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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 Oscillatorsingle-particle basis, which allows for a simple separation of thecenter-of-mass motion from the intrinsic one. A few recent investigations haveshowed that the use of different single-particle bases can bring significantadvantages to numerical nuclear structure computations. In this work, thecomplete analytical expression of the Hamiltonian matrix elements expanded on ageneric spherical basis is presented for the first time. This will allowsystematic studies aimed at the determination of optimal nuclear bases.

Expansion of one-, two- and three-body matrix elements on a generic spherical basis for nuclear ab initio calculations