Excited collective states of heavy even-even nuclei

Quadrupole-type collective excitations of even-even nuclei are analyzed. In this analysis, transverse γ vibrations of the nuclear surface are taken into account effectively, while longitudinal beta vibrations remain free. A potential energy of the exponential form is used for free surface longitudinal beta vibrations. The behavior of the energy levels of excited states in the ground-state, β, and γ bands of heavy nuclei is studied, and the predictive potential of the model used is demonstrated for transfermium nuclei.     

Study of the potential energy of “octupole”-deformed nuclei in a multidimensional deformation space

The collective potential energy of even-even “octupule”-deformed nuclei is studied in a multidimensional deformation space in both radium and barium regions. This energy is calculated by the macroscopic-microscopic method, with the Yukawa-plus-exponential model taken for the macroscopic part and the Strutinski shell correction (based on the Woods-Saxon single-particle potential) used for the microscopic part of the energy. The deformations β_λ of all multipolarity degrees: λ = 2, 3, …, 7 (or even 8) are treated as independent variables. The multipolarities: λ = 5, 6 and 7, usually omitted or treated in an average way up to now, are found to be important for the properties of the nuclei.     

Nuclear shapes and interaction potentials of two colliding208Pb nuclei at finite temperature

The effect of nuclear and Coulomb interactions on the shapes of two colliding²⁰⁸Pb nuclei at finite temperature is investigated. The complex potential energy density derived by Faessler and collaborators and the kinetic energy density and entropy density for two Fermi spheres at finite temperature are used to calculate the free energy of the²⁰⁸Pb +²⁰⁸Pb system in the energy density formalism. Shell corrections are added to the free energy in the framework of the Strutinsky method. The total free energy is minimized with respect to the quadrupole deformation and the diffuseness to determine the density distribution of²⁰⁸Pb nucleus at certain distanceR and temperatureT assuming the deformed Woods-Saxon shape for each nucleus. It is found that the nucleus acquires larger deformation and diffuseness as the temperature increases. The interaction potential between two²⁰⁸Pb nuclei is calculated from the minimized free energy. The total (nuclear + Coulomb) potential is found to decrease with increasing temperature, whereas the real part of the nuclear potential becomes more repulsive as the temperature increases.     

Microscopic quadrupole and hexadecapole moments of rare earth nuclei

The theoretical calculations of multipole moments of even-even rare earth nuclei are presented. The potential energy surface is evaluated by the shell correction method. The condition ensuring the equality of the density distribution of the macroscopic liquid droplet part of the potential energy and the density generated by the single particle potential is added. A single particle Nilsson potential is used. New, less stiff potential surfaces versusε ₄ are obtained while the multipole moments calculated at the equilibrium deformations agree well with experimental data.     

Calculation of multidimensional potential energy surfaces for even-even transuranium nuclei: systematic investigation of the triaxiality effect on the fission barrier

Static fission barriers for 95 even-even transuranium nuclei with charge number Z = 94-118 have been systematically investigated by means of pairing self-consistent Woods-Saxon-Strutinsky calculations using the potential energy surface approach in multidimensional(β_2, γ, β_4) deformation space. Taking the heavier (252)~Cf nucleus(with the available fission barrier from experiment) as an example, the formation of the fission barrier and the influence of macroscopic, shell and pairing correction energies on it are analyzed. The results of the present calculated β_2 values and barrier heights are compared with previous calculations and available experiments. The role of triaxiality in the region of the first saddle is discussed. It is found that the second fission barrier is also considerably affected by the triaxial deformation degree of freedom in some nuclei(e.g., the Z =112-118 isotopes). Based on the potential energy curves, general trends of the evolution of the fission barrier heights and widths as a function of the nucleon numbers are investigated. In addition, the effects of Woods-Saxon potential parameter modifications(e.g.,the strength of the spin-orbit coupling and the nuclear surface diffuseness) on the fission barrier are briefly discussed.     

