A simple analytical formula, a=a¯[1-tan(π/n-2)tan{Φ-[π/2(n-2)]}, is obtained for the scattering length in atomic collisions. Here a¯=cos[π/(n-2)]{ √2Mα /[ħ(n-2)]${\mathrm{\}}}^{2/\left(\mathit{n}\mathrm{-}2\right)}$[Γ(n-3)/(n-2)]/[T(n-1)/(n-2)] is the mean scattering length determined by the asymptotic behavior of the potential U(r)∼-α/${\mathit{R}}^{\mathit{n}}$, (n=6 for atom-atom scattering or n=4 for ion-atom scattering), M is the reduced mass of the atoms, and Φ is the semiclassical phase calculated at zero energy from the classical turning point to infinity. The value of a¯, the average scattering length, also determines the slope of the s-wave phase shifts beyond the near-threshold region. The formula is applicable to the collisions of atoms cooled down in traps, where the scattering length determines the character of the atom-atom interaction. Our calculation shows that repulsion between atoms (a>0) is more likely than attraction with a ‘‘probability’’ of 75%. For the Cs-Cs scattering in the ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{}{}_{}{}^{}$ state, a¯=95.5${\mathit{a}}_{\mathit{B}}$ has been obtained, where ${\mathit{a}}_{\mathit{B}}$ is the Bohr radius. The comparison of the calculated cross-section energy dependence with the experimental data gives evidence for a positive value for the Cs-Cs scattering length, which makes cesium Bose gas stable.

This article presents an overview of current understanding of the interaction of low-energy positrons with molecules with emphasis on resonances, positron attachment, and annihilation. Measurements of annihilation rates resolved as a function of positron energy reveal the presence of vibrational Feshbach resonances (VFRs) for many polyatomic molecules. These resonances lead to strong enhancement of the annihilation rates. They also provide evidence that positrons bind to many molecular species. A quantitative theory of VFR-mediated attachment to small molecules is presented. It is tested successfully for selected molecules (e.g., methyl halides and methanol) where all modes couple to the positron continuum. Combination and overtone resonances are observed and their role is elucidated. Molecules that do not bind positrons and hence do not exhibit such resonances are discussed. In larger molecules, annihilation rates from VFR far exceed those explicable on the basis of single-mode resonances. These enhancements increase rapidly with the number of vibrational degrees of freedom, approximately as the fourth power of the number of atoms in the molecule. While the details are as yet unclear, intramolecular vibrational energy redistribution (IVR) to states that do not couple directly to the positron continuum appears to be responsible for these enhanced annihilation rates. In connection with IVR, experimental evidence indicates that inelastic positron escape channels are relatively rare. Downshifts of the VFR from the vibrational mode energies, obtained by measuring annihilate rates as a function of incident positron energy, have provided binding energies for 30 species. Their dependence upon molecular parameters and their relationship to positron-atom and positron-molecule binding-energy calculations are discussed. Feshbach resonances and positron binding to molecules are compared with the analogous electron-molecule (negative-ion) cases. The relationship of VFR-mediated annihilation to other phenomena such as Doppler broadening of the gamma-ray annihilation spectra, annihilation of thermalized positrons in gases, and annihilation-induced fragmentation of molecules is discussed. Possible areas for future theoretical and experimental investigation are also discussed.

A simple analytical solution for the problem of multiphoton detachment from negative ions by a linearly polarized laser field is found. It is valid in the wide range of intensities and frequencies of the field, from the perturbation theory to the tunneling regime, and is applicable to the excess-photon as well as near-threshold detachment. Practically, the formulas are valid when the number of photons is greater than one. They produce the total detachment rates, relative intensities of the excess-photon peaks, and photoelectron angular distributions for the hydrogen and halogen negative ions, in agreement with those obtained in other, more numerically involved calculations in both perturbative and nonperturbative regimes. Our approach explains the extreme sensitivity of the multiphoton detachment probability to the asymptotic behavior of the bound-state wave function. Rapid oscillations in the angular dependence of the n-photon detachment probability are shown to arise due to interference of the two classical trajectories, which lead to the same final state after the electron emerges at diametrically opposite sides of the atom when the field is close to maximal.

The aim of the present paper is to analyze a realistic model of a quantum chaotic system: the spectrum and the eigenstates of the rare-earth atom of Ce. Using the relativistic configuration-interaction method the spectra and the wave functions of odd and even levels of Ce with J=4 are calculated. It is shown that the structure of the excited states at excitation energies above 1 eV becomes similar to that of the compound states in heavy nuclei. The wave functions of the excited states are chaotic superpositions of the simple basis states (with the number of ‘‘principal’’ components N∼100), built of the 4f, 6s, 5d, and 6p single-electron orbitals. The localization of the eigenstates on the energy scale is characterized by the spread width Γ∼ND, where D is the average level spacing (D∼0.03 eV). The emergence of chaos in the spectrum and the dependence of the N and Γ parameters on the excitation energy are studied. The shape of the localization is shown to be Lorenzian around the maximum (principal components), whereas outside this region the squared components display a faster decrease, in agreement with the perturbation theory treatment of the band random matrix (BRM) model. The structure of the real interaction matrix is compared with that assumed in the BRM models. A formula expressing the mean-squared values of matrix elements between the eigenstates in terms of their parameters and single-particle occupancies is derived, and its applicabilility is checked with the results of numerical calculations. The hypothesis of a Gaussian distribution of the eigenstates’ components and matrix elements between the eigenstates has been checked. The existence of the statistical (dynamical) enhancement of weak perturbations in systems with dense spectra is demonstrated.