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The Journal of Chemical Physics

Long-range interaction of the 39K(4s)+39K(4p) asymptote by photoassociative spectroscopy. I. The g− pure long-range state and the long-range potential constants

H. Wang, P. L. Gould, William C. Stwalley

Published May 15, 1997• 85 citations
Publisher

Abstract

This paper reports on a comprehensive study of the long-range interaction of the K39(4s)+39K(4p) asymptotic system. We present a detailed discussion of the R-dependent angular momentum couplings and correlation between the Hund’s case (a) and case (c) molecular states. Analytical expressions for the 16 adiabatic Hund’s case (c) long-range potential curves are derived including the higher order dispersion forces and the effects of retardation. Experimentally, six Hund’s case (c) long-range molecular states (0u+, 1g, and 0g− dissociating to the 4 2S1/2+4 2P3/2 asymptote and 0u+, 1g, and 0g− to the 4 2S1/2+4 2P1/2 limit) are observed with rovibrational resolution by photoassociative spectroscopy of ultracold K39 atoms in a high density magneto-optical trap (MOT). Among the six observed long-range states, the upper 0g− “pure long-range” state has negligible short-range chemical exchange contributions and the measured molecular binding energies (v=0–26) are used to precisely determine the long-range potential constants of the 4s+4p interaction. We determine: C3Π=8.436(14) a.u., C3Σ=16.872(28) a.u., C6Π=6272(94) a.u., and C6Σ=9365(141) a.u.. Molecular constants for the three special pure long-range states, the 0g− and 1u (dissociating to the 4 2P3/2 limit and with potential minimum) and the 1u (dissociating to the 4 2P1/2 and with potential maximum), 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 1g state obtained in present work (from the 0g− state) and the long-range portion of the RKR potential curve of the 1 1Πg state previously determined by conventional molecular spectroscopy. The radiative lifetime of the K 4p state derived from the dipole–dipole interaction constant C3Π is also in excellent agreement with a recent fast-beam measurement.

