Quadrupole Deformation Parameter Research Articles

Empirical relations for α -decay half-lives: The effect of deformation of daughter nuclei

The influence of the daughter nuclei deformations on the α decay's half-life is modeled by adding the term depending on the quadrupole deformation parameter value to the empirical relations for the α-decay half-lives. It is shown that the addition of the deformation-dependent term led to a better description of the experimental data by the empirical expressions for the half-lives of the α decay than the ones without it. A new empirical expression for a description of the α-decay half-lives is proposed. The empirical relation for the α decay half-lives for the transitions from the ground state to the ground state and the lowest 2+ state of the even-even nuclei is discussed. Published by the American Physical Society 2024

Exploring asymmetric fission in 180Hg⁎ compound nucleus using dynamical cluster-decay model

The observed asymmetric fission of the 180Hg⁎ compound nucleus challenges conventional expectations of symmetric fission, which are attributed to the presence of shell closures at Z=40 (semi-magic) and N=50 (magic). To comprehend this novel phenomenon, the dynamical cluster-decay model has been employed. For the first time, this model incorporates the bulk and neutron-proton asymmetry coefficients of the nuclear shape-dependent mass excess formula which are tuned recently to the ground state mass excess data of AME2020 and/or FRDM(2012) along with the temperature dependence for the nuclear shape and the surface energy coefficient of the nuclear proximity potential. The calculations have considered nuclear shapes as both spherical and deformed (quadrupole), with and without temperature dependence for the quadrupole deformation. A new minimum appears in the symmetric mass region of the fragmentation potential for masses (80, 100), when the fragments are deformed and optimally oriented, at an energy lower than that obtained for masses (90, 90) where the fragments are assumed to be spherical or nearly spherical at higher temperatures. This new minimum seems equivalent to the appearance of a new shell gap with deformation and is responsible for the asymmetric fission of 180Hg⁎. The most probable fission channel and the transition from asymmetric to symmetric mass distribution at higher excitation energies are consistent with experiments for the current temperature dependence assigned to the quadrupole deformation parameter.

Transfer learning and neural networks in predicting quadrupole deformation

Abstract Accurately determining the quadrupole deformation parameters of atomic nuclei is crucial for understanding their structural and dynamical properties. This study introduces an innovative approach that combines transfer learning techniques with neural networks to predict the quadrupole deformation parameters of even-even nuclei. With the application of this innovative technique, the quadrupole deformation parameters of 2331 even-even nuclei are successfully predicted within the nuclear region defined by proton numbers \(8 \leq Z \leq 134\) and neutron numbers \(N \geq 8\). Additionally, the study discusses the impact of nuclear quadrupole deformation parameters on the capture cross-sections in heavy-ion fusion reactions, reconstructing the capture cross-sections for the reactions \(^{48}\text{Ca} + ^{244}\text{Pu}\) and \(^{48}\text{Ca} + ^{248}\text{Cm}\). This research offers new insights into the application of neural networks in nuclear physics and underscores the potential of merging advanced machine learning techniques with both theoretical and experimental data, particularly in fields where experimental data is limited.

Pseudospin symmetry in resonant states in deformed nucleus 154Dy

It is known that pseudospin symmetry plays a crucial role in formation of many physical phenomena. By combining the relativistic mean field theory with the complex momentum representation method, the pseudospin symmetry in the single particle resonant states in the deformed nucleus [Formula: see text]Dy is investigated through the energy and width splittings, the quadrupole deformation parameter, the radial density distributions and occupation probabilities of the pseudospin doublets. Near the continuum threshold, the pseudospin symmetry is well reserved in both bound and resonant states. The energy and width splittings of pseudospin doublets in resonant states exhibit correlations with the deformation and quantum numbers. The good pseudospin symmetry is expected with lower pseudo-orbital angular momentum projection [Formula: see text] and the main quantum number N. In general, an increase in deformation tends to weaken the quality of the pseudospin symmetry. The understanding of the evolution of the pseudospin doublets in the resonant states has been deepened by studying the pseudospin symmetry in the deformed nuclei.