Coherent meson production in antinucleon annihilation on nuclei

A phenomenological optical potential for antinucleon-nucleon (N?N) interaction in an energy range of 1 to 15 GeV is presented in an eikonal model. In addition to the discussion of the strength and energy dependence, the potential is used to describe initial state interactions for coherent meson production on nuclei. To describe nuclear matter effects, Hartree-Fock Bogoliobuv (HFB) densities are used. As a first step we calculate the production of two mesons, namely pions. To cover the large energy range, the final state pion-nucleus ( π A) interaction is improved by adding resonances beyond the Δ resonance to a Kisslinger-type ansatz. Results for N?N and π A cross sections are presented.     

Inclusion of the Δ resonance in the optical potential between two nuclei and its application to medium energy12C-12C scattering

An energy dependent complex optical potential between two nuclei is calculated from the potential energy density for two colliding nuclear matters generated by solving the Bethe-Goldstone equation in whichNΔ and ΔΔ channels are explicitly coupled to theNN channel. By adding the contributions from the third and fourth order ring diagrams and the relativistic correction to the calculated potential energy density, the saturation property of a nuclear matter is reasonably well reproduced. This is used together with the kinetic energy density to calculate the optical potential for the¹²C+¹²C system in the energy density formalism with the local density approximation. The surface correction term and the symmetry energy term in the energy density functional are determined to reproduce the observed binding energy and the rms radius of¹²C. Using this potential, the differential cross sections for elastic¹²C-¹²C scattering atE _lab=1440 and 2400 MeV are calculated and compared with recent experimental data.     

Relativistic mean-field study on proton skins and proton halos in exotic nuclei

We investigate the ground state properties of proton-rich nuclei in the framework of the relativistic mean-field model. Calculations show that the experimental proton halo in the nuclei ^26,27,28P can be reproduced by the model. The proton halos can appear in proton-rich nuclei because the total nuclear potential is attractive up to the radial distance r ≈ 5.5 fm. But the size of proton halos is finite due to the limitation of the Coulomb potential barrier. The mean-square radius of a halo proton is not very sensitive to the separation energy of the last proton in some very proton-rich nuclei due to the effect of the Coulomb barrier. This behavior is different from the case of a neutron halo where the mean-square radius of a halo neutron is inversely proportional to the separation energy of the last halo neutron. We have also analysed the differences of the relativistic mean-field potentials of ²⁵Al and ²⁶P and found that the isovector potential from the p meson has an important effect on the differences.     

A Systematic Study on 1neutron and 2neutron Halo Nuclei Using Coulomb and Nuclear Proximity Potential

The halo-structure of a nucleus is analyzed on the basis of potential energy consideration and separation energy calculations and thereby characterized a nucleus as a halo nucleus. The separation energy analysis showed that ¹¹Be, ¹⁴B, ^{15, 17, 19}C, ²²N, ²³O, ^{24, 26}F, and ²⁹Ne are 1n-halo nuclei since the 1n separation energy S(n) is the lowest and ^{6, 8}He, ¹¹Li, ¹⁴Be, ¹⁷B, ²²C, and ²⁹F are 2n-halo candidates as 2n separation energy S(2n) is the lowest. The potential energy calculations are consistent with the predictions based on separation energy calculations except for ¹²Be, ¹⁹B, and ²⁷F which can be considered as 2n-halo candidates by potential energy consideration. Also, a discrepancy is noticed in the case of the proposed 2n-halo ⁸He and ¹⁷B nuclei. Further, the possibility of emitting halo nucleus via heavy particle decay of heavy nuclei, within the range 82?≤?Z?≤?102, has been studied using the Coulomb and proximity potential model (CPPM). It is observed that the probability of emission of a halo nucleus is lower than that of a normal cluster Nevertheless, there is a finite chance of emission of a halo nucleus in the decay of a heavy nucleus.     

