Precise determination of the dipole matrix element and radiative lifetime of theK394p state by photoassociative spectroscopy

Abstract

Rovibrational levels (v=0–30) of the $0_{\mathrm{g}}^{\mathrm{-}}$ ``pure long-range'' state of ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}_2^{}{}_{}{}^{}$ are observed by photoassociative spectroscopy of ultracold potassium atoms prepared in a high-density magneto-optical trap. The measured molecular binding energies are used to precisely determine the long-range dipole-dipole potential constant ${\mathrm{C}}_3^{\mathrm{\Pi }}$ of the K(4s)+K(4p) asymptote and the radiative lifetime of the 4p state. We determine ${\mathrm{C}}_3^{\mathrm{\Pi }}$=-5.456(9) zJ ${\mathrm{nm}}^3$ (-8.445(14) a.u.), τ(4${\mathrm{}}^2$ ${\mathrm{P}}_{3\mathrm{/}2}$)=26.34(5) ns, and τ(4${\mathrm{}}^2$ ${\mathrm{P}}_{1\mathrm{/}2}$)=26.69(5) ns. Our result is a significant improvement in precision over previous lifetime measurements and agrees well with the recent fast-beam experiment [U. Volz and H. Schmoranzer, Phys. Scr. T65, 48 (1996)].