Even-even Isotopes Research Articles

Shape coexistence in neutron-deficient Hg188 investigated via lifetime measurements

Shape coexistence in the $Z \approx 82$ region has been established in mercury, lead and polonium isotopes. Even-even mercury isotopes with $100 \leq N \leq 106$ present multiple fingerprints of this phenomenon, which seems to be no longer present for $N \geq 110$. According to a number of theoretical calculations, shape coexistence is predicted in the $^{188}$Hg isotope. The $^{188}$Hg nucleus was populated using two different fusion-evaporation reactions with two targets, $^{158}$Gd and $^{160}$Gd, and a beam of $^{34}$S, provided by the Tandem-ALPI accelerators complex at the Laboratori Nazionali di Legnaro. The channels of interest were selected using the information from the Neutron Wall array, while the $\gamma$ rays were detected using the GALILEO $\gamma$-ray array. The lifetimes of the excited states were determined using the Recoil Distance Doppler-Shift method, employing the dedicated GALILEO plunger device. Using the two-bands mixing and rotational models, the deformation of the pure configurations was obtained from the experimental results. The extracted transition strengths were compared with those calculated with the state-of-the-art symmetry-conserving configuration-mixing (SCCM) and five-dimentional collective Hamiltonian (5DCH) approaches in order to shed light on the nature of the observed structures in the $^{188}$Hg nucleus. An oblate, a normal- and a super-deformed prolate bands were predicted and their underlying shell structure was also discussed.

Nuclear structure properties of even-even chromium isotopes and the effect of deformation on calculated electron capture cross sections

In this study, we investigate the role of the nuclear deformation on the calculated electron capture cross section (ECC) of even-even chromium (Cr) isotopes. We first determined the nuclear structure properties of these nuclei within the interacting boson model-1 (IBM-1). The energy spectra and E2 transition probabilities were calculated by fitting the parameters in the model formalism. The analysis of the potential energy surface were also performed to predict the geometric shape of the Cr nuclei by plotting their contour plot in the plane of (β, γ) deformation parameters. Later, we calculated the ECC within the proton-neutron quasiparticle random phase approximation (pn-QRPA) model. In particular we studied how the calculated ECC changed with different values of nuclear deformation parameter. The calculated Gamow-Teller (GT) strength distributions were widely spread among the daughter states. The total GT strength decreased with increasing value of the β parameter. The computed ECC values, however, increased with increase in the β value of the Cr isotopes.

Temperature dependence of the alpha decay half-lives of even-even Th isotopes

Using temperature dependent nuclear and Coulomb potentials the temperature dependence of alpha decay half-lives of even-even Th isotopes were analyzed in framework of WKB method with inclusion of quantization conditions. The temperature dependent double-folding and proximity potentials were used in calculations. In temperature independent calculations, in contrary to prox77, very good agreement between calculated half-lives with double-folding and experiment were observed. The obtained results showed the quantization condition, as an essential condition for WKB, caused the elimination of the effect of temperature dependence of prox77. Considering temperature dependent potentials and Q-value decreasing behavior of half-life with temperature was observed.

Evolution of intrinsic nuclear structure in medium mass even-even Xenon isotopes from a microscopic perspective * * Arun Bharti acknowledges the financial support from the Science and Engineering Research Board, under the project file no. CRG/2019/001231 and Ridham Bakshi acknowledges the financial support from The Department of Science and Technology, Government of India, INSPIRE Fellowship under sanction no. DST/INSPIRE Fellowship/2018/IF180368

In this study, the multi-quasiparticle triaxial projected shell model (TPSM) is applied to investigate -vibrational bands in transitional nuclei of . We report that each triaxial intrinsic state has a -band built on it. The TPSM approach is evaluated by the comparison of TPSM results with available experimental data, which shows a satisfactory agreement. The energy ratios, B(E2) transition rates, and signature splitting of the -vibrational band are calculated.

Microscopic study of shape evolution and ground state properties in even-even Cd isotopes using covariant density functional theory

We have studied the trend of ground state quadrupole deformation and shape transition in even-even 96−136Cd isotopes. Binding energy, two neutrons separation energies, shell closure parameter, rms radii of neutron and proton, charge radii, and nuclear skin thickness have also been studied as a function of the neutron number. We performed the calculations by employing covariant density functional theory with density-dependent meson exchange and point coupling interactions. The ground-state properties are found in good agreement with available experimental data. Our results predict the shape transition from spherical to prolate, prolate to oblate, oblate to prolate, and prolate to spherical in this isotopic mass chain. Besides, the oblate-prolate shape coexistence is also predicted in 110−114Cd isotopes.

