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 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.
The pair potential for helium is computed with accuracy improved by an order of magnitude relative to the best previous determination. For the well region, its uncertainties are now below 1 millikelvin. The main improvement is due to the use of explicitly correlated wave functions at the nonrelativistic Born-Oppenheimer (BO) level of theory. The diagonal BO and the relativistic corrections are obtained from large full configuration interaction calculations. Nonadiabatic perturbation theory is used to predict the properties of the halo state of the helium dimer. Its binding energy and the average value of the interatomic distance are found to be 138.9(5) neV and 47.13(8) Å. The binding energy agrees with its first experimental determination of 151.9(13.3) neV [Zeller et al., Proc. Natl. Acad. Sci. U.S.A. 113, 14651 (2016)PNASA60027-842410.1073/pnas.1610688113].
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.
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.
The precision of the photoassociation spectroscopy of the Yb dimer in degenerate gases is enough to improve the constraints on short-range gravitylike forces if the theoretical knowledge of the Born-Oppenheimer interatomic potential and non-Born-Oppenheimer interactions is refined [Borkowski et al., Sci. Rep. 9, 14807 (2019)]. The ground-state interaction potential of the ytterbium dimer is investigated at the exact two-component core-correlated coupled-cluster method with singles, doubles, and noniterative triples [CCSD(T)] level of ab initio theory in the complete-basis-set limit with extensive augmentation by diffuse functions. For the small basis set the comparison is made with the four-component relativistic finite-nuclei CCSD(T) calculations to identify the contraction of the dimer bond length as the main unrecoverable consequence of the scalar-relativistic approximation. The empirical constraint on the number of bound vibrational energy levels of the
174Yb2 dimer is accounted for by representing the global ab initio--based Born-Oppenheimer potential with the model semianalytical function containing the scale and shift parameters. The results support the previous evaluation of the Yb dimer potentials from the photoassociation spectroscopy data and provide an accurate and flexible reference for future refinement of the constraints on short-range gravitylike forces by ultracold atomic spectroscopy.
Accurate scattering lengths and effective ranges for hydrogen atomic collisions are determined from effective range theory. The precise ab initio b3Σ+u potential energy curve values of H2 calculated by Kolos and Wolniewicz and C6, C8, C10 long-range expansion coefficients are used in obtaining accurate representation of the two-body interaction potential. The s-wave scattering length obtained for this potential (A =1/33455 ao) is used to calculate the zero temperature energy as a function of density of electron spin-polarized ("spin-aligned") atomic hydrogen (H+) using previous many-body perturbation theory results for bosons. Neglecting small potential shape dependent terms, one obtains E/N (energy per particle ) as a function of density, which may be compared with similar results obtained from Monte-Carlo or variational calculations. The scattering lengths and effective ranges for the other hydrogen isotopic systems are also presented. It is shown that the first bound state for the b3Σ+u potential (within the Born-Oppenheimer approximation) only exists for a hypothetical isotopic species with mass larger than a value m = 3.258176 g/mole (where the scattering length becomes infinite). In terms of the quantum parameter, η ≡ [MATH]2/ (2µεσ2), two-body binding occurs in the b3Σ+u potential only for η < 0.17094. The second order liquid-to-gas transition (corresponding to the onset of infinite-body binding) occurs at the accurately determined critical value of the quantum parameter ηCB = 0.43891. This corresponds to zero scattering length.