Effect Of Nuclear Deformation Research Articles

The effect of nuclear deformation on level statistics

We analyze the nearest neighbor spacing distributions of low-lying2+ levelsof even–even nuclei. We grouped the nuclei into classes defined according to the quadrupole deformationparameter (β2). We calculate the nearest neighbor spacing distributions for each class. Then, wedetermine the chaoticity parameter for each class with the help of the Bayesian inferencemethod. We compare these distributions against a formula that describes the transition tochaos by varying a tuning parameter. This parameter appears to depend in anon-trivial way on the nuclear deformation, and takes small values indicatingregularity in strongly deformed nuclei and especially in those having an oblatedeformation.

Nuclear deformation effect on the binding energies in heavy ions

Nuclear deformation effects on the binding energies in heavy ions are investigated. Approximate formulas for the nuclear-size correction and the isotope shift for deformed nuclei are derived. Combined with direct numerical evaluations, these formulas are employed to reanalyze experimental data on the nuclear-charge-distribution parameters in $^{238}\text{U}$ and to revise the nuclear-size corrections to the binding energies in H- and Li-like $^{238}\text{U}$. As a result, the theoretical uncertainties for the ground-state Lamb shift in ${^{238}\text{U}}^{91+}$ and for the $2{p}_{1/2}\ensuremath{-}2s$ transition energy in ${^{238}\text{U}}^{89+}$ are significantly reduced. The isotope shift of the $2{p}_{j}\ensuremath{-}2s$ transition energies for ${^{142}\text{N}\text{d}}^{57+}$ and ${^{150}\text{N}\text{d}}^{57+}$ is also evaluated including nuclear size and nuclear recoil effects within a full QED treatment.

Effect of nuclear deformation on the electric-dipole strength in the particle-emission threshold region

The role of nuclear deformation in the photoabsorption cross section in the tail region of the electric giant dipole resonance (GDR) is studied in terms of a deformed oscillator model and a Nilsson-plus-random-phase-approximation model. It is found within the framework of these approaches that extra electric dipole strength is generated at energies below the GDR maximum if the nuclear system is spatially deformed. This is important in the prediction of stellar photodisintegration rates, knowing that an extra strength can affect these rates even below the particle separation energies through the so-called \ensuremath{\gamma} process. Because the nuclear deformation is governed by shell effects, this extra strength does not directly correlate with the neutron excess.

β-decay in neutron-deficient Hg, Pb, and Po isotopes

The effect of nuclear deformation on the energy distributions of the Gamow-Teller strength is studied in neutron-deficient Hg, Pb, and Po even isotopes. The theoretical framework is based on a self-consistent deformed Skyrme Hartree-Fock mean field with pairing correlations between like nucleons in BCS approximation and residual spin-isospin interactions treated in the proton-neutron quasiparticle random phase approximation. After a systematic study of the Gamow-Teller strength distributions in the low excitation energy region, relevant for beta-decay, we have identified the best candidates to look for deformation signatures in their beta-decay patterns. beta+ half-lives and total Gamow-Teller strengths B(GT+) and B(GT-) are analyzed as well.

Effects of nuclear deformation in dinuclear systems: Application to the fission process

The relative yields of fission fragments, the mean values of their total kinetic energy, and the variances of their distributions with respect to the total kinetic energy are described within the improved scission-point model. It is shown that, for fixed charge and mass numbers of fragments, the potential energy of the prescission configuration as a function of the deformation parameters of the fragments has several minima. The scission at these minima leads to a relative enhancement of the yields of the fragments that have the corresponding values of the total kinetic energy and to the appearance of a fine structure in the mass-energy distribution, this structure being different from that induced by the even-odd effect.

