Reduced Transition Probabilities Research Articles

The shape of the Tz = +1 nucleus 94Pd and the role of proton-neutron interactions on the structure of its excited states

Reduced transition probabilities have been extracted between excited, yrast states in the N=Z+2 nucleus 94Pd. The transitions of interest were observed following decays of the Iπ=14+, Ex=2129-keV isomeric state, which was populated following the projectile fragmentation of a 124Xe primary beam at the GSI Helmholtzzentrum für Schwerionenforschung accelerator facility as part of FAIR Phase-0. Experimental information regarding the reduced E2 transition strengths for the decays of the yrast 8+ and 6+ states was determined following isomer-delayed Eγ1−Eγ2−△T2,1 coincidence method, using the LaBr3(Ce)-based FATIMA fast-timing coincidence gamma-ray array, which allowed direct determination of lifetimes of states in 94Pd using the Generalized Centroid Difference (GCD) method. The experimental value for the half-life of the yrast 8+ state of 755(106) ps results in a reduced transition probability of B(E2:8→+6+) = 205−25+34 e2fm4, which enables a precise verification of shell-model calculations for this unique system, lying directly between the N=Z line and the N=50 neutron shell closure. The determined B(E2) value provides an insight into the purity of (g9/2)n configurations in competition with admixtures from excitations between the (lower) N=3pf and (higher) N=4gds orbitals for the first time. The results indicate weak collectivity expected for near-zero quadrupole deformation and an increasing importance of the T=0 proton-neutron interaction at N=48.

Electromagnetic transition rates in the nucleus 136 58Ce

The half-life of the first 6+ state in 136Ce has been measured as T 1/2 = 41(12) ps using the γ-ray fast-timing technique with the ν-ball spectrometer at the ALTO Tandem Accelerator, Orsay, France. The states of interest in 136Ce have been populated via the 128Te(12C,4nγ) fusion-evaporation reaction. A comparison is made between the value obtained for the reduced transition probability B(E2;61+→41+) = 0.55(21) W.u. and the systematics of the region. In this work, half-lives for the 51− , 71− and 62+ states in 136Ce were also determined.

Systematic study of magnetic and antimagnetic rotational bands

The magnetic and antimagnetic rotational bands are systematically investigated in the present work. Up to now, 253 magnetic rotational bands and 40 antimagnetic rotational bands have been reported in 123 nuclei and 29 nuclei, respectively. The experimental data for these bands are collected and collated, including the level energy, γ-ray energies, spin I, magnetic dipole reduced transition probability B(M1), electric quadrupole reduced transition probability B(E2), B(M1)/B(E2), and J (2)/B(E2), etc. In addition, following the presentation of the kinematic moment-of-inertia J (1), dynamic moment-of-inertia J (2), and I versus rotational frequency ω, as well as energy staggering parameter S(I), B(M1), B(E2), B(M1)/B(E2), and J (2)/B(E2) versus I in A ∼ 60, 80, 110, 140, and 190 mass regions, a discussion is provided in detail. Based on the systematic studies, the main features of magnetic and antimagnetic rotational bands are summarized. Furthermore, some nuclei are also predicted to be candidates for magnetic or antimagnetic rotation.

Triaxiality dynamics in quadrupole deformed heavy even–even nuclei

In the framework of free triaxiality model, branching ratio of reduced E2-transitions probabilities is studied for the full region changes of the triaxiality parameter. The variables of quadrupole deformations [Formula: see text] and [Formula: see text] are dynamic. The Davidson potential for [Formula: see text] and [Formula: see text] variables was used. In the free triaxiality model, the energy levels were obtained by taking into account the high-order terms of the rotational energy operator series, which lead energy levels of ground-state-band, [Formula: see text]- and [Formula: see text]-bands to improve considerably the agreement of the results with experimental data. The quadrupole moment of the nucleus expressed in terms of two internal quadrupole moments: [Formula: see text] is quadrupole moment about the symmetry axis, [Formula: see text] is the measure of the shape asymmetry about the symmetry axis. The intra/inter-band reduced E2-transition probabilities’ ground-state-band, [Formula: see text]- and [Formula: see text]-bands are presented and are expressed in terms of four parameters: [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. The influence of [Formula: see text]-oscillations to the reduced probabilities of E2-transitions is taken into account numerically. The sensitivity of the intra-/inter-band reduced E2-transition probabilities to the triaxiality parameter was analyzed.

