X-Ray Deficiency in Mesonic Atoms

We present an analysis of $\pi$-mesonic atoms, based upon cascade calculations taking into account the known processes of radiation, Auger transitions, and nuclear absorption. This analysis, together with the previous one on $\mu$-mesonic atoms, is intended to provide a deeper insight into the unsolved problem of the deficiency of x rays in mesonic atoms. It is shown that the $\pi$-mesonic $L$ x-ray yields (for $Z\le 20$) are quite insensitive to the strength of nuclear absorption and depend only upon the chosen initial meson population of the higher levels. Similarly, the ratios of basic ($K_{\alpha }$, $L_{\alpha }$, etc.) to higher x-ray yields, both for $\mu$ and $\pi$ mesons, depend strongly on the initial distribution. The best agreement between the calculations and experiment was obtained for a "modified statistical" initial population of the form $\mathrm{}(2l+1)\mathrm{}{e}^{\mathrm{al}}$, with $a=0.2\mathrm{}$, in the $n=14\mathrm{}$ level. From the existing experimental data on $\pi$-mesonic $K$ x rays, the mean life of the $\pi$ meson in nuclear matter was deduced: ${\tau }_c=2.75\mathrm{}\times {10}^{-23\mathrm{}}$ sec. Within the framework of the present theory we are still unable to account for the x ray deficiency in the light atoms. However, it is shown that the quantum loss as a function of energy is different for $\pi$- and $\mu$-mesonic atoms, and therefore it is very probably due to a real physical effect. Furthermore, by comparing our predicted Auger electron yields with the experimental data, we can rule out any hypothetical simple Auger process in which the full energy of the "missing" quantum is given to a single electron.