On the quadrupole moments of nuclear particle-hole states

A method is proposed to calculate in a simple way quadrupole moments and deformations of nuclear particle-hole states. The method can be applied to states described by any linear combination of isotropic harmonic oscillator wave functions belonging to the same energy. The method is illustrated by calculating the quadrupole moments of the 1-( T = 1) and 1-( T = 0) states in ¹⁶O, which are described by the wave functions that Gillet obtained by diagonalizing an adjusted residual interaction. The largest deformations with β ≈ 0.18 and β ≈ -0.16 are found for the 18 MeV and 19 MeV 1-( T = 1) states respectively. The largest deformations of the T = 0 states are somewhat smaller.