Semi-microscopic calculation of the level density in spherical nuclei

The level density at the neutron binding energy for 90 spherical nuclei in the interval 50 < A < 205 is calculated by a method of direct counting of the number of states taking into account collective vibrational excitations. The results of calculations are in satisfactory agreement with the experimental data. The difference in the level density of doubly even and odd-A nuclei is correctly described. The effect of nuclear vibrations on the level density is studied, and it is shown that the account of them leads to an increase in the density by a factor of 1.5–10 and to a decrease in the density fluctuations. It is also studied how the level density depends on excitation energy. With increasing excitation energy, our results come nearer the corresponding values obtained by the statistical model. It is found that the density fluctuations decrease with increasing excitation energy but remain still strong at the neutron binding energy for nuclei with A = 50–70 and for nuclei around closed shells. The density ρ(I^π) is studied as a function of spin and parity. It is shown that at the neutron binding energy the ratio $\text{ρ(I}{}^{\mathrm{+}}\text{)}\text{ρ(I}{}^{\mathrm{?}}\text{)}$ is different from unity for the majority of nuclei. This difference is especially striking for ⁵⁷Fe and ⁵⁸Fe nuclei.     

Emission of helium nuclei in heavy ion interactions at energies ≧ 100 MeV/nucleon

The energy and angular distributions of helium particles emitted in interactions between nuclei in the cosmic radiation and nuclei in photoemulsions at energies ≧ 100 MeV/nucleon have been studied. The data obtained is impossible to interpret on the basis of a statistical decay of excited nuclei. For example, it is found that more than 28% of the helium nuclei are emitted in processes different from simple evaporation. The differential energy distribution of the helium nuclei in the energy interval (40–200) MeV can be represented by the relationN(E)dE=constE ^?a dE, wherea≈1.2. The large spread in angles and energies of the fast helium particles emitted in heavy ion interactions can to a certain degree be understood, if it is assumed that interactions between nucleons and clusters of nucleons occur.     

Unified approach to alpha decay calculations

With the discovery of a large number of superheavy nuclei undergoing decay through α emissions, there has been a revival of interest in α decay in recent years. In the theoretical study of α decay the α-nucleus potential, which is the basic input in the study of α-nucleus systems, is also being studied using advanced theoretical methods. In the light of these, the Wentzel–Kramers–Brillouin (WKB) approximation method often used for the study of α decay is critically examined and its limitations are pointed out. At a given energy, the WKB expression uses barrier penetration formula for the determination of the transmission coefficient. This approach utilizes the α-nucleus potential only at the barrier region and ignores it elsewhere. In the present era, when one has more precise experimental information on decay parameters and better understanding of α-nucleus potential, it is desirable to use a more precise method for the calculation of decay parameters. We describe the analytic S-matrix (SM) method which gives a procedure for the calculation of decay energy and mean life in an integrated way by evaluating the resonance pole of the S-matrix in the complex momentum or energy plane. We make an illustrative comparative study of WKB and S-matrix methods for the determination of decay parameters in a number of superheavy nuclei.     

Nuclei from the barium region: Nonaxial or gamma-soft?

The possibility is studied of describing nuclei from the Ba, Xe region in terms of the quadrupole collective model with theγ-independent potential energy surface. Results show that the nuclei in question can be treated both asγ-soft vibrators and nonaxial rotors.     

Binding energies and modelling of nuclei in semiclassical simulations

We study the binding energies of spin–isospin saturated nuclei with nucleon number 8?A?100$8?A?100$ in semiclassical Monte Carlo many-body simulations. The model Hamiltonian consists of (i) nucleon kinetic energy, (ii) a nucleon–nucleon interaction potential, and (iii) an effective Pauli potential which depends on density. The basic ingredients of the nucleon–nucleon potential are a short-range repulsion, and a medium-range attraction. Our results demonstrate that one can always expect to obtain the empirical binding energies for a set of nuclei by introducing a proper density dependent Pauli potential in terms of a single variable, the nucleon number, A. The present work shows that in the suggested procedure there is a delicate counterbalance of kinetic and potential energetic contributions allowing a good reproduction of the experimental nuclear binding energies. This type of calculations may be of interest in further reproduction of other properties of nuclei such as radii and also exotic nuclei.     