Nuclear structure of even-even Ytterbium isotopes 166−176Yb

A nuclear phenomenological study of the even-even Ytterbium Isotopes Yb166−176 was carried out, in the framework of the interacting Boson model-1 (IBM-1) and modified soft rotor formula (MSRF). The energy levels for ground-state, γ- and β-rotational bands were calculated. Also, electric transition probability B (E2) for these isotopes was calculated. Furthermore, the intrinsic coherent state was used to find the potential energy surfaces. The staggering effect of a γ-band, which is a function of spin, was analyzed. The results obtained by applying the IBM-1 and the MSRF are in good agreement with the corresponding experimental data for most of the nuclear states.

Firm spin and parity assignments for high-lying, low-spin levels in stable Si isotopes

A natural silicon target was investigated in a ^{text {nat}}Si(mathbf {gamma },gamma ^{prime }) photon-scattering experiment with fully linearly-polarised, quasi-monochromatic mathbf {gamma } rays in the entrance channel. The mean photon energies used were langle {E}_{gamma }rangle = 9.33, 9.77, 10.17, 10.55, 10.93, and 11.37 MeV, and the relative energy spread (full width at half maximum) of the incident beam was varDelta E_{gamma }/langle {E}_{gamma }rangle approx 3.5–4 %. The observed angular distributions for the ground-state decay allow firm spin and parity assignments for several levels of the stable even-even silicon isotopes.

Shape isomers in Pt, Hg and Pb isotopes with {hbox {N}}le 126

Deformation-energy surfaces of 54 even-even isotopes of Pt, Hg and Pb nuclei with neutron numbers up to 126 are investigated within a macroscopic-microscopic model based on the Lublin-Strasbourg-Drop macroscopic energy and shell plus pairing-energy corrections obtained from a Yukawa-folded mean-field potential at the desired deformation. A new, rapidly converging Fourier shape parametrization is used to describe nuclear shapes. The stability of shape isomeric states with respect to non-axial and higher-order deformations is investigated.

Systematic study of nuclear structure properties of proton-rich even-even tellurium isotopes with the Gogny energy density functional

The ground state nuclear structure properties of the proton rich even-even tellurium isotopes are studied by using Gogny energy density functional within the framework of Hartree-Fock-Bogoliubov (HFB) method. The HFB equations are solved by using the axial cylindrical transformed deformed harmonic oscillator basis. The full parameterization of Gogny energy density functional is employed in the present study. The evolution of the neutron density distributions with an increase in neutron number is studied and emergence of various nuclear structure phenomena is investigated. Besides this, the ground state nuclear structure properties such as nuclear multipole moments, deformation parameters, binding energies, pairing energies, root mean square radii and charge radii are obtained for the even-even proton-rich tellurium isotopes. The theoretical results on the nuclear ground state properties are compared with the available experimental data and good agreement is found.

Configuration Mixing in Pt Nuclei within Interacting Boson Model-2

This article provides to descript a consistent of the even-even 182-200Pt isotopes. This has been achieved using the interacting boson model-2 (IBM-2) and including configuration mixing (IBM-2 CM). Our attention is paid to describe the nuclei shape and to their connecting with shaping coexistence phenomenon. Ten isotopes are studied, ranging from the middle of the neutron shell to very near the doubly closed shell at 208Pb. The same Hamiltonian is used for all the nuclei studied, with parameters which are constant or smoothly varying. In this study, we showed the transition between more axially symmetric deformed features of light Pt isotopes to γ-unstable and vibrational isotopes (near spherical shape) for 198-200Pt isotopes.

Ground States Structure of Ruthenium Isotopes with Neutron <i>N</i> = 60, 62

In this paper, Ruthenium Isotopes with neutron N = 60, 62 have been studied the ground state bands using Matlab computer code interacting boson model (IBM-1). We apply IBM-1 formula for O(6) symmetry in Ru isotopes with neutron N = 60, 62. The theoretical energy levels up to spin-parity 12+ have been obtained for 104,106Ru isotopes. The yrast states, gamma band, beta band, and B(E2) values are calculated for those nuclei. The experimental and calculated R4/2 values indicate that the even-even 104-106Ru isotopes have O(6) dynamic symmetry. The calculated results are compared to the experimental data and are found in good harmony with each other. The plots of the potential energy surface of both nuclei are O(6) characters.

