Gross Features of Angular Momentum Distribution of Coulomb Captured Mesonic Particles

The gross features of the angular momentum distribution of mesonic particles resulting from Coulomb capture are calculated in closed form. The calculation is based on the semiclas· sical model of Coulomb capture with the energy loss being due to a frictional force the mesonic particle experiences in the atomic electron gas. Atomic structure effects other than the atomic radius, and chemical bonding are neglected. There are two basic questions to be answered by any theory of Coulomb capture of mesonic particles; capture ratio for capture in the individual elements (in the case of a compound, etc.) and angular momentum distribution for capture in a given element. The experimental capture ratio is more directly correlated to the yet unobserved Coulomb capture process, i.e., the transition from an unbound state to the first bound state, than the experimental X-ray intensity pattern: In all theories or models except the large mesic molecule modeF) the capture ratio is only determined by the Coulomb capture processes while there are a large number of yet unobserved Auger transitions between capture and X-ray emission. Although it is not easy to treat, theory and experiment are simplest in the case of muons. Fair agreement between a semiclassical theory and experiment has been obtained for the capture ratio. The situation is worse in the case of the X-ray intensity pattern: There are only some numerical values available as theoretical results, and one cannot speak of good agreement between these values and the experimental results. The field is reviewed, for example, in Refs. 2) ~ 4). It is the aim of the present paper to give a closed-form calculation of the gross features of the initial distribution immediately after Coulomb capture. Detailed effects, such as electron configurations and chemical binding will not be taken into account, but the effect of the atomic radius will be taken into account to some extent. The calculation is based on a semiclassical description of the capture process. 4 )·'9) In this model the mesonic particle is treated classically while the electrons are assumed to be a Fermi gas, with corrections for the atom's finite size in condensed matter. The energy loss and the resulting angular momentum