THE STUDY OF ELECTRIC QUADRUPOLE TRANSITION (E2) IN 58Ce AND 60Nd NUCLEI

Transition strengths 2w.u. M(E2) for gamma transition from first excited 21+statesto the ground states that produced by pure electric quadrupole emission in even –even nuclei of 58Ce and 60Nd have been calculated as a function of neutron number(N). The life times for 21+ excited states together with the intensities of γ0- transitionsmeasurements are used in calculations. The results thus obtained have shown that;the nuclei with magic neutron number such as 58Ce140 and 60Nd142 have minimumvalue for 2w.u. M(E2) . The reduced transition probabilities B(E2) are alsocalculated and compared with the experimental data and other theoretical models.PACS:- 27.60-j, 23.20-g, 23.20.Ck, 23.20.Gq

PROBING THE NUCLEAR STRUCTURE OF EXOTIC 33Mg ISOTOPE

Research on the nuclear structure of exotic isotopes, such as 33Mg, is an exciting and cuttingedge field of nuclear physics. Exotic isotopes are typically those that are far from the stable region of the nuclear chart and often exhibit unique properties that can help us better understand the fundamental forces and structure of atomic nuclei. In this paper the largescale shell model calculations are performed within the model spaces SDPFMU, to study the positive- and negative-parity energy levels and electromagnetic transitions in the exotic 33Mg isotope. Core-polarization effects on reduced transition probability are introduced through first order perturbation theory, which allows for higher energy configurations through excitations of nucleons from core orbits to that outside model space up to . The corepolarization effects have been improved the agreement of B(E2) with their corresponding experimental data, and have ignorable effect on B(M1)

Transitional character of Nd-Dy (N=90) isotones in IBM model

The Interacting Boson Model is used to study the level structure of ground state, beta, and gamma bands in150Nd, 152Sm, 154Gd and 156Dy (N = 90) isotones. The energy ratios R_((I+2)⁄2) and R_(0_2⁄2_1 ) are compared to the predictions of U(5), SU(3), and X(5) symmetry. The calculated reduced transition probabilities as well as quadrupoles moments were compared to experimental data. IBM-1 investigates the properties of the potential energy surface to determine the nuclear shape of the Nd-Dy (N=90) isotones.

High-Precision Spectroscopy of ^{20}O Benchmarking AbInitio Calculations in Light Nuclei.

The excited states of unstable ^{20}O were investigated via γ-ray spectroscopy following the ^{19}O(d,p)^{20}O reaction at 8 AMeV. By exploiting the Doppler shift attenuation method, the lifetimes of the 2_{2}^{+} and 3_{1}^{+} states were firmly established. From the γ-ray branching and E2/M1 mixing ratios for transitions deexciting the 2_{2}^{+} and 3_{1}^{+} states, the B(E2) and B(M1) were determined. Various chiral effective field theory Hamiltonians, describing the nuclear properties beyond ground states, along with a standard USDB interaction, were compared with the experimentally obtained data. Such a comparison for a large set of γ-ray transition probabilities with the valence space in medium similarity renormalization group abinitio calculations was performed for the first time in a nucleus far from stability. It was shown that the abinitio approaches using chiral effective field theory forces are challenged by detailed high-precision spectroscopic properties of nuclei. The reduced transition probabilities were found to be a very constraining test of the performance of the abinitio models.

Electric reduced transition probabilities of \(^{186}\text{W}\) and \(^{186}\text{Os}\) isobars through the interacting boson model-I

