Function Of Neutron Number Research Articles

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

Quadrupole-octupole collective excitations in medium mass nuclei

A quadrupole-octupole axially symmetric collective model is used to describe the alternate parity bands observed in even–even medium mass nuclei. The nature of the octupole correlations in considered nuclei is ascertained from the phenomenology of the adopted model and the obtained parameters. It is found that the model parameters have a regular evolution as a function of neutron number, suggesting that the shape phase transition around N = 90 from low to well deformed shapes is also accompanied by the increase of the vibrational character for the octupole deformation. Model extrapolations are performed for various types of excited states and electromagnetic properties of measured energy levels.

First spectroscopic study of odd-odd Cu78

Nuclei in the vicinity of Ni78 are important benchmarks for nuclear structure, which can reveal changes in the shell structure far from stability. Spectroscopy of the odd-odd isotope Cu78 was performed for the first time in an experiment with the EURICA setup at the Radioactive Isotope Beam Factory at RIKEN Nishina Center. Excited states in the neutron-rich isotope were populated following the β decay of Ni78 produced by in-flight fission and separated by the BigRIPS separator. A level scheme based on the analysis of γ−γ coincidences is presented. Tentative spin and parity assignments were made when possible based on the β-decay feeding intensities and γ-decay properties of the excited states. Time correlations between β and γ decay show clear indications of an isomeric state with a half-life of 3.8(4) ms. Large-scale Monte Carlo shell-model calculations were performed using the A3DA-m interaction and a valence space comprising the full fp shell and the 1g9/2 and 2d5/2 orbitals for both protons and neutrons. The comparison of the experimental results with the shell-model calculations allows interpreting the excited states in terms of spin multiplets arising from the proton-neutron interaction. The results provide further insight into the evolution of the proton single-particle orbitals as a function of neutron number, and quantitative information about the proton-neutron interaction outside the doubly magic Ni78 core.Received 6 October 2022Revised 3 January 2023Accepted 9 January 2023DOI:https://doi.org/10.1103/PhysRevC.107.044301©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBeta decayEnergy levels & level densitiesIsomer decaysNuclear spin & parityNuclear structure & decaysNucleon-nucleon interactionsShell modelProperties59 ≤ A ≤ 89Nuclear Physics

Alpha Decay Half-Lives Calculation of Even-Even Nuclei in the62≤Z≤100Region using Woods-Saxon Potential

Alpha decay properties of even-even nuclei in the 62 ≤ Z ≤ 100 region are investigated within the Unified Fission Model based on a Modified Woods-Saxon potential. The computed alpha decay half-lives are compared to experimental data and are found to be in good agreement with it. The acquired pattern of the variation of alpha decay half-lives as a function of neutron number are explained by the nuclear shell effect. The experimental alpha decay energy Q is found to have an inverse relation with the alpha decay half-lives. This work has shown that the Unified Fission Model based on a Modified Woods-Saxon potential is sufficient to obtain the values of alpha decay half-lives.

Study of static and dynamic properties of even-even 14–24O and 38–54Ca in the frame of Random Phase Approximation (RPA) method with different Skyrme parameterizations

The static and dynamic nuclear properties for neutron rich oxygen and calcium isotopes have been calculated using the framework of the random phase approximation method with different Skyrme parameterizations namely; SyO-, SyO+, BSk17, SLy4, SLy5, and SkX. The nuclear charge radii, the binding energy per nucleon were calculated and compared to the experimental one to choose the best Skyrme interactions used in the calculations of dynamic properties. The two-neutron separation energy for isotopes under study has been calculated and compared to experimental data. Higher modes of the excited states, energy-weighted sum rule, the centroid, constrained, and scaling energies of the resonances have been studied and illustrated together with available experimental data for comparison. For the low-lying excited states, the energy transition densities for J π = 2+ and J π = 3− are reproduced well in 18–24O and 46–54Ca isotopes. The neutron single particle states as a function of neutron number have been also presented. The results show that the random phase approximation calculations with Skyrme-type interactions is a successful method for describing nuclear structure properties of neutron rich nuclei near the drip line.

