physical Society 2024

Description of intruder levels in the 162,164,166Dy nuclei by two different algebraic approaches

In this paper, we tried to describe both normal and intruder levels of the ground and first excited beta and gamma rotational bands of 162,164,166Dy deformed nuclei in the framework of the interacting boson model. A normal Hamiltonian of SU(3) dynamical symmetry limit is extended by adding a 2p-2 h excitation term. Also, the results are compared with the predictions of the partial dynamical symmetry for these levels of considered nuclei. The results show that, this extension removes the degeneracy suggested by the pure SU(3) symmetry and makes satisfactory agreement with the experimental counterparts for the energy levels, too. Also, a comparison between the results of this extended formalism and partial dynamical symmetry shows the advantages of the first one in the description of intruder levels, whereas the latter, makes exact results for the normal energy levels of beta and gamma energy bands. The predictions of pure SU(3), partial dynamical symmetry SU(3) and mixed formalism for different quadrupole transition rates between normal and intruder levels of this nucleus are compared with the predictions of pseudo-SU(3) model and the advantages of each model have explained in detail.

Relativistic energies and information entropy of the inversely quadratic Hellmann potential

The solutions to the Dirac equation are obtained in the spin and pseudospin symmetry limits are presented using the parametric Nikiforov-Uvarov (pNU) method with the inversely quadratic Hellman (IQH) potential. In the exact non-relativistic spin symmetry limit, the energy and wave function of the IQH potential are obtained and used to investigate the Shannon information entropy of the system. Numerical results of the relativistic energies of the spin and pseudospin symmetry limits of the Dirac equation with the IQH potential are presented and observed to exhibit degeneracy. Also, the results of the Shannon entropy for six states (n = 0, 1, 2, 3, 4, 5) show that the momentum space wave function and probability density are better localized than the position space wave function. Also, the Bialynicki-Birula and Mycielski (BBM) inequality is verified for the system. Our results are found to be consistent with those previously reported in the literature.

Spectroscopic quadrupole moments in Xe124

Background: The Xe isotopic chain with four valence protons above the Z=50 shell closure is an ideal laboratory for the study of the evolution of nuclear deformation. At the N=82 shell closure, Xe136 presents all characteristics of a doubly closed shell nucleus with a spherical shape. In the very neutron-deficient isotopes close to N=50, the α-decay chain of Xe was investigated to probe the radioactive decay properties near the drip-line and the magicity of Sn100. Additionally, the Xe isotopes present higher order symmetries in the nuclear deformation such as the octupole degree of freedom near N=60 and N=90 or O(6) symmetry in stable isotopes. Purpose: The relevance of the O(6) symmetry has been investigated by measuring the spectroscopic quadrupole moment of the first excited states in Xe124. In the O(6) symmetry limit, the spectroscopic quadrupole moment of collective states is expected to be null. Method: A stable Xe124 beam with energies of 4.03A MeV and 4.11A MeV was used to bombard a natW target at the GANIL facility. Excited states were populated via the safe Coulomb excitation reaction. The collision of the heavy ions with a large Z at low energy make this reaction sensitive to the diagonal E2 matrix element of the excited states. The recoils were detected in the VAMOS++ magnetic spectrometer and the γ rays in the AGATA tracking array. The least squares fitting code gosia was used for the analysis to extract both E2 and M1 transitional and E2 diagonal matrix elements. Results: The rotational ground state band was populated up to the 81+ state as well as the 22+ and 42+ states. Using high precision spectroscopic data to constrain the gosia fit, the spectroscopic quadrupole moments of the 21+, 41+, and 61+ states were determined for the first time. Conclusions: The spectroscopic quadrupole moments were found to be negative, large, and constant in the ground state band underlining the prolate axially deformed ground state band of Xe124. The present experimental data confirm that the O(6) symmetry is substantially broken in Xe124.1 MoreReceived 21 October 2022Accepted 23 January 2023DOI:https://doi.org/10.1103/PhysRevC.107.014324©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsElectromagnetic transitionsSpectroscopic factors & electromagnetic momentsProperties90 ≤ A ≤ 149Nuclear Physics

