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Structure of Neutral Mesonic Atoms Formed in Liquid Helium. III. More Accurate Treatment of the Electron Wavefunction

### Abstract

The ground‐state energy of a spinless nonrelativistic electron in the field of two fixed spinless nuclei with charges +2 and −1 is computed exactly for a large number of values of the internuclear separation. The calculation is performed using a method devised many years ago by Baber and Hassé. The results of this calculation are then used to estimate values, for a few highly excited states of απ^{−} *e* ^{−} and α*K* ^{−} *e* ^{−} atoms, of a correction to a previous calculation of the binding energy. This energy correction increases, by one unit, a previous estimate of the multipolarity of the most favored Auger transition from a circular orbit of the α*K* ^{−} *e* ^{−} atom with *n* = 29; a similar increase is found to be most likely for circular orbits of the απ^{−} *e* ^{−} atom with *n* = 20 and circular orbits of the α*p̄e* ^{−} atom with *n* = 32, 35, and 37. For α*K* ^{−} *e* ^{−} atoms with *n* = 27 and 29, the energy corrections cause the calculated energy difference between a circular and a nearly circular orbit with the same principal quantum number to be between 15 and 30% smaller than had been estimated previously. Two other corrections are estimated and are found to be probably negligible. One of these corrections is the inaccuracy in the calculated binding energy of a heliumlike mesonic atom, as obtained using the Born‐Oppenheimer approximation, which is associated with the angular correlation between the positions of the electron and the meson. The other correction is the change in the computed value of the mean meson orbital radius which occurs when the interactions responsible for the electron‐meson angular correlation are taken into account.

© 1971 The American Institute of Physics

Received 07 April 1971
Published online 28 October 2003

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http://aip.metastore.ingenta.com/content/aip/journal/jmp/12/9/10.1063/1.1665821

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2003-10-28

2016-10-22

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