Calculation of the interspecies s-wave scattering length in an ultracold Na-Rb vapor

We report the calculation of the interspecies scattering length for the sodium-rubidium (Na-Rb) system. We present improved hybrid potentials for the singlet $X^1\Sigma^+$ and triplet $a^3\Sigma^+$ ground states of the NaRb molecule, and calculate the singlet and triplet scattering lengths $a_{s}$ and $a_{t}$ for the isotopomers $^{23}$Na$^{87}$Rb and $^{23}$Na$^{85}$Rb. Using these values, we assess the prospects for producing a stable two-species Bose-Einstein condensate in the Na-Rb system.Comment: v2: report correct units in Table captions, fix error in conclusions for $^{23}$Na$^{85}$Rb TBEC. Otherwise, more concise presentation, typos fixed. 6 pages, 1 figur

ANALYTICAL RADIAL HAMILTONIANS FOR THE X1Σ+X^{1}\Sigma^{+} STATES OF HF AND HCl

$^{1}$J. A. Coxon and P.G Hajigeorgion, {J. Mol. Spectrosc}. \textbf{142}, 254 (1990). $^{2}$W.T. Zernke, W.C. Stwalley, J.A. Coxon and P.G. Hajigeorgiou, {Chem. Phys. Lett}. \textbf{177}, 412 (1991). $^{3}$J.A. Coxon and P.G. Hajigeorgion, {J. Mol. Spectrosc}. \textbf{139}, 84 (1990) $^{4}$P.G. Hajigeorgiou and R.J. Le Roy (see preceding abstract).Author Institution: Department of Chemistry, Dalhousie University; Guelph-Waterloo Centre for Graduate Work in Chemistry, University of WaterlooOver three years ago, we presented radial Hamiltonians for the $X^{1}\Sigma^{+}$ electronic states of hydrogen $fluoride^{1,2}$ and hydrogen $chloride^{3}$ which represented very accurately the wide range of spectroscopic data available on these important molecules. However, those functions were determined in numerical form on a radial grid, and despite their overall success in representing spectroscopic information, the Hamiltonians lacked compactness. In the present work, this problem is addressed by reducing the several thousand line measurements for HF, HCl and related isotopomers, to Born-Oppenheimer potential functions which are modeled as modified Leannard-Jones (MLJ) $oscillators^{4}$ $$U^{BO}(R) = D_{e} \left[1- \left(\frac{R_{e}}{R}\right)^{e} e^{-\beta(x)x} \right]^{2}$$ where $\beta(z) = \beta_{0} + \beta_{1}z + \beta_{2}z^{2} + \ldots + \beta_{m} z^{m} z = 2(R - R_{e})/(R+ R_{e})$ is the Ogilvie-Tipping expansion parameter. The analysis also furnishes analytical functions which collectively describe adiabatic, homogeneous and heterogeneous non-adiabatic, relativistic, and quantum-electrodynamic effects. In addition to the significant improvement in compactness, improved representations for the radial functions which describe the aforementioned effects have been developed, and fits using the new model yield direct estimates of the dissociation energies, $D_{e}$

ON THE DIRECT DETERMINATION OF ANLYTICA INTERNUCLEAR POTENTIALS FOR DIATOMIC MOLECULES

Author Institution: Department of Chemistry, Dalhousie university; Department of Chemistry, University of British ColumbiaA new method for determining accurate internuclear potentials for diatomic molecules in $^{1}\Sigma$ states directly form spectroscopic measurements is described. The method employs an iterative solution of the radial wave equation in the least-squares adjustment of a nonlinear analytical potential function of the type \begin{equation}U(R)={\cal D}_c[1-{e}^{-\beta(R)(R-R_{e})}]^{2}\end{equation} where\begin{equation}\beta(R)=\beta_{0}+\beta_{1}(R-R_c)+\beta_{2}(R-R_e)^{2}\ldots\end{equation} The quantal eigenvalues of the variable-$\beta$ Morse oscillator in Eq. (1) represent the experimental data over wide ranges of $v$ and $J$ within the measurement accuracies. The method offers distinct advantages over the conventional RKR procedure, or even variational methods such as Inverse Perturbation Analysis (IPA). When data for several isotopomers are considered simultaneously, the method yields the Born--Oppenheimer potential and radial functions describing BornûOppenheimer breakdown effects. The method has been tested for several diatomic molecules for which accurate measurements of pure rotational and rotational-vibrational transitions are available; results are presented for HI/DI, HBr/DBr, CO, SiS, CS NaF and LiI

ACCURATE ANALYTICAL POTENTIAL AND MOLECULAR CONSTANTS FOR THE GROUND X1Σ+X^{1}\Sigma^{+} ELECTRONIC STATE OF CARBON MONOXIDE

Author Institution: Departement of Chemistry, Dalhousie University; Department of Chemistry, IntercollegeAll available infrared and microwave spectroscopic line measurements for seven isotopomers of carbon monoxide in the ground electronic state have been employed in a weighted least squares fit giving directly the Born-Oppenheimer potential in compact analytic form, as well as additional radial functions that describe Born-Oppenheimer breakdown. The 18,858 line positions, which include vibrational levels covering approximately 70% of the well depth, are represented by 29 adjustable parameters with a reduced standard deviation of 0.43. Effective vibrational-rotational Hamiltonian operators constructed for each isotopomer have been employed to calculate accurate and quantum-mechanically meaningful rotational and centrifugal distortion constants that, along with the rotationless vibrational eigenvalues, represent the experimental data with the same degree of success as the eigenvalues of the radial operators

