Resonances of helium in a DC field

A saddle-point complex-rotation method is used to study electric-field effe cts on the doubly excited resonances of He. By using a 892-term wavefunctio n, a seven-angular-symmetry calculation (i.e. L-max = 6) is performed for a comprehensive study around the He (2, 6a) P-1 degrees and (2, 6a) D-1(e) r esonance pair in the presence of an external electric field. A general M-st ate sum rule is shown which suggests the sum of total energy or total width of M-state system is not affected by the presence of a weak static field. The M-state sum rule is used to investigate the sharing of resonance energi es and widths for the locally isolated resonance groups around the He (2, 6 a) P-1 degrees and (2, 6a) D-1(e) resonance pair in the small-field region.