Knowledge Bank

This work describes the application of a weighted least-squares $procedure1$ for the reduction of spectroscopic line positions to effective radial Hamiltonian operators. The method is applied to the $X\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}\Sigma +$ and $B\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}\Sigma +$ states of $H35C1,H37C1,D35C1$, and $D37C1$. 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 $\mathrm{<mrow\; data-mjx-texclass="ORD">35</mrow>}Cl/37Cl$, 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.