Calculation of Effective Coulomb Interaction for $Pr^{3+}$, $U^{4+}$, and $UPt_3$

TL;DR

This paper calculates effective Coulomb interactions for specific ions and a superconductor using screened Coulomb models, providing data useful for many-body calculations in correlated electron systems.

Contribution

It introduces a method to compute effective Coulomb interactions using Yukawa-screened Coulomb integrals, matching experimental spectra and predicting properties of UPt3.

Findings

Good agreement with experimental spectra for Pr^{3+} and U^{4+} ions.

Predicted multiplet spectrum for UPt3 with Coulomb U of 1.6 eV.

Effective Coulomb interactions are simple to calculate and useful for many-body models.

Abstract

In this paper, the Slater integrals for a screened Coulomb interaction of the the Yukawa form are calculated and by fitting the Thomas-Fermi wavevector, good agreement is obtained with experiment for the multiplet spectra of $Pr^{3+}$ and $U^{4+}$ ions. Moreover, a predicted multiplet spectrum for the heavy fermion superconductor $UPt_3$ is shown with a calculated Coulomb U of 1.6 eV. These effective Coulomb interactions, which are quite simple to calculate, should be useful inputs to further many-body calculations in correlated electron metals.