Developing a Hartree-Fock program, additional considerations

Note that $$\langle \alpha\vert\hat{h}_0\vert\beta \rangle$$ denotes the matrix elements of the one-body part of the starting hamiltonian. For self-bound nuclei $$\langle \alpha\vert\hat{h}_0\vert\beta \rangle$$ is the kinetic energy, whereas for neutron drops, $$\langle \alpha \vert \hat{h}_0 \vert \beta \rangle$$ represents the harmonic oscillator hamiltonian since the system is confined in a harmonic trap. If we are working in a harmonic oscillator basis with the same $$\omega$$ as the trapping potential, then $$\langle \alpha\vert\hat{h}_0 \vert \beta \rangle$$ is diagonal.