DECAY OF NEGATIVE MESOTRONS IN MATTER *)

A joint article by three of the leading theorists discusses the results of recent experimental studies of the passage of negative mesotrons through matter and points out a fundamental discrepancy between theory and experiment.

Recently Conversi, Pancini, and Piccioni 1 published a paper devoted to the passage of negative and positive mesotrons through iron and graphite. In iron, decay electrons (i.e., electrons arising in the spontaneous decay of mesotrons) were observed only for positive mesotrons. The absence of decay electrons for negative mesotrons is in complete agreement with theory, since theoretical calculations imply that negative mesotrons, having slowed down, must be captured by nuclei before they have time to decay. However, in observing the passage of mesotrons through graphite, the Italian experimenters found approximately the same number of decay electrons for both positive and negative mesotrons. This indicates that the probability of capture for negative mesotrons in graphite is smaller than the probability of decay.

Sigurgeirsson and Yamakawa 2, who studied the decay of mesotrons in Be, C, S, Al, NaOH, and SiC, likewise came to the conclusion that the probability of capture of negative mesotrons by nuclei of light elements (with atomic number \(Z < 10\)) is smaller than the probability of decay, and only for \(Z > 10\) does the ratio between these probabilities become the reverse.

Fermi, Teller, and Weisskopf analyze the theoretical calculations of the interaction of mesotrons with nuclei and come to the conclusion that the contradiction between theory and experiment can be eliminated only by a radical revision of the theory.

The process leading to the capture of a negative mesotron by a nucleus may be divided into two stages: 1) the approach of the mesotron to the nucleus, which is determined by electromagnetic interaction, and 2) capture of the mesotron by the nucleus owing to the non-electromagnetic interaction between mesotrons and heavy particles at short distances. The energy losses in the first stage are easily calculated on the basis of ordinary theory. The time during which the mesotron must reach its innermost orbit around the nucleus, according to theoretical estimates for most solids, does not exceed \(10^{-12}\) sec. The radius of this orbit, as is not difficult to see, is approximately 200 times smaller than the radius of the \(K\)-shell and, for carbon, is 10 times, and for iron 2 times, larger than the nuclear radius.

) E. Fermi, E. Teller, and V. Weisskopf, Phys. Rev. 71*, No. 5, 315 (1947).

According to present-day ideas, capture of a mesotron by a nucleus can occur according to two schemes: 1) proton \(+\) negative mesotron \(=\) neutron \(+\gamma\)-quantum; 2) nucleus in the initial state \(+\) negative mesotron \(=\) neutron \(+\) nucleus in the final state. The first calculations for these processes were made by Kobayasi and Okayama\(^3\) and by Sakata and Tanikawa\(^4\). The results depend somewhat on the spin of the mesotron and on the form of the interaction. For pseudoscalar mesotrons and a definite form of interaction of mesotrons with heavy particles, the capture time of a mesotron from its lower orbit in the first case turns out to be of the order of \(10^{-18}\) sec for graphite and \(10^{-20}\) sec for iron. The second process gives a capture time 10 times smaller. These times are negligibly small in comparison with the decay time of the mesotron, which is equal to \(2.15\cdot 10^{-6}\) sec. The experimental data cited above, however, indicate that the capture time for graphite is greater than the lifetime of the mesotron (the lifetime being equal to the reciprocal of the decay probability). Consequently, the theoretical value of the capture time is smaller than the value following from experiment by at least \(10^{12}\) times. This factor can be reduced only to \(10^{10}\) if another form of interaction is chosen.

The authors point out that the theoretical value of the probability for the processes inverse to the first and second, i.e., for the production of mesotrons by x-rays and slow protons, is evidently also greater than the actual value by approximately \(10^{12}\) times.

Thus, it follows from experiment that the interaction of mesotrons with heavy particles is considerably weaker than follows from theory. Therefore, if the experimental data on the capture of negative mesotrons by light nuclei are correct, the present theory of the interaction of mesotrons with heavy particles must be changed in the most radical way.

In the same issue of Physical Review there is a letter to the editor by Wheeler\(^5\), in which considerations of the same character are presented. Wheeler gives the following estimate for the dependence of the capture time of negative mesotrons \(\tau\) on the atomic number of the element \(Z\):

\[ \frac{1}{\tau}=\frac{1}{\tau_0}\left[1+\left(\frac{Z_0}{Z}\right)^s\right], \qquad Z \simeq 10,\quad s \simeq 4. \]

B. Geilikman

CITED LITERATURE

1. M. Conversi, E. Pancini, O. Piccioni, Phys. Rev. 71, 209 (1947).
2. T. Sigurgeirsson, A. Jamakawa, Phys. Rev. 71, 319 (1947).
3. Kobayasi, Okayama, Proc. Phys. Math. Soc. Japan 21, 1 (1939).
4. Sakata, Tanikawa, Proc. Phys. Math. Soc. Japan 21, 58 (1939).
5. Y. A. Wheeler, Phys. Rev. 71, 320 (1947).