Developing a Hartree-Fock program, a simple Python program

An example of a function written in python which performs the Hartree-Fock calculation is shown here. In setting up your code you will need to write a function which sets up the single-particle basis, the matrix elements \( t_{\alpha\gamma} \) of the one-body operator (called \( h0 \) in the function below) and the antisymmetrized TBMEs (called nninteraction in the code link below) and the density matrix elements \( \rho_{\beta\delta} \) (called densityMatrix below). The python program shows how one can, in a brute force way read in matrix elements in \( m \)-scheme and compute the Hartree-Fock single-particle energies for four major shells. The interaction which has been used is the so-called N3LO interaction of Machleidt and Entem using the Similarity Renormalization Group approach method to renormalize the interaction, using an oscillator energy \( \hbar\omega=10 \) MeV.

The nucleon-nucleon two-body matrix elements are in \( m \)-scheme and are fully anti-symmetrized. The Hartree-Fock programs uses the density matrix discussed above in order to compute the Hartree-Fock matrix. Here we display the Hartree-Fock part only, assuming that single-particle data and two-body matrix elements have already been read in.