Quadrupole Deformation Parameter Research Articles

Evidence of a Proton Halo in 23Al: A Mean Field Analysis

We have studied the nuclear structure properties like binding energy, charge radius, quadrupole deformation parameter for various isotopes of Al from the valley of stability to drip line region using the well known relativistic mean field formalism (RMF) with NL3 parameter set. We have compared our results with experimental data and found reasonable agreement. Further, we have taken spherical and deformed RMF densities to estimate the reaction dynamics of $^{23-28}$Al isotopes as projectiles and $^{12}$C as target by conjunction in Glauber model. The estimated results are also compared with the experimental data. The analysis of angular elastic differential and one proton removal cross sections are also studied with Glauber model many body system to investigate the structural feature of $^{23}$Al. The evidence of enhanced total reaction cross section, higher value of rms radius, narrow longitudinal momentum distribution and small proton separation energy of $^{23}$Al support its proton halo structure.

A study of some nuclear structure properties of 11C, 13N, 15O, 18F, 52Mn, 52Fe, 60Cu, 62Zn, 63Zn, 66Ga, 68Ga, 76Br, 81Rb, 82Rb, 82Sr, 83Sr, 86Y, 89Zr and 92Rb nuclei used for PET in the axial deformation

In this paper, we mainly investigated important nuclear structure properties of nuclide used in positron-emission tomography for 13 different Skyrme force parameters in the axial deformation such as the binding energy, root mean square charge, proton and density radii, neutron skin thicknesses, quadrupole deformation parameter (β2), proton and neutron quadrupole moments (Qm). To analyze accuracy of the obtained results, the calculated data also were compared with available experimental and the theoretical results in the literature, such as relativistic mean-field theory and the finite-range liquid-drop model. According to Hartree–Fock–Bogolyibov approach with the axial deformation, we discussed Skyrme force parameters on the basis of the obtained result. Further, when taking into account the enormous number of the existing Skyrme-force parameterizations, it has been noticed the obtained results reveal appropriate Skyrme force parameters for each nucleus.

Study of hot thermally fissile nuclei using relativistic mean field theory

We have studied the properties of hot 234,236U and 240Pu nuclei in the framework of relativistic mean field formalism. The recently developed FSUGarnet and IOPB-I parameter sets are implemented for the first time to deform nuclei at finite temperature. The results are compared with the well known NL3 set. The said isotopes are structurally important because of the thermally fissile nature of 233,235U and 239Pu as these nuclei (234,236U and 240Pu) are formed after the absorption of a thermal neutron, which undergoes fission. Here, we have evaluated the nuclear properties, such as shell correction energy, neutron-skin thickness, quadrupole and hexadecapole deformation parameters and asymmetry energy coefficient for these nuclei as a function of temperature.

Decay properties and reaction dynamics of zirconium isotopes in the relativistic mean-field model

In the framework of relativistic mean-field theory, the ground state properties like binding energy, charge radius and quadrupole deformation parameter for various isotopes of zirconium from the valley of stability to drip-line region have been studied. The results are compared with the experimental data and we found reasonable agreement. The calculations are carried out for [Formula: see text]-decay energy and [Formula: see text]-decay half-life up to the drip-line. Total reaction and elastic differential cross-sections are also studied for few zirconium isotopes as projectiles with [Formula: see text] as target, using different parameter sets namely NL3*, DD-ME2 and DD-PC1 in conjunction with Glauber model.

Fast-timing measurements in neutron-rich odd-mass zirconium isotopes using LaBr3:Ce detectors coupled with Gammasphere

A fast-timing experiment was performed at the Argonne National Laboratory to measure the lifetimes of the lowest lying states of nuclei belonging to the deformed regions around mass number A≃110 and A≃150. These regions were populated via spontaneous fission of 252Cf and the gamma radiation following the decay of excited states in the fission fragments was measured using 51 Gammasphere detectors coupled with 25 LaBr3:Ce detectors. A brief description of the acquisition system and some preliminary results from the fast-timing analysis of the fission fragment 100Zr are presented. The lifetime value of τ = 840(65) ps was found for the 2+ state in 100Zr consistent within one standard deviation of the adopted value with 791 +26 -35ps. This is associated with a quadrupole deformation parameter of 0.36(2) which is within one standard deviation of the literature value of 0.3556+82 -57.

