Deltafunction model for the helium dimer

Abstract

rnThe helium dimer 'Hez has recently been detected, confirming earlier ab initio predictions of stability for a single bound state with binding energy of 1.310 mK. The predicted potential minimum is at 2.96 A, with a radial distribution function peaking at 6.96 A. We model this system using a Dirac bubble potential, which also admits just one bound J = 0 state. With the bubble located at 6.96 A, an overlap of 0.9994 with the ab initio wave function is obtained. An average internuclear distance of 52.6 A is calculated, in good agreement with the ab initio result. The root mean square deviation from the mean, 48.0 A, indicates an enormous spread of the radial wave function. Also consistent with our model is the absence of bound states for the isotopic variants 'He'He and ?Hez. Cross sections for helium-helium scattering are also computed, using both a partial-wave expansion and the Born approximation. General trends in the energy dependence of the total cross section are accounted for, in qualitative agreement with experimental results. 0 1995 John Wiley & Sons, Inc.

Models for low‐temperature helium dimers and trimers

“…We have revised the pairwise deltafunction potential we previously employed 25 to obtain better estimates of the binding energy of the helium trimer. We now calculate binding energies of 96.1 and 11.4 mK for the ground states of 4 He 3 and 4 He 2 3 He, respectively.…”

“…In an earlier contribution to this journal 25, the authors proposed a “Dirac bubble potential” in which the interatomic interaction is idealized as an attractive deltafunction on a sphere of radius r 0 , viz. V ( r )=−const δ( r − r 0 ).…”

Dirac bubble potential for He–He and inadequacies in the continuum: Comparing an analytic model with elastic collision experiments

“…One of the most insightful and fascinating potential models for pairwise interactions in helium consists of an attractive deltafunction in the shape of a spherical bubble of radius r 0 to mimic the interatomic potential. [35][36][37][38] At the origin of this model is the observation that 4 He- 4 He supports but a single bound state, a property that is highly evocative of a deltafunction (which has the same property). 35 However, it is still very surprising that such an oversimplified model can reproduce distinctive features of the helium dimers 35 and trimers.…”

“…[35][36][37][38] At the origin of this model is the observation that 4 He- 4 He supports but a single bound state, a property that is highly evocative of a deltafunction (which has the same property). 35 However, it is still very surprising that such an oversimplified model can reproduce distinctive features of the helium dimers 35 and trimers. [36][37][38] In fact, the Dirac bubble potential (Dbp) is renowned for its capability to reproduce, without the need for elaborate computations, a wealth of stability properties in helium clusters, viz., the binding energies of 4 He 3 (96.1 mK) and 4 He 2 3 He (11.4 mK), 36,37 an Efimov state 39 for 4 He 2 3 He (Ref.…”

Analytic representation of the Efimov effect in the helium trimer

“…Cornelius and Glöckle [6] used the HFDHE2 helium diatomic potential of Aziz et al [7] scaled by a parameter to solve the Faddeev equations in momentum space. The present authors have studied models for low-temperature helium dimers and trimers based on approximations of the interatomic potentials by ␦ functions [8].…”