Direct potential fit analysis of the X 1Σg+ state of Rb2: Nothing else will do!

Abstract

High resolution A-X emission data involving vibrational levels of the ground X 1Σg+ electronic state up to v″=113, spanning 99.8% of the potential well, have been acquired for three isotopomers of Rb2. While a good fit (σ̄f=1.03) to the 12 148 transition frequencies (with uncertainties ±0.001 cm−1) is obtained from an unconstrained combined-isotopomer Dunham-type analysis, it requires a large number (62) of expansion parameters, and the resulting empirical centrifugal distortion constants (CDCs) are unreliable for extrapolation to higher-J. Moreover, Dunham expansion fits using constrained theoretical values of the first six CDCs (up to Ov) fail to properly represent the data, as even higher-order CDCs are required. However, a direct fit of these data to an analytical “modified Lennard-Jones” potential energy function involving only 16 fitted parameters yields essentially the same quality of fit as did the unconstrained Dunham fit, and should be reliable for extrapolation to arbitrarily high J. This potential form incorporates the proper R−6 asymptotic behavior of the potential, and is constrained to have the theoretically predicted C6 dispersion coefficient. Although the dataset involves the three isotopomers 85,85Rb2, 85,87Rb2, and 87,87Rb2, none of the present analyses was able to determine any Born–Oppenheimer breakdown effects.

Contrasting the wide Feshbach resonances inLi6andLi7

“…For heavy diatomic molecules, the differences between the binding energies for different isotopes can be well accounted for by retaining the same potential curves and simply changing the masses used in the calculation [28][29][30][31][32][33][34]. However, it is known that mass corrections due to the breakdown of the BornOppenheimer approximation are important for light species such as H 2 [35,36] and also have significant effects in LiK [37] and LiRb [38].…”

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

“…We thus effectively include the bound states of Ref. [7] with outer turning points in the range considered. In the search we take C 12 equal to the theoretical value 11.9×10 9 of Ref.…”

“…The second experiment is the improved characterization [6] of the elastic scattering near a Feshbach resonance in 85 Rb, leading to a more precise determination of the resonance field B 0 = 154.9(4) G and the nearby field strength B ′ 0 ≡ B 0 + ∆ = 165.85(5) G, where the scattering length goes through zero (∆ is the (elastic) resonance width). The third experimental ingredient going into our analysis is the measurement [7] of 12148 transition frequencies between X 1 Σ + g vibrational levels of the ( 85 Rb) 2 , ( 87 Rb) 2 , and 85 Rb 87 Rb molecules, leading to a highly accurate singlet Rb + Rb potential [8]. Moreover, within the accuracy of this experiment a comparison of levels for the three studied isotopomers shows no sign of BornOppenheimer break-down effects, i.e., the observed levels agree with a simple radial Schrödinger equation containing a common singlet potential V S (r) and the reduced atomic mass.…”

“…[7] with a long-range part equal to the difference V disp −V exch of a dispersion term and an exchange term, starting at a variable radius r S between 21 and 23.5 a 0 (1 a 0 = 0.529Å). The part V disp (r) includes C 6 , C 8 , C 10 terms and retardation, while V exch (r) is given by the analytic form 1 2 Jr 7/2α−1 exp(−2αr) derived by Smirnov and Chibisov [9], in which 1 2 α 2 is the ionization potential of the Rb atom in atomic units (au).…”

Probing Weakly Bound Molecules with Nonresonant Light

“…Based on the molecular constants and a combination of the potential energy curve of Ref. [13] with the long-range exchange and dispersion terms of Ref. [14], a single potential curve for the ground 1 AE þ g electronic state was found, with a dissociation energy D e ¼ 3993:53 cm À1 and an equilibrium distance r e ¼ 4:21 #…”