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

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. •Analytical expressions for ab initio matrix elements on any spherical basis.•Discussions of the main differences with respect to standard basis used in the field.•Pedagogical introductions to the main mathematical expressions.