Two neutrino double-βdecay in deformed nuclei with an angular momentum projected basis

Four nuclei which are proved to be $2\nu\beta\beta$ emitters ($^{76}$Ge, $^{82}$Se, $^{150}$Nd, $^{238}$U), and four suspected, due to the corresponding Q-values, to have this property ($^{148}$Nd, $^{154}$Sm, $^{160}$Gd, $^{232}$Th), were treated within a proton-neutron quasiparticle random phase approximation (pnQRPA) with a projected spherical single particle basis. The advantage of the present procedure over the ones using a deformed Woods Saxon or Nilsson single particle basis is that the actual pnQRPA states have a definite angular momentum while all the others provide states having only K as a good quantum number. The model Hamiltonian involves a mean field term yielding the projected single particle states, a pairing interaction for alike nucleons and a dipole-dipole proton-neutron interaction in both the particle-hole (ph) and particle-particle (pp) channels. The effect of nuclear deformation on the single beta strength distribution as well as on the double beta Gamow-Teller transition amplitude (M$_{{\rm GT}}$) is analyzed. The results are compared with the existent data and with the results from a different approach, in terms of the process half life T$_{1/2}$. The case of different deformations for mother and daughter nuclei is also presented.

Dependence of Heavy-Ion Fusion Reaction on Nuclear Deformation

In order to study the effect of nuclear deformation on complete fusion between spherical projectiles and well-deformed targets, we have measured the excitation functions at energies around the Coulomb barrier in the same compound nuclear system of 6 0 Ni+ 1 5 4 Sm and 3 2 S+ 1 8 2 W (the compound nucleus 2 1 4 Th), 7 6 Ge+ 1 5 0 Nd and 2 8 Si+ 1 9 8 Pt (the compound nucleus 2 2 6 U), and 6 4 Ni+ 1 5 4 Sm. To get the direct evidence that the heavy projectile really fuses with the deformed target, the fusion evaporation residues emitted to the beam direction were measured by using the JAERI recoil mass separator and identified on the basis of time- and position-correlated α-decays. The angular distribution of fission fragments was also measured to obtain the total fusion cross section. The measured cross sections of the fission and the evaporation residue were compared with the results of a coupled channel calculation and a statistical model calculation, respectively. In 3 2 S+ 1 5 2 W and 2 8 Si+ 1 9 8 Pt reactions having enough smaller charge product Z 1 Z 2 than 1800, good agreements between the data and the calculated results were obtained. In the large Z 1 Z 2 systems of 6 4 , 6 0 Ni+ 1 5 4 Sm and 7 6 Ge+ 1 5 0 Nd, on the other hand, large fusion hindrance was observed up to about three orders of magnitude in the lowest energy region where only collisions around the tip of the deformed target are possible. The fusion hindrance gradually decreased in the high energy region where near side collisions become possible. By assuming of an extra-extra push energy around 20 MeV in the tip collisions and nearly zero in the side collision, the excitation function was reasonably reproduced. This is consistent with the theoretical speculation of hugging fusion or gentle fusion that the compact touching configuration of the side collision is more favorable for complete fusion than the elongated configuration of the tip collision.

Effects of Nuclear Deformation on the Fusion Probability in the Reactions of 76Ge+150Nd and 82Se+natCe

Evaporation residue (ER) cross sections for the 76Ge+150Nd and 82Se+natCe reactions were measured near the Coulomb barrier in order to investigate the effects of nuclear deformation on the fusion process. The first reaction represents fusion involving the prolately deformed target 150Nd, whereas the latter reaction is the fusion with the spherical target natCe. We obtained fusion probabilities from the experimental data with the aid of calculated survival probabilities. The system 82Se+natCe showed fusion hindrance in the form of the extra-extra-push energy of 27±5 MeV, whereas the system 76Ge+150Nd does not show any hindrance at the bombarding energy corresponding to the Coulomb barrier for the collision of 76Ge on the side of 150Nd. Since the side collision is compact in configuration at touching, our results suggest that the reaction starting from the compact touching point results in a higher fusion probability.

