## Hartree-Fock algorithm

Solving the Hartree-Fock eigenvalue problem yields then new eigenvectors $$C_{i\alpha}^{(1)}$$ and eigenvalues $$\epsilon_i^{HF(1)}$$.

• With the new eigenvalues we can set up a new Hartree-Fock potential
$$\sum_{j = 1}^A\sum_{\gamma\delta} C_{j\gamma}^{(1)}C_{j\delta}^{(1)}\langle \alpha\gamma|\hat{v}|\beta\delta\rangle_{AS}.$$ The diagonalization with the new Hartree-Fock potential yields new eigenvectors and eigenvalues. This process is continued till for example $$\frac{\sum_{p} |\epsilon_i^{(n)}-\epsilon_i^{(n-1)}|}{m} \le \lambda,$$ where $$\lambda$$ is a user prefixed quantity ($$\lambda \sim 10^{-8}$$ or smaller) and $$p$$ runs over all calculated single-particle energies and $$m$$ is the number of single-particle states.