{U}_{mathfrak{q}}{mathfrak{sl}}_2 -invariant non-compact boundary conditions for the XXZ spin chain

We introduce new {U}_{mathfrak{q}}{mathfrak{sl}}_2 -invariant boundary conditions for the open XXZ spin chain. For generic values of mathfrak{q} we couple the bulk Hamiltonian to an infinite-dimensional Verma module on one or both boundaries of the spin chain, and for mathfrak{q}={e}^{frac{ipi}{p}} a 2p-th root of unity — to its p-dimensional analogue. Both cases are parametrised by a continuous “spin” α ∈ ℂ.To motivate our construction, we first specialise to mathfrak{q} = i, where we obtain a modified XX Hamiltonian with unrolled quantum group symmetry, whose spectrum and scaling limit is computed explicitly using free fermions. In the continuum, this model is identified with the (η, ξ) ghost CFT on the upper-half plane with a continuum of conformally invariant boundary conditions on the real axis. The different sectors of the Hamiltonian are identified with irreducible Virasoro representations.Going back to generic q we investigate the algebraic properties of the underlying lattice algebras. We show that if mathfrak{q} α ∉± mathfrak{q} ℤ, the new boundary coupling provides a faithful representation of the blob algebra which is Schur-Weyl dual to {U}_{mathfrak{q}}{mathfrak{sl}}_2 . Then, modifying the boundary conditions on both the left and the right, we obtain a representation of the universal two-boundary Temperley-Lieb algebra. The generators and parameters of these representations are computed explicitly in terms of mathfrak{q} and α. Finally, we conjecture the general form of the Schur-Weyl duality in this case.This paper is the first in a series where we will study, at all values of the parameters, the spectrum and its continuum limit, the representation content of the relevant lattice algebras and the fusion properties of these new spin chains.

Study some of the nuclear characters of Samarium 148,150,152,154Sm isotopes in the IBM-1 framework

The interacting boson model IBM-1 has been applied to some 62Sm even-even isotopes .This study has included calculation of the positive-parity collectiv g-band and β,γ –degenerate bands of 148 62Sm, 150 62Sm, 152 62Sm and 154 62Sm isotopes and compared with experimental values of energy level. The used Hamiltonian parameters correspond to description close to the U(5)-SU(3). The potential energy surfaces E(β,γ) as function of geometrical parameter β and γ for these isotopes can be obtained where they were represented by contour lines and the minimum value of deformation factor βmin was fixed , which was in front of Emin, and so the γ factor. The transition from the spherical to the rotational shape can be observed in these isotopes. In the framework of IBM-1 , what we conclude from the energy spectra study and the geometrical picture of potential energy surface for these nuclei is that these nuclei are spherical shape (U(5)symmetry), prolate rotational shape (SU(3)symmetry) and deformed shape between these two symmetry limits in the U(5)-SU(3)transitional region .

Deformation in 92−128Pd isotopes

The purpose of the study further explores the quadrupole transition rates and effective deformation within the framework of a simple interacting boson model to the Pd isotopic chain. We used the spherical U(5) and deformed O(6) dynamical symmetry limits. Results indicate a significant relationship between the effective quadrupole deformation values and effective boson charge. Results suggest that 106Pd is a good candidate for the E(5) critical point of the U(5)-O(6) shape phase transitional region and also has the largest variation of the quadrupole shape constants. A close relationship between the ground- and excited-state quantum phase transitions is found, as evidenced by the ratios of different energy levels.

Semileptonic Bs→K0*(1430) transitions with the light-cone sum rules

In the $\rm SU(3)_F$ symmetry limit, using two- and three-particle distribution amplitudes of $B^{\pm}$-meson for $B_s$, the transition form factors of semileptonic $B_{s}\to K_{0}^*(1430)$ decays are calculated in the framework of the light-cone sum rules. The two-particle distribution amplitudes, $\varphi_{_{+}}(\omega)$ and $\varphi_{_{-}}(\omega)$ have the most important contribution in estimation of the form factors $f_{+}(q^2)$, $f_{-}(q^2)$ and $f_{T}(q^2)$. The knowledge of the behavior of $\varphi_{_+}(\omega)$ is still rather limited. Therefore, we consider three different parametrizations for the shapes of $\varphi_{_+}(\omega)$ that are derived from the phenomenological models. Using the form factors $f_{+}$, $f_{-}$ and $f_{T}$, the semileptonic $B_s \to K_0^*(1430) l \bar{\nu_{l}}$ and $B_s \to K_0^*(1430) l \bar{l}/\nu \bar{\nu}$, $l=e, \mu, \tau$ decays are analyzed. The branching fractions for the aforementioned decays, in addition the longitudinal lepton polarization asymmetries are calculated. A comparison between our results with predictions of other approaches is provided.

