Even-even Isotopes Research Articles

Quadrupole and octupole collectivity and cluster structures in neon isotopes

The lowest positive- and negative-parity bands of $^{20}$Ne and neutron-rich even-even Ne isotopes are investigated using a theoretical framework based on energy density functionals. Starting from a self-consistent relativistic Hartree-Bogoliubov calculation of axially-symmetric and reflection-asymmetric deformation energy surfaces, the collective symmetry-conserving states are built using projection techniques and the generator coordinate method. Overall a good agreement with the experimental excitation energies and transition rates is obtained. In particular, the model provides an accurate description of the excitation spectra and transition probabilities in $^{20}$Ne. The contribution of cluster configurations to the low-energy states is discussed, as well as the transitional character of the ground state. The analysis is extended to $^{22}$Ne and the shape-coexisting isotope $^{24}$Ne, and to the drip-line nuclei $^{32}$Ne and $^{34}$Ne. The role of valence neutrons in the formation of molecular-type bonds between clusters is discussed.

Signatures of octupole correlations in neutron-rich odd-mass barium isotopes

Octupole deformation and the relevant spectroscopic properties of neutron-rich odd-mass barium isotopes are investigated in a theoretical framework based on nuclear density functional theory and the particle-core coupling scheme. The interacting-boson Hamiltonian that describes the octupole-deformed even-even core nucleus, as well as the single-particle energies and occupation probabilities of an unpaired nucleon, are completely determined by microscopic axially-symmetric $(\beta_{2},\beta_{3})$-deformation constrained self-consistent mean-field calculations for a specific choice of the energy density functional and pairing interaction. A boson-fermion interaction that involves both quadrupole and octupole degrees of freedom is introduced, and their strength parameters are determined to reproduce selected spectroscopic data for the odd-mass nuclei. The model reproduces recent experimental results both for the even-even and odd-mass Ba isotopes. In particular, for $^{145,147}$Ba our results indicate, in agreement with recent data, that octupole deformation does not determine the structure of the lowest states in the vicinity of the ground state, and only becomes relevant at higher excitation energies.

Evolution of Shapes and Search for Shape Coexistence in Sd-Shell Nuclei

A detailed and systematic study has been performed using state dependent Relativistic Mean-Field plus BCS (RMF+BCS) approach to investigate shape evolution for even-even isotopes of Ne, Mg, Si and S. We perform quadrupole constraint calculation using NL3* parameter and look into the variation of binding energy with respect to deformation and find the shape and deformation corresponding to energy minima. We find various isotopes showing shape coexistence and shape transition while moving from proton drip-line to neutron drip-line. These results are compared with Macroscopic-microscopic approach (Mac-Mic) with Nilson Strutinsky (NS) prescription and some other works and are found consistent for these sd-shell nuclei.

Neutron knockout from 68,70Ni ground and isomeric states.

Neutron-rich isotopes are an important source of new information on nuclear physics. Specifically, the spin-isospin components in the nucleon-nucleon (NN) interaction, e.g., the proton-neutron tensor force, are expected to modify shell structure in exotic nuclei. These potential changes in the intrinsic shell structure are of fundamental interest. The study of the excitation energy of states corresponding to specific configurations in even-even isotopes, together with the single-particle character of the first excited states of odd-A, neutron-rich Ni isotopes, probes the evolution of the neutron orbitals around the Fermi surface as a function of the neutron number a step forward in the understanding of the region and the nature of the NN interaction at large N/Z ratios.In an experiment carried out at the National Superconducting Cyclotron Laboratory [1], new spectroscopic information was obtained for 68Ni and the distribution of single-particle strengths in 67,69Ni was characterized by means of single-neutron knockout from 68,70Ni secondary beams. The spectroscopic strengths, deduced from the measured partial cross sections to the individual states tagged by their de-exciting gamma rays, is used to identify and quantify configurations that involve neutron excitations across the N = 40 harmonic oscillator shell closure. The de-excitation γ rays were measured with the GRETINA tracking array [2].The results challenge the validity of the most current shell-model Hamiltonians and effective interactions, highlighting shortcomings that cannot yet be explained. These results suggest that our understanding of the low-energy states in such nuclei is not complete and requires further investigation.

Role of the excitation energy of the compound nucleus in binary decay processes

Employing the improved scission-point model, the isotopic and excitation energy trends of the charge distribution of fission fragments are studied in fission of even-even Th isotopes at low and high excitation energies.

