sarkas.tools.observables.RadialDistributionFunction.compute_sum_rule_integrals

RadialDistributionFunction.compute_sum_rule_integrals(potential)

Compute integrals of the RDF used in sum rules.

The species dependent integrals are

\[I_{AB}^{\rm (Hartree, k)} = 2^{D - 2} \pi n_{A} n_{B} \int_0^{\infty} dr \, r^{D - 1 + k} \frac{d^k}{dr^k} \phi_{AB}(r),\]

\[I_{AB}^{\rm (Corr, k)} = 2^{D - 2} \pi n_{A} n_{B} \int_0^{\infty} dr \, r^{D - 1 + k} h_{AB} (r) \frac{d^k}{dr^k} \phi_{AB}(r),\]

where \(D\) is the number of dimensions, \(k = {0, 1, 2}\), and \(\phi_{AB}(r)\) is the potential between species \(A\) and \(B\).

Only Coulomb and Yukawa potentials are supported at the moment.

Parameters

potential (sarkas.potentials.core.Potential) – Sarkas Potential object. Needed for all its attributes.

Returns

• hartrees (numpy.ndarray) – Hartree integrals with \(k = {0, 1, 2}\).

  Shape = ( sarkas.tools.observables.Observable.no_obs, 3).

• corrs (numpy.ndarray) – Correlational integrals with \(k = {0, 1, 2}\).

  Shape = ( sarkas.tools.observables.Observable.no_obs, 3).