Hexadecapole Deformation Parameters Research Articles

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.

Hexadecapole strength in the rare isotopes 74,76Kr

In the Ge-Sr mass region, isotopes with neutron number N≤40 are known to feature rapid shape changes with both nucleon number and angular momentum. To gain new insights into their structure, inelastic proton scattering experiments in inverse kinematics were performed on the rare isotopes 74,76Kr. This work focuses on observables related to the Jπ=41+ states of the Kr isotopes and, in particular, on the hexadecapole degree of freedom. By performing coupled-channels calculations, hexadecapole deformation parameters β4 were determined for the Jπ=41+ states of 74,76Kr from inelastic proton scattering cross sections. Two possible coupled-channels solutions were found. A comparison to predictions from nuclear energy density functional theory, employing both non-relativistic and relativistic functionals, clearly favors the large, positive β4 solutions. These β4 values are unambiguously linked to the well deformed prolate configuration. Given the β2−β4 trend, established in this work, it appears that β4 values could provide a sensitive measure of the nuclear shell structure.

Neuro-fuzzy modeling of deformation parameters for fusion-barriers

The fusion-barrier distribution is very sensitive to the structure of the colliding nuclei such as nuclear quadrupole and hexadecapole deformation parameters and their signs. If the nuclei that enter the fusion reaction are deformed, the barrier problem becomes complicated. Therefore the deformation parameters are taken into account in the calculations. In this study, Neuro-Fuzzy approach, ANFIS, method has been used for the estimation of ground-state quadrupole (ε2) and hexadecapole (ε4) deformation parameters for the nuclei. According to the results, the method is suitable for this task and one can confidently use it to obtain the data that is not available in the literature.

Subbarrier fusion reactions of an aligned deformed nucleus

We discuss heavy-ion fusion reactions of a well-deformed odd-mass nucleus at energies around the Coulomb barrier. To this end, we consider the $^{16}$O+$^{165}$Ho reaction and take into account the effect of deformation of $^{165}$Ho using the orientation average formula. We show that fusion cross sections are sensitive to magnetic substates of the target nucleus, and cross sections for the side collision, which are relevant to a synthesis of superheavy elements, may be enhanced by a factor of around two by aligning the deformed target nuclei. We also discuss the effect of alignment on the fusion barrier distribution. We find that, for a particular choice of alignment, the shape of barrier distribution becomes similar to a typical shape of barrier distribution for a deformed nucleus with a negative hexadecapole deformation parameter, $\beta_4$, even if the intrinsic $\beta_4$ is positive in the target 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.

Nonaxial hexadecapole deformation effects on the fission barrier

Fission barrier of the heavy nucleus [Formula: see text]Cf is analyzed in a multi-dimensional deformation space. This space includes two quadrupole ([Formula: see text]) and three hexadecapole deformation ([Formula: see text]) parameters. The analysis is performed within an unpaired macroscopic–microscopic approach. Special attention is given to the effects of the axial and non-axial hexadecapole deformation shapes. It is found that the inclusion of the nonaxial hexadecapole shapes does not change the fission barrier heights, so it should be sufficient to minimize the energy in only one degree of freedom in the hexadecapole space [Formula: see text]. The role of hexadecapole deformation parameters is also discussed on the Lublin–Strasbourg drop (LSD) macroscopic and the Strutinsky shell energies.

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.

Effect of deformations on the binding energy of centrally depressed nuclei

The energy density formalism is implemented to study the binding energy of some heavy, superheavy and hyperheavy nuclei. The macroscopic contribution of binding energy is derived in the presence of a depression parameter in the nuclear density distribution, and the total energy is obtained by adding the shell and pairing correction to the macroscopic part. Total energy is studied with the variation of quadrupole and hexadecapole deformation parameters using different values of depression parameter. The addition of the shell and pairing corrections affects the behavior of the total energy especially the minimum position at specific deformation parameters, a second minimum in some cases are close to the first one, suggesting the possible existence of shape isomers. We minimized the total energy with respect to deformation and density depression parameters and obtained the binding energy of 208Pb, 238U, 252Cf, 280Cn, , 298Fl, 306120, 320126, 339136, 500174 and 700226. The binding energies obtained are in good agreement with the available experimental data. The difference between the binding energies obtained by this simple method and experimental ones is less than 0.13%.