A Study of Alpha-Particle Scattering on 10B Nuclei at an Energy of 29 MeV

The angular distributions of the elastic and inelastic scattering of α-particles on 10B nuclei were measured at an energy of 29 MeV (with excitation of the 0.718 MeV (1+) state). The data obtained by us, together with the angular distributions of the elastic scattering measured earlier in a wide range of energies from 24 to 90 MeV, were described using an optical model, the coupled-channel method, and parameterized phase analysis. The optimal parameters of optical potentials were found, and a good description of the experimental data in the specified energy range of α-particles was achieved. By taking into account the contribution of the elastic transfer mechanism of the 6Li cluster, it was possible to correctly reproduce the rise of the cross section at the backward angles in the elastic channel. The value of the quadrupole deformation parameter was extracted from the analysis of inelastic scattering using the coupled-channel method. The geometric parameters of the interaction potentials were determined using parameterized phase analysis. The radii of the 10B nuclei in the high-energy region (30 MeV and above) obtained by PPA are in good agreement with the radii calculated in the framework of the optical model.

Deformation studies on thorium isotopes

The study of the deformation on thorium nuclei are important in nuclear physics due to its fissile nature. Thermally fissile isotopes have importance in energy production. The quadrupole and hexadecapole deformation parameters are important as they provide information on nuclear shape, size and moments of nuclei. The shape degree of freedom plays an important role in determining the fission barrier. In the present study, the quadrupole and hexadecapole deformation parameters of thorium nuclei were estimated by using the relativistic mean-field theory, with density dependent meson exchange interaction DD-ME2 and the density dependent point-coupling interaction DD-PC1. The estimated results of quadrupole deformation parameter are comparable with the available data and the minima point towards the neutron numbers N=126 and 184. The hexadecapole deformation parameter of thorium nuclei are positive along the stability line, negative towards the drip lines and zero at neutron number N=126 and 184.

Correlation between the nuclear structure and reaction dynamics of Ar-isotopes as projectile using the relativistic mean-field approach

This theoretical study is devoted to bridging the gap between the nuclear structure and reaction dynamics and unravelling their impact on each other, considering the neutron-rich light mass 30−60Ar isotopes. Using the relativistic mean-field with the NL3⁎ parameter set, several bulk properties such as binding energies, charge radii, quadrupole deformation parameter, two neutron separation energy, and differential two neutron separation energy with the shell closure parameter are probed for the mentioned isotopic chain. For validation, the RMF (NL3⁎) results are compared with those obtained from the finite range droplet model (FRDM), Weizsäcker-Skyrme model with WS3, WS⁎ parameters, and the available experimental data. Most of the participating isotopes are found to be prolate in structure, and neutron shell closures are conspicuously revealed at N=14,20,40 but weakly shown at N=24,28,34. From our analysis, a central depletion in the nucleonic density is identified in 32 Ar and 42−58 Ar, indicating that they are possible candidates for a semi-bubble-like structure. Interestingly, these results are consistent with recent theoretical and experimentally measured data. Furthermore, using the Glauber model, the reaction cross-sections are determined by taking 26−48Ar as projectiles and stable targets such as 12C, 16O, 40Ca, 90Zr, 124,132Sn, 208Pb and 304120. Although there is no experimental evidence for the stability of 304120, it was predicted by Bhuyan and Patra (2012) [115] as a stable nucleus. A relatively higher cross-section value is noticed between 30 Ar and 32 Ar, which infers that 32Ar is the most stable isotope among the considered chain. Moreover, we noticed that the profile of the differential cross-sections and scattering angle are highly influenced by the mass of the target nuclei and the magnitude of the incident energy of the projectile nucleus.