Neutron–proton interaction, bubble structure and neutron skin properties of Co in a Supernova

In the present paper, we investigated the neutron skin properties, central depletion effects, residual and average neutron–proton interactions for Co in a Type II Supernova 1987A. The neutron skin thicknesses performed by Skyrme–Hartree–Fock model for the isotopic chain of Co $$(17\le N\le 82)$$ are obtained with different methods to investigate the bulk and surface contributions to neutron skin thicknesses as a function of neutron number N and relative neutron excess I = (N-Z)/A. For this purpose, two-parameter Fermi (2pF) distributions for each nucleus are obtained by the proton and neutron density distributions. Since the neutron skin thickness demonstrates the dependency on the symmetry pressure of neutron matter and sensitive to the symmetry energy at the sub-saturation density, the neutron skin properties lead to the investigation on the formation and composition of the crusts in Supernova and neutron stars. For a proper understanding of surface effects of nuclei, the central depletion (or bubble structure) effects on neutron skin of nuclei in the Supernova are explained by calculating the bubble parameters b and b′. Furthermore, in order to illustrate accuracy of theoretical model used in the current work, the mass model approach is also analyzed by the calculating residual and average neutron–proton interactions, where the fluctuations in the mass model approaches have also been compared with the experimental and theoretical results in the literature. In order to evaluate more nuclear properties, we also analyzed the charge form factors and the single- particle energy levels for Co isotopes in the Supernova for providing nuclear data for electron-nucleus scattering experimental processes.

Nuclear shape evolution and shape coexistence in Zr and Mo isotopes

The phenomena of shape evolution and shape coexistence in even–even $$^{88-114}$$ Zr and $$^{90-116}$$ Mo isotopes are studied by employing covariant density functional theory (CDFT) with density-dependent point-coupling parameter set, DD-PCX, and with separable pairing interaction. The results for the rms deviation in binding energies, two-neutron separation energy, the differential variation of two-neutron separation energy, and rms charge radii, as a function of neutron number, are presented and compared with available experimental data. In addition to the oblate–prolate shape coexistence in $$^{96-110}$$ Zr isotopes, the correlations between shape transition and discontinuity in the observables are also examined. A smooth trend of charge radii in Mo isotopes is found to be due to the manifestation of triaxiality softness. The observed oblate and prolate minima are related to the low single-particle energy level density around the Fermi level of neutron and proton, respectively. The rapid shape transition in Zr isotopes near N $$\approx $$ 60 is identified to be caused by the evolution of the shell structure associated with massive proton excitations to 1 $$\pi g_{9/2}$$ orbit. The present calculations also predict a deformed semi-bubble structure in the $$^{100}$$ Zr isotope.

Evolution of E2 strength in the rare-earth isotopes Hf174,176,178,180

Mean lifetimes of yrast states of the isotopes 174,176,178,180Hf have been measured using fast- electronic scintillation timing. Excited states of 74,176,178Hf were populated via β decay, while 180Hf was populated via Coulomb excitation. The lifetimes of the 2+ 1 and 4+ 1 states of all isotopes and the lifetimes of the 6+ 1 states of 174,178Hf were measured, using the slope and the centroid shift methods. The mean lifetime, τ (4+ 1 ) = 85(13) ps, of 178Hf has been determined for the first time. In addition, the mean lifetimes of the 2− 1 and the 3− 1 states of 176Hf have been determined. Systematic uncertainties on the evolution of data as a function of neutron number were reduced by using the same setup for all the isotopes of interest. The data are in agreement with other recent lifetime measurements where available and shows a shift of the maximum of collectivity for the Hf isotopic chain from neutron midshell at N = 104 to N = 100.

Investigating the fusion enhancement for neutron-rich mid-mass nuclei using the dynamical cluster-decay model

The mechanism involved in compound nucleus formation through heavy ion induced fusion reactions at near- and sub-barrier energies has been stimulating the interest of both experimentalists and theoreticians. The study of fusion reactions is important not only for the production of superheavy elements but also to unfold the mysteries involved in the evolution of neutron stars and nucleosynthesis of elements in astrophysical scenarios. The detection of gravitational waves originating from the merging of two black holes, and the possibility of observing similar events originating from black-hole--neutron-star mergers, highlighted the necessity of understanding the behavior of neutron-rich nuclear matter. One of the potential methods to understand the character of neutron-rich matter is through the study of fusion of an isotopic chain of reactions. Recently, the first experimental evidence of fusion enhancement at near-barrier energies for neutron-rich nuclei was reported for the light and mid-mass regime. To understand the dynamics involved in such reactions, the investigation of K-induced reactions has been performed using the quantum mechanical fragmentation based dynamical cluster-decay model (DCM). The experimental fusion cross sections of $^{39,47}\mathrm{K}+^{28}\mathrm{Si}$ are reproduced using DCM and, further, the fusion cross sections are predicted for other isotopes of K beam on $^{28}\mathrm{Si}$ to investigate the fusion enhancement as a function of neutron number. It has been observed that fusion enhancement is significant at near-barrier energies for neutron-rich nuclei. The fusion enhancement observed is larger for odd neutron number nuclei as compared to adjacent neutron nuclei. This indicates the influence of unpaired neutrons on fusion cross sections. Also, the fusion cross sections predicted in the present work will act as input for planning more experimental measurements.

