Energy spectrum of stopping negative mesons and the concentration dependence of capture fractions

The physics that determines the shape of the energy spectrum of stopping negative mesons is discussed. We note that a white energy spectrum, for arrival probability $F\left(E\right)\mathrm{}$, not flux $P\left(E\right)\mathrm{}$, follows for a large class of models. The importance of distinguishing between $F\left(E\right)\mathrm{}$ and $P\left(E\right)\mathrm{}$ is stressed: $P\left(E\right)\mathrm{}$ reflects the energy ($E$) dependence of the total inelastic and capture cross sections, while $F\left(E\right)\mathrm{}$ is independent of these. The $F\left(E\right)\mathrm{}\propto E$ behavior found in some models is due to meson capture at positive energies, i.e., capture behind a positive centrifugal barrier. We explore the possibility of a concentration effect on capture ratios in binary mixtures, and conclude that, as long as the energy losses in meson-atom collisions are not much smaller than the barrier height, such concentration effects are negligibly small.