Pairing phase transition in an odd–even hot 69Zn nucleus

The pairing phase transition in an odd–even hot-rotating 69Zn nucleus has been investigated by using the reported nuclear level density (NLD) data, which were experimentally extracted from the γ-gated particle spectra. The experimental NLDs have been compared with those obtained within the microscopic exact pairing plus independent-particle model at finite temperature (EP+IPM) along with the results of other microscopic calculations such as the Hartree–Fock BCS (HFBCS) and Hartree–Fock–Bogoliubov plus combinational (HFBC) methods. It is found that the experimental NLDs can be well described by the EP+IPM using the recommended quadrupole deformation parameter β 2 = −0.164. Intriguingly, the heat capacity calculated using the EP+IPM NLD exhibits a sharp S-shape, which is not expected in such odd–even hot or hot-rotating system as reported earlier. Changing the deformation parameter β 2 does not change much this S-shape. However, increasing or decreasing the pairing gaps could enhance or destroy the S-shaped heat capacity. Therefore, the S-shaped heat capacity in odd–even 69Zn nucleus is explained due to the deformation-induced pairing correlation.

Theoretical studies on structural properties and decay modes of $$^{284-375}$$119 isotopes

Within the axially deformed relativistic mean field with $$\hbox {NL3}^*$$ parametrisation, the different bulk properties like binding energy, quadrupole deformation parameter, separation energies, density profile and shape co-existence for Z = 119 isotopic chain within the mass range 284 $$\le$$ A $$\le$$ 375 are computed. Further, a competition between possible decay modes such as α-decay, $$\beta$$ -decay and spontaneous fission (SF) of the isotopic chain of Z = 119 superheavy nuclei under study is systematically analysed within self-consistent relativistic mean field model and a close agreement is noticed among the calculations performed using various semi-empirical formulae and also with the estimations made by finite range droplet model (FRDM) wherever available. Our analysis confirmed that α–decay is restricted within the mass range 284 $$\le$$ A $$\le$$ 375 and thus being the dominant decay channel in this mass range and there is no possibility of $$\beta$$ –decay for the considered isotopic chain. In addition, we forecasted the α–decay chain of fission survival nuclides, i.e. $$^{284-296}119$$ and found as one α chain from $$^{284} 119$$ and $$^{296} 119$$ , $$2 \alpha$$ chains from $$^{285}119$$ and $$^{295} 119$$ consistently, $$3\alpha$$ chains from $$^{286} 119$$ and $$^{294} 119$$ consistently, $$4 \alpha$$ chains from $$^{287} 119$$ consistently, six consistent α chains from $$^{288-293} 119$$ . A comparative study of SF and α-decay half-live computed using the formula of Santhosh et al and Coulomb proximity potential model (CPPM), respectively, for the fission surviving isotopic chain reveals that isotopes $$^{288-293} 119$$ exhibit $$6\alpha$$ chains followed by SF, isotopes $$^{295,296} 119$$ exhibit $$4\alpha$$ chains followed by SF, and the rest of the nuclei show continuous α chains. This study has also established that the alpha half-life values computed using $$\hbox {Q}_\alpha$$ (RMF) agree with half-life values computed using experimental $$\hbox {Q}_\alpha$$ values within 1 order difference. Thus, such studies can be of great significance to the experimentalists in very near future for synthesizing the isotopes of Z = 119 superheavy nuclei.

Investigation of giant dipole resonance in Mo isotopes within TDHF theory

The isovector giant dipole resonance (IVGDR) in the chain of even-even Mo isotopes is investigated within the time-dependent Hartree-Fock (TDHF) using the Skyrme force Sly6. The GDR calculated in Mo92−108 are presented, and compared with the available experimental data. An overall agreement between them is obtained. Moreover, the dipole strength in Mo102−108 is predicted. Shape phase transition from spherical to oblate as well as shape coexistence (A ∼ 100) in Mo isotopes are also investigated in this work. In addition, the correlation between the deformation splitting ΔE and the quadrupole deformation parameter β2 is studied. The results confirm that ΔE is proportional to the deformation of nucleus. We also discuss the dependence of GDR strength on some nuclear properties of Skyrme forces, such as the asymmetry energy as. We find that as=32 MeV, corresponding to SLy6, is quite consistent with experimental data.

