VAMPIR describes shape coexistence in nuclei

The measurements of shape coexistence of the Vanderbilt-Oak Ridge-LSU-Georgia-Tech-Group is shortly reviewed for the Hg isotopes and the mass 70 region. Then this contribution concentrates on the description of shape coexistence with the help of refined self-consistent fields plus correlations. The basic approach is VAMPIR which starts from an angular momentum, proton and neutron number and parity projected Hartree-Fock-Bogoliubov quasi-particle Slater determinant. VAMPIR stands for Variation After Mean field Projection In Realistic models spaces. Minimization of orthogonalized projected HFB states yields also shape coexistence exited states of the same symmetries. Those states can then be diagonalized to include correlations (excited VAMPIR=EV). One can even improve on EV by adding in a second step to VAMPIR a second projected HFB-Slater determinant with unknown Bogoliubov transformation coefficients. The energy is now minimized by varying the mixing coefficients of the two Slater determinants and the Bogoliubov transformation in the second state. This can be continued step by step always using the previously fixed HFB-Slater determinants and determining only one in addition and the mixing coefficients of all the projected HFB-Slater determinants. The method is tested in sd-shell nuclei and applied in the A=70 region to the Ge and Se isotopes, where the Vanderbilt-Oak Ridge-group found a large number of different shapes in nuclei