Concerning 10C and 10Be, the experimental B(E2;0+ -> 2+) values indicate large deformations: |a20|=0.82 for 10C and 1.1 for 10Be. However, the potential energy curves in the figure have only the spherical minimum. The quantum fluctuation in shape may be able to account for the large B(E2) since the curves are very soft toward prolate deformations.
For 12C, the experimental B(E2) is very large (corresponding to |a20|=0.59) and an oblate intrinsic deformation with a triangular three-alpha-cluster configuration has been suggested. However, the HF+BCS calculation with the SIII force, as well as other widely-used Skyrme forces of the SkM* and the SGII, gives a potential energy curve which has only one minimum at the spherical shape. Consequently, the largest deviation from the experimental |a20| occurs in this nucleus. An old Skyrme force SII gives an oblate minimum with delta=-0.27 [Va73].
Let us briefly report on the three-alpha-cluster linear-chain state of 12C. By extending the potential energy curve in the figure to larger delta, we have found the first excited minimum at delta ~ 1.0, in good agreement with the result of the Nilsson model for the linear-chain state (delta=1.1) [ZZC91]. The excitation energy from our calculation is 21 MeV. Though it is much larger than the experimental value of 7.654 MeV, the overestimation will be improved by the angular momentum projection.