The interaction between atoms behaves as −α/r n at large distances, and, owing to the large reduced mass µ of the collision pair, allows semiclassical treatment within the potential well. As a result, the low-energy scattering is governed by two large parameters: the asymptotic parameter γ = √ 2µα/h ≫ a (n−2)/2 0 (a 0 is the Bohr radius), and the semiclassical zero-energy phase Φ ≫ 1. In our previous work [Phys. Rev. A 48, 546 (1993)] we obtained an analytical expression for the scattering length a, which showed that it has 75% preference for positive values for n = 6, characteristic of collisions between ground-state neutral atoms. In this paper we calculate the effective range and show that it is a function of a, r e = F n − G n /a + H n /a 2 , where F n , G n and H n depend only on γ. Thus, we know the s phase shift at low momenta k ≪ γ −2/(n−2) from the expansion k cot δ 0 ≃ −1/a +

We report a joint test of local Lorentz invariance and the Einstein equivalence principle for electrons, using long-term measurements of the transition frequency between two nearly degenerate states of atomic dysprosium. We present many-body calculations which demonstrate that the energy splitting of these states is particularly sensitive to violations of both special and general relativity. We limit Lorentz violation for electrons at the level of 10(-17), matching or improving the best laboratory and astrophysical limits by up to a factor of 10, and improve bounds on gravitational redshift anomalies for electrons by 2 orders of magnitude, to 10(-8). With some enhancements, our experiment may be sensitive to Lorentz violation at the level of 9 × 10(-20).

Including the Breit interaction leads to a 0.6% reduction in the magnitude of the 6s-7s paritynonconservation ͑PNC͒ amplitude in 133 Cs, confirming a result recently obtained by A. Derevianko ͓Phys. Rev. Lett. 85, 1618 ͑2000͔͒. A revised value of the theoretical PNC amplitude for 133 Cs is given; the corresponding value of the weak charge shows no noticeable deviation from the standard model.

We show that a dense spectrum of chaotic multiply excited eigenstates can play a major role in collision processes involving many-electron multicharged ions. A statistical theory based on chaotic properties of the eigenstates enables one to obtain relevant energy-averaged cross sections in terms of sums over single-electron orbitals. Our calculation of low-energy electron recombination of Au 25ϩ shows that the resonant process is 200 times more intense than direct radiative recombination, which explains the recent experimental results of Hoffknecht et al. ͓J. Phys. B 31, 2415 ͑1998͔͒.

A statistical theory of resonant multielectron recombination based on properties of chaotic eigenstates is developed. The level density of many-body states increases exponentially with the number of excited electrons. When the residual electron-electron interaction exceeds the interval between these levels, the eigenstates (called compound states or compound resonances if these states are in the continuum) become "chaotic" superpositions of large numbers of Hartree-Fock configurational basis states. This situation takes place in some rare-earth atoms and many open-shell multiply charged ions excited in the process of electron recombination. Our theory describes resonant multielectron recombination via dielectronic doorway states leading to such compound resonances. The result is a radiative capture cross section averaged over a small energy interval containing several compound resonances. In many cases individual resonances are not resolved experimentally (since the interval between them is small, e.g., 1 meV, possibly even smaller than their radiative widths); therefore, our statistical theory should correctly describe the experimental data. We perform numerical calculations of the recombination cross sections for tungsten ions W q+ , q = 18-25. The recombination rate for W 20+ measured recently [Schippers et al. Phys. Rev. A 83, 012711 (2011)] is 10 3 greater than the direct radiative recombination rate at low energies, and our result for W 20+ agrees with the measurements.