Precise determination of the dipole matrix element and radiative lifetime of the ³⁹K 4p state by photoassociative spectroscopy

Rovibrational levels (v=0–30) of the 0_g^- ``pure long-range'' state of ³⁹K₂ 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 C₃^Π of the K(4s)+K(4p) asymptote and the radiative lifetime of the 4p state. We determine C₃^Π=-5.456(9) zJ nm³ (-8.445(14) a.u.), τ(4 ²P_3/2)=26.34(5) ns, and τ(4 ²P_1/2)=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)].