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The Journal of Chemical Physics

Predissociations in u+ and 1g states of K2

T. H. Bergeman, Paul S. Julienne, Carl J. Williams, Eite Tiesinga, M. Riad Manaa, H. Wang, P. L. Gould, William C. Stwalley

Published Oct 10, 2002• 18 citations
Publisher

Abstract

Recently Wang, Gould, and Stwalley [Phys. Rev. Lett. 80, 476 (1998)] showed by exciting atomic fragments that predissociation occurs in the 1g and 0u+ states of K2. In this study, we supplement the interpretation given in the original report with a more detailed discussion. The calculations presented here use discrete variable representation, close coupling, and semiclassical methods, and incorporate an ab initio calculation of diagonal and off-diagonal spin–orbit elements. The predicted predissociation widths for the 1g state are too narrow to be observed directly, but may be correlated with the strength of the spectral lines observed by exciting atomic fragments. The missing v=90 level of the 1g state in the observed fragmentation spectrum, where the predissociation rate is calculated to be nearly maximum, is attributed to a node in the absorption line strength close to this vibrational level. Since the available information on K2 electronic states (despite recent progress) gives inadequate information on the inner walls of the A state and especially of the b state, calculations of predissociation in the 0u+ state can give only a range of possible widths. We fit widths to 0u+ spectral lines observed by monitoring trap loss. The fitted experimental widths are significantly larger than the maximum calculated predissociation widths, suggesting that there was line broadening associated with the laser power required for the observation.

