The present work is devoted to a study of the Heisenberg model of the He atom. We consider the subset of the singlet states, in which one of the electron is kept on its 1s orbital. This spectrum is treated as a pseudo two-body problem. Use is made of a method designed to solve the inverse problem from bound states to determine the local equivalent potential seen by the second electron. The problem is simplified by the use of parametric expressions instead of a full numerical determination of the local equivalent potential. It keeps the numerical effort to a reasonable level. By construction, the local equivalent potential should fit the experimental eigenvalues, which is well achieved with the proposed simplified expressions. It shows the validity of the Heisenberg model for the excited states. It yields also a value for the mean square radius of the He atom. This one is in good qualitative agreement with the value derived from large basis calculations of the He ground state