Novel Shape Evolution in Sn Isotopes from Magic Numbers 50 to 82.

A novel shape evolution in the Sn isotopes by the state-of-the-art application of the MonteCarlo shell model calculations is presented in a unified way for the ^{100-138}Sn isotopes. A large model space consisting of eight single-particle orbits for protons and neutrons is taken with the fixed Hamiltonian and effective charges, where protons in the 1g_{9/2} orbital are fully activated. While the significant increase of the B(E2;0_{1}^{+}→2_{1}^{+}) value, seen around ^{110}Sn as a function of neutron number (N), has remained a major puzzle over decades, it is explained as a consequence of the shape evolution driven by proton excitations from the 1g_{9/2} orbital. A second-order quantum phase transition is found around N=66, connecting the phase of such deformed shapes to the spherical pairing phase. The shape and shell evolutions are thus described, covering topics from the Gamow-Teller decay of ^{100}Sn to the enhanced double magicity of ^{132}Sn.

Lifetime Measurements of Excited States in ^{172}Pt and the Variation of Quadrupole Transition Strength with Angular Momentum.

Lifetimes of the first excited 2^{+} and 4^{+} states in the extremely neutron-deficient nuclide ^{172}Pt have been measured for the first time using the recoil-distance Doppler shift and recoil-decay tagging techniques. An unusually low value of the ratio B(E2:4_{1}^{+}→2_{1}^{+})/B(E2:2_{1}^{+}→0_{gs}^{+})=0.55(19) was found, similar to a handful of other such anomalous cases observed in the entire Segré chart. The observation adds to a cluster of a few extremely neutron-deficient nuclides of the heavy transition metals with neutron numbers N≈90-94 featuring the effect. No theoretical model calculations reported to date have been able to explain the anomalously low B(E2:4_{1}^{+}→2_{1}^{+})/B(E2:2_{1}^{+}→0_{gs}^{+}) ratios observed in these cases. Such low values cannot, e.g., be explained within the framework of the geometrical collective model or by algebraic approaches within the interacting boson model framework. It is proposed that the group of B(E2:4_{1}^{+}→2_{1}^{+})/B(E2:2_{1}^{+}→0_{gs}^{+}) ratios in the extremely neutron-deficient even-even W, Os, and Pt nuclei around neutron numbers N≈90-94 reveal a quantum phase transition from aseniority-conserving structure to a collective regime as a function of neutron number. Although a system governed by seniority symmetry is the only theoretical framework for which such an effect may naturally occur, the phenomenon is highly unexpected for these nuclei that are not situated near closed shells.

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.

De-excitation of the strongly coupled band in Au177 and implications for core intruder configurations in the light Hg isotopes

Excited states in the proton-unbound nuclide $^{177}$Au were populated in the $^92}$Mo($^{88}$Sr, p2n) reaction and identified using the Jurogam-II and GREAT spectrometers in conjunction with the RITU gas-filled separator at the University of Jyvaskyla Accelerator Laboratory. A strongly coupled band and its decay path to the 11/2−α-decaying isomer have been identified using recoil-decay tagging. Comparisons with cranked Hartree-Fock-Bogoliubov (HFB) calculations based on Skyrme energy functionals suggest that the band has a prolate deformation and is based upon coupling the odd 1h11/2 proton hole to the excited 02+ configuration in the $^{178}$Hg core. Although these configurations might be expected to follow the parabolic trend of core Hg(02+) states as a function of neutron number, the electromagnetic decay paths from the strongly coupled band in $^{177}$Au are markedly different from those observed in the heavier isotopes above the midshell. This indicates that a significant change in the structure of the underlying A+1Hg core occurs below the neutron midshell.