Solutions of the Dirac equation with position-dependent mass for q-deformed Pöschl–Teller and Coulomb-like tensor potentials

We consider the Dirac equation with position-dependent mass for a q-deformed Pöschl–Teller potential plus a Coulomb-like tensor interaction in the limits of spin and pseudospin symmetries. Under the condition of spin symmetry, the bound state energy eigenvalue equation and the two radial components of the Dirac wave function in terms of the Jacobi polynomials are obtained approximately for an arbitrary shifted spin-orbit quantum number λκ = κ + H and for any value of the deformation parameter q ≥ 1. In the case of the pseudospin symmetry limit, there are no bound states. The Dirac equation describes a free physical system and the two components of the wave function are expressed in terms of the spherical Bessel functions.

A theoretical study on the effective quadrupole deformations of 100−128Cd isotopic chain

In this paper, we have applied a simple interacting boson model (IBM) to Cadmium (Cd) isotopic chain to obtain the quadrupole transition rates and effective deformation. To this aim, we use the U(5) and O(6) dynamical symmetry limits of this model to classify the considered states. Also, the energy spectra of some levels are determined which their experimental counterparts are available. The results describe the regular states with high accuracy but suggest notable deviation in the prediction of intruder energy levels. Also, our results show the advantages of this formalism in the description of quadrupole transition rates and indicate a significant relationship between the values of effective quadrupole deformations and effective boson charge. Also, for the [Formula: see text]Cd, [Formula: see text]Cd and [Formula: see text]Cd isotopes, we have the largest variation of the quadrupole shape constants which are located in the region of shape coexistence. The study of the ratios of different energy levels indicates that there is a close relationship between ground and excited-state quantum phase transitions (ESQPTs).

S K-edge XAS of CuII, CuI, and ZnII oxidized Dithiolene complexes: Covalent contributions to structure and the Jahn-Teller effect

Reduced dithiolene ligands are bound to high valent Mo centers in the active site of the oxotransferase family of enzymes. Related model complexes have been studied with great insight by Prof. Holm and his colleagues. This study focuses on the other limit of dithiolene chemistry: an investigation of the 2-electron oxidized dithiolene bound to low-valent late transition metal (TM) ions (ZnII, CuI, and CuII). The bonding descriptions of the oxidized dithiolene [N,N-dimethyl piperazine 2,3-dithione (Me2Dt0)] complexes are probed using S K-edge X-ray absorption spectroscopy (XAS) and the results are correlated to density functional theory (DFT) calculations. These experimentally supported calculations are then extended to explain the different geometric structures of the three complexes. The ZnII(Me2Dt0)2 complex has only ligand-ligand repulsion so it is stabilized at the D2d symmetry limit. The CuI(Me2Dt0)2 complex has additional weak backbonding thus distorts somewhat from D2d toward D2h symmetry. The CuII(Me2Dt0)2 complex has a strong σ donor bond that leads to both a large Jahn-Teller stabilization to D2h and an additional covalent contribution to the geometry. The combined strong stabilization results in the square planar, D2h structure. This study quantifies the competition between the ligand-ligand repulsion and the change in electronic structures in determining the final geometric structures of the oxidized dithiolene complexes, and provides quantitative insights into the Jahn-Teller stabilization energy and its origin.

Relativistic Solutions of Dirac Equation with the Molecular Hua Potential in the Spin Symmetry Limit

The study presents solutions of Dirac equation with the Molecular Hua potential energy model using the Formula method. In the non-relativistic limit, the relativistic energy equation becomes the non-relativistic rotation-vibrational energy expression. Numerical results for some molecules are also presented. Interestingly, our results agree with those in literature.

