Collective multipole expansions and the perturbation theory in the quantum three-body problem

The perturbation theory with respect to the potential energy of three particles is considered. The first-order correction to the continuum wave function of three free particles is derived. It is shown that the use of the collective multipole expansion of the free three-body Green function over the set of Wigner $D$-functions can reduce the dimensionality of perturbative matrix elements from twelve to six. The explicit expressions for the coefficients of the collective multipole expansion of the free Green function are derived. It is found that the $S$-wave multipole coefficient depends only upon three variables instead of six as higher multipoles do. The possible applications of the developed theory to the three-body molecular break-up processes are discussed.Comment: 20 pages, 2 figure

Factorized representation for parity-projected Wigner d\u3csup\u3e\u3ci\u3ej\u3c/i\u3e\u3c/sup\u3e (β) matrices

An alternative representation for the parity-projected Wigner dj(β) rotation matrix is derived as the product of two triangular matrices composed of Gegenbauer polynomials with negative and positive upper indices, respectively. We relate this representation for dj(β) to the one presented by Matveenko [Phys. Rev. A 59, 1034 (1999)], which, in contrast with our result, requires for its evaluation a matrix inversion. In addition, identities for bilinear sums of Gegenbauer polynomials are derived. This work is based on our recently introduced invariant representations for finite rotation matrices [Phys. Rev. A 57, 3233 (1998)]

Nondipole effects in double photoionization of He at 450 eV excess energy

Convergent close-coupling results for the triply differential cross section for double photoionization of He that include dipole-quadrupole terms are shown to have improved agreement (as compared to dipole approximation results) with recent experiments using linearly polarized light (Knapp A et al 2005 J. Phys. B: At. Mol. Opt. Phys. 38 615) for a number of kinematical configurations

Nondipole effects in double photoionization of He at 450 eV excess energy

Convergent close-coupling results for the triply differential cross section for double photoionization of He that include dipole–quadrupole terms are shown to have improved agreement (as compared to dipole approximation results) with recent experiments using linearly polarized light (Knapp A et al 2005 J. Phys. B: At. Mol. Opt. Phys. 38 615) for a number of kinematical configurations

Expressing Crystallographic Textures through the Orientation Distribution Function: Conversion between the Generalized Spherical Harmonic and Hyperspherical Harmonic Expansions

In the analysis of crystallographic texture, the orientation distribution function (ODF) of the grains is generally expressed as a linear combination of the generalized spherical harmonics. Recently, an alternative expansion of the ODF, as a linear combination of the hyperspherical harmonics, has been proposed, with the advantage that this is a function of the angles that directly describe the axis and angle of each grain rotation, rather than of the Euler angles. This article provides the formulas required to convert between the generalized spherical harmonics and the hyperspherical harmonics, and between the coefficients appearing in their respective expansions of the ODF. A short discussion of the phase conventions surrounding these expansions is also presented.National Science Foundation (U.S.) (contract DMR- 0346848)National Science Foundation (U.S.) (contract DMR-0855402