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

Journal of Physics B Atomic Molecular and Optical Physics

Scattering lengths for collisions between sodium and potassium atoms

V. Venturi, M. J. Jamieson, Robin Côté

Published Nov 13, 2001• 9 citations
Publisher

Abstract

The scattering lengths that characterize the low-energy elastic scattering of 23 Na atoms by 39 K, 40 K and 41 K atoms, when they interact via the X 1 Σ + and a 3 Σ + states of the NaK dimer, are calculated. The systematic variation of the short- and long-range parts of the interaction potentials reveals that the calculated scattering lengths are sensitive to uncertainties in the potentials. It is concluded that precise spectroscopic measurements of the least-bound ro-vibrational levels supported by the ground electronic state, which would reduce the uncertainties in both the molecular potentials, are needed for an accurate determination of the scattering lengths.

DOI
10.1088/0953-4075/34/22/305

Related papers

S-wave scattering lengths and effective ranges for collisions of ground state Be atoms

Michael J. Jamieson, A. S.‐C. Cheung, Henni Ouerdane +2 more

The scattering lengths and effective ranges for collisions of ground state Be atoms interacting via the X 1Σ + g molecular state of the Be 2 dimer are calculated for two published X 1Σ + g potentials. A new ab initio X 1Σ + g potential is presented with its vibrational energies and rotational constants. The scattering parameters calculated with it and with the existing potentials are compared. Simple formulae showing how the scattering parameters are influenced by adiabatic coupling to electronic motion are derived within the semi-classical formulation and evaluated for the potentials considered. The formulae imply that a semi-classical account of adiabatic coupling can be made by increasing each atomic mass by one electron mass. © 2007 IOP Publishing Ltd.

Journal of Physics B Atomic Molecular and Optical Physics•Aug 28, 2007•5 citations

Elastic scattering of cold caesium and rubidium atoms

M. J. Jamieson, Hamid Sarbazi‐Azad, Henni Ouerdane +3 more

For elastic scattering of 133 Cs atoms by 85 Rb and 87 Rb atoms, interacting via the X 1 Σ + and a 3 Σ + molecular states of RbCs, calculations are presented of the scattering length and the effective range and also of two volume parameters, one for low energy p-wave scattering and one for the energy of an ensemble of fermions. The calculations are performed by various methods, with several representations of the interatomic potentials, including new ab initio potentials presented here. It is shown how the calculated data may be corrected to include the influence of the long range interactions, thus removing the need for numerical solutions of the radial Schrödinger equation at very large interatomic separations. The sensitivity of the results to the choice of potentials, to the van der Waals dispersion coefficient C 6 and to the reduced mass of the colliding atoms is explored, and is found to be great.

Journal of Physics B Atomic Molecular and Optical Physics•Feb 25, 2003•45 citations

A spectroscopic determination of scattering lengths for sodium atom collisions

Eite Tiesinga, Carl J. Williams, Paul S. Julienne +3 more

We report a preliminary value for the zero magnetic field Na 2 S(f = 1, m = Ϫ 1) + Na 2 S(f = 1, m = Ϫ 1) scattering length, a1,Ϫ1.This parameter describes the lowenergy elastic two-body processes in a dilute gas of composite bosons and determines, to a large extent, the macroscopic wavefunction of a Bose condensate in a trap.Our scattering length is obtained from photoassociative spectroscopy with samples of uncondensed atoms.The temperature of the atoms is sufficiently low that contributions from the three lowest partial waves dominate the spectrum.The observed lineshapes for the purely long-range 0g Ϫ molecular state enable us to establish key features of the ground state scattering wavefunction.The fortuitous occurrence of a p -wave node near the deepest point (Re = 72 a0) of the 0g Ϫ potential curve is instrumental in determining a1,Ϫ1 = (52 Ϯ 5) a0 and a2,2 = (85 Ϯ 3) a0, where the latter is for a collision of two Na 2 S(f = 2, m = 2) atoms.

