Determination of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>s</mml:mi></mml:math>-Wave Scattering Length of Chromium

Abstract

We have measured the deca-triplet $s$-wave scattering length of the bosonic chromium isotopes $^{52}\mathrm{C}\mathrm{r}$ and $^{50}\mathrm{C}\mathrm{r}$. From the time constants for cross-dimensional thermalization in ultracold atomic samples, we have determined the magnitudes $|a(^{52}\mathrm{C}\mathrm{r})|=(170\ifmmode\pm\else\textpm\fi{}39){a}_{0}$ and $|a(^{50}\mathrm{C}\mathrm{r})|=(40\ifmmode\pm\else\textpm\fi{}15){a}_{0}$, where ${a}_{0}=0.053\text{ }\mathrm{n}\mathrm{m}$. By measuring the rethermalization rate of $^{52}\mathrm{C}\mathrm{r}$ over a wide temperature range and comparing the temperature dependence with the effective-range theory and numerical single-channel calculations, we have obtained strong evidence that the sign of $a(^{52}\mathrm{C}\mathrm{r})$ is positive. Rescaling our $^{52}\mathrm{C}\mathrm{r}$ model potential to $^{50}\mathrm{C}\mathrm{r}$ strongly suggests that $a(^{50}\mathrm{C}\mathrm{r})$ is positive also.