Structure and reaction dynamics of zirconium in the relativistic mean field model

In the framework of relativistic mean field theory using NL3, NL3*, NLSH, DD-PC1 and DD-ME2 parameter sets, the ground state binding energy, charge radius, quadrupole deformation parameter of three key isotopes of Zr, i.e., 90,92,94Zr has been studied. The results are compared with the experimental data and are found in reasonable agreement. The two-neutron separation energy and β-decay half-life of these isotopes are also evaluated. Total reaction and elastic differential scattering cross-section are also studied for these isotopes as projectile with 12C as target, using above parameter sets in conjunction with Glauber model and results are compared with the experimental data. All these investigations support the abundance of these three isotopes of zirconium.

Triaxial quadrupole dynamics and the inner fission barrier of some heavy even-even nuclei

Background: Inner fission barriers of actinide nuclei have been known for a long time to be unstable with respect to the axial symmetry. On the other hand, taking into account the effect of the relevant adiabatic mass parameter reduces or even may wash out this instability. A proper treatment of the dynamics for both axial and triaxial modes is thus crucial to accurately determine the corresponding fission barriers. This entails in particular an accurate description of pairing correlations.Purpose: We evaluate the potential energies, moments of inertia, and vibrational mass parameters in a two-dimensional relevant deformation space (corresponding to the usual $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ quadrupole deformation parameters) for four actinide nuclei ($^{236}\mathrm{U}, ^{240}\mathrm{Pu}, ^{248}\mathrm{Cm}$, and $^{252}\mathrm{Cf}$). We assess the relevance of our approach to describe the dynamics for a triaxial mode by computing the low energy spectra (exploring thus mainly the equilibrium deformation region). We evaluate the inner fission barrier heights releasing the axial symmetry constraint.Method: Calculations within the Hartree-Fock plus BCS approach are performed using the SkM* Skyrme effective interaction in the particle-hole channel and a seniority force in the particle-particle channel. The intensity of this residual interaction has been fixed to allow a good reproduction of some odd-even mass differences in the actinide region. Adiabatic mass parameters for the rotational and vibrational modes are calculated using the Inglis-Belyaev formula supplemented by a global renormalization factor taking into account the so-called Thouless-Valatin corrections. Spectra are obtained through the diagonalization of the corresponding Bohr collective Hamiltonian.Results: The experimental low energy spectra are qualitatively well reproduced by our calculations for the considered nuclei. Inner fission barrier heights are calculated and compared with available estimates from various experimental data. The reproduction of the data is better for $^{236}\mathrm{U}$ and $^{240}\mathrm{Pu}$ (up to about 300 keV) than for $^{248}\mathrm{Cm}$ and $^{252}\mathrm{Cf}$ (up to about one MeV).Conclusions: While these results are encouraging, they call for, in particular, a better treatment of pairing correlations, especially as far as the particle number conservation is concerned. Besides, these results could provide a basis for the determination of the least action trajectories which would generate better grounds for the evaluation of fission half lives.

16O + 16O molecular structures of superdeformed states in S isotopes

Structures of excited states in S isotopes are investigated by using the antisymmetrized molecular dynamics and generator coordinate method (GCM). The GCM basis wave functions are calculated via energy variation with a constraint on the quadrupole deformation parameter β. By applying the GCM after parity and angular momentum projections, the coexistence of positive- and negative-parity superdeformed (SD) bands are predicted in 33-36S except for negative-parity states in 36S. The SD bands have structures of 16O + 16O + valence neutron(s) in molecular orbitals around the two 16O cores in a cluster picture. The configurations of the valence neutron(s) in the SD states are δ and/or π molecular orbitals.

