Mathematical and computational science issues in high precision Hylleraas–configuration interaction variational calculations: II. Kinetic energy and electron–nucleus interaction integrals

Abstract

Three-electron kinetic energy and electron-nucleus interaction integrals arising in Hylleraas-configuration interaction (Hy-CI) calculations are discussed. We show that the electron-nucleus interaction operators introduce no new integral complications and that the kinetic energy operators lead to integrals which have much in common with electron interaction integrals treated in the first paper of this series. We discuss the efficient evaluation of the kinetic energy integrals and give selected values of the integrals to 30 digit accuracy. The one new W auxiliary function which arises in treating the kinetic energy operator is discussed in appendix B. We also give a few details on accurate evaluations of the Condon and Shortley c k s which arise in Hy-CI calculations in appendix A.

Atomic excitations during the nuclearβ−decay in light atoms

“…Expressions for all these integrals are given in Refs. [13][14][15]. The calculation of the overlap between the wave functions of bound states require only the usual two-and three-electron integrals.…”

Evaluation of Hylleraas–CI atomic integrals by integration over the coordinates of one electron. IV. An improved algorithm for three-electron kinetic energy integrals

“…Some of the integrals of Table I are the same ones than in Table 6 of Ref. [6], some are reproduced values of integrals from Table 1 of the paper of Sims and Hagstrom [8], and the last values are new integrals obtained with non-vanishing I ϕ contributions, which represent rare cases. The agreement with previous values of paper I of this series and the ones of Sims and Hagstrom is complete (about 30 decimal digits in our computer using quadruple precision).…”

“…[6] and several integrals of Table 1 of Ref. [8]. The charge distributions are constructed with the exponents ω i =1.40 for orbitals with , otherwise ω i = 2.86.…”

“…Finally, computed values of selected integrals of Refs. [6,8] and of new kinetic energy integrals are given in this work.…”

“…The earlier method is the one of Sims and Hagstrom [8,9], where the interelectronic distances r ij are expanded into one-electron distances. The expansion of the interelectronic distances is a concept they use systematically in the evaluation of all kind of integrals.…”