Vibrations and potential energy surfaces (with Argonne V18) of⁴He and³He

A potential energy surface is constructed for^3,4He with the two-body Argonne V18 potential. The minimization suggests a semi-rigid asymmetric top structure for⁴He, where the appropriate pointgroup symmetry is C ₂. We calculate the Hessian matrix, determining the 6 normal modes of vibration (in the range 300-700 MeV). The breathing mode is found to lie at too high an energy to be observable and the nature of the $0_2^{+}$ excited states of the alpha particle at 20 MeV should probably be sought elsewhere. Similar investigations have been carried out for the A=3 system, finding a planar C_s configuration (scalene triangle) and three excited vibrational states (in the range 600-1900 MeV). (paper)