Role of neutron transfer on fusion barrier distributions of theSi28,30 + Sn124systems

The fusion barrier distributions for $^{28,30}\mathrm{Si}$ + $^{124}\mathrm{Sn}$ systems were extracted from quasielastic excitation function measurements at backward angles. The experimental barrier distributions were then compared with coupled-channel (CC) calculations. The fusion barrier distribution for the $^{30}\mathrm{Si}$ + $^{124}\mathrm{Sn}$ reaction was well reproduced by the CC calculations with the inclusion of projectile and target inelastic couplings and only one possible positive $Q$-value 2$n$-transfer channel coupling using the ccfull code. However, CC calculations with similar coupling schemes for inelastic excitation of target and projectile with the 4$n$-transfer channel corresponding to the highest positive $Q$ value failed to reproduce the barrier distribution for the $^{28}\mathrm{Si}$ + $^{124}\mathrm{Sn}$ reaction, because it has many positive $Q$-value multi-neutron transfer channels. A better agreement between the experimental fusion barrier distribution for the $^{28}\mathrm{Si}$ + $^{124}\mathrm{Sn}$ system and the prediction of semiempirical CC calculations based on the Zagrebaev framework [V. I. Zagrebaev, Phys. Rev. C 67, 061601(R) (2003)] was obtained only after considering positive $Q$-value multi-neutron transfer couplings. The sensitivity of the fusion barrier distribution to the hexadecapole deformation parameter ${\ensuremath{\beta}}_{4}$ of the projectile was also discussed.

Examples of the failure of proximity approach when the nuclear surface is irregular or has concave regions

Abstract We study the results of the proximity approach in calculating the fusion barrier parameters (the height of Coulomb barrier V B and its radius R B ) compared with the results of double folding model (DFM). We considered five interaction systems as examples and made our study at several relative orientations for the interacting deformed nuclei. We found that V B and R B , evaluated by using the proximity approach, have nonphysical Φ -dependence when the value of hexadecapole deformation parameter β 4 0 or at least one nucleus has octupole deformation order, β 3 . The results almost agree with those of DFM when β 4 = 0 . For positive β 4 values the results of the two models almost agree in behavior but differ in values. The reason for failure when β 4 has negative value is due to the existence of concave region in the nuclear surface, which does not satisfy the requirement of proximity approach based on gently-curved surface. Since the existence of β 6 and β 8 induce irregularity and concave regions in the surface, we expect failure of proximity approach in this case, for an example, β 6 was given.

ROLE OF HIGHER-MULTIPOLARITY DEFORMATIONS IN THE POTENTIAL ENERGY OF HEAVIEST NUCLEI

Potential energy of the superheavy nucleus 284114 is analyzed in a 6-dimensional deformation space. This space includes two quadrupole, three hexadecapole and one multipolarity-6 deformation parameter. The energy is minimized simultaneously in all 6 degrees of freedom. The analysis is done within a macroscopic-microscopic approach. As in the studies of other superheavy nuclei, the result is found to be very individual for a given nucleus. A more general feature is a small effect of one (γ4) of the hexadecapole deformation parameters on the energy of the nucleus.

Scattering of α particles on 11B nuclei at energies 40 and 50 MeV

The differential cross sections for elastic and inelastic scattering of α particles on 11B nuclei at energies of 40 and 50 MeV were measured in the entire angular range. The measured angular distributions were analyzed in terms of the optical model, the distorted-wave Born approximation, and the coupled-channel-method. Optical model potentials and quadrupole (β2) and hexadecapole (β4) deformation parameters were found from this analysis. The rise in the cross sections at backward angles was shown to be associated with the transfer mechanism of the heavy 7Li cluster.

FUSION BARRIER DISTRIBUTIONS IN 20,22Ne+natNi

Barriers height distributions for 20,22 Ne on nat Ni have been measured using quasi-elastic scattering at backward angles. The results have been compared to coupled-channels calculations performed with the CCQUEL code. A fair agreement with data has been obtained if the values of a hexadecapole deformation parameters of 20 Ne and 22 Ne are reduced by a factor of 2 with respect to their previously quoted values.

Effect of β 6 Deformation Parameter on Fusion Cross-Section and Barrier Distribution

The effect of hexacontatetrapole deformation parameter on both the fusion cross-section and the barrier distribution have been studied for U238 + O16 nuclear pair using microscopically derived heavy ion (HI) potential. A method was described to extend the calculation of HI potential between two spherical nuclei using density dependent finite range NN forces to the spherical-deformed interacting pair. Density dependent and density independent effective NN forces were used in the generalized double folding model to derive the HI potential. We found that positive β6 has large effect on both the fusion cross-section and the barrier distribution in the presence of a small value of hexadecapole deformation parameter β4. In this case the fusion cross-section is less sensitive to the negative value of β6. In the presence of a large value of β4, negative and positive β6 values affect the fusion cross-section and have a small effect on the barrier distribution.