Correlated-Gaussian approach to linear-chain states: Case of four α particles

We show that correlated Gaussians with good angular momentum and parity provide flexible basis functions for specific elongated shape. As its application we study linear-chain states of four-alpha particles in variation-after-projection calculations in which all the matrix elements are evaluated analytically. We find possible chain states for $J=0^+$, $2^+$, $4^+$ and perhaps $6^+$ with the bandhead energy being about 33 MeV from the ground state of $^{16}$O. No chain states with $J\geq 8$ are found. The nature of the rotational sequence of the chain states is clarified in contrast to a rigid-body rotation. The quadrupole deformation parameters estimated from the chain states increase from 0.59 to 1.07 for $2^+$ to $6^+$. This work suggests undeveloped fields for the correlated Gaussians beyond those problems which have hitherto been solved successfully.

Beyond-mean-field study of the hyperon impurity effect in hypernuclei with shape coexistence

[Background] The hyperon impurity effect in nuclei has been extensively studied in different mean-field models. Recently, there is a controversy about whether the $\Lambda$ hyperon is more tightly bound in the normal deformed (ND) states than that in the superdeformed (SD) states.[Purpose] This article is aimed to provide a beyond-mean-field study of the low-lying states of hypernuclei with shape coexistence and to shed some light on the controversy.[Method] The models of relativistic mean-field and beyond based on a relativistic point-coupling energy functional are adopted to study the low-lying states of both $^{37}_\Lambda$Ar and $^{36}$Ar. The wavefunctions of low-lying states are constructed as a superposition of a set of relativistic mean-field states with different values of quadrupole deformation parameter. The projections onto both particle number and angular momentum are considered.[Results] The $\Lambda$ binding energies in both ND and SD states of $^{37}_{\Lambda}$Ar are studied in the case of the $\Lambda$ hyperon occupying $s, p$, or $d$ state in the spherical limit, respectively. For comparison, four sets of nucleon-hyperon point-coupling interactions are used respectively. Moreover, the spectra of low-lying states in $^{36}$Ar and $^{37}_{\Lambda_s}$Ar are calculated based on the same nuclear energy density functional. The results indicate that the SD states exist in $^{37}_{\Lambda}$Ar for all the four effective interactions. Furthermore, the $\Lambda_s$ reduces the quadrupole collectivity of ND states to a greater extent than that of SD states. For $^{37}_{\Lambda}$Ar, the beyond-mean-field decreases the $\Lambda_s$ binding energy of the SD state by 0.17 MeV, but it almost has no effect on that of the ND state. [Conclusions] In $^{37}_{\Lambda_s}$Ar, the $\Lambda_p$ and $\Lambda_d$ binding energies of the SD states ...

Study of B(E2) Values of Even-Even <img width="84" height="43" src="http://article.sciencepublishinggroup.com/journal/122/1221113/image001.png" /> Isotopes Using Interacting Boson Model-1

The Electric Reduced Transition Probabilities have been estimated for the even neutron numbers of isotopes using Interacting Boson Model-1 (IBM-1). The U(5) symmetry, values, intrinsic quadrupole moments and deformation parameters of even neutron of isotopes have been studied. The R4/2 values of isotopes have been calculated for the first and energy states and thus U(5) limit is identified.

Structural and decay properties of Z = 132, 138 superheavy nuclei

In this paper, we analyze the structural properties of Z = 132 and Z = 138 superheavy nuclei within the ambit of axially deformed relativistic mean-field framework with NL3 * parametrization and calculate the total binding energies, radii, quadrupole deformation parameter, separation energies, density distributions. We also investigate the phenomenon of shape coexistence by performing the calculations for prolate, oblate and spherical configurations. For clear presentation of nucleon distributions, the two-dimensional contour representation of individual nucleon density and total matter density has been made. Further, a competition between possible decay modes such as $\alpha$ -decay, $\beta$ -decay and spontaneous fission of the isotopic chain of superheavy nuclei with Z = 132 within the range $ 312 \le A \le 392$ and $318 \le A \le 398$ for Z = 138 is systematically analyzed within self-consistent relativistic mean-field model. From our analysis, we inferred that the $\alpha$ -decay and spontaneous fission are the principal modes of decay in majority of the isotopes of superheavy nuclei under investigation apart from $\beta$ -decay as dominant mode of decay in 318-322138 isotopes.