A test for correction made to spin systematics for coupled band in doubly-odd nuclei

Systematic Spin Assignments were generally made by using the argument that the energy of levels is a function of neutron number. In the present systematics, the excitation energy of the levels incorporated the effect of nuclear deformation and signature splitting. The nuclear deformation changes toward the mid-shell, therefore a smooth variation in the excitation energy of the levels is observed towards the mid-shell, that intended to make systematics as a function of neutron number towards the mid-shell. Another term “signature splitting” that push the energy of levels for odd- and even-spin sequences up and down, caused the different energy variation pattern for odd- and even-spin sequences. The corrections made in the spin systematics were tested for the known spins of various isotopic chain. In addition, the inconsistency in spin assignments made by the spin systematics and other methods of the configuration π h 11/2 ⊗ νh 11/2 band belonging to 112,114,116Cs, 126Pr, and 138Pr, as an example, was resolved by the correctionmade in the present spin systematics.

Pygmy resonance and low-energy enhancement in theγ-ray strength functions of Pd isotopes

Background: An unexpected enhancement in the $\ensuremath{\gamma}$-ray strength function, as compared to the low-energy tail of the giant dipole resonance (GDR), has been observed for Sc, Ti, V, Fe, and Mo isotopes for ${E}_{\ensuremath{\gamma}}l4$ MeV. This enhancement was not observed in subsequent analyses on Sn isotopes, but a pygmy dipole resonance (PDR) centered at ${E}_{\ensuremath{\gamma}}\ensuremath{\approx}8$ MeV was however detected. The $\ensuremath{\gamma}$-ray strength functions measured for Cd isotopes exhibit both features over the range of isotopes, with the low-energy enhancement decreasing and PDR strength increasing as a function of neutron number. This suggests a transitional region for the onset of low-energy enhancement, and also that the PDR strength depends on the number of neutrons.Purpose: The $\ensuremath{\gamma}$-ray strength functions of $^{105--108}\mathrm{Pd}$ have been measured in order to further explore the proposed transitional region.Method: Experimental data were obtained at the Oslo Cyclotron Laboratory by using the charged particle reactions $(^{3}\mathrm{He},\phantom{\rule{0.16em}{0ex}}^{3}\mathrm{He}{}^{\ensuremath{'}}\ensuremath{\gamma})$ and ($^{3}\mathrm{He},\phantom{\rule{0.16em}{0ex}}\ensuremath{\alpha}\ensuremath{\gamma}$) on $^{106,108}\mathrm{Pd}$ target foils. Particle-$\ensuremath{\gamma}$ coincidence measurements provided information on initial excitation energies and the corresponding $\ensuremath{\gamma}$-ray spectra, which were used to extract the level densities and $\ensuremath{\gamma}$-ray strength functions according to the Oslo method.Results: The $\ensuremath{\gamma}$-ray strength functions indicate a sudden increase in magnitude for ${E}_{\ensuremath{\gamma}}g4$ MeV, which is interpreted as a PDR centered at ${E}_{\ensuremath{\gamma}}\ensuremath{\approx}8$ MeV. An enhanced $\ensuremath{\gamma}$-ray strength at low energies is also observed for $^{105}\mathrm{Pd}$, which is the lightest isotope measured in this work.Conclusions: A PDR is clearly identified in the $\ensuremath{\gamma}$-ray strength functions of $^{105--108}\mathrm{Pd}$, and a low-energy enhancement is observed for $^{105}\mathrm{Pd}$. Further, the results correspond and agree very well with the observations from the Cd isotopes, and support the suggested transitional region for the onset of low-energy enhancement with decreasing mass number. The neutron number dependency of the PDR strength is also evident.

COMPARISONS OF THE ODD–EVEN STAGGERING PATTERNS BETWEEN THE Ba–Dy REGION WITH 88 NEUTRONS AND Ra ISOTOPES WITH 88 PROTONS

Useful information about the shape transitions of even–even isotones 144 Ba , 146 Ce , 148 Nd , 150 Sm , 152 Gd , 154 Dy with 88 neutrons and 218-226 Ra isotopes with 88 protons are obtained from the ratios of [Formula: see text] as a function of neutron number N or proton number Z and the relations [Formula: see text] and r((I+2)/I) as a function of the angular momentum I. Interacting Boson Model (IBM-1), Bohr–Mottelson Model (BM) and Interacting Vector Boson Model (IVBM) have been employed to study the energy levels for the ground and octupole bands of the above nuclei. The best input parameters for the above approaches which lead to the best fit to experimental data are determined. The ΔI = 1 staggering (odd–even staggering) in octupole bands of the studied nuclei is found to exhibit a "beat" behavior as a function of angular momentum I. Comparisons of the displacement energies δE(I) and the staggering factor ΔE1, γ(I) are presented between the Ba–Dy region with 88 neutrons and Ra isotopes with 88 protons.