Fission fragment mass and total kinetic energy distributions of spontaneously fissioning plutonium isotopes

The fission-fragment mass and total kinetic energy (TKE) distributions are evaluated in a quantum mechanical framework using elongation, mass asymmetry, neck degree of freedom as the relevant collective parameters in the Fourier shape parametrization recently developed by us. The potential energy surfaces (PES) are calculated within the macroscopic-microscopic model based on the Lublin-Strasbourg Drop (LSD), the Yukawa-folded (YF) single-particle potential and a monopole pairing force. The PES are presented and analysed in detail for even-even Plutonium isotopes with A = 236–246. They reveal deep asymmetric valleys. The fission-fragment mass and TKE distributions are obtained from the ground state of a collective Hamiltonian computed within the Born-Oppenheimer approximation, in the WKB approach by introducing a neck-dependent fission probability. The calculated mass and total kinetic energy distributions are found in good agreement with the data.

Probable Decay Modes at Limits of Nuclear Stability of the Superheavy Nuclei

The modes of decay for the even-even isotopes of superheavy nuclei of Z = 118 and 120 with neutron number $160 \leq N \leq 204$ are investigated in the framework of the axially deformed relativistic mean field model. The asymmetry parameter $\eta$ and the relative neutron-proton asymmetry of the surface to the center ($R_{\eta}$) are estimated from the ground state density distributions of the nucleus. We analyze the resulting asymmetry parameter $\eta$ and the relative neutron-proton asymmetry $R_{\eta}$ of the density play a crucial role in the mode(s) of decay and its half-life. Moreover, the excess neutron richness on the surface facets a superheavy nucleus for $\beta^-$ decays.

Emergence of low-energy monopole strength in the neutron-rich calcium isotopes

The isoscalar monopole response of neutron-rich nuclei is sensitive to both the incompressibility coefficient of symmetric nuclear matter and the density dependence of the symmetry energy. The main goal of this paper is to explore the emergence, evolution, and origin of low energy monopole strength along the even-even calcium isotopes: from 40Ca to 60Ca. The distribution of isoscalar monopole strength is computed in a relativistic random phase approximation (RPA) using three effective interactions that have been calibrated to the properties of finite nuclei and neutron stars. A non-spectral approach is adopted that allows for an exact treatment of the continuum without any reliance on discretization. For the stable calcium isotopes, no evidence of low-energy monopole strength is observed, even as the 1f7/2 neutron orbital is being filled and the neutron-skin thickness progressively grows. Further, in contrast to experimental findings, a mild softening of the monopole response with increasing mass number is predicted. Beyond 48Ca, a significant amount of low-energy monopole strength emerges as soon as the weak-binding neutron orbitals (2p and 1f5/2) become populated. The emergence and evolution of low-energy strength is identified with transitions from these weakly-bound states into the continuum. Moreover, given that models with a soft symmetry energy tend to reach the neutron-drip line earlier than their stiffer counterparts, we identify an inverse correlation between the neutron-skin thickness and the inverse energy weighted sum.

Shell-model-based deformation analysis of light cadmium isotopes

Large-scale shell-model calculations for the even-even Cadmium isotopes 98 Cd - 108 Cd have been performed with the ANTOINE code in the {\pi}(2p 1/2 ; 1g 9/2 ) {\nu}(2d 5/2 ; 3s 1/2 ; 2d 3/2 ; 1g 7/2 ; 1h 11/2 ) model space without further truncation. Known experimental energy levels and B(E2) values could be well reproduced. Taking these calculations as a starting ground we analyze the deformation parameters predicted for the Cd isotopes as a function of neutron number N and spin J using the methods of model independent invariants introduced by K. Kumar and D. Cline.

Search for $\alpha$ α + core states in even-even Cr isotopes

The $\alpha + \mathrm{core}$ structure is investigated in even-even Cr isotopes from the viewpoint of the local potential model. The comparison of $Q_{\alpha}/A$ values for even-even Cr isotopes and even-even $A = 46,54,56,58$ isobars indicates that $^{46}$Cr and $^{54}$Cr are the most favorable even-even Cr isotopes for $\alpha$-clustering. The ground state bands of the two Cr isotopes are calculated through a local $\alpha + \mathrm{core}$ potential with two variable parameters. The calculated spectra give a very good description of most experimental $^{46}$Cr and $^{54}$Cr levels. The reduced $\alpha $-widths, rms intercluster separations and $B(E2)$ transition rates are determined for the ground state bands. The calculations reproduce the order of magnitude of the available experimental $B(E2)$ values without using effective charges and indicate that the first members of the ground state bands present a stronger $\alpha$-cluster character. The volume integral per nucleon pair and rms radius obtained for the $\alpha+^{50}$Ti potential are consistent with those reported previously in the analysis of $\alpha$ elastic scattering on $^{50}$Ti.

