Photoassociative spectroscopy of highly excited vibrational levels of alkali-metal dimers: Green-function approach for eigenvalue solvers

Understanding high-precision photoassociative spectroscopy of laser-cooled alkali-metal atoms involves modeling an extremely dense level structure of weakly bound molecules in the region where coriolis and hyperfine interactions become comparable to electronic interactions. We describe an iterative eigenvalue solver suitable for resolving these bound states that is based on finding eigenvalues of the shifted inverse or Green-function operator. Nonlinear coordinate transformations applied to the nuclear motion are introduced to minimize the dimensionality of the discretized Hamiltonian. The formalism is applied to resolve the hyperfine structure of rovibrational levels of the $\mathrm{Na}{(}^{2}P)+\mathrm{Na}{(}^{2}S)$ dimer.