DOI
10.1063/1.1508375

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Recently Wang, Gould, and Stwalley [Phys. Rev. Lett. 80, 476 (1998)] showed by exciting atomic fragments that predissociation occurs in the 1g and 0u+ states of K2. In this study, we supplement the interpretation given in the original report with a more detailed discussion. The calculations presented here use discrete variable representation, close coupling, and semiclassical methods, and incorporate an ab initio calculation of diagonal and off-diagonal spin–orbit elements. The predicted predissociation widths for the 1g state are too narrow to be observed directly, but may be correlated with the strength of the spectral lines observed by exciting atomic fragments. The missing v=90 level of the 1g state in the observed fragmentation spectrum, where the predissociation rate is calculated to be nearly maximum, is attributed to a node in the absorption line strength close to this vibrational level. Since the available information on K2 electronic states (despite recent progress) gives inadequate information on the inner walls of the A state and especially of the b state, calculations of predissociation in the 0u+ state can give only a range of possible widths. We fit widths to 0u+ spectral lines observed by monitoring trap loss. The fitted experimental widths are significantly larger than the maximum calculated predissociation widths, suggesting that there was line broadening associated with the laser power required for the observation.
Photoassociation resonances in the 87{}^{87}87Rb2{}_{2}2​ 1g{1}_{g}1g​ state dissociating to 52S+52P1/25{\phantom{\rule{0.16em}{0ex}}}^{2}S+5{}^{2}{P}_{1/2}52S+52P1/2​ were produced by the excitation of colliding 87{}^{87}87Rb atoms in a far-off resonance trap. Levels down to 31 cm${}^{\ensuremath{-}1}$ below the dissociation limit were measured with resonance linewidths of 15 to 20 MHz, and have been located to a one-sigma combined systematic and statistical uncertainty of 50 MHz relative to the 52S+52P1/25{\phantom{\rule{0.16em}{0ex}}}^{2}S+5{}^{2}{P}_{1/2}52S+52P1/2​ limit. Electron and nuclear spins were fixed to a space-fixed axis by circularly polarized optical pumping, so that only states with total nuclear spin I=3I=3I=3 were excited, thereby greatly simplifying the spectrum. The analysis of the data yielded hyperfine coupling parameters A(v)A(v)A(v), vibrational G(v)G(v)G(v), and rotational B(v)B(v)B(v) parameters. The G(v)G(v)G(v) parameters could be fit to an rms accuracy of about 0.01 cm${}^{\ensuremath{-}1}$ to a potential constructed from current C3{C}_{3}C3​ and C6{C}_{6}C6​ long-range dispersion parameters plus an ab initio potential that was adjusted in depth and with quadratic terms in the internuclear distance added to the inner wall.
The treatment of the dynamics of ultracold molecules requires new theoretical tools. Previous work of the present authors [J. Chem. Phys. 110, 9865 (1999)] for calculation of vibrational levels by a Fourier grid representation with use of adaptative coordinates is generalized here to the treatment of the bound-continuum interaction in a two-channel problem. Two numerical methods are presented: a time-dependent method using a Chebyshev propagator to compute the correlation function and a time-independent method with diagonalization of a Hamiltonian that includes an absorbing optical potential. In both cases the adaptative coordinate is defined by a numerical rather than an analytical procedure. Lifetimes are reported for the predissociated levels of the Rb2{\mathrm{Rb}}_{2}Rb2​ and Cs20u+(ns+np2P3/2){\mathrm{Cs}}_{2}{0}_{u}^{+}{(ns+np}^{2}{P}_{3/2})Cs2​0u+​(ns+np2P3/2​) spectra, where n=5,6.n=5,6.n=5,6. The two numerical methods give similar results. The lifetimes increase with the vibrational quantum number proportionally to the classical vibration period estimated from the Le Roy--Bernstein law for an asymptotic ${R}^{\ensuremath{-}3}$ potential, and the energy variation can be fitted to an analytical formula. The results are shown to be very sensitive to the molecular parameters, potentials, and couplings. The measured width of 8.5 GHz reported by Cline et al. [Phys. Rev. Lett. 73, 632 (1994)] for one predissociated level of 87Rb2{}^{87}{\mathrm{Rb}}_{2}87Rb2​ is reproduced. A strong isotopic effect is found for the rubidium dimer, the lifetimes of 85Rb2{}^{85}{\mathrm{Rb}}_{2}85Rb2​ and 87Rb2{}^{87}{\mathrm{Rb}}_{2}87Rb2​ levels differing by a factor of 3. Finally, we present a third approach, in the framework of a generalized two-channel quantum-defect theory, where lifetimes are determined by extrapolation of parameters fitted to Lu-Fano plots of computed bound levels below the P1/2{P}_{1/2}P1/2​ dissociation limit. Excellent agreement is obtained with the numerical results, suggesting the possibility of fitting to experimental spectra.
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.
PHOTOASSOCIATIVE SPECTROSCOPY OF THE PURE LONG-RANGE STATES OF THE 39K2{^{39}}K_{2}39K2​ DIMER
1^{1}1 H. Wang, J. Li, X.T. Wang, C.J. Williams, P.L. Gould, and W.C. Stwalley, Phys. Rev. A 55, R1569(1997). 2^{2}2 H. Wang, X.T. Wang, P.L. Gould, and W.C. Stwalley, Phys. Rev. Lett., 78, 4173(1997).
We report the first observation of fragmentation spectra of the fine-structure predissociated long-range 1g{1}_{g}1g​ and 0u+{0}_{u}^{+}0u+​ $(b^{3}\ensuremath{\Pi}_{{0}^{+}u})$ states of ultracold (T<1mK)(T<1\mathrm{mK})(T<1mK) 39K2{}^{39}{\mathrm{K}}_{2}39K2​ molecules. The 1g{1}_{g}1g​ state predissociates via the curve crossing at long range $(R\ensuremath{\sim}23\AA{})$ with the repulsive 0g+{0}_{g}^{+}0g+​ state. The 0u+{0}_{u}^{+}0u+​ state, however, predissociates predominantly through molecular fine-structure mixing at short range with the $b^{3}\ensuremath{\Pi}_{1u}$ component. Our technique of fragmentation spectroscopy is a sensitive and selective tool for ultracold photoassociation and fine-structure-changing collisions.