Continuum wavefunctions for one-electron two-centre molecular ions from the Killingbeck - Miller method

Hadinger, G.; Aubert‐Frécon, M.

doi:10.1088/0953-4075/29/14/008

Cited by 20 publications

(17 citation statements)

References 27 publications

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“…The coefficient J agrees with the most recent theoretical value in Ref. [15]. Table I also gives the values of the pure singlet and triplet scattering lengths for both 85 Rb and 87 Rb, following from C 6 , C 8 , J, φ 0 T ( 87 Rb), as well as the fractional vibrational quantum numbers at dissociation v D and the numbers of bound states n b .…”

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confidence: 85%

Interisotope Determination of Ultracold Rubidium Interactions from Three High-Precision Experiments

et al. 2002

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Combining the measured binding energies of four of the most weakly bound rovibrational levels of the 87 Rb2 molecule with the results of two other recent high-precision rubidium experiments, we obtain exceptionally strong constraints on the atomic interaction parameters in a highly model independent analysis. The comparison of 85 Rb and 87 Rb data, where the two isotopes are related by a mass scaling procedure, plays a crucial role. Using the consistent picture of the interactions that thus arises we are led to predictions for scattering lengths, clock shifts, Feshbach resonance fields and widths with an unprecedented level of accuracy. To demonstrate this, we predict two Feshbach resonances in mixed-spin scattering channels at easily accessible magnetic field strengths, which we expect to play a role in the damping of coherent spin oscillations. Suggested PACS Numbers: 03.75.Fi, 34.20.Cf, 32.80.Pj After the first realization of Bose-Einstein condensation (BEC) in a dilute ultracold gas of rubidium atoms [1], experiments with the two isotopes 87 Rb and 85 Rb further lead to an amazingly rich variety of BEC phenomena, ranging from the controlled collapse of a condensate with tunable attractive interactions [2] to the realization of an atomic matter wave on a microchip [3]. Because of the large number of groups that have started doing experiments with these atomic species and the growing complexity and subtlety of the planned experiments, there is a clear need for a more precise knowledge of the interactions between ultracold rubidium atoms in the electronic ground state, since these determine most of the properties of the condensate. For instance, despite a widespread interest, until now to our knowledge no experimental group has been able to locate the predicted [4] magnetic-field induced Feshbach resonances that can be used to tune the interactions between ultracold 87 Rb atoms. Being able to switch on or off these interactions at will by a mere change of magnetic field may well be one of the main assets of matter waves compared to light waves in the new matter wave devices. In an atomic interferometry device, in particular, a nonlinear interaction between interfering waves may be introduced or eliminated by changing a field applied at the intersection point.In this Letter, combining the results of three very recent high-precision observations, we come close to a complete and model-independent specification of the interaction properties of ultracold rubidium atoms. The fact that two isotopes 85 Rb and 87 Rb are involved in the measurements makes the constraints exceptionally strong and also increases the predictive power: the interaction properties of any other fermionic or bosonic isotope with mass number 82, 83, 84, or 86 are now known with about the same precision. Using mass scaling to relate the different isotopes we are able for the first time to deduce for each of the isotopes the exact numbers of bound Rb 2 states with total spin S = 0 (singlet) and 1 (triplet). As an illustration of the predictive ...

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confidence: 85%

Interisotope Determination of Ultracold Rubidium Interactions from Three High-Precision Experiments

et al. 2002

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“…We found by interpolation the detuning D theor i which would correspond to a zero-dipole-moment integral and we adjusted the value of a T to make it match the corresponding experimental value. A first trial was made using in turn the various theoretical values found in the literature for the multipole expansion parameters [17][18][19][20][21] and for the exchange terms [22,23]. The values of the scattering length that were obtained for the various sets of parameters and also, in general, for the various minima were all different and incompatible with the experimental error bars.…”

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“…We have used in turn the exchange terms found in Refs. [23] and [22], which differ by roughly a factor of two. The latter is preferable because the corresponding value of x 2 is twice as small, whereas the results for a T and C 6 are almost identical.…”

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Photoassociative Spectroscopy as a Self-Sufficient Tool for the Determination of the Cs Triplet Scattering Length

et al. 2000

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In photoassociation spectroscopy, the line intensities of a given vibrational progression exhibit zero-signal modulation reflecting the node structure of the s-wave ground state wave function of two free colliding atoms. This leads to the determination of the scattering length. We performed photoassociation of cold Cs atoms polarized in the Zeeman sublevel f = 4, m(f) = 4. We analyzed the intensities of the lines associated with the Cs2 0(-)(g) state dissociating to the 6s(1/2)+6p(3/2) asymptote. This yields a value of the Cs triplet state scattering length, a(T) = -530a(0), while consistency requirements impose a value of the multipole ground state molecular coefficient, C6 = 6510 a.u.

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“…, whose expression is given by equation (13) in [48]. The computation methods of the scattering states can be found in [60,61]. However, to save the computation effort, during the propagation of the wavefunction at some time t i , we use a splitting scheme in the asymptotic region [62,63]:…”

Section: Computation Of Physical Observablesmentioning

confidence: 99%

Accurate computation of above threshold ionization spectra for stretched ${{\rm{H}}}_{2}^{+}$ in strong laser fields

Liang

Xiao

Gong

et al. 2017

J. Phys. B: At. Mol. Opt. Phys.

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Investigations on the simplest benchmark system can reveal most underlying mechanisms for the intricate dynamics of molecular systems induced by strong laser pulses. However, due to the two-center Coulomb potential and the highly nonlinear nature of the electron dynamics, the accurate computation of the above threshold ionization spectra remains challenging, especially at large internuclear distances and high laser intensities. In the present work, we implement a new Gauss-quadrature approximation (GA) in the framework of finite element discrete variable representation to solve the time-dependent Schrödinger equation of in strong laser fields. By using this GA, one can arrive at a matrix representation of the first derivative operator that keeps its anti-hermiticity. This crucial feature allows a very stable propagation of the wavefunction under the usual Lanczos scheme. Combining with a wavefunction splitting in the asymptotic region, we show that our present numerical method can reliably deal with the electronic dynamics of stretched molecules at large internuclear distances for high laser intensities and long pulse durations. Accurate photoelectron momentum distributions under these conditions are presented and the distinct features due to the two-center potential are discussed.

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Continuum wavefunctions for one-electron two-centre molecular ions from the Killingbeck - Miller method

Cited by 20 publications

References 27 publications

Interisotope Determination of Ultracold Rubidium Interactions from Three High-Precision Experiments

Interisotope Determination of Ultracold Rubidium Interactions from Three High-Precision Experiments

Photoassociative Spectroscopy as a Self-Sufficient Tool for the Determination of the Cs Triplet Scattering Length

Accurate computation of above threshold ionization spectra for stretched ${{\rm{H}}}_{2}^{+}$ in strong laser fields

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