Elastic scattering of hydrogen atoms at low temperatures

Jamieson, M. J.; Dalgarno, A.; Yukich, John N.

doi:10.1103/physreva.46.6956

Cited by 50 publications

(38 citation statements)

References 25 publications

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“…As the value of 0 R decreases, the strength of attractive van der Waals interaction gradually increases. It is to be observed that the scattering length is gradually decreasing and being closer to the reported accurate values [17][18][19][20][21] as the strength of van der Waals interaction increases with decreasing 0 R . In Figure 7, the plot applying effective range theory for different values of 0 R is presented.…”

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confidence: 83%

The Elastic Collision of Two H-Like Atoms Including the Exotic Ps and Mu

Ray

2017

Acta Phys. Pol. A

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Elastic collision between two H-like atoms using the ab initio static-exchange model (SEM) and a modified static-exchange model (MSEM) at cold energies are investigated in the center of mass frame considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly. The importance of an exact calculation to find basic physics is highlighted. In addition, the dependence of scattering length on the van der Waals interaction between the atoms and the dependence of scattering length on reduced-mass of the system are derived which is completely new information in the field of science.

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confidence: 83%

The Elastic Collision of Two H-Like Atoms Including the Exotic Ps and Mu

Ray

2017

Acta Phys. Pol. A

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“…The calculation of the scattering length is ill-conditioned with respect to these small discrepancies for spin-polarized H(1 S) atoms [24]; such ill-conditioning is also present in the present calculations and its removal requires ab initio potential calculations to be made to greater interatomic separations than are presently published.…”

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confidence: 95%

Scattering lengths for collisions of ground state and metastable state hydrogen atoms

1996

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Scattering lengths for the collisions of ground and metastable state hydrogen ,1 + EF xy~, e Z u and h3E + molecular potentials are atoms interacting via the B E u, 3 + evaluated from published ab initio Born-Oppenheimer potentials with adiabatic corrections, matched to multipole expansions at large interatomic separations. It is demonstrated that the scattering lengths are very sensitive to the connections between the ab initio potentials and their asymptotic forms and the need is shown for accurate interatomic potential calculations at greater separations than are currently available. The density-dependent shift and broadening of the 1S-2S transition frequency in atomic hydrogen caused by two-body elastic collisions are presented.

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“…(17). Alternatively, and discarding the exceptional outliers for α 0 [24,25,26] (Li-Li,Na-Na), [27] (Cs-Cs), [28] (Na-Rb), [29] (Be-Be), [30] (Cs-Rb), [31] (Cr-Cr), [32] (Fr-Fr), [33,34,35,36] (H-H), [36] (He-He). The line corresponds to Eq.…”

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confidence: 99%

Low-energy universality and scaling of van der Waals forces

2010

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At long distances interactions between neutral ground state atoms can be described by the Van der Waals potential V (r) = − P ∞ n=6 Cn/r n . In the ultra-cold regime atom-atom scattering is dominated by s-waves phase shifts given by an effective range expansion p cot δ0(p) = −1/α0 + r0p 2 /2 + . . . in terms of the scattering length α0 and the effective range r0. We show that while for these potentials the scattering length cannot be predicted, the effective range is given by the universal low energy theorem r0 = A + B/α0 + C/α 2 0 where A,B and C depend on the dispersion coefficients Cn and the reduced di-atom mass. We confront this formula to about a hundred determinations of r0 and α0 and show why the result is dominated by the leading dispersion coefficient C6. Universality and scaling extends much beyond naive dimensional analysis estimates. Van der Waals (VdW) forces appear ubiquitously in many contexts of atomic, molecular, nuclear and particle physics. They account for long range dipole fluctuations between charge neutral atomic and molecular systems [1] with implications on the production of Bose-Einstein condensates of ultra-cold atoms and molecules [2]. The intermediate range nucleon-nucleon interaction due to two pion exchange also exhibits this VdW behaviour based on chiral symmetry [3] providing a justification for the liquid drop model of nuclei [4]. The short distance gluon exchange interaction between (colour neutral) hadrons also display this kind of interaction [5,6]. Van der Waals forces, however, diverge when naively extrapolated to short distance scales [7,8]. The study of such problems in a variety of situations will certainly shed light on the usefulness of renormalization ideas within the specific context of quantum mechanics (see e.g. Ref.[9]).Fundamental work for neutral atoms was initiated in Refs. [10,11,12] (see also [13]),within a quantum-defect theoretical viewpoint. In this letter we systematically show that these simplified approaches work and analyze why they succeed. VdW forces are extremely simple in this case and are described by the potentialwhere C n are the VdW coefficients which are computed ab initio from intensive electronic orbital atomic structure calculations (see e.g. Ref.[14] for a compilation). Usually, only the terms with n = 6, 8, 10 are retained although the series is expected to diverge asymptotically, C n ∼ n! [15]. The impressive calculation in Hydrogen up to C 32 [16] exhibits the behaviour C n ∼ (1/2) n n! at relatively low n-values. The potential (1) holds for distances much larger than the ionization length l I = / √ 2m e I (I is the ionization potential) which usually is a few a.u. In the Born-Oppenheimer approximation the quantum mechanical problem consists of solving the Schrödinger equation for the two atoms apart a distance r,where U (r) = 2µV (r)/ 2 is the reduced potential, µ = m 1 m 2 /(m 1 + m 2 ) the reduced di-atom mass, k = p/ = 2π/λ the wavenumber, and u k (r) the reduced wave function. For our purposes, it is convenient to write the reduce...

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Elastic scattering of hydrogen atoms at low temperatures

Cited by 50 publications

References 25 publications

The Elastic Collision of Two H-Like Atoms Including the Exotic Ps and Mu

The Elastic Collision of Two H-Like Atoms Including the Exotic Ps and Mu

Scattering lengths for collisions of ground state and metastable state hydrogen atoms

Low-energy universality and scaling of van der Waals forces

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