Isospin Dependence of Proton and Neutron Radii within Relativistic Mean Field Theory

The binding energies, shapes and sizes of even-even beta-stable nuclei with A >= 40 and a few chains of isotopes with Z=50, 56, 82, 94 protons and isotones with N=50, 82, 126 neutrons are analyzed. The average isospin dependence of the radii of protons and neutrons evaluated within the relativistic mean field theory is studied. A simple, phenomenological formula for neutron radii is proposed.Comment: 10 pages in Latex and 14 figures in the eps forma

Simple Formula for Nuclear Charge Radius

A new formula for the nuclear charge radius is proposed, dependent on the mass number (A) and neutron excess (N-Z) in the nucleus. It is simple and it reproduces all the experimentally available mean square radii and their isotopic shifts of even--even nuclei much better than other frequently used relations.Comment: The paper contains 7 pages in LateX and 6 figures (available upon request) in postscript. Email: [email protected]

Interaction Strengths for the Fock-Space Formulation of the Nuclear Pairing Problem

A realistic nuclear mean-field hamiltonian with pairing has been diagonalized using Fock space representation that allows for nearly exact treatment of the problem. Calculations were performed for all the even-even nuclei with Z in (20, 100), whose pairing gaps were possible to extract out of the experimental masses. The optimal values of the pairing strength constants for the protons and neutrons have been found.Comment: Seminar given at XXXVII School of Physics in Zakopane, Poland. Paper in LaTeX, 4 pages including one figure, submitted to Acta Physica Polonica

Global Properties of Spherical Nuclei Obtained from Hartree-Fock-Bogoliubov Calculations with the Gogny Force

Selfconsistent Hartree-Fock-Bogoliubov (HFB) calculations have been performed with the Gogny force for nuclei along several constant Z and constant N chains, with the purpose of extracting the macroscopic part of the binding energy using the Strutinsky prescription. The macroscopic energy obtained in this way is compared to current liquid drop formulas. The evolution of the single particle levels derived from the HFB calculations along the constant Z and constant N chains and the variations of the different kinds of nuclear radii are also analysed. Those radii are shown to follow isospin-dependent three parameter laws close to the phenomenological formulas which reproduce experimental data.Comment: 17 pages in LaTeX and 17 figures in eps. Phys. Rev. C, accepted for publicatio

Ground state properties of the β\beta stable nuclei in various mean field theories

The separation energies of neutrons and protons, binding energies, mean square charge radii, electric quadrupole moments and deformation parameters of the proton and neutron distributions are evaluated for $\beta$ stable even-even nuclei with $16 \leq A \leq 256$. We compare the theoretical estimates obtained within the Hartree-Fock plus BCS model with a few sets of Skyrme forces, relativistic mean-field theory and frequently used Saxon-Woods and Nilsson potentials with experimental data.Comment: 15 pages, latex, 3 tables, 14 figures in thr eps format include

Parametrizations of triaxial deformation and E2 transitions of the wobbling band

By the very definition the triaxial deformation parameter $\gamma$ is related to the expectation values of the K=0 and K=2 components of the intrinsic quadrupole tensor operator. On the other hand, using the same symbol "$\gamma$", various different parametrizations of triaxial deformation have been employed, which are suitable for various types of the mean-field potentials. It is pointed out that the values of various "$\gamma$" are quite different for the same actual triaxial deformation, especially for the large deformation; for example, the difference can be almost a factor two for the case of the triaxial superdeformed bands recently observed in the Hf and Lu nuclei. In our previous work, we have studied the wobbling band in Lu nuclei by using the microscopic framework of the cranked Nilsson mean-field and the random phase approximation, where the most serious problem is that the calculated B(E2) value is about factor two smaller. It is shown that the origin of this underestimation can be mainly attributed to the small triaxial deformation; if is used the same triaxial deformation as in the analysis of the particle-rotor model, the calculated B(E2) increases and gives correct magnitude compared with the experimental data.Comment: 10 pages, 9 figure

Effect of differences in proton and neutron density distributions on fission barriers

The neutron and proton density distributions obtained in constrained Hartree-Fock-Bogolyubov calculations with the Gogny force along the fission paths of 232Th, 236U, 238U and 240Pu are analyzed. Significant differences in the multipole deformations of neutron and proton densities are found. The effect on potential energy surfaces and on barrier heights of an additional constraint imposing similar spatial distributions to neutrons and protons, as assumed in macroscopic-microscopic models, is studied.Comment: 5 pages in Latex, 4 figures in ep