Spin-orbit interaction assumes Hydrogenic potential

[gerardhiggins]

In the code nvwcpp.c and on the primer on the website, the spin-orbit interaction

V_{so}(r)= \frac{\alpha \vec{L} \cdot \vec{S}}{2r^3}

It should be

V_{so}(r)= \frac{\alpha^2 \vec{L} \cdot \vec{S}}{2r^3} \frac{dV}{dr}

In a Hydrogenic potential

\frac{dV}{dr} =  \frac{e^2}{4\pi \epsilon_0 r^2} =  \frac{1}{\alpha}

Which matches the formula in the code (I think the minus signs are all fine).

Anyway why not use the screened potential when calculating the spin-orbit interaction?
Then one would change nvwcpp.c to

inline double Potenital(double r, double step){
	// l<4
	double V1 = CorePotential(r);
	double V2 = CorePotential(r+step);
	double dVdr = (V2-V1)/step;
	double Vso = pow(alpha,2)*commonTerm1*dVdr/(2*r);
	return V1 + Vso;
}

or if one wants to have a spin-orbit interaction which is well-behaved as r->0 an extra term can be included as is done in eq 3.31 of Aymar et al Rev. Mod. Phys. 68, 1015 (1996)

inline double Potenital(double r, double step){
	// l<4
	double V1 = CorePotential(r);
	double V2 = CorePotential(r+step);
	double dVdr = (V2-V1)/step;
	double Vso = pow(alpha,2)*commonTerm1*dVdr/(2.0*r*pow((1.0-pow(alpha,2)*V1/2.0),2));
	return V1 + Vso;
}

[nikolasibalic]

One would have to test if the simplest numerical approximation of dVdr = (V2-V1)/step is not introducing more errors than current implementation. The current implementation is done in this way since spin-orbit interaction can have (relatively) significant effect only for high l states anyway, and this states are essentially a Hydrogen states (quantum defects go to 0).

@gerardhiggins Do you any specific example showing that this is introducing observable inaccuracy in calculation?

[nikolasibalic]

I am closing this issue due to inactivity. In my tests I couldn't see need for change (due to above explained reasoning), but please reopen this issue if you have example where this causes some known inaccuracies.