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Toward an accurate calculation of the mean lifetime of the H ion in an electric field. Mullen, Brian Charles

Abstract

The lifetime of the negative hydrogen ion in an electric field is of crucial importance for the design and performance of negative ion sector-focussed cyclotrons. The v x B force of the ion moving with a velocity v in a magnetic field B acts like an electric field which removes an electron from the ion. In previous calculations of the dissociation rate, a simple one-electron picture, in which the escaping electron moves in the field of a neutral H atom and tunnels through the barrier formed by the combination of the electric potential and the potential well of the neutral atom was used. We improve the best potential previously chosen by requiring the one-electron state of the second electron to be properly bound with the ionization energy of the H ̄ ion in the absence of the external field. The methods of nuclear reaction theory are then applied in an accurate calculation of the width. The disagreement between the calculated mean lifetime and the experimental values indicates this simple picture of the H ̄ ion is inadequate and the correlations between the two electrons are important. Therefore these are included by using an accurate two electron variational wavefunction. The form of the single particle state from which one of the electrons is removed is then defined unambiguously and a spectroscopic factor results which includes the two electron aspects of the problem. The calculated mean lifetime is then found to agree with the experimental values to within the accuracy of the two sets of results.

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