Theory and computation of electric-field-induced tunneling rates of polyelectronic atomic states

It is shown how to obtain efficiently quantum-mechanical tunneling rates (and energy shifts) induced by electric fields for arbitrary polyelectronic states. The problem is formulated as one of solving nonperturbatively a complex-eigenvalue matrix equation, constructed in terms of two separately optimized multidimensional function spaces, Q and P. The theory is demonstrated on two prototypical ground states, He 1s² ¹S and Li 1s²2s ²S, as well as on the Li 1s² 2p ²P^∘{} excited levels (ML=0,±{}1). For example, for field strengths F=3.86×{}10⁷--3.86×{}10⁸ V/cm the He ¹S tunneling rates range from 5.79×{}10⁷ to 7.75×{}10¹⁰ s^-1.