In this study, we applied the Interacting Boson Model (IBM-I) to compute the electric reduced transition probabilities B(E2)\(\downarrow\) of even-even neutron rich \(^{186}\text{W}\) and \(^{186}\text{Os}\) isobars. The ratio \(R_{4/2} = E(4_{1}^{+}) / E(2_{1}^{+})\) has also been calculated for those isobars and the SU(3) symmetry for those isobars has been reported. \(E(4_{1}^{+})\) and \(E(2_{1}^{+})\) indicate the energy level of \(4_{1}^{+}\) and \(2_{1}^{+}\), respectively. We have described the strength of B(E2) in W.u. for \(^{186}\text{W}\) and \(^{186}\text{Os}\) isobars of some of the low-lying quadrupole collective states in contrast to obtainable measured data. The electric reduced transition probabilities B(E2)\(\downarrow\) from yrast state gamma transition from \(12_1^{+} \rightarrow 10_1^{+}\), \(10_1^{+} \rightarrow 8_1^{+}\), \(8_1^{+} \rightarrow 6_1^{+}\), \(6_1^{+} \rightarrow 4_1^{+}\), \(4_1^{+} \rightarrow 2_1^{+}\) and \(2_1^{+} \rightarrow 0_1^{+}\) and other bands states and B(E2) ratio of \(^{186}\text{W}\) and \(^{186}\text{Os}\) isobars have been compared with obtainable measured data and other previous studies. Also calculated were the systematic strength of B(E2), intrinsic quadrupole moments, and deformation parameters of even-even \(^{186}\text{W}\) and \(^{186}\text{Os}\) isobars. The data from these calculations are in good matching with the obtainable measured data. The IBM-I model for the strength of B(E2) has been systematically deduced in SU(3) limit for a few yrasts states transitions in \(^{186}\text{W}\) and \(^{186}\text{Os}\) isobars.

Proton inelastic scattering on 68,70,72Ni

The proton inelastic scattering on 68,70,72Ni isotopes was measured at the NSCL at MSU, employing the S800 spectrometer coupled to the GRETINA γ-ray array. The aim of the experiment was to determine the degree of collectivity in these neutron-rich Z = 28 isotopes. The use of a hadronic probe allows to complement previous Coulomb excitation measurements of the reduced transition probability B(E2; 0+ → 2+) and deduce the neutron-to-proton transition matrix elements ratio. The high resolution in γ-ray energy achievable with GRETINA gives large control on feeding transitions, thus reducing possible systematics errors in the determination of transition strengths.

An alternative viewpoint on the nuclear structure towards 100Sn: Lifetime measurements in 105Sn

This work aims at presenting an alternative approach to the long standing problem of the B(E2) values in Sn isotopes in the vicinity of the N=Z double-magic nucleus 100Sn, until now predominantly measured with relativistic and intermediate-energy Coulomb excitation reactions. The direct measurement of the lifetime of low-lying excited states in odd-even Sn isotopes provides a new and precise guidance for the theoretical description of the nuclear structure in this region. Lifetime measurements have been performed in 105Sn for the first time with the coincidence Recoil Distance Doppler Shift technique. The lifetime results for the 7/21+ first excited state and the 11/21+ state, 2+(104Sn) ⊗ν1g7/2 multiplet member, are discussed in comparison with state-of-the-art shell model and mean field calculations, highlighting the crucial contribution of proton excitation across the core of 100Sn. The reduced transition probability B(E2) of the 11/21+ core-coupled state points out an enhanced staggering with respect to the B(E2; 21+→01+) in the even-mass 104Sn and 106Sn isotopes.

Altered Brain Dynamics and Their Ability for Major Depression Detection Using EEG Microstates Analysis

Major depressive disorder (MDD) may be driven by dysfunction in intrinsic dynamic properties of the brain, and EEG microstate is a promising method for analyzing brain dynamics. However, the alterations in EEG microstate is still not entirely clear, and its ability for MDDs detection is worth probing. Moreover, the mechanism behind the neural networks contributing to microstates remains poorly understood in MDDs. Therefore, we applied microstate analysis and Topographic Electrophysiological State Source-imaging (TESS) on EEG data of 27 MDDs and 28 healthy controls (HCs). Compared to HCs, MDDs had apparent increase in microstate C and decrease in microstate D. Furthermore, TESS results showed that the underlying network of microstate C in MDDs overlapped with the anterior cingulate cortex and left insula gyrus, whereas main source of microstate D was in the orbital part of inferior frontal gyrus. The reduced transition probability from C to D in MDDs may reveal an imbalance between the networks of microstates. The microstate parameters as features reached good performance in identifying MDD (89.09% accuracy, 92.86% sensitivity, 85.19% specificity), indicating their potential as biomarkers of depression pathology. Collectively, these results highlight alteration of brain activity patterns and provide new insights into abnormal EEG dynamics in MDDs.