Shape change in Hf, W and Os-isotopes: A non-relativistic Hartree-Fock versus relativistic Hartree approximation

We have investigated the ground-state structures of even-even Hf, W and Os isotopes within the framework of a deformed non-relativistic Hartree-Fock and a relativistic mean field formalism. A majority of the nuclei are predicted to be prolate in shape in the relativistic calculations. On the other hand, contrary to the relativistic results, we predict a shape change in a cyclic order in the non-relativistic calculations. However, in both the cases, the magnitude of the quadrupole deformation parameter agrees well with the experimental data. We also evaluated the hexadecapole deformation parameter for Hf, W and Os isotopes and irrespective of the shape change in quadrupole moments, we find a cyclic change in hexadecapole shape from positive to negative and vice versa in both the relativistic and non-relativistic formalisms.

Microscopic study of low-lying yrast spectra in 100–108Mo isotopes

Variation-after-projection (VAP) calculations in conjunction with Hartree-Bogoliubov (HB) ansatz have been carried out for A=100−108 molybdenum (Mo) isotopes. In this framework, the yrast spectra with Jmaxπ≥10+, B(E2) transition probabilities, quadrupole (β2) and hexadecapole (β4) deformation parameters, moment of inertia (I) and square of cranking frequency (ω2) for even-even Mo isotopes have been obtained. The results of the calculation give an indication that it is important to include the hexadecapole-hexadecapole component of the two-body interaction for obtaining various nuclear structure quantities in these Mo isotopes.

MICROSCOPIC STUDY OF THE EFFECT OF HEXADECAPOLE DEFORMATION ON BOTH FUSION CROSS-SECTION AND BARRIER DISTRIBUTION

The interaction potential for deformed-spherical nuclear pair is derived microscopically in the framework of double folding model with M3Y-Paris nucleon–nucleon interaction. The heavy target nucleus 238 U together with the light projectile nucleus 16 O are considered as an example. The exchange part of the heavy ion (HI) potential has been calculated using finite-range exchange NN force instead of the zero-range pseudoforce. Neutron thickness and the difference in kinetic energy densities between neutrons and protons have been taken into consideration in calculating the exchange HI potential. For this pair the fusion cross-section as well as the barrier distribution are calculated. These calculations have been done using three different values of hexadecapole deformation parameter of 238 U . The effect of using both the finite-range exchange NN force and the hexadecapole deformation on the fusion cross-section and the barrier distribution have been discussed.

GROUND-STATE PROPERTIES OF EVEN–EVEN NUCLEI IN THE RELATIVISTIC MEAN-FIELD THEORY

The ground-state properties of 1315 even–even nuclei with 10 ≤Z≤ 98 have been calculated in the framework of the relativistic mean-field (RMF) theory. The Lagrangian parametrization NL3 was used in the calculations. Pairing correlations are accounted within the Bardeen–Cooper–Schrieffer approach. The calculated values for the total binding energy, rms proton radius, rms neutron radius, rms charge radius, neutron quadrupole moment, proton quadrupole moment, charge (proton) hexadecapole moment, quadrupole deformation parameter, and hexadecapole deformation parameter are given in Table I. The RMF predictions of some rare-earth nuclei have been compared with the available experimental information.

Description of the Hexadecapole Deformation Parameter in the sdg Interacting Boson Model

The hexadecapole deformation parameter β4 of the rare-earth and actinide nuclei is investigated in the framework of the sdg interacing boson model. An explicit relation between the geometric hexadecapole deformation parameter β4 and the intrinsic deformation parameters ϵ4, ϵ2 are obtained. The deformation parameters β4 of the rare-earths and actinides are determined without any free parameter. The calculated results agree with experimental data well. It also shows that the SU(5) limit of the sdg interacting boson model can describe the β4 systematics as well as the SU(3) limit.

Parametrization of nonaxial deformations in rotational nuclei

A parametrization is proposed for hexadecapole tensors, which observes symmetries coming from the O{sub h} group of transformations of the frame of reference defined through the quadrupole deformation and/or the rotation axes. A possible dependence of the hexadecapole deformation parameters on the quadrupole deformation is discussed. The inclusion of octupole deformation is considered. {copyright} {ital 1997} {ital The American Physical Society}