Zr isotopes as a region of intertwined quantum phase transitions

The zirconium isotopes with $A=92--110$ have one of the most complicated evolution of structure in the nuclear chart. In order to understand the structural evolution of these isotopes, we carry a detailed calculation in a definite symmetry-based framework, the interacting boson model with configuration mixing (IBM-CM). We compare our calculation to a large range of experimental data, such as energy levels, two-neutron separation energies, $E2$ and $E0$ transition rates, isotope shifts, and magnetic moments. The structural evolution of the low lying spectra of these isotopes is explained using the notion of intertwined quantum phase transitions (IQPTs), for which a QPT involving a crossing of two configurations (Type II) is accompanied by a QPT involving a shape evolution of each configuration separately (Type I). In our study, we find the occurrence of Type I QPT within the intruder configuration, changing from weakly deformed to prolate deformed and finally to $\ensuremath{\gamma}$-unstable, associated with the U(5), SU(3) and SO(6) dynamical symmetry limits of the IBM, respectively. Alongside the Type I QPT, we also find the occurrence of Type II QPT between the normal and intruder configurations, where both Types I and II have a critical point near $A\ensuremath{\approx}100$. The good agreement of our calculation with the vast empirical data along the chain of isotopes demonstrates the relevance of IQPTs to the zirconium isotopes, and can serve as a case study to set path for new investigations of IQPTs in other nuclei and other physical systems.

Exploring multi-Higgs models with softly broken large discrete symmetry groups

We develop methods to study the scalar sector of multi-Higgs models with large discrete symmetry groups that are softly broken. While in the exact symmetry limit, the model has very few parameters and can be studied analytically, proliferation of quadratic couplings in the most general softly broken case makes the analysis cumbersome. We identify two sets of soft breaking terms which play different roles: those which preserve the symmetric vacuum expectation value alignment, and the remaining terms which shift it. Focusing on alignment preserving terms, we check which structural features of the symmetric parent model are conserved and which are modified. We find remarkable examples of structural features which are inherited from the parent symmetric model and which persist even when no exact symmetry is left. The general procedure is illustrated with the example of the three-Higgs-doublet model with the softly broken symmetry group Sigma (36).

Dirac equation and thermodynamic properties with the Modified Kratzer potential

In this work, we present the analytical solutions of Dirac equation for modified Kratzer potential in the pseudospin and spin symmetry limits using the formula method. The energies of the pseudospin and spin symmetry limit are obtained analytically and numerically. The numerical values are compared with those obtained in literature. Furthermore, we study the thermodynamic properties of some diatomic molecules within the nonrelativistic spin symmetry limits.

Properties of giant dipole resonances within an extended pairing model with a focus on spectral statistics

In this paper, we report on a study of the spectral features associated with dipole resonances in medium-mass nuclei $(E\ensuremath{\le}12 \mathrm{MeV})$, as revealed in the framework of the spd-interacting boson model. The effect of pairing correlations on the theory follows from solutions obtained through an application of the Bethe ansatz equation. In general, calculated spectra around the critical point of the vibrational to $\ensuremath{\gamma}$-soft transitions appear to approach those of a Gaussian orthogonal ensemble, while near the rotational and vibrational limits of the theory the spectra show more regular behavior. Specifically, the results reveal that the statistical features of the spectra are sensitive to the vector boson pairing strength ${c}_{p}$ in the transition region; that is, when ${c}_{p}$ is zero, or when the system approaches one of its dynamical symmetry limits, the spectra display regular features, while for stronger ${c}_{p}$ values, or when near to the critical phase transition region, the spectral features show more chaotic behavior. Overall, our results indicate that the statistical features are governed by the interplay between dipole resonant energies, pairing correlations, and interactions between and among the single and vector boson modes of the theory. As part of this work we also found out that chaoticity occurred when results were fit to a Berry-Robnik distribution. Throughout our analyses, we used experimentally known information about both positive- and negative-parity states. Our findings suggest that dipole resonances appear to be best-described by Poisson statistics for $A\ensuremath{\approx}32--138$ nuclei.