Pseudopotential Theory for Interionic Interionic Interaction Potentials in Metals at Non-Zero Temperature. I. : Elementary Derivation of Asymptotic Expressions on Basis of Hilbert Transforms

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An asymptotic expression F..j...,(r; 7') oj' a pair potential between ions in metals atnon-zero temperature 7:0 is given approximately by a form V,..,..,(r; C))D(r; 7'),where ]/......,(r; 0)= F.cos (2k.x')/(lk.r)' is the Friedel oscillatory potential atT=0, D(r; 7')=,v=cosech (,x') with x=n0c.T/E7)k.r is a danaping factor, k. theBoltzmann constant, k. and E. the Fermi wave number and the Fermi level.Lighthill's method for estimating asymptotic form of Fourier transforms of f (X) thatincludes a singular point is proved to be applicable also to transformed functionsFCx)=I fix -z)t<z; 7')dz,wherev(z; 7')=J(z)as7'=0.Ther>roofisdoneb>'theuse of Hilbert transforms, in which f(x)=1/x. This modifued Lighthill's methodderives V,.,...,(r; T) in the usual way thal. is used in pseudopotential treatment ofV,.?,..,(r; 0). Earlmer works by Kohn and Vosko, March and Murray, and Flynn andOdle are examined.[pseudopotentia1' poten- ll fiats, 'Hilbert [Z transfltheory, dielectric functions, asymptotic ex)cressxon, paurunteruonic potentials, interatomic potentials, temperature effects,orms
社団法人日本物理学会の論文
1992-11-15