Modern He–He potentials: Another look at binding energy, effective range theory, retardation, and Efimov states

Abstract

We compare a number of helium–helium potentials with respect to their predictions of dimer binding energy, scattering length, effective range and Efimov states. We also study the effect of retardation on the ‘‘best’’ potential. All realistic potentials support a weakly bound dimer, while none supports an Efimov state. We agree with other authors that retardation decreases the binding energy by about 10%. Finally, we investigated the effect on the binding energy from the application of retardation over different ranges of separation. The precise effects of retardation at short range in realistic potentials require further study.

Quantum second virial coefficient calculation for the 4He dimer on a recent potential

“…Data in the literature [16][17][18][19][20] show that the He dimer potential well at 10.9 K and a nuclear equilibrium distance of 2.97 Å only support a single bound rovibrational state with a binding energy of approximately -1.176 mK, 34 which is the weakest bound state ever discovered. Due to this extremely weak interaction, the wave function must be delocalized over a large intermolecular distance.…”

“…364 Several He-He intermolecular potentials are discussed in the literature. [16][17][18][19][20] The most recent potential has not been tested against thermodynamic and transport property data, 21 such as the quantum second virial coefficients. In the present work, a study of this recent potential was conducted using second virial coefficient data at low temperature.The quantum virial coefficient can be determined by evaluating the quantum ideal gas term, the scattering phase shift dependence on angular momentum [22][23][24][25][26][27][28][29] and the bound states by Levinson's theorem.…”

Some Energy Inequalities for Two-Body Problems and Helium Dimer

“…Using Lennard-Jones and several modern potentials we showed that dimer is bound in 2D. For the Aziz "best" potential HFD-Β3-FCI1 [13,14] S. Kilić Although the binding of two atoms in 3D, for the same class of radial wave functions and zero angular momentum, is not found, we can estimate the quality of our calculation and use it later for an excited state. (Of course another appropriate class of trial wave functions could give a bound state in 3D, but they are unknown).…”

“…It means that the absolute value of the first term is about 2/3 of the second term. Since the experimental value of Ε3 is -1 mK, what is the left hand side of the relation (14), one may conclude that the function Ψ2(r), used as a trial function, leads to the result which is about 67% of the right value. (Evidently the "error" of about 33% comes out because of the form of our trial function which influences stronger on the kinetic energy term in 3D than in 2D.…”

“…(Of course another appropriate class of trial wave functions could give a bound state in 3D, but they are unknown). As the dimer was discovered experimentally with a binding energy of 1 mK [8], or calculated 1.7 mK [15], one may estimate the trial function using the relation (14). Namely, on the right hand side of the relation (14) only a part of the first term and the second term survive for 1 = 0.…”