APPLICATION OF A DIRECT POTENTIAL FITTING METHOD TO THE B1Σ+B^{1}\Sigma^{+} AND X1Σ+X^{1}\Sigma^{+} ELECTRONIC STATES OF HF AND DF

$^{a}$J. K. G. Watson, J. Mol. Spectrosc. 80, 411 (1980). $^{b}$R. J. Le Roy, J. Mol. Spectrosc. 194, 189 (1999).Author Institution: Department of Chemistry, Dalhousie University; Department of Biosciences, IntercollegeA collection of 6070 spectroscopic line positions for hydrogen fluoride and deuterium fluoride, which consists of all microwave and infrared $X^{1}\Sigma^{+}$ ground electronic state data, and the $B^{1}\Sigma^{+} X^{1}\Sigma^{+}$ emission band system data, has been employed in a weighted least-squares fit directly to the radial Hamiltonian operators of the $B^{1}\Sigma^{+}$ and $X^{1}\Sigma^{+}$ electronic states. The radial Hamiltonian operator model includes first- and second-order corrections to the Born-Oppenheimer approximation and was derived from the landmark theoretical work of $Watson^{a}$. The principle isotopomer fitting strategy of Le $Roy^{b}$ was incorporated in the least-squares fit. A total of 54 adjustable parameters was required to obtain a satisfactory representation of the experimental data, with a reduced standard deviation of 1.03. In addition, a collection of highly accurate quantum-mechanically meaningful rotational and centrifugal distortion constants was calculated from the derived Hamiltonian operators of the two electronic states

THE RADIAL HAMILTONIAN OPERATOR OF HeH+HeH^{+}

Author Institution: Department of Chemistry, Dalhousie University; Department of Chemistry, University of British ColumbiaExperimental line positions for $^{3}HeH^{+}, ^{4}HeH^{+}, ^{3}HeD^{+}$, and $^{4}HeD^{+}$ have been employed in the determination of an effective non-adiabatic radial Hamiltonian operator for the ground $X^{1}\Sigma^{+}$ electronic state in compact analytic form. The procedure considers a Born-Oppenheimer potential and isotopically invariant Born-Oppenheimer breakdown functions for each atomic centre. The nuclear mass-independent potential is represented by the modified Morse $function^{1}$ $U^{BO}(R)= D_{r}[1 - e^{-\beta(R)(R-R_{e})}]^{2}$ where a Pad\'{e} approximant is adopted for $\beta(R)$. The spectroscopic data base, which samples the entire potential well, includes a number of transitions from quasibound levels. The experimental line positions are reproduced to within their experimental uncertainties and calculated quasibound level widths are in excellent agreement with experimental measurements. Results are compared to recent ab initio calculations. $^{1}$. J.A. Coxon and P.G. Hajigeorgiou, J. Mol. Spectrosc. 150, 1 (1991)

THE ISOTOPIC BEHAVIOUR OF BORN-OPPENHEIMER BREAKDOWN EFFECTS: APPLICATION OF A LEAST-SQUARES PROCEDURE TO THE HC1 ISOTOPOMERS

$^{1}$ J.A. Coxon, J. Mol. Spectrosc. 117, 361-387 (1986).Author Institution: Department of Chemistry, Dalhousie UniversityThis work describes the application of a weighted least-squares $procedure^{1}$ for the reduction of spectroscopic line positions to effective radial Hamiltonian operators. The method is applied to the $X{^{1}}\Sigma^{+}$ and $B{^{1}}\Sigma^{+}$ states of $H^{35}C1, H^{37}C1, D^{35}C1$, and $D^{37}C1$. Extensive spectroscopic data are now available for all four isotopomers; these data have been employed to determine an isotope independent rotationless potential, U(BO), and isotopically invariant radial functions U(H) and U(Cl) which result in effective potential functions U(eff) for each isotopomer according to Eq. (1). \begin{equation}U(eff) = U(BO) + U(H)/M_{a} + U(Cl)/M_{b},\end{equation} where Ma and Mb are the atomic masses of H/D and $^{35}Cl/^{37}Cl$, respectively. In addition, J- dependent non-adiabatic effects are described in terms of a radial function q(R) containing contributions from both atoms, that modifies the conventional rotational Hamiltonian, as in Eq. (2). \begin{equation}H(rot) = (\hbar^{2}/2\mu R^{2})[1 + q(R)][J(J+1)].\end{equation} The effective rotationless potential of each isotopomer in combination with the appropriate rotational Hamiltonian, yield eigenvalues that reproduce spectroscopic line positions within estimated experimental errors

HIGH RESOLUTION SPECTROSCOPY OF SrOD RADICAL BY SUPERSONIC EXPANSION

Author Institution: University of Waterloo, Waterloo, Ontario, Canada, N2L 3GlThe high resolution spectrum of gas phase SrOD has been recorded in a supersonic beam spectrometer. The $\tilde{B}^{2}\Sigma^{+}-\tilde{X}^{2}\sigma^{+} (000)-(000)$ and (100) - (000) bands have been rotationally analyzed. The accuracy of the rotational line positions was about $0.003 cm^{-1}$, The measured line positions together with the microwave data for the ground state have been fitted to give molecular constants for both electronic states. The Q branch of the (000)-(000) band was resolved for the first time and the ratio between the perpendicular and parallcll transition dipole moments was estimated to be about 0.2