Exact ground state of several N-body problems with an N-body potential

I consider several N-body problems for which exact (bosonic) ground state and a class of excited states are known in case the N-bodies are also interacting via harmonic oscillator potential. I show that for all these problems the exact (bosonic) ground state and a class of excited states can also be obtained in case they interact via an N-body potential of the form $-e^2/\sqrt{\sumr^2_i}$ (or $-e^2/\sqrt{\sum_{i