Canonical-basis Time-Dependent Hartree-Fock-Bogoliubov Theory and Linear-Response Calculation for Light to Heavy Nuclei

Abstract

We have developed a new theory to study excited states and dynamics of atomic nuclei, which we call the Canonical-basis time-dependent Hartree-Fock-Bogoliubov (Cb-TDHFB). The CbTDHFB is a simplified theory of the full TDHFB theory, treating pairing energy functional with a BCS-like approximation which is assumed to be diagonal in the canonical basis. Implementing the theory with a real-space and real-time method, we can describe nuclear excitations and dynamics taking account of deformation effects and pairing correlations, even for heavy nuclei with a reasonable computational costs. In this thesis, we first present a derivation of the CbTDHFB theory and we apply the method to linear-response calculations for even-even light to heavy nuclei and demonstrate its capability and accuracy by comparing our results with recent calculations of the quasi-particle random-phase approximation (QRPA) which is equivalent to the small amplitude limit of TDHFB, with Skyrme functionals. We derived the Cb-TDHFB equations starting with the full TDHFB equations, introducing a simplified form for the pairing energy functional. In the derivation, we start with the ordinary TDHFB equation written in terms of the time-dependent generalized density matrix R(t) which is composed of the time-dependent normal density matrix ρ(t) and the pairing tensor κ(t). We then rewrite the equation in the canonical basis, which diagonalize ρ(t). The derived TDHFB equations in the canonical basis has a very simple form. However, they are not useful practically for a general case since it costs much to obtain the canonical basis themselves at each time. Solving the time-dependent equation for the canonical basis is as difficult as solving the full TDHFB equation. This difficulty disappears if we employ a simplified pairing energy density functional, which is equivalent to that employed in the BCS approximation for ground state calculations. For linear response calculations, we present results of the Cb-TDHFB calculations for excited states of some spherical and deformed nuclei to show performance of the method. We show strength functions of isovector dipole and isoscalar quadrupole excitations for some spherical and deformed nuclei. First, we show the comparison results of Cb-TDHFB with the QRPA in order to confirm the justification of canonical-basis formulation and the reduction of computational cost with this new framework. We show isoscalar quadrupole strength functions of neutron-rich nucleus 34Mg for confirmation of our new method, and also discuss full self-consistent calculations of 24Mg as an example of light nucleus and 208Pb and 154Sm as an example of heavy nuclei, in order to be clear, especially, the effects of spin-orbit and Coulomb residual interaction. Next, in order to show typical strength functions for spherical and deformed nuclei, we discuss isovector dipole and isoscalar quadrupole mode for 34Si as an example of spherical nucleus, for 34Mg as an example of prolate deformed nucleus and for 24Ne as an example of oblate deformed nucleus. For a confirmation of computational cost of the calculation using Cb-TDHFB, we isovector dipole strength functions of deformed heavy nuclei 172Yb and 236−240U. We show then the comparison our results with experimental data for photo-nuclear reaction cross sections. And we also show systematic calculations low-energy E1 strength which is often called Pygmy dipole resonance and which is well-known as a important strength to understand nucleosynthesis. In this thesis, we discuss the appearance of low-energy E1 strength functions of C, O, Ne, Mg, Si, S, Ar and Ca isotopes which are relatively light nuclei.