Pre-Scission Model Calculation of Fission Fragment Mass and Total Kinetic Energy Distributions for Even-Even Fm, No and Rf Isotopes

The main properties of the fission fragments in spontaneous fission of even-even isotopes of Fm (Z=100), No (Z=102) and Rf (Z=104) are estimated using a pre-scission point model. The underlying potential energy surfaces are calculated with Strutinsky’s shell correction procedure. The parametrization of the nuclear shapes is based on Cassini ovals generalized by the inclusion of three additional shape parameters: α1, α4 and α6. It represents a natural way to describe scission configurations. The corresponding fragment-mass distributions are estimated supposing they are due to thermal fluctuations in the mass asymmetry degree of freedom. A detailed comparison with all existing data for Fm, No and Rf isotopes is presented. For these three series of isotopes the experimentally observed transition from asymmetric to symmetric fission, that happens with increasing mass number A, is well reproduced. In lighter isotopes (e.g. 254Fm and 254Rf) two mass-asymmetric fission modes are predicted to occur with comparable yields: one having relatively compact and the other relatively elongated scission configurations. On the other hand, in heavier isotopes (e.g. 264Fm and 264Rf) the fragment-mass distributions are predicted to be narrow single-peaked around A/2 corresponding to essentially one compact fission mode. We call this type of fission ”super-symmetric”. The corresponding distributions of the total kinetic energy of the fragments are also calculated (in the point-charge approximation) and compared with measurements. Despite the fact that the dynamical effects were neglected, we have obtained a quantitative agreement with the experimental data.

Calculations of the β-decay half-lives of neutron-deficient nuclei**Supported by National Nature Science Foundation of China (11535004, 11375086, 11120101005, 11175085 and 11235001), 973 Nation Major State Basic Research and Development of China (2013CB834400) and Science and Technology Development Fund of Macau (020/2014/A1 and 039/2013/A2)

In this work, β+/EC decays of some medium-mass nuclei are investigated within the extended quasiparticle random-phase approximation (QRPA), where neutron-neutron, proton-proton and neutron-proton (np) pairing correlations are taken into consideration in the specialized Hartree-Fock-Bogoliubov (HFB) transformation. In addition to the pairing interaction, the Brückner G-matrix obtained with the charge-dependent Bonn nucleon-nucleon force is used for the residual particle-particle and particle-hole interactions. Calculations are performed for even-even proton-rich isotopes ranging from Z=24 to Z=34. It is found that the np pairing interaction plays a significant role in β-decay for some nuclei far from stability. Compared with other theoretical calculations, our calculations show good agreement with the available experimental data. Predictions of β-decay half-lives for some very neutron-deficient nuclei are made for reference.

Lifetime measurement of neutron-rich even-even molybdenum isotopes

Background: In the neutron-rich $A\ensuremath{\approx}100$ mass region, rapid shape changes as a function of nucleon number as well as coexistence of prolate, oblate, and triaxial shapes are predicted by various theoretical models. Lifetime measurements of excited levels in the molybdenum isotopes allow the determination of transitional quadrupole moments, which in turn provides structural information regarding the predicted shape change.Purpose: The present paper reports on the experimental setup, the method that allowed one to measure the lifetimes of excited states in even-even molybdenum isotopes from mass $A=100$ up to mass $A=108$, and the results that were obtained.Method: The isotopes of interest were populated by secondary knock-out reaction of neutron-rich nuclei separated and identified by the GSI fragment separator at relativistic beam energies and detected by the sensitive PreSPEC-AGATA experimental setup. The latter included the Lund-York-Cologne calorimeter for identification, tracking, and velocity measurement of ejectiles, and AGATA, an array of position sensitive segmented HPGe detectors, used to determine the interaction positions of the $\ensuremath{\gamma}$ ray enabling a precise Doppler correction. The lifetimes were determined with a relativistic version of the Doppler-shift-attenuation method using the systematic shift of the energy after Doppler correction of a $\ensuremath{\gamma}$-ray transition with a known energy. This relativistic Doppler-shift-attenuation method allowed the determination of mean lifetimes from 2 to 250 ps.Results: Even-even molybdenum isotopes from mass $A=100$ to $A=108$ were studied. The decays of the low-lying states in the ground-state band were observed. In particular, two mean lifetimes were measured for the first time: $\ensuremath{\tau}=29.{7}_{\ensuremath{-}9.1}^{+11.3}$ ps for the ${4}^{+}$ state of $^{108}\mathrm{Mo}$ and $\ensuremath{\tau}=3.{2}_{\ensuremath{-}0.7}^{+0.7}$ ps for the ${6}^{+}$ state of $^{102}\mathrm{Mo}$.Conclusions: The reduced transition strengths $B(E2)$, calculated from lifetimes measured in this experiment, compared to beyond-mean-field calculations, indicate a gradual shape transition in the chain of molybdenum isotopes when going from $A=100$ to $A=108$ with a maximum reached at $N=64$. The transition probabilities decrease for $^{108}\mathrm{Mo}$ which may be related to its well-pronounced triaxial shape indicated by the calculations.