Effects of Nuclear Deformation on Fusion Probability in the Reactions of 76Ge+150Nd and 82Se+natCe near the Coulomb Barrier

Evaporation residue (ER) cross sections for 76Ge+150Nd and 82Se+natCe were measured near the Coulomb barrier in order to investigate the effects of nuclear deformation on fusion process. The former reaction represents fusion involving the prolately deformed target l50Nd, whereas the latter reaction is the fusion using spherical target natCe. We obtained fusion probability from the experimental data with the aid of calculated survival probability. The system 82Se+natCe showed fusion hindrance in the form of extra-extra-push energy of 27±5 MeV, whereas the system 76Ge+150Nd does not show any hindrance at the bombarding energy corresponding to the Coulomb barrier of the collision of 76Ge on the side of 150Nd. Since the side collision is compact in configuration at touching, our results indicates that the reaction starting from the compact touching point results in higher fusion probability.

Effects of Nuclear Deformation on the Fusion Probability in the Reactions of 76Ge + 150Nd and 82Se + natCe

Evaporation residue (ER) cross sections for the 76Ge+150Nd and 82Se+natCe reactions were measured near the Coulomb barrier in order to investigate the effects of nuclear deformation on the fusion process. The first reaction represents fusion involving the prolately deformed target 150Nd, whereas the latter reaction is the fusion with the spherical target natCe. We obtained fusion probabilities from the experimental data with the aid of calculated survival probabilities. The system 82Se+natCe showed fusion hindrance in the form of the extra-extra-push energy of 27±5 MeV, whereas the system 76Ge+150Nd does not show any hindrance at the bombarding energy corresponding to the Coulomb barrier for the collision of 76Ge on the side of 150Nd. Since the side collision is compact in configuration at touching, our results suggest that the reaction starting from the compact touching point results in a higher fusion probability.

Kinetics in sub-barrier fusion of spherical nuclei

The semiclassical transport theory is applied to the description of heavy-ion fusion at energies below and above the Coulomb barrier. The paths connecting entrance and exit fusion reaction channels are found as a continuous solution of the Vlasov transport equation in classically allowed and forbidden regions associated with suitably defined collective variables. The effects of nuclear deformation, neck formation, and nonlocality are quantified on the basis of microscopic simulations and analyzed. The results of calculations give good fits to experimental data for fusion of nearly symmetric oxygen and nickel isotope pairs.

Evaporation of light particles from a hot, deformed and rotating nucleus

The dependence of the transmission coefficient on the deformation, the collective rotation and excitation energy of the compound nucleus emitting light particles is introduced in the framework of Wei{\ss}kopf's evaporation theory. The competition between fission and particle evaporation is treated by a~Langevin equation for the fission variable coupled to the emission process. Detailed calculations are presented on the decay of different Gd and Yb isotopes at an excitation energy of about 250~MeV. These calculations demonstrate the importance of the effects of nuclear deformation and of the initial spin distribution on the evaporation.

The (e, eṕ) reaction on 142Nd and 146Nd: A search for deformation effects

In a search for nuclear deformation effects in the (e, e'p) reaction, proton knockout from the spherical nucleus 142Nd and the transitional isotope 146Nd has been investigated. Momentum distributions for the transitions to the discrete states below 1.3 MeV excitation energy in 141Pr and below 0.6 MeV in 145Pr have been measured and compared to results of calculations with the Nilsson + BCS model, assuming 146Nd to be deformed and including Coriolis coupling. For the transitions to the 7 2 + states ( 1g 7 2 knockout) the spectroscopic strength changes in going from 142Nd to 146Nd but the shape of the momentum distribution remains fairly unchanged. The same is true for the 5 2 + states. For the transition to the 3 2 + state at 0.348 MeV in 145Pr, the measured momentum distribution is influenced by a mixture of ∼ 25% s-wave in agreement with the prediction of a close-lying 1 2 + state in the deformed shell model. The theory is well able to account for the increased level density in 145Pr and for the other experimental features observed, but the calculated spectroscopic factors are systematically larger than the experimental ones.

On the fine-structure splitting in $$\bar p$$ atoms

Recent measurements of fine-structure splitting in $$\bar p$$ atoms of174Yb are analysed. Effects of nuclear deformation are calculated. The strength of nuclear spin-orbit coupling is determined and its implications on theN $$\bar N$$ potential are discussed.

