Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Comment on "Scattering length for fermionic alkali atoms" by S. Gautam and D. Angom

Henni Ouerdane, M. J. Jamieson

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

We suggest that Gautam and Angom [Eur. Phys. J. D 56, 173 (2010)] underestimated the influence of the van der Waals dispersion forces at long range on their calculated low energy scattering parameters and we provide numerical evidence in support. We also provide a simple proof of the relation between s-wave and p-wave scattering parameters and we comment briefly on the semiclassical formula derived by these authors.

Related papers

Low-energy universality and scaling of van der Waals forces

A. Calle Cordón, E. Ruiz Arriola

At long distances, interactions between neutral ground-state atoms can be described by the van der Waals potential. In the ultracold regime, atom-atom scattering is dominated by $s$-waves phase shifts given by an effective range expansion in terms of the scattering length ${\ensuremath{\alpha}}_{0}$ and the effective range ${r}_{0}$. We show that while the scattering length cannot be predicted for these potentials, the effective range is given by the universal low-energy theorem ${r}_{0}=A+B/{\ensuremath{\alpha}}_{0}+C/{\ensuremath{\alpha}}_{0}^{2}$, where $A$, $B$, and $C$ depend on the dispersion coefficients ${C}_{n}$ and the reduced diatom mass. We confront this formula to about 100 determinations of ${r}_{0}$ and ${\ensuremath{\alpha}}_{0}$ and show why the result is dominated by the leading dispersion coefficient ${C}_{6}$. Universality and scaling extend much beyond naive dimensional analysis estimates.

arXiv:0912.1714•Physical Review A•Apr 23, 2010•18 citations

Comment on ‘‘Relation between the electron scattering length and the van der Waals approximation to the equation of state’’

Igor T. Iakubov, Alexey G. Khrapak

In a recent paper, Reisfeld and Asaf [Phys. Rev. A 49, 348 (1994)] have undertaken an attempt to explain the linear dependence of the electron-atom scattering length on the atomic polarizability. They used the Born approximation, which is valid only for small atomic or molecular polarizabilities. Using the exact formula for the scattering length, we offer a simple expression for estimation of the scattering length by known values of the polarizability and ionization potential.

Physical Review A•Jun 1, 1995•10 citations

The van der Waals force between positronium and light atoms

D W Martin, P A Fraser

The long-range interaction energies of H-Ps, Ps-He and Ps-Ps are calculated using the Hylleraas variational method. Implications for low-energy H-Ps and Ps-He scattering theory are discussed.

Journal of Physics B Atomic and Molecular Physics•Sep 14, 1980•35 citations

Relation between the electron scattering length and the van der Waals approximation to the equation of state

G. Reisfeld, Uri Asaf

A theoretical relation between the electron scattering length and the van der Waals approximation to the equation of state is described. The theory provides a simple calculation for the scattering length of neutral atomic scatterers such as rare gases, using two experimental parameters: the hard-core radius (calculated from the van der Waals equation of state, using critical data) and the atomic polarizability. The results for the calculated electron scattering length agree with measured values derived either from the energy shifts of highly excited molecular Rydberg states, perturbed by He, Ne, Ar, Kr, and Xe, or from swarm electron cross-section data for the same gases.

Physical Review A•Jan 1, 1994•13 citations

Binding energy and scattering length for diatomic systems

Bo Gao

We discuss the relationship between scattering length and binding energy for a diatomic system with long-range van der Waals interaction. The well-known relation, 0 = −(ℏ 2 /2μ)(1/ a 0 ) 2 , is generalized to much higher orders for the s wave. Analytic results for the binding energies of p and higher angular momentum states are also presented.

Journal of Physics B Atomic Molecular and Optical Physics•Oct 27, 2004•46 citations

Long-range dispersion interactions. II. Alkali-metal and rare-gas atoms

J. Mitroy, J.-Y. Zhang

The dispersion coefficients for the van der Waals interactions between the rare gases Ne, Ar, Kr, and Xe and the low-lying states of Li, Na, K, and Rb are estimated using a combination of ab initio and semiempirical methods. The rare-gas oscillator strength distributions for the quadrupole and octupole transitions were derived by using high-quality calculations of rare-gas polarizabilities and dispersion coefficients to tune Hartree-Fock single-particle energies and expectation values.

Physical Review A•Sep 11, 2007•63 citations
We suggest that Gautam and Angom [Eur. Phys. J. D 56, 173 (2010)] underestimated the influence of the van der Waals dispersion forces at long range on their calculated low energy scattering parameters and we provide numerical evidence in support. We also provide a simple proof of the relation between s-wave and p-wave scattering parameters and we comment briefly on the semiclassical formula derived by these authors.
At long distances, interactions between neutral ground-state atoms can be described by the van der Waals potential. In the ultracold regime, atom-atom scattering is dominated by sss-waves phase shifts given by an effective range expansion in terms of the scattering length ${\ensuremath{\alpha}}_{0}$ and the effective range r0{r}_{0}r0​. We show that while the scattering length cannot be predicted for these potentials, the effective range is given by the universal low-energy theorem ${r}_{0}=A+B/{\ensuremath{\alpha}}_{0}+C/{\ensuremath{\alpha}}_{0}^{2}$, where AAA, BBB, and CCC depend on the dispersion coefficients Cn{C}_{n}Cn​ and the reduced diatom mass. We confront this formula to about 100 determinations of r0{r}_{0}r0​ and ${\ensuremath{\alpha}}_{0}$ and show why the result is dominated by the leading dispersion coefficient C6{C}_{6}C6​. Universality and scaling extend much beyond naive dimensional analysis estimates.
A theoretical relation between the electron scattering length and the van der Waals approximation to the equation of state is described. The theory provides a simple calculation for the scattering length of neutral atomic scatterers such as rare gases, using two experimental parameters: the hard-core radius (calculated from the van der Waals equation of state, using critical data) and the atomic polarizability. The results for the calculated electron scattering length agree with measured values derived either from the energy shifts of highly excited molecular Rydberg states, perturbed by He, Ne, Ar, Kr, and Xe, or from swarm electron cross-section data for the same gases.