the equipotentials.

In a second step, let us consider how to circumvent the difficulty of the angular expansion of the above PES, in order to obtain reliable expansions for He and H$_2$ (eqs \[eq:pot\] and \[eq:pot2\]).

Using the angular spline representation, we first expressed each PES over a fine $\theta_1$ mesh suitable for a subsequent high $l_1$ expansion. As expected from the work of @chapman77, high $l_1$ expansions (\[eq:pot\]) resulted in severe Gibbs oscillations for $R$ in the range 5–7 Bohr, spoiling completely the description of the low energy features of the PES. Then, having in mind low energy scattering applications, we regularized the PES by introducing a scaling function $S_f$. We replaced $V(R,\theta_1,...)$ by $S_f(V(R,\theta_1,...))$, where $S_f(V)$ returns $V$ when $V$ is lower than a prescribed threshold, and then smoothly saturates to a limiting value when $V$ grows up into the repulsive walls. Consequently, the regularized PES retains only the low energy content of the original PES, unmodified up to the range of the threshold energy; it should not be used for higher collisional energies. However, in contrast to the original PES, it can be easily expanded over Legendre functions to an excellent accuracy and is thus suitable for 