A theoretical study is performed to re-evaluate the scattering length for spin-polarized metastable helium. The Σ5g+ potential is calculated with three huge basis sets, as well as one previously proposed, using two ab initio approaches: a large configuration interaction method and a coupled-cluster method. The influence of a dummy basis set is analyzed and shown to yield spurious behavior in the energy decrease, roughly Gaussian with changing separation of the dummy basis from the molecule. The scattering length is found to be extremely sensitive here even to tiny details of the potential because the potential is very close to supporting a fifteenth rotationless vibrational level. This behavior can be rationalized using semiclassical methods. From this study we conclude that there are certainly 15 vibrational levels and that the dissociation energy is most probably 1045.2±1 cm−1, while our final result for the scattering length, a=291 a0, is best considered as an upper limit.
Upper and lower bounds are estimated for the scattering length, a , for the various isotopes of spin-polarized metastable helium. From a previous study involving various large basis sets and two ab initio approaches, and paying special attention to combine them with the accurate long-range potential, we get, for 4 He*– 4 He* collisions (in Bohr) 152 < 4−4 a < 230 and for 3 He*– 3 He* collisions 94 < 3−3 a < 113, while a surprising result arises for mixed collisions, 3 He*– 4 He*, 3−4 a < −488 and 3−4 a > 865. Indeed, the scattering length for this species is very close to the divergence occurring at the binding of a 14th vibrational level. Within these limits, our approach suggests that the values for 4−4 a and 3−3 a are closer to their upper bounds than to their lower bounds, and that the value for 3−4 a is negative and very large (>500) in magnitude. Sympathetic cooling could therefore be very efficient for the mixed species. Cooling-rate coefficients are also evaluated: they are large, of order 10 −9 cm 3 s −1 at mK temperatures for all combinations.
We developed a series of correlation-consistent, polarized multiple zeta basis sets optimized specifically for the energy of the 2 3S state of helium atom. These basis sets were subsequently augmented with diffuse functions optimized for the van der Waals constants C6 through C14 which determine the asymptotic behavior of the second-order dispersion interaction between 2 3S helium atoms at large interatomic separation R. The resulting bases were applied to compute the Born-Oppenheimer (BO) potential for the lowest 5Sigmag+ state of the helium dimer. The coupled cluster and the full configuration-interaction techniques were employed to account for the electron correlation effects. The cardinal number extrapolation technique was used to obtain the complete-basis-set limit V(R) for the interaction potential and to find its lower VL(R) and upper VU(R) bounds. The resulting potentials were fitted to an analytical function containing accurate van der Waals constants C6 through C12 (including C11). We found that the complete-basis-set BO potential has a well depth De=1048.24+/-0.36 cm-1. The highest rotationless vibrational level is bound by D14=90.2+/-4.7 MHz, much stronger than the previous most accurate estimation of 15.2 MHz. The error bounds for De and D14 were obtained using the VL(R) and VU(R) potentials. The S-wave scattering length computed using the VL(R), V(R), and VU(R) potentials (assuming atomic masses) is aL=7.41 nm, a=7.54 nm, and aU=7.69 nm, respectively. We also computed the adiabatic, relativistic, and quantum electrodynamics (QED) corrections to the BO potential. When these corrections are taken into account the values of D14 and of a (both computed assuming nuclear masses) are 87.4+/-6.7 MHz and 7.64+/-0.20 nm; the error bounds reflect now also the uncertainty of the included adiabatic, relativistic, and QED corrections. The value of the scattering length resulting from our investigation lies outside the error bounds of all experimental determinations based on the properties of Bose-Einstein condensate of spin-polarized helium atoms.
A theoretical study is performed for the photoassociation of metastable helium. Combining short-range, high-level, ab initio calculations for 5 Σ g / u + and 5 Π g / u symmetries and long-range behaviour, better described in Hund's case (c), potential-energy curves for attractive, 5 Σ u + and 5 Π g , as well as repulsive, 5 Π u and 5 Σ g + , states of quintet metastable helium molecules dissociating to 2 3 S + 2 3 P are obtained. Taking into account the atomic spin-orbit couplings, vibrational levels are derived for near-dissociation levels at the 3 P 2 asymptote. Comparison with results from three recent photoassociation experiments obtained under different conditions (μK temperatures with spin alignment and mK temperatures without) allowed for an assignation of about three quarters of the observed levels. The robustness of the vibrational numbering is confirmed by testing a modification of the short-range potentials.
A new theoretical study for the photoassociation of metastable helium is presented, based on fully ab initio short-range potentials. Optimization of the exponents of the Gaussian orbitals of a smaller basis set than employed previously allowed the calculation of potentials dissociating to He(2 3 S)+He(2 3 P) at the multi-reference configuration interaction level down to internuclear separations of 3.5 a 0 . The good agreement with observed near-dissociation levels obtained previously using extrapolated short-range potentials is confirmed and almost all levels observed to the red of the He D 2 line, associated with the He 2 3 S + 2 3 P 2 dissociation limit, are assigned. The agreement is less satisfactory with the levels observed to the red of the He D 1 line, although vibrational levels have been found in the outer ultra-long-range well of a double-well potential with the He 2 3 P 1 dissociation limit. A semiclassical analysis is presented to explain the limited sensitivity of the near-dissociation binding energies to the short-range potential.
Helium dimer in its metastable triplet electronic state, He
2(a 3Σu+), is a promising candidate for direct laser cooling and precision measurements. Interactions and collisions involving He
2(a 3Σu+) remain unexplored in ultracold and cold energy domains. Here, we present the first theoretical investigation of intermolecular interactions and collision dynamics of He
2(a 3Σu+)+Ne van der Waals complex. For the ground electronic state,
X 3A′, we employ a spin-restricted coupled cluster method with single, double, and noniterative triple excitations. The resulting interaction potential exhibits an extremely shallow well with a depth of 4.612 cm
−1. We construct a three-dimensional vibrationally averaged potential energy surface. Using this surface, we perform full close-coupling calculations including fine-structure levels of He
2(a 3Σu+) to investigate collisional excitation and quenching induced by Ne. We analyze the low-energy scattering dynamics and model resonant features associated with quasi-bound states supported by interaction potential. Propensity rule for fine-structure conserving transitions is established. We additionally consider He
2+Ar collisions and compare their energy dependence and resonance structure with those of He
2+Ne. The He
2+Ar system exhibits a richer resonance structure, highlighting the sensitivity of low-energy scattering to interaction potential and reduced mass. Calculated PES and scattering properties provide a reliable benchmark for description of He
2+Ne van der Waals complex and may be useful for interpretation of future experimental spectra and collision measurements.
We calculate accurate potential-energy curves for a ground-state
He+ ion interacting with a He atom in the lowest-energy metastable
3S electronic state. We employ the full configuration-interaction method, equivalent to exact diagonalization, with results extrapolated to the complete basis set limit. The leading relativistic and adiabatic corrections are included using perturbation theory. We calculate rovibrational levels and spectroscopic constants of the
He2+ molecular ion in excited electronic states for three stable isotopologues. We predict the scattering lengths for ultracold ion-atom collisions. The theoretical data are presented with their uncertainties and agree well with previous results for the ground state. The reported results may be useful for the spectroscopy of the
He2+ molecular ion in the excited electronic state and collisional studies of
He+ ions immersed in ultracold gases of metastable He atoms.