Investigation of the Mg isotopes using the shell-model-like approach in relativistic mean field theory**Supported by NSFC (11465001,11275098, 11275248, 11505058,11165001) and Natural Science Foundation of Inner Mongolia of China (2016BS0102)

Ground state properties for Mg isotopes, including binding energies, one- and two-neutron separation energies, pairing energies, nuclear matter radii and quadrupole deformation parameters, are obtained from the self-consistent relativistic mean field (RMF) model with the pairing correlations treated by a shell-mode-like approach (SLAP), in which the particle-number is conserved and the blocking effects are treated exactly. The experimental data, including the binding energies and the one- and two-neutron separation energies, which are sensitive to the treatment of pairing correlations and block effects, are well reproduced by the RMF+SLAP calculations.

Shape evolution with angular momentum in Lu isotopes

The nuclear potential energies of Lu isotopes with neutron number [Formula: see text] up to high spins are computed within the framework of the unpaired cranked Nilsson–Strutinsky method. The potential and the macroscopic Lublin–Strasbourg drop (LSD) energy-surface diagrams are analyzed in terms of quadrupole deformation and triaxiality parameter. The shape evolution of these isotopes with respect to angular momentum, as well as the neutron number is studied.

Properties of superdeformed bands in A ∼ 190 region within the framework of three parameters nuclear softness model

The three parameters nuclear softness model (NS3) have been applied to eleven superdeformed (SD) bands of A ≈190 mass region namely: 191Hg(SD2,SD3), 192Hg(SD1), 194Hg(SD1,SD2), 193Tl(SD1,SD2), 194Tl(SD1,SD3, SD5) and 194Pb(SD1). The level spins and the model parameters are determined by fitting the electric quadrupole transition energies Eγ with the experimental ones, by using a computer simulated search program. Rotational frequencies ħω, kinematic J(1) and dynamic J(2)moments of inertia and the quadrupole deformation parameter β2 have been calculated. In all cases of our selected SD bands the results obtained are in good agreement with experimental ones. J(2) reveal a steady increase with ħω, this can be attributed to the successive alignment of πi13/2 (N = 6) and υj15/2 (N = 7) intruder orbitals in the presence of dynamical pairing correlations. The presence of ΔI = 2 staggering in the two SD bands 1,2 of 194Hg and in the three SD bands 1,3,5 of 194Tl have been investigated by calculating the staggering parameter which represent the fourth order derivative of the gamma-ray transition energies. Also the ΔI = 1 staggering in SD bands of odd nuclei has been investigated in the signature partner pairs 191Hg (SD2, SD3) and 193Tl (SD1, SD2). The yrast SD bands in the isotones 194Pb and 192Hg have almost identical transition energies which implies that their J(2) are also identical. This indicates that either the two occupied 5/2+[642] protons have a very weak influence on Eγ and J(2).

Theoretical study of fusion reactions 32S + 94,96Zr and 40Ca + 94,96Zr and quadrupole deformation of 94Zr

The dynamic coupling effects on fusion cross sections for reactions $^{32}$S + $^{94,96}$Zr and $^{40}$Ca + $^{94,96}$Zr are studied with the universal fusion function formalism and an empirical coupled channel (ECC) model. An examination of the reduced fusion functions shows that the total effect of couplings to inelastic excitations and neutron transfer channels on fusion in $^{32}$S + $^{94}$Zr ($^{40}$Ca + $^{94}$Zr) is almost the same as that in $^{32}$S + $^{96}$Zr ($^{40}$Ca + $^{96}$Zr). The enhancements of the fusion cross section at sub-barrier energies due to inelastic channel coupling and neutron transfer channel coupling are evaluated separately by using the ECC model. The results show that effect of couplings to inelastic excitations channels in the reactions with $^{94}$Zr as target should be similar as that in the reactions with $^{96}$Zr as target. This implies that the quadrupole deformation parameters $\beta_2$ of $^{94}$Zr and $^{96}$Zr should be similar to each other. However, $\beta_2$'s predicted from the finite-range droplet model, which are used in the ECC model, are quite different. Experiments on $^{48}$Ca + $^{94}$Zr or $^{36}$S + $^{94}$Zr are suggested to solve the puzzling issue concerning $\beta_2$ for $^{94}$Zr.

