Long-range interaction of the 39K(4s)+39K(4p) asymptote by photoassociative spectroscopy. I. The 0g− pure long-range state and the long-range potential constants This paper reports on a comprehensive study of the long-range interaction of the 39 K(4s) ϩ 39 K(4p) asymptotic system. We present a detailed discussion of the R-dependent angular momentum couplings and correlation between the Hund's case ͑a͒ and case ͑c͒ molecular states. Analytical expressions for the 16 adiabatic Hund's case ͑c͒ long-range potential curves are derived including the higher order dispersion forces and the effects of retardation. Experimentally, six Hund's case ͑c͒ long-range molecular states ͑0 u ϩ , 1 g , and 0 g Ϫ dissociating to the 4 2 S 1/2 ϩ4 2 P 3/2 asymptote and 0 u ϩ , 1 g , and 0 g Ϫ to the 4 2 S 1/2 ϩ4 2 P 1/2 limit͒ are observed with rovibrational resolution by photoassociative spectroscopy of ultracold 39 K atoms in a high density magneto-optical trap ͑MOT͒. Among the six observed long-range states, the upper 0 g Ϫ ''pure long-range'' state has negligible short-range chemical exchange contributions and the measured molecular binding energies (vϭ0 -26) are used to precisely determine the long-range potential constants of the 4sϩ4 p interaction. We determine: C 3 ⌸ ϭ8.436(14) a.u., C 3 ⌺ ϭ16.872(28) a.u., C 6 ⌸ ϭ6272(94) a.u., and C 6 ⌺ ϭ9365(141) a.u.. Molecular constants for the three special pure long-range states, the 0 g Ϫ and 1 u ͑dissociating to the 4 2 P 3/2 limit and with potential minimum͒ and the 1 u ͑dissociating to the 4 2 P 1/2 and with potential maximum͒, are reported. The internal consistency of the theoretical model used in this work is confirmed by the excellent agreement between the long-range potential curve of the 1 g state obtained in present work ͑from the 0 g Ϫ state͒ and the long-range portion of the RKR potential curve of the 1 1 ⌸ g state previously determined by conventional molecular spectroscopy. The radiative lifetime of the K 4 p state derived from the dipole-dipole interaction constant C 3 ⌸ is also in excellent agreement with a recent fast-beam measurement.
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