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

Possibility of an ultra-precise optical clock using the 61S0→63P0o6 ^1S_0 \to 6 ^3P^o_0 transition in 171,173^{171, 173}Yb atoms held in an optical lattice

We report calculations designed to assess the ultimate precision of an atomic clock based on the 578 nm $6 ^1S_0 --> 6 ^3P^o_0$ transition in Yb atoms confined in an optical lattice trap. We find that this transition has a natural linewidth less than 10 mHz in the odd Yb isotopes, caused by hyperfine coupling. The shift in this transition due to the trapping light acting through the lowest order AC polarizability is found to become zero at the magic trap wavelength of about 752 nm. The effects of Rayleigh scattering, higher-order polarizabilities, vector polarizability, and hyperfine induced electronic magnetic moments can all be held below a mHz (about a part in 10^{18}), except in the case of the hyperpolarizability larger shifts due to nearly resonant terms cannot be ruled out without an accurate measurement of the magic wavelength.Comment: 4 pages, 1 figur

Observed photodetachment in parallel electric and magnetic fields

We investigate photodetachment from negative ions in a homogeneous 1.0-T magnetic field and a parallel electric field of approximately 10 V/cm. A theoretical model for detachment in combined fields is presented. Calculations show that a field of 10 V/cm or more should considerably diminish the Landau structure in the detachment cross section. The ions are produced and stored in a Penning ion trap and illuminated by a single-mode dye laser. We present preliminary results for detachment from S- showing qualitative agreement with the model. Future directions of the work are also discussed.Comment: Nine pages, five figures, minor revisions showing final publicatio

Dynamic hyperpolarizability and two-photon detachment in the presence of a strong static electric field: Application to H\u3csup\u3e-\u3c/sup\u3e

Our recent analysis [J. Phys. B 33, R141 (2000)] of the problem of H- in both laser and strong static electric fields, which treated effects that are linear in the laser intensity l (e.g., the dynamic polarizability and the single-photon detachment cross section), is extended here to treat effects of higher order (∼l2) in the laser intensity (e.g., the dynamic hyperpolarizability, the two-photon detachment cross section, the linear in l corrections to the single-photon detachment rate, etc). We introduce the concept of the dynamic hyperpolarizability of an atom in the presence of a strong electric field based on the complex quasienergy approach with properly normalized, quasistationary quasienergy wave functions. Our analysis of the general structure of the dynamic hyperpolarizability tensor of an atom in a nondegenerate (S-) state is performed for arbitrary field geometries and laser polarizations. The connection of the hyperpolarizability γ(F;ω) to the complex quasienergy and to atomic ionization rates is established. Analytic results (in terms of Airy functions) are obtained for five irreducible components of a hyperpolarizability tensor (that are independent of the laser polarization and the field geometry) for the case of a weakly bound electron in a three-dimensional, zero-range potential. These results are used for the analysis of the frequency, field geometry, and laser polarization dependence of the two-photon detachment rate as well as of the linear in laser intensity corrections to the single-photon detachment rate. It is shown that the oscillatory behavior of the frequency dependence of both the real and the imaginary parts of γ(F;ω) exists for both the coplanar and orthogonal field geometries, and that this behavior is qualitatively different for frequencies below and above the single-photon detachment threshold. The threshold behavior of the two-photon detachment rate is analyzed in detail and the static electric-field-induced modification of Wigner’s threshold law for a short-range potential is discussed

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)]

Threshold-Related Enhancement of the High-Energy Plateau in Above-Threshold Detachment

We present nonperturbative theoretical results showing a resonant-like enhancement of above-threshold detachment spectra in the region of the high-energy plateau as the laser intensity sweeps across channel thresholds. This enhancement has a pure quantum origin stemming from well-known threshold phenomena in multichannel problems whose features are clearly demonstrated in our numerical results. Similar well-known anomalies at neutral atom thresholds are expected to explain experimentally observed resonant-like enhancements of above-threshold ionization spectra

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