s-wave and p-wave scattering in a cold gas of Na and Rb atoms

Ouerdane, Henni; Jamieson, M. J.

doi:10.1140/epjd/e2009-00042-8

Cited by 11 publications

(7 citation statements)

References 34 publications

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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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confidence: 99%

Low-energy universality and scaling of van der Waals forces

2010

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“…Thus, the short distance cut-off r c is a parameter for kR 6 ≫ 1 but becomes innocuous otherwise when r c ≪ R 6 implying that universality is robust. We show for a sample case in [37] (Li-Li,Na-Na), [38] (Na-Na), [39] (Cs-Cs), [40] (Cs-Cs), [41] (Na-Rb), [42] (Be-Be), [43] (Cs-Rb), [44] (Cr-Cr), [45] (Fr-Fr), [46] (H-H), [47] (H-H), [48] (H-H), [49] (H-H). Fig.…”

Section: The Pure −1/r 6 Vdw Forcementioning

confidence: 99%

“…The VdW universal effective range in units of the VdW radius R defined by 2µV(r) = −R 4 /r 6 . Compared to several calculations[37] (Li-Li,Na-Na),[38] (Na-Na),[39] (Cs-Cs),[40] (Cs-Cs),[41] (Na-Rb),[42] (Be-Be),[43] (Cs-Rb),[44] (Cr-Cr),[45] (Fr-Fr),[46] (H-H),[47] (H-H),[48] (H-H),[49] (H-H).…”

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confidence: 96%

Renormalization and Universality of Van der Waals forces

Arriola

Cordón

2010

EPJ Web of Conferences

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Abstract. Renormalization ideas can profitably be exploited in conjunction with the superposition principle of boundary conditions in the description of model independent and universal scaling features of the singular and long range Van der Waals force between neutral atoms. The dominance of the leading power law is highlighted both in the scattering as well as in the bound state problem. The role of off-shell two-body unitarity and causality within the Effective Field Theory framework on the light of universality and scaling at low energies is analyzed.

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“…At ultracold temperatures, scattering between two heteronuclear atoms is characterized by the s-wave scat-tering length, the effective range and the p-wave scattering length, the contributions from higher angular momenta are negligible at very low energy. [20,21] Those scattering parameters are very sensitive to the interaction potentials between the colliding systems over an extended range of internuclear distances. The elastic scattering and spin-change cross sections are also important for cold atom experiments, which control the thermalisation of the atoms and lead to atom loss, respectively.…”

Section: Introductionmentioning

confidence: 99%