Canonical-basis solution of the Hartree-Fock-Bogoliubov equation on three-dimensional Cartesian mesh

A method is presented to obtain the canonical-form solutions of the HFB equation for atomic nuclei with zero-range interactions like the Skyrme force. It is appropriate to describe pairing correlations in the continuum in coordinate-space representations. An improved gradient method is used for faster convergences under constraint of orthogonality between orbitals. To prevent high-lying orbitals to shrink into a spatial point, a repulsive momentum dependent force is introduced, which turns out to unveil the nature of high-lying canonical-basis orbitals. The asymptotic properties at large radius and the relation with quasiparticle states are discussed for the obtained canonical basis.Comment: 23 pages including 17 figures, REVTeX4, revised version, scheduled to appear in Phys. Rev. C, Vol.69, No.

Gamma-ray Polarimetry

An astrophysics application of a low noise Double-sided Silicon Strip Detector (DSSD) is described. A Semiconductor Multiple-Compton Telescope (SMCT) is being developed to explore the gamma-ray universe in the 0.1-20 MeV energy band. Excellent energy resolution and polarization sensitivity are key features of the SMCT. We have developed prototype modules for a low noise DSSD system, which reached an energy resolution of 1.3 keV (FWHM) for 122 keV at 0 degree C. Results of a gamma-ray imaging test are also presented.Comment: 6 pages, 9 figures. Contributed to International Workshop on Vertex Detectors, Kailua-Kona, Hawaii USA, November 3-8, 200

Hartree-Fock+BCS approach to unstable nuclei with the Skyrme force

We reanalyze the results of our extensive Hartree-Fock + BCS calculation from new points of view paying attention to the properties of unstable nuclei. The calculation has been done with the Skyrme SIII force for the ground and shape isomeric states of 1029 even-even nuclei ranging 2 <= Z <= 114. We also discuss the advantages of the employed three-dimensional Cartesian-mesh representation, especially on its remarkably high precision with apparently coarse meshes when applied to atomic nuclei. In Appendices we give the coefficients of finite-point numerical differentiation and integration formulae suitable for Cartesian mesh representation and elucidate the features of each formula and the differences from a method based on the Fourier transformation.Comment: 31 pages including 21 figures, Latex2

Analytical formula for numerical evaluations of the Wigner rotation matrices at high spins

The Wigner d function, which is the essential part of an irreducible representation of SU(2) and SO(3) parameterized with Euler angles, has been know to suffer from a serious numerical errors at high spins, if it is calculated by means of the Wigner formula as a polynomial of cos and sin of half of the second Euler angle. This paper shows a way to avoid this problem by expressing the d functions as the Fourier series of the half angle. A precise numerical table of the coefficients of the series is obtainable from a web site.Comment: 5 pages, 5 figure