Radioactivities by light fragment (C, Ne, Mg) emission

Recently, heavy nuclei known as α-emitters like Ra and U isotopes have been found to present parallel emissions of 14C, 24Ne and 28Mg with very low branching ratios (< 10-9). Today, the spontaneous emission by heavy nuclei of fragments intermediate between 4He and fission fragments has become a well established field of research. The theory has been developed since 1980 and the first experimental discovery was published in 1984. Now, there are four known 14C emitters (222,223,224, 226Ra) and four 24Ne emitters (230Th, 231Pa, 232, 233U). Probably 25Ne is present in the results of 233U. Two kinds of radioactivity, 28Mg and Ne (probably 24Ne and 26Ne), have been measured from 234U, previously known for its cold fission. Some measurements gave upper limits in branching ratios ; in particular, an upper limit for the Si emission from 241 Am of ~ 10-15 relative to α emission has been set. After a brief review of the theoretical models which have oriented the experimental discoveries, the experiments are described. They are grouped according to the technique used to identify the emitted fragment : ΔE x E telescope in direct view of the source, magnetic spectrometers and solid state track detectors. The experimental results are compared with the theoretical predictions. We present the systematics studies which have given evidence of odd-even effects in the parent nucleus, have analysed the nuclear deformation effects and have proposed a unified approach of α-decay, fragment emissions and cold fission. Finally, it is shown how these new radioactivities are being used to test and refine very elaborate models of α-decay and fission.

Effect of nuclear deformation on few-quasiparticle state densities.

A microscopic combinatorial approach is used to investigate the influence of the nuclear deformation on the distributions of quasiparticle states. It is shown that nuclear deformation tends to suppress strong fluctuations observed in the similar calculations performed in the space of spherical shell-model basis vectors. The dependence of the pairing effects on the deformation is analyzed. The applicability of the formula by Williams is examined and found to be only valid for strongly deformed medium and heavy nuclei.

Effects of nuclear deformation in quasi-elastic electron scattering

We discuss effects due to nuclear deformation that can be observed in quasi-elastic electron scattering from deformed nuclei. To simplify the discussion we restrict ourselves to the plane wave impulse approximation (PWIA) and compare the form of the spectral function for axially symmetric deformed nuclei with that for spherical nuclei in the independent particle model. We point out that a strong dependence on deformation can be expected for momentum distributions measured in narrow missing energy ranges. This is illustrated taking 28Si as an example.

Effect of rotation on the isovector giant dipole resonance in certain calcium isotopes.

The isovector giant dipole resonances in certain rapidly rotating calcium isotopes wherein the bulk of the angular momentum is of an aligned nature are analyzed microscopically in the framework of the random phase approximation. The shape and deformation of the above nuclei at high spins are determined by the Mottelson-Nilsson method for rotating light nuclei. The allowed angular velocities for these deformations are obtained by the Fermi liquid drop model. The splitting of the resonance energies and the changes in the photoabsorption cross sections caused by rotation are studied in these nuclei by a simple schematic model of a rotating anisotropic harmonic oscillator which is justifiable in the case of the light nuclei considered. The results obtained show the general broadening of resonance widths in these light nuclei similar to that observed in the case of rare earth nuclei. The narrowing down of resonance widths in certain cases at higher angular momenta, suspected in lighter nuclei experimentally, is also theoretically observed and explained in the case of $^{40}\mathrm{Ca}$ as due to the shrinking effect of nuclear deformation at high spins.

Double beta decay in the interacting boson approximation

In order to include the effects of nuclear deformation in the calculation of the nuclear many-body matrix element involved in the double beta proay process, we have performed a calculation in the interacting boson approximation. An explicit expression for the boson image of the 2ϵB transition operator is given. Results for the 128,130TeåXe decays are presented. The calculation indicates that the nuclear deformation strongly hinders the double beta decay.

The RMS radii of the charge distribution in nuclei

A semi-empirical formula for calculating the RMS radii of the charge distribution in stable nuclei and nuclei close to stability with Z, N>or=5 is presented. The results of calculations of the RMS radii for a spherical distribution of charge in deformed and diffused nuclei under rotation, which is assumed to be the Fermi distribution, are also presented. In both calculations the neutron shell effect is observed in addition to the nuclear deformation effect.