Journal of Research of the National Institute of Standards and Technology•Jul 1, 1996•212 citations

Elastic Scattering of Ultracold 23 Na and 39 K Atoms in the Singlet State

Hu Qiu-Bo, Zhang Yong-Sheng, Sun Jin-Feng

The elastic scattering properties for collisions between ultracold Na and K atoms in the singlet state are investigated. Based on the recent theoretical and experimental results, the improved hybrid potential is presented for the singlet X 1 Σ g + ground state of NaK. By means of the Numerov and semiclassical methods, the values of the s-wave scattering length a for the singlet state are calculated to be 33.3757 a 0 and 37.9399 a 0 , respectively. Pronounced shape resonances appear for the l = 1 partial wave for the X 1 Σ g + state. In addition, the s-wave scattering cross section, total cross section and energy positions of shape resonances for the X 1 Σ g + state are discussed.

Chinese Physics Letters•Feb 1, 2010•1 citation

Treasure of the past X - A spectroscopic determination of scattering lengths for sodium atom collisions (Reprinted from the Journal of Research of the National Bureau of Standards, vol 101, pg 505-520, 1996

Eite Tiesinga, Carl J. Williams, Paul S. Julienne +3 more

We report a preliminary value for the zero magnetic field Na (2)S(f = 1, m = - 1) + Na (2)S(f = 1, m = - 1) scattering length, a 1,-1. This parameter describes the low-energy elastic two-body processes in a dilute gas of composite bosons and determines, to a large extent, the macroscopic wavefunction of a Bose condensate in a trap. Our scattering length is obtained from photoassociative spectroscopy with samples of uncondensed atoms. The temperature of the atoms is sufficiently low that contributions from the three lowest partial waves dominate the spectrum. The observed lineshapes for the purely long-range [Formula: see text] molecular state enable us to establish key features of the ground state scattering wavefunction. The fortuitous occurrence of a p-wave node near the deepest point (R e = 72 a 0) of the [Formula: see text] potential curve is instrumental in determining a 1,-1 = (52 ± 5) a 0 and a 2.2 = (85 ± 3) a 0, where the latter is for a collision of two Na (2)S(f = 2, m = 2) atoms.

Journal of Research of the National Institute of Standards and Technology•Jan 1, 2002•1 citation

Potentials for modeling cold collisions between Na (3S) and Rb (5S) atoms

A. Pashov, O. Docenko, M. Tamanis +3 more

The experimental characterization of the electronic states correlated to the asymptote of ground state Na (3S) and Rb (5S) atoms was expanded by spectroscopic data on $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ state levels using a high resolution Fourier transform spectroscopy technique. The hyperfine splitting of the $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ state levels was partially resolved and analyzed for both $\mathrm{Na}\phantom{\rule{0.2em}{0ex}}^{85}\mathrm{Rb}$ and $\mathrm{Na}\phantom{\rule{0.2em}{0ex}}^{87}\mathrm{Rb}$ isotopomers. Transitions to high lying levels of the $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ and $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ states were recorded simultaneously which enables one to determine long range parameters of the molecular potentials. Coupled channels calculations based on the Fourier grid method were finally applied for deriving accurate potential energy curves of the $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ and $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ states capable of a reliable description of cold collisions between Na and Rb atoms in their ground states. Scattering lengths and Feshbach resonances were calculated for some quantum states.

