Shape transitions in neutron-rich Yb, Hf, W, Os, and Pt isotopes within a Skyrme Hartree-Fock + BCS approach

9 pages, 1 table, 7 figures.-- PACS nrs.: 21.60.Jz; 27.70.+q; 27.80.+w.Self-consistent axially symmetric Skyrme Hartree-Fock plus BCS calculations are performed to study the evolution of shapes with the number of nucleons in various chains of Yb, Hf,W, Os, and Pt isotopes from neutron number N = 110 up to N = 122. Potential energy curves are analyzed in a search for signatures of oblate-prolate phase shape transitions, and results from various Skyrme and pairing forces are considered. Comparisons with results obtained with the Gogny interaction as well as with relativistic mean field calculations are presented. The role of the γ degree of freedom is also discussed.This work was partly supported by Ministerio de Educación y Ciencia (Spain) under Contract Nos. FIS2005-00640 and FPA2007-66069.Peer reviewe