Theoretical complex Stark energies of lithium by a complex scaling plus the B-spline approach

Abstract

The B-spline-based coordinate rotation method plus the model potential approach is applied to investigate the complex energies of low-lying resonances of the lithium atom in an electric field. Our results are compared with two recent calculations by a state-specific complex eigenvalue Schrödinger equation (CESE) (Themelis and Nicolaides 2001 J. Phys. B: At. Mol. Opt. Phys. 34 2905) and complex absorbing potential (CAP) (Sahoo and Ho 2000 J. Phys. B: At. Mol. Opt. Phys. 33 5151) methods, which are in controversy. The positions of resonances by the present calculation are found to be in agreement with theoretical data obtained by both the CESE and CAP methods. Our investigation clarifies that the contradiction about ‘4f0’ resonant position varies with the electric field. However, for the width of resonances, our results are only consistent with those by the CESE method for all strengths of the electric field under consideration. A detailed comparison on the m = 0 state among these three calculations shows that the unusual behaviour of width of resonances in the weak-field case by the CAP method is not a ‘new’ finding but a misguiding resulting from nonconvergent results. The systematic agreement between our model potential calculation and the ab initio calculation by the CESE for lithium indicates that the present proposed method is reliable and appropriate to simplify the calculation of the alkali metal atom in external fields.