Total muon capture rates for N = Z nuclei in the 1p shell

The approach to total muon capture rates by means of sum rule techniques is applied systematically to 1p shell nuclei. Explicit calculations involve ground-state wave functions extracted from Cohen-Kurath effective interactions. For the double commutator expectation value we use a form of the potential consistent with the effective interaction and the giant dipole resonance energy.Results are given for N = Z nuclei, studying the minimal sensitivity with the parameter of the improved closure approach. The manifestations of SU(4) breaking are quantitatively shown. Within the uncertainties of the model the rates thus obtained compare reasonably well with experiment.     

Energetics of the fission process

The mass asymmetry of fragments from nuclear fission of heavy nuclei is reviewed. While mass asymmetry is a common and well-known phenomenon for low-energy fission of the lighter actinides, more recent experiments have demonstrated that, for the heaviest actinides, the mass distribution switches to a symmetric one. On the other hand, it has been discovered that, though for fissioning nuclei with mass numbersA225 the mass distribution is basically symmetric, an asymmetric component is clearly to be identified for nuclei down to the Pb-region. In the absence of a generally accepted dynamical theory of fission, the above experimental findings are discussed in terms of static energy considerations. Triggered from the outset by the structure of the potential energy surface at the saddlepoint, the energy balance at the scission point between the available energy (Q-value) of the reaction and the Coulomb and deformation energy of the nascent fragments is shown to steer the characteristics of the fragment mass distributions.     

Level-density parameters in the back-shifted Fermi gas model

The parameters a and δ_eff appearing in the back-shifted Fermi gas model are determined for about 3000 nuclei on the basis of modern estimated experimental data and the proposed systematics. For 272 of these nuclei, the parameters are deduced from experimental data on the cumulative numbers of low-lying levels and on mean spacings between S-wave neutron resonances at the neutron binding energy in the nuclei. For 952 nuclei, the parameter δ_eff is calculated by using the cumulative numbers of low-lying levels and values of the parameter a that were obtained via an interpolation from the points corresponding to the aforementioned 272 nuclei. For the remaining nuclei, the parameters a and δ_eff are obtained on the basis of the proposed systematics. An expression is constructed for taking into account the damping of shell effects with increasing excitation energy of nuclei. The results are compared with those from other studies.     

Effects of shell correction on α decay properties

The shell correction effects on the α decay properties of heavy and superheavy nuclei have been studied in a macroscopic-microscopic manner. The macroscopic part is constructed from the generalized liquid drop model(GLDM), whereas the microscopic part, namely, the shell correction energy, brings about certain effects on the potential barriers and half-lives under a WKB approximation, which is emphasized in this work. The results show that the shell effects play a significant role in the estimation of the α decay half-lives within the actinide region.Predictions of the α decay half-lives are then generated for superheavy nuclei, which will provide useful information for future experiments.     

Estimating the occupation probabilities of single-particle orbits in nuclei

Occupation probabilities of neutron and proton single-particle orbits are estimated for a number of spherical and close to spherical nuclei with 20 ≤ Z ≤ 50 and 20 ≤ N ≤ 82 near the Fermi energy. The estimates are made according to the formula of the BCS theory with single-particle energies calculated using the mean-field model with dispersive optical potential. The closeness of the occupation probabilities to 0 and 1 is demonstrated for nuclei with traditional and new magic numbers.     

Nuclear Structure of 12,14Be Within Deformed Quasi-Particle Random Phase Approximation (DQRPA)

We developed a deformed quasi-particle random phase approximation (DQRPA) to describe the Gamow–Teller (GT) transitions on even–even neutron-rich nuclei. To describe deformed nuclei, we exploited the deformed axially symmetric Woods–Saxon potential, the deformed BCS, and the deformed QRPA with realistic two-body interaction calculated by Brueckner G-matrix based on Bonn CD potential. The deformed single particle states are expanded in terms of the spherical harmonic oscillator basis in order to take the realistic G-matrix stored in the spherical basis. We calculated GT strength distributions, B(GT), of two nuclei ^12,14Be for many different deformation parameter β ₂ values as a function of the excitation energy E _ex w.r.t. the ground state of a parent nucleus. Our results for ¹²Be predict to prefer a prolate shape and B(GT) results of ¹⁴Be turn out to be independent of the β ₂ values.