Resonances in a positron-lithium $(e^{+}-\mathrm{Li})$ system

The method of complex scaling is used to calculate $S$- and $P$-wave resonance energies and widths below the $\mathrm{Li}(3s,3p,4s,4p)$ excitation thresholds and positronium $n=2$ formation threshold in the positron-lithium system. We use two different types of model potentials to determine the interaction between the core and the valence electron. Explicitly correlated Gaussian basis functions are used to represent the correlation effects between the valence electron, the positron, and the ${\mathrm{Li}}^{+}$ core. A dipole series of resonances are found under the positronium $n=2$ threshold. Furthermore, these resonances are found to agree well with an analytically derived scaling law. The present results are compared with those in the literature.