DOI
10.1063/1.473804

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This paper reports on a comprehensive study of the long-range interaction of the K39(4s)+39K(4p) asymptotic system. We present a detailed discussion of the R-dependent angular momentum couplings and correlation between the Hund’s case (a) and case (c) molecular states. Analytical expressions for the 16 adiabatic Hund’s case (c) long-range potential curves are derived including the higher order dispersion forces and the effects of retardation. Experimentally, six Hund’s case (c) long-range molecular states (0u+, 1g, and 0g− dissociating to the 4 2S1/2+4 2P3/2 asymptote and 0u+, 1g, and 0g− to the 4 2S1/2+4 2P1/2 limit) are observed with rovibrational resolution by photoassociative spectroscopy of ultracold K39 atoms in a high density magneto-optical trap (MOT). Among the six observed long-range states, the upper 0g− “pure long-range” state has negligible short-range chemical exchange contributions and the measured molecular binding energies (v=0–26) are used to precisely determine the long-range potential constants of the 4s+4p interaction. We determine: C3Π=8.436(14) a.u., C3Σ=16.872(28) a.u., C6Π=6272(94) a.u., and C6Σ=9365(141) a.u.. Molecular constants for the three special pure long-range states, the 0g− and 1u (dissociating to the 4 2P3/2 limit and with potential minimum) and the 1u (dissociating to the 4 2P1/2 and with potential maximum), 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 1g state obtained in present work (from the 0g− state) and the long-range portion of the RKR potential curve of the 1 1Πg state previously determined by conventional molecular spectroscopy. The radiative lifetime of the K 4p state derived from the dipole–dipole interaction constant C3Π is also in excellent agreement with a recent fast-beam measurement.
Rovibrational levels (v=0--30) of the ${0}_{\mathrm{g}}^{\mathrm{\ensuremath{-}}}$ ``pure long-range'' state of 39K2^{39}\mathrm{K}_{2}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 ${\mathrm{C}}_{3}^{\mathrm{\ensuremath{\Pi}}}$ of the K(4s)+K(4p) asymptote and the radiative lifetime of the 4p state. We determine ${\mathrm{C}}_{3}^{\mathrm{\ensuremath{\Pi}}}$=-5.456(9) zJ nm3{\mathrm{nm}}^{3}nm3 (-8.445(14) a.u.), \ensuremath{\tau}(42{\mathrm{}}^{2}2P3/2{\mathrm{P}}_{3\mathrm{/}2}P3/2​)=26.34(5) ns, and \ensuremath{\tau}(42{\mathrm{}}^{2}2P1/2{\mathrm{P}}_{1\mathrm{/}2}P1/2​)=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)].
Photoassociation spectroscopy with high resolution for 0u+(6P3/2) long-range state of ultracold cesium molecules has been measured experimentally using the modulated trap loss fluorescence spectroscopy technology. The spectral range has been extended over 60 cm-1 below the 6S1/2 + 6P3/2 dissociation limit as compared with other groups. twenty-five new observations of the Cs2 0u+ in long-range state are reported. The vibrational binding energies of these states are analyzed by using the LeRoy-Bernstein formula. The long-range parameter C3 in molecular 0u+(6P3/2) state is derived for 16.1030.010, and the corresponding molecular potential curve is depicted.
We report the first observation of optical-optical double resonance photoassociative spectroscopy of ultracold 39{}^{39}39K atoms near the highly excited 39K(4s)+39K(4d,5d,6d,6s,7s)^{39}K(4s)+^{39}K(4d,5d,6d,6s,7s)39K(4s)+39K(4d,5d,6d,6s,7s) asymptotes in a high density magneto-optical trap. Using the ${v}^{\ensuremath{'}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ level of the ${0}_{g}^{\ensuremath{-}}$ ``pure long-range'' state (a localized long-range Franck-Condon window) as the intermediate state, we observe simple and assignable rovibrational progressions dissociating to these asymptotes. The dominant long-range potential constants are determined. Line broadening, presumably due to autoionization, and rotational excitations due to strong field effects are observed.
We report on new observations of the photoassociation spectroscopy of ultracold cesium molecules using a highly sensitive detection technique and a combined analysis with all observed electronic states. The technique is achieved by directly modulating the frequency of the trapping lasers of a magneto-optical trap. New observations of the Cs2 0g(-), 0u(+), and 1g states at the asymptotes 6S1/2 + 6P1/2 and 6S1/2 + 6P3/2 are reported. The spectral range is extended to the red detuning of 112 cm(-1) below the 6S1/2 + 6P3/2 dissociation limit. Dozens of vibrational levels of the ultracold Cs2 0g(-), 0u(+), and 1g states are observed for the first time. The available experimental binding energies of these states are analyzed simultaneously in a framework of the generalized LeRoy-Bernstein theory and the almost degenerate perturbation theory by Marinescu and Dalgarno [Phys. Rev. A: At., Mol., Opt. Phys. 52, 311 (1995)]. The unique atomic-related parameter c3 governing the dispersion forces of all the molecular states is estimated as (10.29 ± 0.05) a.u.
Very high-lying vibrational levels of the 1g∼1 1Πg electronic state of K2 have been observed in a photoassociation experiment using an ion detection scheme. The photoassociation measurements have been treated together with laser induced fluorescence data recorded by Fourier transform spectrometry to construct a pointwise potential curve for this electronic state. Several vibrational levels were observed by both techniques, so the dissocation energy can be deduced without extrapolation, from the sum of binding energies measured in photoassociation and vibrational energies established with respect to the potential minimum (defined by the fluorescence data), giving De=1290.292±0.002 cm−1 (1 standard deviation). The potential curve reproduces over 2000 term values (up to v=138) with a root mean square error of 0.0025 cm−1. Nevertheless, small differences are found between the rotational constants generated from the potential curve and the effective rotational constants deduced from binding energy measurements at very high v. The smoothness of the outermost part of the pointwise potential energy curve has been investigated through fits to a Hund’s case (c) asymptotic model.