Physical Review A•Dec 21, 2005•77 citations
The scattering lengths that characterize the low-energy elastic scattering of 23 Na atoms by 39 K, 40 K and 41 K atoms, when they interact via the X 1 Σ + and a 3 Σ + states of the NaK dimer, are calculated. The systematic variation of the short- and long-range parts of the interaction potentials reveals that the calculated scattering lengths are sensitive to uncertainties in the potentials. It is concluded that precise spectroscopic measurements of the least-bound ro-vibrational levels supported by the ground electronic state, which would reduce the uncertainties in both the molecular potentials, are needed for an accurate determination of the scattering lengths.
The scattering lengths and effective ranges for collisions of ground state Be atoms interacting via the X 1Σ + g molecular state of the Be 2 dimer are calculated for two published X 1Σ + g potentials. A new ab initio X 1Σ + g potential is presented with its vibrational energies and rotational constants. The scattering parameters calculated with it and with the existing potentials are compared. Simple formulae showing how the scattering parameters are influenced by adiabatic coupling to electronic motion are derived within the semi-classical formulation and evaluated for the potentials considered. The formulae imply that a semi-classical account of adiabatic coupling can be made by increasing each atomic mass by one electron mass. © 2007 IOP Publishing Ltd.
For elastic scattering of 133 Cs atoms by 85 Rb and 87 Rb atoms, interacting via the X 1 Σ + and a 3 Σ + molecular states of RbCs, calculations are presented of the scattering length and the effective range and also of two volume parameters, one for low energy p-wave scattering and one for the energy of an ensemble of fermions. The calculations are performed by various methods, with several representations of the interatomic potentials, including new ab initio potentials presented here. It is shown how the calculated data may be corrected to include the influence of the long range interactions, thus removing the need for numerical solutions of the radial Schrödinger equation at very large interatomic separations. The sensitivity of the results to the choice of potentials, to the van der Waals dispersion coefficient C 6 and to the reduced mass of the colliding atoms is explored, and is found to be great.
We report a preliminary value for the zero magnetic field Na 2 S(f = 1, m = Ϫ 1) + Na 2 S(f = 1, m = Ϫ 1) scattering length, a1,Ϫ1.This parameter describes the lowenergy elastic two-body processes in a dilute gas of composite bosons and determines, to a large extent, the macroscopic wavefunction of a Bose condensate in a trap.Our scattering length is obtained from photoassociative spectroscopy with samples of uncondensed atoms.The temperature of the atoms is sufficiently low that contributions from the three lowest partial waves dominate the spectrum.The observed lineshapes for the purely long-range 0g Ϫ molecular state enable us to establish key features of the ground state scattering wavefunction.The fortuitous occurrence of a p -wave node near the deepest point (Re = 72 a0) of the 0g Ϫ potential curve is instrumental in determining a1,Ϫ1 = (52 Ϯ 5) a0 and a2,2 = (85 Ϯ 3) a0, where the latter is for a collision of two Na 2 S(f = 2, m = 2) atoms.
The elastic scattering properties for collisions between ultracold Na and K atoms in the singlet state are investigated. Based on the recent theoretical and experimental results, the improved hybrid potential is presented for the singlet X 1 Σ g + ground state of NaK. By means of the Numerov and semiclassical methods, the values of the s-wave scattering length a for the singlet state are calculated to be 33.3757 a 0 and 37.9399 a 0 , respectively. Pronounced shape resonances appear for the l = 1 partial wave for the X 1 Σ g + state. In addition, the s-wave scattering cross section, total cross section and energy positions of shape resonances for the X 1 Σ g + state are discussed.
We report a preliminary value for the zero magnetic field Na (2)S(f = 1, m = - 1) + Na (2)S(f = 1, m = - 1) scattering length, a 1,-1. This parameter describes the low-energy elastic two-body processes in a dilute gas of composite bosons and determines, to a large extent, the macroscopic wavefunction of a Bose condensate in a trap. Our scattering length is obtained from photoassociative spectroscopy with samples of uncondensed atoms. The temperature of the atoms is sufficiently low that contributions from the three lowest partial waves dominate the spectrum. The observed lineshapes for the purely long-range [Formula: see text] molecular state enable us to establish key features of the ground state scattering wavefunction. The fortuitous occurrence of a p-wave node near the deepest point (R e = 72 a 0) of the [Formula: see text] potential curve is instrumental in determining a 1,-1 = (52 ± 5) a 0 and a 2.2 = (85 ± 3) a 0, where the latter is for a collision of two Na (2)S(f = 2, m = 2) atoms.
The experimental characterization of the electronic states correlated to the asymptote of ground state Na (3S) and Rb (5S) atoms was expanded by spectroscopic data on $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ state levels using a high resolution Fourier transform spectroscopy technique. The hyperfine splitting of the $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ state levels was partially resolved and analyzed for both Na85Rb\mathrm{Na}\phantom{\rule{0.2em}{0ex}}^{85}\mathrm{Rb}Na85Rb and Na87Rb\mathrm{Na}\phantom{\rule{0.2em}{0ex}}^{87}\mathrm{Rb}Na87Rb isotopomers. Transitions to high lying levels of the $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ and $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ states were recorded simultaneously which enables one to determine long range parameters of the molecular potentials. Coupled channels calculations based on the Fourier grid method were finally applied for deriving accurate potential energy curves of the $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ and $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ states capable of a reliable description of cold collisions between Na and Rb atoms in their ground states. Scattering lengths and Feshbach resonances were calculated for some quantum states.