We produce giant helium dimers by photoassociation of metastable helium atoms in a magnetically trapped, ultracold cloud. The photoassociation laser is detuned red of the atomic 2 3 S1−2 3 P0 line and produces strong heating of the sample when resonant with molecular bound states. The temperature of the cloud serves as an indicator of the molecular spectrum. We report good agreement between our spectroscopic measurements and our calculations of the five bound states belonging to a 0 + u purely long-range potential well. These previously unobserved states have classical inner turning points of about 150 a0 and outer turning points as large as 1150 a0.PACS numbers: 34.20. Cf, 32.80.Pj, 34.50.Gb In the purely long-range molecules first proposed by Stwalley et al.[1], the binding potential depends only on the long-range part of the atom-atom interaction, and the internuclear distance is always large compared with ordinary chemical bond lengths. Theoretical description of these molecules involves only the leading C 3 /R 3 terms of the electric dipole-dipole interaction and the fine structure inside each atom. These well-known interactions allow precise calculation of potential wells and rovibrational energies. Previous experimental studies of such spectra in alkali atoms have utilized the technique of laser-induced photoassociation (PA) in a magneto-optical trap (MOT) [2,3]. In addition to testing calculations of molecular structure, that work has produced precise measurements of excited-state lifetimes [4,5,6,7] and has led to accurate determinations of s-wave scattering lengths for alkali systems, which are of interest for studies of Bose Einstein condensates (BECs) [8,9]. This letter reports novel spectroscopic measurements and calculations for extraordinarily long-range molecules that are produced when two 4 He atoms in the metastable 2 3 S 1 state absorb laser light tuned close to the 2 3 S 1 − 2 3 P 0 (D 0 ) atomic line at λ = 1083 nm. As compared with the alkali dimers considered previously, the potential wells are shallower, and molecules are much more tenuous, with an internuclear distance reaching values as large as 1150 a 0 (a 0 ≃ 0.53Å, the Bohr radius). At such large distances, retardation clearly influences the dipole-dipole interaction. Moreover, these purely longrange molecular states of metastable helium are distinctive in that each atom carries a high internal energy (the 2 3 S 1 state lies 20 eV above the ground state). While one normally expects Penning ionization to destabilize such * Electronic address: leonard@lkb.ens.fr † Permanent address: Calvin College, Grand Rapids, MI, USA. ‡ Permanent address: FOM instituut voor plasmafysica Rijnhuizen, and University of Twente, The Netherlands. § Present address: Institut für Quantenoptik, Universität Hannover, Germany.energetic molecules, we note that purely long-range interactions might rather suppress this process, since the atoms are effectively held apart by the same potential that binds them together. The absence of purely longrange resonances ...

For potentials with attractive tails, as occur in typical atomic interactions, we present a simple formula for the s-wave phase shift δ 0 . It exposes a universal dependence of δ 0 (E) on the potential tail and the influence of effects specific to a given potential, which enter via the scattering length a, or equivalently, the noninteger part th of the threshold quantum number n th . The formula accurately reproduces δ 0 (E) from threshold up to the semiclassical regime, far beyond the validity of the effective-range expansion. We derive the tail functions occurring in the formula for δ 0 (E) and demonstrate the validity of the formula for attractive potential tails proportional to 1/r 6 or to 1/r 4 , and also for a mixed potential tail consisting of a 1/r 4 term together with a non-negligible 1/r 6 contribution.

The influence of the electron spin degree of freedom on nonperturbative electron-positron pair production by high-energy proton impact on an intense laser field of circular polarization is analyzed. Predictions from the Dirac and Klein-Gordon theories are compared and a spin-resolved calculation is performed. We show that the various spin configurations possess very different production probabilities and discuss the transfer of helicity in this highly nonlinear process. Our predictions could be tested by combining the few-TeV proton beam at CERN-LHC with an intense laser pulse from a table-top petawatt laser source.