Analytical calculations of scattering lengths in atomic physics

Szmytkowski, Radosław

doi:10.1088/0305-4470/28/24/027

Cited by 42 publications

(47 citation statements)

References 16 publications

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“…However, only N ≈ 100 grid points are required to converge the present a s -value to 7 significant digits. The present estimate agrees with the value reported by Szmytkowski [13] to within the 6 significant digit that he reports (see row 2 of Table II).…”

Section: B Applications To 'Real' Systemssupporting

confidence: 94%

“…(44) correspond to the familiar charge/induced-dipole and charge/induced-quadrupole interactions, where α 1 = 27.292 and α 2 = 128.255 are the static dipole and quadrupole polarizabilities of the Xe atom, while β 1 = 29.2 is the dynamical correction to the dipole polarizability. This shallow U Xe-e − (r) interaction potential supports no bound levels and its scattering length is negative, as was determined by Szmytkowski using an asymptotic method [13].…”

Section: B Applications To 'Real' Systemssupporting

confidence: 70%

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Rapid, accurate calculation of the s-wave scattering length

Meshkov

Stolyarov

Roy

2011

The Journal of Chemical Physics

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Transformation of the conventional radial Schrödinger equation defined on the interval r ∈ [0, ∞) into an equivalent form defined on the finite domain y(r) ∈ [a, b] allows the s-wave scattering length a(s) to be exactly expressed in terms of a logarithmic derivative of the transformed wave function φ(y) at the outer boundary point y = b, which corresponds to r = ∞. In particular, for an arbitrary interaction potential that dies off as fast as 1/r(n) for n ≥ 4, the modified wave function φ(y) obtained by using the two-parameter mapping function r(y; ̄r,β) = ̄r[1 + 1/β tan(πy/2)] has no singularities, and a(s) = ̄r[1 + 2/πβ 1/φ(1) dφ(1)/dy]. For a well bound potential with equilibrium distance r(e), the optimal mapping parameters are ̄r ≈ r(e) and β ≈ n/2 - 1. An outward integration procedure based on Johnson's log-derivative algorithm [J. Comp. Phys. 13, 445 (1973)] combined with a Richardson extrapolation procedure is shown to readily yield high precision a(s)-values both for model Lennard-Jones (2n, n) potentials and for realistic published potentials for the Xe-e(-), Cs(2)(aΣ(u)(+)(3)), and (3, 4)He(2)(XΣ(g)(+)(1)) systems. Use of this same transformed Schrödinger equation was previously shown [V. V. Meshkov et al., Phys. Rev. A 78, 052510 (2008)] to ensure the efficient calculation of all bound levels supported by a potential, including those lying extremely close to dissociation.

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Section: B Applications To 'Real' Systemssupporting

confidence: 94%

Section: B Applications To 'Real' Systemssupporting

confidence: 70%

Rapid, accurate calculation of the s-wave scattering length

Meshkov

Stolyarov

Roy

2011

The Journal of Chemical Physics

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“…The analytical solutions of the Schrödinger equation are known for several class of potentials, thus allowing the derivations of compact expressions for the scattering length [54]. Van der Waals systems such as those discussed here can be nicely described and very well understood using analytical theory.…”

Section: Ground State Scattering Wave Functionmentioning

confidence: 99%

Line shapes of optical Feshbach resonances near the intercombination transition of bosonic ytterbium

Borkowski¹,

Ciuryło²,

Julienne

et al. 2009

Phys. Rev. A

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The properties of bosonic Ytterbium photoassociation spectra near the intercombination transition 1 S0-3 P1 are studied theoretically at ultra low temperatures. We demonstrate how the shapes and intensities of rotational components of optical Feshbach resonances are affected by mass tuning of the scattering properties of the two colliding ground state atoms. Particular attention is given to the relationship between the magnitude of the scattering length and the occurrence of shape resonances in higher partial waves of the van der Waals system. We develop a mass scaled model of the excited state potential that represents the experimental data for different isotopes. The shape of the rotational photoassociation spectrum for various bosonic Yb isotopes can be qualitatively different.

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“…The correction in the form of the numerator of Eq. (22) was derived in a different way by Szmytkowski [21] (whose scattering length is B…”

Section: Inverse Power Potentialmentioning

confidence: 99%

Scattering parameters for cold Li–Rb and Na–Rb collisions derived from variable phase theory

Ouerdane

Jamieson

2004

Phys. Rev. A

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We show how the scattering phase shift, the s-wave scattering length and the p-wave scattering volume can be obtained from Riccati equations derived in variable phase theory. We find general expressions that provide upper and lower bounds for the scattering length and the scattering volume. We show how, in the framework of the variable phase method, Levinson's theorem yields the number of bound states supported by a potential. We report new results from a study of the heteronuclear alkali dimers NaRb and LiRb. We consider ab initio molecular potentials for the X 1 Σ + and a 3 Σ + states of both dimers and compare and discuss results obtained from experimentally based X 1 Σ + and a 3 Σ + potentials of NaRb. We explore the mass dependence of the scattering data by considering all isotopomers and we calculate the numbers of bound states supported by the molecular potentials for each isotopomer.

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Analytical calculations of scattering lengths in atomic physics

Cited by 42 publications

References 16 publications

Rapid, accurate calculation of the s-wave scattering length

Rapid, accurate calculation of the s-wave scattering length

Line shapes of optical Feshbach resonances near the intercombination transition of bosonic ytterbium

Scattering parameters for cold Li–Rb and Na–Rb collisions derived from variable phase theory

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