Theoretical Atomic Collisions Laboratory

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The zero-energy Born exchange amplitude for electron-helium scattering in the forward direction has been calculated using a multi-parameter Hylleraas-type wavefunction. Up to 125 terms are used and the result is extrapolated to be 3.9430+or-0.0016. The present calculation substantiates the conclusion reached in several recent papers that the zero-energy form of the Gerjuoy-Krall dispersion relation (1960, 1962) does not hold for e - -He scattering.

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The complex rotation method is applied to calculate autoionisation states ( 1 S e , 1 P o and 3 P o ) of the helium isoelectronic sequence (Z=2-10) below the n=3 hydrogenic thresholds. The Hylleraas-type wavefunctions are employed and up to 161 terms for S states and 165 terms for P states are used, so that several lower-lying states are determined. For He and Li + states, comparisons are made with other calculations and experiments. The width of the lowest 1 P o state of helium below the n=3 threshold is determined to be (191+or-7) meV which differs quite significantly from the experimental value of (132+or-14) meV of Dhez and Ederer (1973). Furthermore, it is concluded that the width computed by the complex rotation method would not reduce to the experimental value even if more terms in the wavefunction are used.

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