Calculations of The Shell Model for 27Mg Isotope

Using shell-model calculations, the nuclear structure (energy levels and reduced transition probability) of 27Mg isotope has been studied. Shell-model codes, Oxbash for Windows operating system, were utilized to calculate the outcomes. Using a harmonic oscillator, the wave functions of radial single-particle matrix elements have been calculated. The calculated energy levels and available experimental data up to 5 MeV for 27Mg are compared. Core-polarization effects on reduced transition probability are introduced via first-order perturbation theory, which permits higher energy configurations via nucleon excitations from core orbits to those outside model space up to 9ℏω. The core-polarization effects have improved the agreement between B(E2) and their corresponding experimental data, but have no effect on B(M1), B(M2), and B(E1).

Electroexcitation Form Factors and Deformation of 20,22Ne Isotopes Based on the Shell Model and Hartree-Fock plus BCS Calculations

Nuclear structure of 20,22Ne isotopes has been studied via the shell model with Skyrme-Hartree-Fock calculations. In particular, the transitions to the low-lying positive and negative parity excited states have been investigated within three shell model spaces; sd for positive parity states, spsdpf large-basis (no-core), and zbme model spaces for negative parity states. Excitation energies, reduced transition probabilities, and elastic and inelastic form factors were estimated and compared to the available experimental data. Skyrme interaction was used to generate a one-body potential in the Hartree-Fock calculations for each selected excited states, which is then used to calculate the single-particle matrix elements. Skyrme interaction was used to calculate the radial wave functions of the single-particle matrix elements, from which a one-body potential in Hartree-Fock theory with SLy4 parametrization can be generated. Furthermore, we have explored the interplays among neutron and proton density profiles in two dimensions, along with the deformations of 20,22Ne using Hartree-Fock plus BCS calculations.

Hamiltonian sensitivity in calculating the electromagnetic moments and electroexcitation form factor for the sd nuclei using shell model with Skyrme–Hartree–Fock

In this work, the nuclear electromagnetic moments for the ground and low-lying excited states for sd shell nuclei have been calculated, resulting in a revised database with 56 magnetic dipole moments and 41 electric quadrupole moments. The shell model calculations are performed for each sd isotope chain, considering the sensitivity of changing the sd two-body effective interactions USDA, USDE, CWH and HBMUSD in the calculation of the one-body transition density matrix elements. The calculations incorporate the single-particle wave functions of the Skyrme interaction to generate a one-body potential in Hartree–Fock theory to calculate the single-particle matrix elements. For most sd shell nuclei, the experimental data are well reproduced, except for those spans near the island of inversion. In order to interpret the structure of low-lying excited states, the electric quadrupole and magnetic dipole transition form factors and the corresponding reduced transition probabilities in the sd shell nuclei have also been calculated, for which the experimental data are available. The present results demonstrate the nuclear electromagnetic moments’ sensitivity to many forms of the understanding of nucleon–nucleon interactions and provide a crucial baseline for future improvements in conceptual calculations.

Core-proton coupled nature of the 11/2+ state in 131 Sb probed by lifetime measurements

The structure of the state in 131Sb was investigated at the LOHENGRIN spectrometer of Institut Laue-Langevin via neutron-induced fission of 235U and lifetime measurements, yielding , at the edge of the sensitivity of the experimental method. This first result for the state half-life in neutron-rich Sb isotopes provides a quadrupole reduced transition probability to the ground state of W.u., very close to the in 130Sn. Realistic shell-model calculations reproduce well both the experimental level scheme of 131Sb and the value, indicting a dominant core-proton coupled configuration for the state.

Nuclear structure aspects of the heaviest N∼Z nuclei south of 100Sn

Ever-lasting interest in the structure of 100Sn and neighbouring nuclei is still well justified by the fact that it is the heaviest doubly-magic nucleus with N=Z. State-of-the-art experimental techniques involving stable and radioactive beam facilities have enabled access to these exotic nuclei. In particular, the analysis of experimental data obtained in two DESPEC experiments at GSI Darmstadt extends the information on the shell structure and its evolution towards N = Z = 50, and allows the study of seniority conservation and proton-neutron interaction in the g9/2 orbit. Several theoretical approaches for shell-model investigations are discussed and their predictive power assessed. The calculated systematics of the reduced transition probabilities for high- to medium-spin states in N∼Z isotopes with active g9/2 orbit is presented for the first time.