Upward Transition Probabilities B(E2)↑ Properties Study of Even-Even <sup>104-114</sup>Ru Nuclei

In this research work, the upward transition probabilities for the transition levels, 0+ → 2+, 2+ → 4+, 4+ → 6+ and 6+ → 8+ levels of even-even neutron rich 104-114Ru isotopes have been calculated by using the Global Best Fit (GBF) method. In addition, the associated parameters such as, Quadrupole moment and Deformation parameter of even-even 104-114Ru have been calculated. The dependency of these nuclear parameters shows the nuclear magic number tendency.

γ-vibration in 126Xe: A revisit

The electromagnetic properties of the γ-transitions, decaying from the γ-vibrational states of 126Xe, have been studied via 122Sn(9Be, 5nγ) fusion-evaporation reaction at a beam energy of 48 MeV. The level scheme has been updated by placing the 82+→81+ (ΔI=0) and the 71+→61+ (ΔI=1) γ-transitions. Spin and parity of several excited states have been assigned on the basis of angular correlation and linear polarization results. Systematic of the γ-band in even-even Xe isotopes has been discussed.

Neutrino scattering off the stable even-even Mo isotopes

A systematic study of neutrino-nucleus reaction rates at low and intermediate energies are presented and discussed, focusing on the even-even Mo isotopes. Contributions coming from both the vector and axial-vector components of the corresponding hadronic currents have been included. The response of these detectors to supernova neutrino is also studied, by exploiting the above results and utilizing the folding procedure assuming a two parameter Fermi-Dirac distribution for the supernova neutrino energy-spectra.

Effects of the γ -soft isomeric states on the giant monopole resonances in even-even cadmium isotopes Cd110,112,114,116

The shape evolutions of the even-even cadmium isotopes $^{110--116}\mathrm{Cd}$ are investigated in this work. The giant monopole resonances built on different shape isomeric states are studied using the quasiparticle random phase approximation, which is implemented with a finite amplitude method. We find the local minima corresponding to the prolate, oblate, and triaxial-deformed isomeric states in the even-even cadmium isotopes. Their responses to external monopole perturbations are quite different. Larger deformation tends to make the energy of the giant monopole resonance to shift lower. It is well known that the density functional models have some difficulties in predicting the right positions of the monopole resonances in cadmium isotopes: the centroid energies always seem too large compared to the experimental results. Our calculations show the giant monopole resonances built on the $\ensuremath{\gamma}$ soft isomeric states in the cadmium isotopes have centroid energies even lower than the experimental measurements. Therefore, if the isomeric branching of these $\ensuremath{\gamma}$ soft isomeric states turns out to be prominent, isomer mixing may be a good explanation to the longstanding puzzle.

Empirical proton-neutron interaction of even Ra isotopes probed by the quadrupole-octupole collective Hamiltonian based on the covariant density functional

The empirical proton-neutron interaction $\ensuremath{\delta}{V}_{pn}$ for even-even Ra isotopes is analyzed by using the covariant density functional theory and the quadrupole-octupole collective Hamiltonian approach. It is shown that the static deformation and collective fluctuation are crucial ingredients for good reproduction of the data. Particularly, the introduction of octupole deformation ${\ensuremath{\beta}}_{3}$ dramatically changes the $\ensuremath{\delta}{V}_{pn}$ with $N=134,136,140$. The collective fluctuation smoothly corrects the $\ensuremath{\delta}{V}_{pn}$ with good trend. Taking $^{224}\mathrm{Ra}$ as an example, the detailed contributions from the static deformation and the collective fluctuation are analyzed, and the microscopic single-particle levels, the octupole driving pairs, and the enhancement of proton-neutron interaction are discussed.