In-gas-cell laser resonance ionization spectroscopy of Pt200,201

The KEK Isotope Separation System (KISS) was used to produce neutron-rich platinum group isotopes via multinucleon transfer reactions. Mass-spectrometry-assisted in-gas-cell laser resonance ionization spectroscopy was utilized to perform the first experimental determinations of the magnetic dipole moment $\ensuremath{\mu}$ and the differential mean-square charge radii $\ensuremath{\delta}{\ensuremath{\langle}{r}^{2}\ensuremath{\rangle}}^{198,A}$ of $^{200,201}\mathrm{Pt}$. The quadrupole deformation parameters $|\ensuremath{\langle}{\ensuremath{\beta}}_{2}^{2}\ensuremath{\rangle}{|}^{1/2}$ were evaluated from the measured $\ensuremath{\delta}{\ensuremath{\langle}{r}^{2}\ensuremath{\rangle}}^{198,A}$ of $^{200,201}\mathrm{Pt}$ by using a droplet model. The ${\ensuremath{\beta}}_{2}$ values were estimated from a comparison of the experimentally determined magnetic dipole moment $\ensuremath{\mu}$ with values calculated in a strong coupling model. Comparison of the $|\ensuremath{\langle}{\ensuremath{\beta}}_{2}^{2}\ensuremath{\rangle}{|}^{1/2}$ and ${\ensuremath{\beta}}_{2}$ values determined from the laser spectroscopy data with theoretical calculations indicates the likely spin-parity value for $^{201}\mathrm{Pt}$ to be ${I}^{\ensuremath{\pi}}=1/{2}^{\ensuremath{-}}$ or $5/{2}^{\ensuremath{-}}$.

Structure of $$^{128,129,130}$$Xe through multi-reference energy density functional calculations

Recently, values for the Kumar quadrupole deformation parameters of the nucleus $^{130}$Xe have been computed from the results of a Coulomb excitation experiment, indicating that this xenon isotope has a prominent triaxial ground state. Within a different context, it was recently argued that the analysis of particle correlations in the final states of ultra-relativistic heavy-ion collisions performed at the Large Hadron Collider (LHC) points to a similar structure for the adjacent isotope, $^{129}$Xe. In the present work, we report on state-of-the-art multi-reference energy density functional calculations that combine projection on proton and neutron number as well as angular momentum with shape mixing for the three isotopes $^{128,129,130}$Xe using the Skyrme-type pseudo-potential SLyMR1. Exploring the triaxial degree of freedom, we demonstrate that the ground states of all three isotopes display a very pronounced triaxial structure. Moreover, comparison with experimental results shows that the calculations reproduce fairly well the low-energy excitation spectrum of the two even-mass isotopes. By contrast, the calculation of $^{129}$Xe reveals some deficiencies of the effective interaction.

Lifetime measurements in the tungsten isotopes W176,178,180

Lifetimes of yrast states in the rare-earth midshell isotopes $^{176,178,180}\mathrm{W}$ have been measured with fast-timing methods using the Cologne iron-free Orange spectrometer and the Cologne HORUS spectrometer and with the recoil distance Doppler shift method using the Cologne coincidence plunger setup. Different fusion evaporation reactions have been used to populated excited states in the investigated nuclei. Lifetimes of the ${2}_{1}^{+}$, ${4}_{1}^{+}$, ${6}_{1}^{+}$, and ${8}_{1}^{+}$ yrast states were measured in all three tungsten isotopes and in addition the lifetime of the ${10}_{1}^{+}$ state was measured in $^{176}\mathrm{W}$. Quadrupole deformation parameters, reduced transition probabilities, and ${\text{B}}_{4/2}$ ratios are extracted and discussed in the context of interacting boson model 1 calculations. The results with newly determined signatures largely confirm the investigated tungsten isotopes to be deformed prolate rotors.

