# Three-Body Contribution to the Helium Interaction Potential †

**ABSTRACT** Two nonadditive three-body analytic potentials for helium were obtained: one based on three-body symmetry-adapted perturbation theory (SAPT) and the other one on supermolecular coupled-cluster theory with single, double, and noniterative triple excitations [CCSD(T)]. Large basis sets were used, up to the quintuple-zeta doubly augmented size. The fitting functions contain an exponentially decaying component describing the short-range interactions and damped inverse powers expansions for the third- and fourth-order dispersion contributions. The SAPT and CCSD(T) potentials are very close to each other. The largest uncertainty of the potentials comes from the truncation of the level of theory and can be estimated to be about 10 mK or 10% at trimer's minimum configuration. The relative uncertainties for other configurations are also expected to be about 10% except for regions where the nonadditive contribution crosses zero. Such uncertainties are of the same order of magnitude as the current uncertainties of the two-body part of the potential.

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**ABSTRACT:**The triatomic 4He system and its isotopic species ${^4{\rm He}_2^3{\rm He}}$ are theoretically investigated. By adopting the best empirical helium interaction potentials, we calculate the bound state energy levels as well as the rates for the three-body recombination processes: 4He + 4He + 4He → 4 He2 + 4He and 4He + 4He + 3He → 4He2 + 3He. We consider not only zero total angular momentum J = 0 states, but also J > 0 states. We also extend our study to mixed helium-alkali triatomic systems, that is 4He2X with X = 7Li, 23Na, 39K, 85 Rb, and 133Cs. The energy levels of all the J ≥ 0 bound states for these species are calculated as well as the rates for three-body recombination processes such as 4He + 4He + 7Li → 4 He2 + 7Li and 4He + 4He + 7Li → 4 He7Li + 4He. In our calculations, the adiabatic hyperspherical representation is employed but we also obtain preliminary results using the Gaussian expansion method.Few-Body Systems 08/2013; 54(7-10). DOI:10.1007/s00601-013-0708-z · 0.77 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Helium is the only substance that has been observed on macroscopic scale to form the fourth state of matter, the superfluid state. However, until recently superfluid helium had not found any practical applications, mainly because it expels all other atoms or molecules. Only in the 1990s was it discovered that it is possible to mix in other substances with superfluid helium if helium is prepared as small droplets, called nanodroplets, containing only a few thousand atoms. This discovery led to the development of a new and very powerful experimental technique, called helium-nanodroplet spectroscopy. Superfluid helium creates a gentle matrix around the impurities and - due to superfluidity and to very weak interactions of helium atoms with other atoms or molecules - allows measurements of the spectra with precision not much lower than in the gas phase. Consequently, helium-nanodroplet spectroscopy enables very accurate probing of molecules or clusters which cannot be investigated in the gas phase due to their instability. This category includes `fragile' molecules, isomers, radicals, and clusters in secondary minima. The major experimental developments will be described, emphasizing their importance for understanding basic principles of physics and new insights into chemically relevant processes. The experiments have been assisted by theoretical work on impurity-Hen clusters. Most such work involves first-principles quantum simulations. Although the number of helium atoms that can be included in such simulations is significantly smaller than in a typical nanodroplet, theory explains most of the observed trends reasonably well. Theoretical results can also be compared directly and much more precisely than in the case of the droplets with the results of molecular beam experiments on clusters of controllable size, with the number of helium atoms ranging from 1 to almost 100. Most of the simulations published to date will be discussed and the level of agreement with experiment will be critically evaluated. The results of the simulations are very sensitive to details of the He-He and impurity-He interaction potentials used, and most of the current discrepancies between theory and experiment can be traced down to the uncertainties of the potentials. Thus, an important component of this review will be an analysis of various sources of errors in potential energy surfaces.International Reviews in Physical Chemistry 04/2008; 27(2):273-316. DOI:10.1080/01442350801933485 · 7.03 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The 4He3 system is studied using the adiabatic hyperspherical representation. We adopt the current state-of-the-art helium interaction potential including retardation and the nonadditive three-body term, to calculate all low-energy properties of the triatomic 4He system. The bound state energies of the 4He trimer are computed as well as the 4He+4He2 elastic scattering cross sections, the three-body recombination and collision induced dissociation rates at finite temperatures. We also treat the system that consists of two 4He and one 3He atoms, and compute the spectrum of the isotopic trimer 4He2 3He, the 3He+4He2 elastic scattering cross sections, the rates for three-body recombination and the collision induced dissociation rate at finite temperatures. The effects of retardation and the nonadditive three-body term are investigated. Retardation is found to be significant in some cases, while the three-body term plays only a minor role for these systems. Comment: 24 pages 6 figures Submitted to Physical Review APhysical Review A 09/2008; 78(6). DOI:10.1103/PhysRevA.78.062701 · 2.81 Impact Factor