Satoshi Takahara

Extensive Hartree-Fock+BCS calculation with Skyrme SIII force

Abstract We have performed deformed Hartree-Fock+BCS calculations with the Skyrme SIII force for the ground states of even-even nuclei with 2 ⩽ Z ⩽ 114 and N ranging from outside the proton drip line to beyond the experimental frontier in the neutron-rich side. We obtained spatially localized solutions for 1029 nuclei, together with the second minima for 758 nuclei. The single-particle wavefunctions are expressed in a three-dimensional Cartesian-mesh representation, which is suitable to describe nucleon skins, halos, and exotic shapes as well as properties of ordinary stable nuclei. After explaining some of the practical procedures of the calculations, we compare the resulting nuclear masses with experimental data and the predictions of other models. We also discuss the quadrupole ( m =0, 2) and hexadecapole ( m =0, 2, 4) deformations, the skin thicknesses, the halo radii, and the energy difference between the oblate and prolate solutions. Our results can be obtained via internet.

Pairing correlation in nuclear matter from Skyrme force

Abstract The properties of pairing correlation in nuclear matter are investigated by using various versions of Skyrme forces. Truncation of states involving pairing correlation, necessary due to zero range nature of the Skyrme force, is discussed in detail. A plateau appears in pairing gap versus cutoff for each force. We propose to choose the cutoff parameter in the middle of the plateau so that the parameterization is independent of nuclides.

Improved microscopic-macroscopic approach incorporating the effects of continuum states

The Woods-Saxon-Strutinsky method (the microscopic-macroscopic method) combined with the Kruppa prescription for positive-energy levels, which is necessary to treat neutron-rich nuclei, is studied to clarify the reason for its success and to propose improvements for its shortcomings. The reason why the plateau condition is met for the Nilsson model but not for the Woods-Saxon model is understood in a new interpretation of the Strutinsky smoothing procedure as a low-pass filter. Essential features of the Kruppa level density is extracted in terms of the Thomas-Fermi approximation modified to describe spectra obtained from diagonalization in truncated oscillator bases. A method is proposed, which weakens the dependence on the smoothing width by applying the Strutinsky smoothing only to the deviations from a reference level density. The BCS equations are modified for the Kruppa spectrum, which is necessary to treat the pairing correlation properly in the presence of a continuum. The potential depth is adjusted for the consistency between the microscopic and macroscopic Fermi energies. It is shown, with these improvements, that the microscopic-macroscopic method is now capable to reliably calculate binding energies of nuclei far from stability.

Study of superdeformation in non-rotating states using the Skyrme-Hartree-Fock method

Abstract Superdeformation (SD) in non-rotating states is studied with the HF + BCS method using the Skyrme interaction. In applying the BCS theory, the seniority pairing force is employed, of which strengths are determined in order to reproduce the empirical pairing gap formula, Δ − = 12A − 1 2 , through a smooth level density obtained in the Thomas-Fermi approximation. Properties of superdeformation are investigated by calculating potential energy surfaces (PES) for various sets of the pairing force strengths and the Skyrme force parameter for 194Hg and 236,238U. The best results are obtained using both the SkM∗ force and the pairing force strength determined in this paper. By making use of this set of forces, a systematic calculation of SD states is carried out extensively for even-even nuclei for 20 ⩽ Z ⩽ 82. From our calculation, the barriers preventing the decay into the normally deformed states are about twice as high as those predicted by Krieger et al., who used the same Skyrme interaction but a pairing force stronger than ours.

Nuclear prolate-shape dominance with the Woods-Saxon potential

We study the prolate-shape predominance of the nuclear ground-state deformation by calculating the masses of more than 2000 even-even nuclei using the Strutinsky method, modified by Kruppa, and improved by us. The influences of the surface thickness of the single-particle potentials, the strength of the spin-orbit potential, and the pairing correlations are investigated by varying the parameters of the Woods-Saxon potential and the pairing interaction. The strong interference between the effects of the surface thickness and the spin-orbit potential is confirmed to persist for six sets of Woods-Saxon potential parameters. The observed behavior of the ratios of prolate, oblate, and spherical nuclei versus potential parameters are rather different in different mass regions. The ratio of spherical nuclei is found to increase for weakly bound unstable nuclei. Differences from the results of calculations performed using the Nilsson potential are described in detail.

Relation between Density-Matrix Theory and Pairing Theory

The time-dependent density-matrix theory (TDDM) gives a correlated ground state as a stationary solution of the time-dependent equations for one-body and two-body density matrices. The small amplitude limit of TDDM (STDDM) is a version of extended RPA theories which include the effects of ground state correlations. It is shown that the solutions of the Hartree-Fock Bogoliubov theory and the quasi-particle RPA satisfy the TDDM and STDDM equations, respectively, when only pairing-type correlations are taken into account in TDDM and STDDM.

On the Error of the Dixon Plot for Estimating the Inhibition Constant between Enzyme and Inhibitor.

In textbook treatments of enzyme inhibition kinetics, adjustment of the initial inhibitor concentration for inhibitor bound to enzyme is often neglected. For example, in graphical plots such as the Dixon plot for estimation of an inhibition constant, the initial concentration of inhibitor is usually plotted instead of the true inhibitor concentration. Justification for this approximation should be presented to students, because in certain conditions it can be inaccurate.

Deformed Hartree-Fock calculation of proton-rich nuclei

Abstract We perform Hartree-Fock+BCS calculations for even-even nuclei with 2 ≤ Z ≤ 82 and N ranging from outside the proton drip line to the experimental frontier on the neutron-rich side. The ground state solutions are obtained for 737 nuclei, together with shape-coexistence solutions for 480 nuclei. Our method features the Cartesian-mesh representation of single-particle wavefunctions, which is advantageous in treating nucleon skins and exotic shapes. The results are compared with those of the finite-range droplet model of Moller et al. as well as the experimental values.