Mapping the N=40 island of inversion: Precision mass measurements of neutron-rich Fe isotopes

Nuclear properties across the chart of nuclides are key to improving and validating our understanding of the strong interaction in nuclear physics. We present high-precision mass measurements of neutron-rich Fe isotopes performed at the TITAN facility. The multiple-reflection time-of-flight mass spectrometer (MR-ToF-MS), achieving a resolving power greater than 600000 for the first time, enabled the measurement of Fe63–70, including first-time high-precision direct measurements (δm/m≈10−7) of Fe68–70, as well as the discovery of a long-lived isomeric state in Fe69. These measurements are accompanied by both mean-field and ab initio calculations using the most recent realizations which enable theoretical assignment of the spin-parities of the Fe69 ground and isomeric states. Together with mean-field calculations of quadrupole deformation parameters for the Fe isotope chain, these results benchmark a maximum of deformation in the N=40 island of inversion in Fe and shed light on trends in level densities indicated in the newly refined mass surface.Received 19 July 2021Revised 24 December 2021Accepted 16 March 2022DOI:https://doi.org/10.1103/PhysRevC.105.L041301©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBinding energy & massesNuclear structure & decaysRare & new isotopesProperties59 ≤ A ≤ 89TechniquesAb initio calculationsMean field theoryTime-of-flight mass spectrometryNuclear Physics

Deuteron scattering and (d,t) reaction on 11B at an energy of 14.5 MeV

At an energy of 14.5 MeV, the elastic and inelastic scattering of deuterons and the (d, t) reaction on 11B nuclei were studied. Experimental angular distributions with transitions to the states of the 11B nucleus (ground state (3/2−), 4.445 (5/2−) MeV, 6.743 (7/2−) MeV) and to the states of the 10B nucleus (ground state (3+), 0.718 MeV (1+), 1.74 MeV (0+, T = 1), 2.15 MeV (1+)) were analyzed by the coupled channel method. The value of the quadrupole deformation parameter β2= 0.80 ± 0.2 was extracted. The assumption of a direct mechanism for picking up a neutron in the reaction (d, t) made it possible to describe rather well the measured angular distributions for the states of the 10B nucleus. The values of the spectroscopic amplitudes for the transitions to these states have been extracted. It is shown that the mechanism of 8Be transfer both in the form of a whole cluster and in the sequential transfer of two α-particles does not play a significant role. It was found that the deformation of the 10B and 11B nuclei noticeably affects the calculated cross sections for the (d, t) reaction.

Structural evolution and shape transition in even-even Hf-isotopes within the relativistic mean-field approach

In this theoretical study, we calculate the ground state parameters like binding energy, charge radii, neutron skin-thickness, chemical potentials, quadrupole deformation parameter, neutron separation energy, and single-particle energy for Hf isotopes of mass 170 ⩽ A ⩽ 220. The potential energy surface in parallel with the Fermi energy as a function of the quadrupole deformation parameter is estimated to determine the ground state configuration. The Relativistic Hartree-Bogoliubov approach with density-dependent DD-ME2 and the relativistic mean-field formalism with the popular NL3 and NL3⁎ parameter sets are used for the present analysis. The study involves a constant gap BCS approach within NL3, & NL3⁎ and Bogoliubov transformation within DD-ME2 parameter sets to examine the effect of pairing correlations. The calculated bulk quantities are reasonably good agreement with available experimental data, the finite range droplet model predictions, and the Weizsäcker-Skyrme mass formula. We find the signature of shell/sub-shell closure at N = 126 for all the parameter sets, which indicates the stability of 198Hf in the neutron drip-line region of the Hf-isotopes.

Probing nuclear quadrupole deformation from correlation of elliptic flow and transverse momentum in heavy ion collisions

In heavy ion collisions, elliptic flow $v_2$ and radial flow, characterized by event-wise average transverse momentum $[p_{\mathrm{T}}]$, are related to the shape and size of the overlap region, which are sensitive to the shape of colliding atomic nuclei. The Pearson correlation coefficient between $v_2$ and $[p_{\mathrm{T}}]$, $\rho_2$, was found to be particularly sensitive to the quadrupole deformation parameter $\beta$ that is traditionally measured in low energy experiments. Built on earlier insight that the prolate deformation $\beta>0$ reduces the $\rho_2$ in ultra-central collisions (UCC), we show that the prolate deformation $\beta<0$ enhances the value of $\rho_2$. As $\beta>0$ and $\beta<0$ are the two extremes of triaxiality, the strength and sign of $v_2^2-[p_{\mathrm{T}}]$ correlation can be used to provide valuable information on the triaxiality of the nucleus. Our study provide further arguments for using the hydrodynamic flow as a precision tool to directly image the deformation of the atomic nuclei at extremely short time scale ($<10^{-24}$s).

