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Frank E Harris

Publications and source records attributed to Frank E Harris.

4 recordsLinked to original sources
PubMed2005

Highly compact wave functions for He-like systems.

Wave functions which are compact, but still quite accurate, are extremely valuable as tools for gaining understanding of quantum systems. This paper investigates the use for that purpose of functions that depend exponentially on all the interparticle distances of a few-body system, illustrated by a study of the ground electronic states of the He isoelectronic series (Z from 1 to 10). Using as few as 4 exponential basis functions, it is found that nonrelativistic energies are reproduced to within 38 microhartrees of the exact values, an error far less than for previously reported compact wave functions. Other properties are also well-represented.

Journal Article↗
PubMed2004

Singular and nonsingular three-body integrals for exponential wave functions.

Integrals which are individually singular, but which may be combined to yield convergent expressions, are needed for computations of relativistic effects and various properties of atomic and quasiatomic systems. As computations become more detailed and precise, more such integrals are required. This paper presents general formulas for the radial parts of the singular and nonsingular (regular) integrals that occur when three-body systems are described using wave functions that include exponentials in all three interparticle coordinates. Our results are compared with those found in the literature for some of the integrals, and are also shown to be consistent with previously reported results for Hylleraas functions (a limiting case in which one of the exponential parameters is set to zero).

Journal Article↗
PubMed2004

Highly accurate evaluation of atomic three-electron integrals of lowest orders.

Calculations of three-electron atomic systems in Hylleraas coordinates require integrals involving all the interparticle distances r(ij), which have usually been evaluated by introducing series expansions. For integrals with the smallest powers of r(ij) these expansions do not converge at a satisfactory rate, leading some investigators to introduce convergence-acceleration procedures. This paper recommends the alternative of evaluating these integrals in closed form and presents stable explicit formulas for so doing. Some of the formulas are more compact versions of those in the literature; others have not been previously reported. It is also shown that finite-difference methods can be used with advantage to obtain additional low-order integrals. Sample integral values have been provided for test purposes.

Journal Article↗