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In this paper, the Slater integrals for a screened Coulomb interaction of thethe Yukawa form are calculated and by fitting the Thomas-Fermi wavevector, goodagreement is obtained with experiment for the multiplet spectra of $Pr^{3+}$and $U^{4+}$ ions. Moreover, a predicted multiplet spectrum for the heavyfermion 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 correlatedelectron metals.Comment: 8 pages, revtex, 3 uuencoded postscript figure

physical review. b, condensed matter

Calculation of effective Coulomb interaction for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Pr</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">U</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn><mml:mo>+</mml:mo></mml…

Calculation of effective Coulomb interaction forPr3+,U4+