Three-body calculation of elastic and inelastic scattering of deuterons on 24Mg

Deuteron–nucleus scattering is described using exact three-particle equations. The theory is formulated in an extended Hilbert space allowing the excitation of the target nucleus. Alt, Grassberger, and Sandhas equations for transition operators are solved in the momentum-space framework including the Coulomb interaction via the screening and renormalization method. The calculations are performed for elastic and inelastic scattering of deuterons on 24Mg using the rotational model for the excitation potential. A reasonable agreement with the experimental data for the first excited state 2+ of 24Mg is achieved when the quadrupole deformation parameter β2=0.47 is used. This new value is more consistent with the inelastic proton scattering data requiring β2≈0.5 than previous determinations β2≈0.4 based on two-body deuteron–nucleus models.

16O +16O molecular structures of positive- and negative-parity superdeformed bands in34S

The structures of excited states in 34 S are investigated using the antisymmetrized molecular dynamics and generator coordinate method(GCM). The GCM basis wave functions are calculated via energy variation with a constraint on the quadrupole deformation parameter β . By applying the GCM after parity and angular momentum projections, the coexistence of two positive- and one negative-parity super de formed(SD) bands are predicted, and low-lying states and other deformed bands are obtained. The SD bands have structures of 16 O + 16 O + two valence neutrons in molecular orbitals around the two 16 O cores in a cluster picture. The configurations of the two valence neutrons are δ 2 and π 2 for the positive-parity SD bands and π 1 δ 1 for the negative parity SD band.

Comparison between different proximity potentials and the double-folding model for spherical–deformed interacting nuclei

The Coulomb barrier parameters have been calculated for a spherical–deformed interacting pair of nuclei using 14 different versions of the proximity approaches and a simple analytical formula for the Coulomb part of the heavy ion potential. The results of these proximity versions have been compared with more accurate results obtained from the double-folding model (DFM). We have considered the interacting pair 48Ca + 238Pu as an example and assumed the presence of the quadrupole, octupole, and hexadecapole deformation parameters for 238Pu. The orientation angle dependence of the Coulomb barrier parameters has been computed for different sets of deformation parameters. We found that the proximity types named Prox77, BW Prox91, AW Prox95, Bass Prox77, and Bass Prox80 are the best ones of the available 14 versions of the proximity approaches for calculating the nuclear part of the interaction potential for a spherical–deformed pair of nuclei.

BruecknerG-matrix approach for neutron-proton pairing correlations in the deformed BCS approach

Ground states of even-even Ge isotopes with mass number $A=64\text{--}76$ have been studied in the deformed Bardeen-Cooper-Schrieffer (BCS) theory by taking neutron-proton $(np)$ pairing correlations as well as neutron-neutron $(nn)$ and proton-proton $(pp)$ pairing correlations. The $np$ pairing has two different modes $J=0,\phantom{\rule{4pt}{0ex}}T=1$ (isotriplet) and $J=1,\phantom{\rule{4pt}{0ex}}T=0$ (isosinglet). In this work, the Brueckner $G$ matrix, based on the CD-Bonn potential, has been exploited to reduce the ambiguity regarding nucleon-nucleon interactions inside nuclei compared to the results by a simple schematic phenomenological force. We found that the $G$ matrix plays important roles to obtain reasonable descriptions of even-even nuclei compared to the schematic force. The $np$ pairing strength has been shown to have a clear correlation with quadrupole deformation parameter ${\ensuremath{\beta}}_{2}$ for the isotopes, and affects the smearing of the Fermi surfaces of not only $N=Z$ nuclei but also $N\ensuremath{\ne}Z$ nuclei. In particular, the coexistence of the like particle ($nn$ and $pp$) and the $np$ pairing modes was found to become more salient by the $G$-matrix approach than by the schematic force approach.