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.