5. Gribakin and Flambaum’s Semiclassical Scattering Length a class (eq ) Closely Agrees with the Fully Quantum Mechanical Scattering Length a quant with Low Relative Error for Various Parametrizations of the Cs2 3Σ u Potential (eq ) .
| R c [au] | Rmin [au] | Umin [10–3 au] | aclass [au] | aquant [au] | Relative Error |
|---|---|---|---|---|---|
| 23.215 | 11.93 | –1.273 | 376 | 352.5 | 6.7% |
| 23.190 | 11.91 | –1.286 | 140 | 144.2 | 2.9% |
| 23.165 | 11.88 | –1.300 | 65 | 68.0 | 4.4% |
| 23.140 | 11.86 | –1.313 | –69 | –67.7 | 1.9% |
| 23.115 | 11.83 | –1.327 | 467 | 485.3 | 3.8% |
a
Results are shown for parameters B = 0.0016, α = 5.53, β = 1.072, C 6 = 6.5, C 8 = 1.1 · 106, and C 10 = 1.7 · 108 from ref , with stated cutoff radii R c resulting in shifted potential minima (R min, U min). The quantum result follows from extrapolation of the s-wave phase shift at k = 0.005 au (12 μK) to k = 0 au (zero Kelvin). Reproduced table with permission from G. F. Gribakin and V. V. Flambaum, Physical Review A, 48, 1, 546, 1993. Copyright 1993 by the American Physical Society.