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INTERACTION OF $\pi$-MESONS WITH THE CARBON NUCLEUS*
Most of the experimental data accumulated at present concerning the interaction of $\pi$-mesons (both charged and neutral) with nucleons, as well as experiments on the photoproduction of $\pi$-mesons on nucleons**, apparently testify in favor of the assumption that $\pi$-mesons are pseudoscalar with a pseudovector type of coupling (this means that derivatives of the meson wave function enter into the term describing the interaction of mesons with nucleons in the Hamiltonian). The article reviewed, in which the interaction of $\pi$-mesons of both signs with carbon nuclei was studied, sheds additional light on this question. It should be emphasized, however, that, owing to the poor statistics, the results are for the most part only qualitative in character.
The $\pi$-mesons were produced by means of betatron bremsstrahlung with an upper limit of 320 MeV. The beam of $\pi$-mesons was then focused in a constant magnetic field and directed into a Wilson chamber containing nine carbon plates. The energy of the mesons striking the chamber was $65 \pm 5$ MeV. Their energy in the chamber was on the average 48 MeV. A total of 9443 tracks were processed, and only those mesons whose energy lay in the range from 35 to 60 MeV were selected.
Taking into account possible errors connected mainly with $\pi$-$\mu$ decay and with contamination of the initial beam of $\pi$-mesons (due to the decay of $\pi$-mesons in flight) and electrons, the nuclear-interaction cross section and the elastic-scattering cross section of $\pi$-mesons on the carbon nucleus were calculated (see table).
Table
| Nuclear-interaction cross section | Elastic-scattering cross section (in $10^{-27}\ \text{cm}^2$) | |
|---|---|---|
| $\pi^+$ | $214 \pm 37$ | $78 \pm 23$ |
| $\pi^-$ | $240 \pm 54$ | $96 \pm 34$ |
| Total | $223 \pm 32$ | $84 \pm 19$ |
It is evident from the table that the interaction cross sections of $\pi^+$- and $\pi^-$-mesons prove to be equal within the limits of statistical errors. This agrees with the results of other, earlier experiments.
Proceeding from these data, under certain assumptions about the character of the interaction of $\pi$-mesons with the nucleus, it is possible to calculate the average effective potential in the nucleus; knowing this, one may find the scattering cross section on a single nucleon. It is found to be $1.7^{+2.6}_{-1.5}$, if the nucleon radius is taken to be $1.47 \cdot 10^{-13}$ cm.
Taking further into account that the amplitudes for scattering of a pseudoscalar $\pi$-meson on a proton and neutron have identical or opposite signs depending on whether the coupling is pseudoscalar or pseudovector, and taking into account other data, according to—
* A. M. Shapiro, Phys. Rev. 84 (No. 1), 1063–64 (1951).
** See review by A. Baldin and V. Mikhailov, UFN, XLIV, p. 200 (1951).
for which the total scattering cross section of $\pi$-mesons with energy $50\ \mathrm{MeV}$ on protons is equal to $(11 \pm 5)\cdot 10^{-27}\ \mathrm{cm}^2$ for $\pi^-$ and $(37 \pm 8)\cdot 10^{-27}\ \mathrm{cm}^2$ for $\pi^+$ mesons, the author calculated the total scattering cross section of a meson on a nucleon in the carbon nucleus (the number of protons is equal to the number of neutrons and is equal to 6) and obtained that it is equal to
\[ \left| \frac{1}{2}\left(37^{\frac{1}{2}} + 11^{\frac{1}{2}}\right) \right|^2 = 22 \pm 5 \]
(in units of $10^{-27}\ \mathrm{cm}^2$), if a pseudoscalar coupling is assumed, and
\[ \left| \frac{1}{2}\left(37^{\frac{1}{2}} - 11^{\frac{1}{2}}\right) \right|^2 = 1.9 \pm 1.4, \]
if the coupling is considered pseudovector. Comparing these values with the results of his measurements, the author comes to the conclusion that the amplitudes of the interaction of $\pi$-mesons with protons and neutrons have opposite signs and that the coupling is apparently pseudovector.
V. F.