Exploring the ground state bulk and decay properties of the nuclei in superheavy island

The α-decay half-lives of 204 superheavy nuclei covering the range 114≤Z≤126 have been investigated using the relativistic mean-field model (RMF) for NL3⁎ parameter set. The ground state bulk properties such as binding energy, quadrupole deformation parameter (β2), and root-mean-square charge radii for these nuclei are analyzed. Four different semi-empirical formulae, namely, the universal decay law (UDL), the Viola-Seaborg (VSS) formula, the modified universal decay law (MUDL), and the modified Brown formula (MBrown), are used to obtain the α-decay half-lives for the considered nuclei. To examine the applicability of relativistic mean-field model within NL3⁎ parametrization, the α-decay energies, and the half-lives of a few known superheavy nuclei within the range 102 ≤ Z ≤ 118 are calculated and the results are compared with the experimental data along with the theoretical predictions. The α-decay energies (Q-values) are estimated from the binding energies of the parent, and daughter from the RMF (NL3⁎) parameter set. The calculated results are compared with macroscopic-microscopic Finite-Range-Droplet-Model (FRDM), Global Nuclear Mass Model (WS3, WS4), Weizsacker-Skyrme mass model (WS⁎) predictions, and the experimental data, wherever available. The possible standard deviations are also estimated for experimental and various theoretical predictions. We find a good consistency for the experimental-to-UDL, FRDM-to-UDL, and WS4-to-UDL estimates of the decay energy and corresponding half-life. The present analysis provides the theoretical predictions within the microscopic model for the upcoming experiments on the superheavy region.

Structural and decay properties of Z = 124 isotopes using RMF densities

We investigate various ground state characteristics of Z = 124 super-heavy nuclei in the region 296 ⩽ A ⩽322 using the relativistic mean field (RMF) formalism with NL3∗ parametrization. First, the calculation was carried out for the binding energy per nucleon, root-mean-square charge (rms) radii, quadrupole deformation parameter, two-neutron separation energies and other observables.The outcomes are comparable to the macro–microscopic predictions made by the Finite Range Droplet Model (FRDM) and the Weizsȧcker-Skyrme (WS) mass model. The binding energies of the parent and daughter nuclei are used to estimate the α-decay energies. Then, the Viola-Seaborg (VSS) formula and the universal decay law (UDL) have been used to explore the α-decay half-lives of two isotopes 124304,305, and the comparison is made with FRDM and WS predictions. The maximum half-lives of 124292,297 isotopes indicate the signature of shell closure.

Study the Nuclear Structure of Some Even-Even Ca Isotopes Using the Microscopic Theory

The root-mean square-radius of proton, neutron, matter and charge radii, energy level, inelastic longitudinal form factors, reduced transition probability from the ground state to first-excited 2+ state of even-even isotopes, quadrupole moments, quadrupole deformation parameter, and the occupation numbers for some calcium isotopes for A=42,44,46,48,50 are computed using fp-model space and FPBM interaction. 40Ca nucleus is regarded as the inert core for all isotopes under this model space with valence nucleons are moving throughout the fp-shell model space involving 1f7/2, 2p3/2, 1f5/2, and 2p1/2 orbits. Model space is used to present calculations using FPBM interaction, and with the effects of core-polarization are obtained by the first order core polarization through a microscopic theory is called modified surface delta interaction which allows all higher orbits are excited by particle-hole excitation from the core and model space orbits. Also, each isotope's effective charge is determined by using the collective model by Bohr and Mottelson formula. The current result corresponds to the experimental data by taking into account core polarization effects.