β and γ bands in N=88 , 90, and 92 isotones investigated with a five-dimensional collective Hamiltonian based on covariant density functional theory: Vibrations, shape coexistence, and superdeformation

A comprehensive systematic study is made for the collective β and γ bands in even-even isotopes with neutron numbers N=88 to 92 and proton numbers Z=62(Sm) to 70 (Yb). Data, including excitation energies, B(E0) and B(E2) values, and branching ratios from previously published experiments are collated with new data presented for the first time in this study. The experimental data are compared to calculations using a five-dimensional collective Hamiltonian (5DCH) based on the covariant density functional theory (CDFT). A realistic potential in the quadrupole shape parameters V(β,γ) is determined from potential energy surfaces (PES) calculated using the CDFT. The parameters of the 5DCH are fixed and contained within the CDFT. Overall, a satisfactory agreement is found between the data and the calculations. In line with the energy staggering S(I) of the levels in the 2γ+ bands, the potential energy surfaces of the CDFT calculations indicate γ-soft shapes in the N=88 nuclides, which become γ rigid for N=90 and N=92. The nature of the 02+ bands changes with atomic number. In the isotopes of Sm to Dy, they can be understood as β vibrations, but in the Er and Yb isotopes the 02+ bands have wave functions with large components in a triaxial superdeformed minimum. In the vicinity of Sm152, the present calculations predict a soft potential in the β direction but do not find two coexisting minima. This is reminiscent of Sm152 exhibiting an X(5) behavior. The model also predicts that the 03+ bands are of two-phonon nature, having an energy twice that of the 02+ band. This is in contradiction with the data and implies that other excitation modes must be invoked to explain their origin.20 MoreReceived 4 July 2018Revised 5 June 2019DOI:https://doi.org/10.1103/PhysRevC.100.044324©2019 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsCollective modelsElectromagnetic transitionsLow & intermediate energy heavy-ion reactionsNuclear density functional theoryNuclear spin & parityNucleon induced nuclear reactionsProperties150 ≤ A ≤ 189Nuclear Physics

Variational approximations to exact solutions in shell-model valence spaces: Calcium isotopes in the pf shell

We study the performance of self-consistent mean-field and beyond-mean-field approximations in shell-model valence spaces. In particular, Hartree-Fock-Bogolyubov, particle-number variation after projection and projected generator coordinate methods are applied to obtain ground-state and excitation energies for even-even and odd-even Calcium isotopes in the pf-shell. The standard (and non-trivial) KB3G nuclear effective interaction has been used. The comparison with the exact solutions -- provided by the full diagonalization of the Hamiltonian -- shows an outstanding agreement when particle-number and angular-momentum restorations are performed and both quadrupole and neutron-neutron pairing degrees of freedom are explicitly explored as collective coordinates.

A study of charge radii and neutron skin thickness near nuclear drip lines

We studied the charge radius, rms radius and neutron skin thickness Δrnp in even-even isotopes of Si, S, Ar and Ca and isotones of N = 20, 28, 50 and 82. The Δrnp in doubly-magic 48Ca, 68Ni, 120,132Sn and 208Pb nuclei has also been calculated. Theoretical calculations are done with the Hartree-Fock-Bogoliubov theory with the effective Skyrme interactions. Calculated theoretical estimates are in good agreement with the recently available experimental data. The charge radii for Si, S, Ar and Ca isotopes is observed to be minimum at neutron number N = 14. The theoretically computed results with UNEDF0 model parameterization of functional are reasonably reproducing the experimental data for Δrnp in 48Ca, 68Ni and 120,132Sn. The energy density functional of UNEDF1 model provides much improved result of Δrnp for 208Pb.

Parameter optimization for the latest quark-meson coupling energy-density functional

The Quark--Meson--Coupling (QMC) model self-consistently relates the dynamics of the internal quark structure of a hadron to the relativistic mean fields arising in nuclear matter. It offers a natural explanation to some open questions in nuclear theory, including the origin of many-body nuclear forces and their saturation, the spin-orbit interaction and properties of hadronic matter at a wide range of densities. The QMC energy density functionals QMC-I and QMC$\pi$-I have been successfully applied to calculate ground state observables of finite nuclei in the Hartree-Fock + BCS approximation, as well as to predict properties of dense nuclear matter and cold non-rotating neutron stars. Here we report the latest development of the model, QMC$\pi$-II, extended to include higher order self-interaction of the $\sigma$ meson. A derivative-free optimization algorithm has been employed to determine a new set of the model parameters and their statistics, including errors and correlations. QMC$\pi$-II predictions for a wide range of properties of even-even nuclei across the nuclear chart, with fewer adjustable parameters, are comparable with other models. Predictions of ground state binding energies of even-even isotopes of superheavy elements with Z$>$96 are particularly encouraging.