Transition Probabilities, and Potential Energy Surfaces for 120-126Xe Even-Even Isotopes

Transition Probabilities, and Potential Energy Surfaces for 120-126Xe Even-Even Isotopes

Tetrahedral shapes of neutron-rich Zr isotopes from a multidimensionally constrained relativistic Hartree-Bogoliubov model

We develop a multidimensionally constrained relativistic Hartree-Bogoliubov (MDC-RHB) model in which the pairing correlations are taken into account by making the Bogoliubov transformation. In this model, the nuclear shape is assumed to be invariant under the reversion of $x$ and $y$ axes; i.e., the intrinsic symmetry group is $V_4$ and all shape degrees of freedom $\beta_{\lambda\mu}$ with even $\mu$ are included self-consistently. The RHB equation is solved in an axially deformed harmonic oscillator basis. A separable pairing force of finite range is adopted in the MDC-RHB model. The potential energy curves of neutron-rich even-even Zr isotopes are calculated with relativistic functionals DD-PC1 and PC-PK1 and possible tetrahedral shapes in the ground and isomeric states are investigated. The ground state shape of $^{110}$Zr is predicted to be tetrahedral with both functionals and so is that of $^{112}$Zr with the functional DD-PC1. The tetrahedral ground states are caused by large energy gaps around $Z=40$ and $N=70$ when $\beta_{32}$ deformation is included. Although the inclusion of the $\beta_{30}$ deformation can also reduce the energy around $\beta_{20}=0$ and lead to minima with pear-like shapes for nuclei around $^{110}$Zr, these minima are unstable due to their shallowness.

β -decay properties of neutron-rich rare-earth isotopes

In this paper, beta-decay properties of even-even neutron-rich isotopes in the rare-earth mass region are studied within a microscopic theoretical approach based on a proton-neutron quasiparticle random-phase approximation. The underlying mean field is constructed selfconsistently from a deformed Hartree-Fock calculation with Skyrme interactions and pairing correlations to which particle-hole and particle-particle residual interactions are added. Nuclei in this mass region participate in the astrophysical rapid neutron capture process and are directly involved in the generation of the rare-earth peak in the isotopic abundance pattern centered at A=160. The energy distributions of the Gamow-Teller strength as well as the beta-decay half-lives and the beta-delayed neutron-emission probabilities are discussed and compared with the available experimental information and with calculations based on different approaches.

Theoretical Studies on the α-decay Half-Lives of Even-Even Lv Isotopes

The α-decay half-lives for even-even Lv isotopes within the range 290 ≤ A ≥ 314 which have Z = 116, have been evaluated using Gamow-like model (GLM) which is based on Gamow theory, the different semi-empirical formula for α-decay half-lives also was used. The half-lives were evaluated using theoretical Q-value. The computed α-decay half-lives were compared with CPPM, and also with empirical formula, the result was achieved in a good agreement.

Physical Origin of the Transition from Symmetric to Asymmetric Fission Fragment Charge Distribution

Using an improved scission-point model, we describe the charge distribution of fission fragments produced in the electromagnetic-induced fission of even-even thorium isotopes. The transition from a symmetric fission mode to an asymmetric one is explained. A three-peaked charge distribution is predicted for several fissioning nuclei at low excitation energy.

Unexpected asymmetry of the charge distribution in the fission of Th222,224 at high excitation energies

Using the improved scission-point model, the isotopic trends of the charge distribution of fission fragments are studied in induced fission of even-even Th isotopes. The calculated results are in good agreement with available experimental data. With increasing neutron number the transition from symmetric to asymmetric fission mode is shown to be related to the change of the potential energy surface. The change of the shape of mass distribution with increasing excitation energy is discussed for fissioning $^{A}\mathrm{Th}$ nuclei. At high excitation energies, there are unexpected large asymmetric modes in the fission of neutron-deficient Th isotopes considered.

The Total β-Half-Lives for Some Nickel Isotopes

Abstract . The first-forbidden transitions can play an important role in decreasing the calculated half-lives specially in environments. We calculate the allowed Gamow-Teller transitions in pn-QRPA model for even-even neutron-rich isotopes of nickel. The first forbidden transitions for even-even neutron-rich isotopes of nickel are calculated assuming the nuclei to be spherical. The Woods-Saxon potential basis has been used in our calculations. The calculated half-lives have been compared with the schematic model calculations and corresponding experimental data. Keywords: pn-QRPA approximation, Gamow-Teller, First forbidden transitions