The β⁴ potential at the U(5)-O(6) critical point of the Interacting Boson Model

Exact numerical results of the interacting boson model Hamiltonian along the integrable line from U(5) to O(6) are obtained by diagonalization within boson seniority subspaces. The matrix Hamiltonian reduces to a block tridiagonal form which can be diagonalized for large number of bosons. We present results for the low energy spectrum and the transition probabilities for systems up to 10000 bosons, which confirm that at the critical point the system is equally well described by the Bohr Hamiltonian with a $\beta^4$ potential.