Yasutoshi Tanaka

Hartree–Fock–Bogoliubov calculation of charge radii of Sn, Ba, Yb and Pb isotopes

Abstract Charge radii of Sn, Ba, Yb and Pb isotopes are calculated within Hartree–Fock–Bogoliubov theory with a Skyrme force and a density-dependent delta-force pairing. We investigate mean-field effects of the pairing upon odd–even staggering of isotope shifts. HFB equations are solved in the canonical basis. Odd nuclei are treated in the blocking approximation.

Nuclear polarization in hydrogenlike 82 208 Pb 8 1

We calculate nuclear-polarization energy shifts for the hydrogenlike 2 0 8 8 2 Pb 8 1 + . The retarded transverse part as well as the longitudinal part is taken into account as the electromagnetic interaction between an electron and the nucleus. With a finite charge distribution for the nuclear ground state and the random-phase approximation to describe the nuclear excitations, we obtain nuclear-polarization energy of the 1s 1 / 2 state as -38.2 (-37.0) meV in the Feynman (Coulomb) gauge. For the 2s 1 / 2 , 2p 1 / 2 , and 2p 3 / 2 states, they are -6.7 (-6.4), -0.2 (-0.2), and +0.0 (+0.0) meV, respectively. The transverse contribution is small in comparison with the longitudinal nuclear-polarization correction. It is about 12% both for the 1s 1 / 2 and 2s 1 / 2 states. The seagull term in the two-photon exchange diagrams is also shown to be quite important to obtain the gauge-invariant nuclear-polarization energies.

Transverse nuclear polarization in muonic 208Pb

Abstract In light of the recent finding of the discrepancies between theory and experiment in the Δ2p and Δ3p fine-structure splitting energies of muonic 208Pb, we have studied the effect of the electromagnetic transverse interaction on the nuclear-polarization energy shifts of muonic 208Pb. The reasons for this study are that the electric transverse interaction interferes coherently with the Coulomb interaction giving rise to large nuclear-polarization energy shifts, and that the transverse interaction may give nuclear-polarization energies of different muon-spin dependences from those of the Coulomb interaction. The calculation is based on the transition charge and current densities constructed from the random-phase approximation with the density-dependent contact interaction of Migdal and with particle-hole excitations of nearly a full 3 h ω space. The real part of the Feynman propagator was employed in the electromagnetic transverse interaction. The transverse interaction is found to explain 111 eV of the Δ2p binding-energy anomaly, which is one third of the total discrepancy, while it reduces the Δ3p anomaly by 32 eV. Large portions ofthe discrepancies still remain in both cases.

Oblate–prolate transition in odd-mass light mercury isotopes

Abstract Anomalous isotope shifts in the chain of light Hg isotopes are investigated by using the Hartree–Fock–Bogoliubov method with the Skyrme SIII, SkI3 and SLy4 forces. The sharp increase in the mean-square radius of the odd mass 181–185Hg isotopes is well explained in terms of the transition from an oblate to a prolate shape in the ground state of these isotopes. We discuss the polarization energy of time-odd mean-field terms in relation to the blocked level by the odd neutron.

Nuclear polarization in hydrogenlike 20882Pb81

We calculate nuclear-polarization energy shifts for the hydrogenlike 2 0 8 8 2 Pb 8 1 + . The retarded transverse part as well as the longitudinal part is taken into account as the electromagnetic interaction between an electron and the nucleus. With a finite charge distribution for the nuclear ground state and the random-phase approximation to describe the nuclear excitations, we obtain nuclear-polarization energy of the 1s 1 / 2 state as -38.2 (-37.0) meV in the Feynman (Coulomb) gauge. For the 2s 1 / 2 , 2p 1 / 2 , and 2p 3 / 2 states, they are -6.7 (-6.4), -0.2 (-0.2), and +0.0 (+0.0) meV, respectively. The transverse contribution is small in comparison with the longitudinal nuclear-polarization correction. It is about 12% both for the 1s 1 / 2 and 2s 1 / 2 states. The seagull term in the two-photon exchange diagrams is also shown to be quite important to obtain the gauge-invariant nuclear-polarization energies.

Nuclear polarization in hydrogenlike82208Pb81

We calculate nuclear-polarization energy shifts for the hydrogenlike 2 0 8 8 2 Pb 8 1 + . The retarded transverse part as well as the longitudinal part is taken into account as the electromagnetic interaction between an electron and the nucleus. With a finite charge distribution for the nuclear ground state and the random-phase approximation to describe the nuclear excitations, we obtain nuclear-polarization energy of the 1s 1 / 2 state as -38.2 (-37.0) meV in the Feynman (Coulomb) gauge. For the 2s 1 / 2 , 2p 1 / 2 , and 2p 3 / 2 states, they are -6.7 (-6.4), -0.2 (-0.2), and +0.0 (+0.0) meV, respectively. The transverse contribution is small in comparison with the longitudinal nuclear-polarization correction. It is about 12% both for the 1s 1 / 2 and 2s 1 / 2 states. The seagull term in the two-photon exchange diagrams is also shown to be quite important to obtain the gauge-invariant nuclear-polarization energies.

Charge conservation for nonrelativistic RPA theory

Abstract Charge conservation for nonrelativistic RPA theory of finite nuclei is investigated. Charge conservation of the RPA is proved with effective one-body operators by taking the angular momentum coupling into account. For LS-closed shell nuclei, it is proved that this charge conservation is valid also in truncated particle-hole spaces.