Testing the predictive power of realistic shell model calculations via lifetime measurement of the 11/2+ state in Sb131

The lifetime of the $11/{2}_{1}^{+}$ state in the $^{131}\mathrm{Sb}$ nucleus was measured at the LOHENGRIN spectrometer of the Institut Laue-Langevin via neutron-induced fission of $^{235}\mathrm{U}$ using $\ensuremath{\gamma}$-ray fast-timing techniques. The obtained value of ${T}_{1/2}=3\phantom{\rule{0.16em}{0ex}}$(2) ps, at the edge of the sensitivity of the experimental method, is the first result for the $11/{2}_{1}^{+}$ state half-life in neutron-rich Sb isotopes. The corresponding quadrupole reduced transition probability to the ground state is $B(E2)=1.{4}_{\ensuremath{-}0.6}^{+1.5}$W.u., indicating a noncollective nature of this state. Realistic shell-model calculations performed in a large valence space reproduce well the experimental value and point to a dominant ${2}^{+}(^{130}\mathrm{Sn})\ensuremath{\bigotimes}\ensuremath{\pi}{\mathrm{g}}_{7/2}$ configuration for the $11/{2}_{1}^{+}$ state, as expected in a weak-coupling scenario. At the same time, the sum of the quadrupole strength of the multiplet states is predicted to exceed the one of the $^{130}\mathrm{Sn}$ core as a consequence of the equal contribution of the proton and the proton-neutron quadrupole matrix elements, pointing to possible development of collectivity already in the close neighborhood of $^{132}\mathrm{Sn}$.

The Particle-Rotor-Quadrupole-Coupling Model for Transitional Odd-A Nuclei

The particle-rotor-quadrupole-coupling model, in which the quadrupole–quadrupole interaction of the even-even core is described by a triaxial rotor with a single-j particle, is adopted to describe low-lying spectra of odd-A nuclei within the vibrational to triaxial transition region. In contrast to the particle-plus-rotor-model, the quadrupole–quadrupole interaction introduced in the particle-rotor-quadrupole-coupling model keeps the rotational symmetry in the collective model framework without approximation. To demonstrate the usability, low-lying level energies, reduced E2 transition probabilities, and ground-state quadrupole moments of 135Ba and 131Xe are fit by the model, of which the results are compared with the experimental data and those of other models. It is shown that the fitting results of the particle-rotor-quadrupole-coupling model to the low-lying level energies, reduced E2 transition probabilities, and ground-state electric quadrupole moments of 135Ba and 131Xe are the best, of which the model parameters of the even-even core are determined by the triaxial rotor model in fitting the low-lying spectra of 134Ba and 130Xe. In comparison with the E(5/4) model results of 135Ba, it is also shown that the quadrupole–quadrupole interaction of the even-even core with the single particle adopted can indeed reproduce the E(5/4) critical point behavior. The fitting quality of the reduced E2 transition probabilities among low-lying states by the particle-rotor-quadrupole-coupling model is also noticeably improved. Thus, it can be concluded that the particle-rotor-quadrupole-coupling model is suitable to describe low-lying properties of odd-A nuclei within the transitional region.

Description of Nuclear Properties for 114-128Cd Isotopes

In this paper, the energy levels of the ground-state band (GSB) and other states for 114−128Cd isotopes have been determined using the Interacting Boson Model (IBM-1) with a New Empirical Equation (NEE). The GSB results showed that the IBM-1, NEE, and available experimental data were all in fairly consistent. The NEE and IBM-1 calculations for the high states above 6+ state are slightly overestimated compared to the experimental data, with the exception of the 114Cd and 118Cd nuclei. Furthermore, the reduced transition probabilities B(E2) extracted from the IBM-1 model agree well with the available experimental data. The potential energy surface (EPS) was also examined with the IBM-1. The EPS contour results for Cd isotopes demonstrate that the Cd isotopes under investigation represent a smooth transition behavior from light Cd nuclei toward a more collective vibrational mode as the neutron number increases.