  Ab initio studies of atomic nuclei are based on Hamiltonians including one-,
two- and three-body operators with very complicated structures. Traditionally,
matrix elements of such operators are expanded on a Harmonic Oscillator
single-particle basis, which allows for a simple separation of the
center-of-mass motion from the intrinsic one. A few recent investigations have
showed that the use of different single-particle bases can bring significant
advantages to numerical nuclear structure computations. In this work, the
complete analytical expression of the Hamiltonian matrix elements expanded on a
generic spherical basis is presented for the first time. This will allow
systematic studies aimed at the determination of optimal nuclear bases.
