E2 core polarization for sd-shell single-particle states calculated with a skyrme-type interaction

We have studied the core-polarization effect on the 1s0d-shell single-particle electromagnetic quadrupole transitions due to coupling with the quadrupole giant resonances. The self-consistent Hartree-Fock + RPA method is applied for the calculations of the single-particle wave functions and the response functions of the giant resonances. The particle-vibration-coupling model is used to calculate the core-polarization effect in the vicinity of ¹⁶O and ⁴⁰Ca. The effective coupling hamiltonian is determined by the SGII Skyrme-type interaction which is used in the HF + RPA and particle-vibration-coupling calculation. The results are discussed for the proton and neutron effective charges and for the longitudinal and transverse form factor for the $\text{0}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{→ 1}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ pro single-particle transition in ³⁹K. Good agreement with recent longitudinal data for this transition is obtained.