Beyond relativistic mean-field studies of low-lying states in neutron-deficient krypton isotopes

Neutron-deficient krypton isotopes are of particular interest due to the coexistence of oblate and prolate shapes in low-lying states and the transition of ground-state from one dominate shape to another as a function of neutron number. A detailed interpretation of these phenomena in neutron-deficient Kr isotopes requires the use of a method going beyond a mean-field approach that permits to determine spectra and transition probabilities. The aim of this work is to provide a systematic calculation of low-lying state in the even-even 68-86Kr isotopes and to understand the shape coexistence phenomenon and the onset of large collectivity around N=40 from beyond relativistic mean-field studies. The starting point of our method is a set of relativistic mean-field+BCS wave functions generated with a constraint on triaxial deformations (beta, gamma). The excitation energies and electric multipole transition strengths of low-lying states are calculated by solving a five-dimensional collective Hamiltonian (5DCH) with parameters determined by the mean-field wave functions. To examine the role of triaxiality, a configuration mixing of both particle number (PN) and angular momentum (AM) projected axially deformed states is also carried out within the exact generator coordinate method (GCM) based on the same energy density functional. The energy surfaces, the excitation energies of 0^+_2, 2^+_1, 2^+_2 states, as well as the E0 and E2 transition strengths are compared with the results of similar 5DCH calculations but with parameters determined by the non-relativistic mean-field wave functions, as well as with the available data...

Prediction of alpha-decay energy and decay half-life for unknown superheavy nuclei using resonances of exactly solvable α+nucleus potential

Predictions of the results of alpha-decay energy (Q-value) and decay half-life (t1/2) are made for experimentally unknown alpha decaying systems of superheavy nuclei. Following a theoretical method proposed recently by B. Sahu, the calculations are performed using the analytical expression of the potential that simulates the nuclear+Coulomb potential of the α + daughter nucleus system. The Q-value considered as resonance energy is calculated using the behavior of the wave function, and the t1/2 is expressed analytically using the exact solutions of the potential. A global formula for the potential parameter as a function of neutron number in a given isotopic chain of nuclei is developed for the calculation of Q and t1/2. Calculations of the latter two quantities are made for the decay chain of newly discovered superheavy elements 294117, 293117, and for the isotopic chains of Z = 74 and 102. Predictions of the same parameters are made for Z = 113 and some other still unknown superheavy nuclei. It is observed that the global formula works well in evaluating correct results of Q and t1/2 for various alpha emitters.

Collective structural evolution in neutron-rich Yb, Hf, W, Os, and Pt isotopes

An interacting-boson-model Hamiltonian determined from Hartree-Fock-Bogoliubov calculations with the microscopic Gogny energy density functional D1M is applied to the spectroscopic analysis of neutron-rich Yb, Hf, W, Os, and Pt isotopes with mass $A\ensuremath{\sim}180$--200. Excitation energies and transition rates for the relevant low-lying quadrupole collective states are calculated by this method. Transitions from prolate to oblate ground-state shapes are analyzed as a function of neutron number $N$ in a given isotopic chain by calculating excitation energies, $B(E2)$ ratios, and correlation energies in the ground state. It is shown that such transitions tend to occur more rapidly for the isotopes with lower proton number $Z$ when departing from the proton shell closure $Z=82$. The triaxial degrees of freedom turn out to play an important role in describing the considered mass region. Predicted low-lying spectra for the neutron-rich exotic Hf and Yb isotopes are presented. The approximations used in the model and the possibilities to refine its predictive power are addressed.

Spectroscopic calculations of the low-lying structure in exotic Os and W isotopes

Structural evolution in neutron-rich Os and W isotopes is investigated in terms of the interacting boson model (IBM) Hamiltonian determined by (constrained) Hartree-Fock-Bogoliubov calculations with the Gogny-D1S energy density functional (EDF). The interaction strengths of the IBM Hamiltonian are produced by mapping the potential energy surface (PES) of the Gogny-EDF with quadrupole degrees of freedom onto the corresponding PES of the IBM system. We examine the prolate-to-oblate shape/phase transition which is predicted to take place in this region as a function of neutron number $N$ within the considered Os and W isotopic chains. The onset of this transition is found to be more rapid compared to the neighboring Pt isotopes. The calculations also allow the prediction of spectroscopic variables (excited state energies and reduced transition probabilities) which are presented for the neutron-rich $^{192,194,196}\mathrm{W}$ nuclei, for which there is only very limited experimental data available to date.