From Current Literature

SCATTERING OF HIGH-ENERGY $\pi$-MESONS BY PROTONS

The study of the scattering of elementary nuclear particles of high energy is a method for investigating nuclear forces. Therefore, work on the scattering of $\pi$-mesons by protons, making it possible to clarify the character of the forces acting between these particles, is of considerable interest.

The first investigations[^1] of this question, carried out for $\pi$-mesons with kinetic energy $55$–$85$ MeV, led to an unexpected result: the effective cross section for the scattering of such mesons proved to be considerably smaller than the “geometrical” cross section

$$ \pi \left( \frac{\hbar}{Mc} \right)^2 $$

for the $\pi$-meson.

In the papers reviewed[^2][^3][^4], the measurements were extended into the region of higher $\pi$-meson energies, up to $E = 220$ MeV. Mesons produced in a copper or beryllium target bombarded by a proton beam of energy $450$ MeV were deflected by the magnetic field of the cyclotron and led into the room intended for the experiments described. Further monochromatization and focusing of the meson beam was carried out by means of a deflecting magnet. In this way a well-collimated beam of $\pi$-mesons was obtained, with energy $E$ constant within $\pm 3\%$, and with an insignificant admixture of $\mu$-mesons and electrons. The scheme of the experiment is shown in Fig. 1.

Fig. 1.

The $\pi$-meson beam passed through a telescope consisting of two scintillation counters (1 and 2), behind which was placed the scatterer—a glass vessel filled with liquid hydrogen. Particles that did not undergo scattering were registered by a second telescope made of liquid scintillation counters (3, 4), placed after the vessel with liquid hydrogen.

The attenuation of the meson beam in this experiment is equal to the ratio of the number of quadruple coincidences $1—2—3—4$ to the number of double coincidences $1—2$. The total scattering cross section in hydrogen is equal to the difference between the attenuations produced by the vessel filled with liquid hydrogen and by the empty glass vessel. The data obtained by the authors, after the introduction of the necessary corrections connected with the geometrical conditions of the experiment and the inhomogeneity of the meson beam, are shown in Fig. 2, on whose abscissa axis the $\pi$-meson energy in MeV is plotted, and on the ordinate axis—the effective cross section in $10^{-27}\ \text{cm}^2$.

Let us consider the data for negative $\pi$-mesons. In Fig. 2 they are plotted in the form of rectangles whose sides are equal to the standard

error in the measurement of the energy \(E\) and of the effective cross section \(\sigma_{\pi^-}\). We see that \(\sigma_{\pi^-}\) increases with increasing \(E\) and at \(E = 150\) MeV becomes equal to the “geometrical” cross section of the \(\pi\)-meson:

\[ \sigma_{\pi^-}=\pi\left(\frac{\hbar}{Mc}\right)^2 \simeq 60\cdot 10^{-27}\ \text{cm}^2. \]

Analyzing the results of these measurements, the authors point out that \(\pi\)-mesons may be scattered by protons owing to the following three principal processes:

\[ \pi^- + p \to \pi^- + p, \tag{1} \]

\[ \pi^- + p \to \pi^0 + n \to 2\gamma + n, \tag{2} \]

\[ \pi^- + p \to n + \gamma . \tag{3} \]

The last process (3) is the reverse of the process of production of negative \(\pi^-\)-mesons in the interaction of \(\gamma\)-quanta with neutrons. The effective cross section of this process is known from experiment\(^5\), and therefore the effective cross section for process (3) can be estimated from the principle of detailed balance. It is equal to several units of \(10^{-27}\ \text{cm}^2\), i.e. it constitutes only a small part of the observed cross section. Process (1) is simple scattering (elastic or inelastic), while process (2) is scattering connected with charge exchange.

Fig. 2.

The magnitude of the relative contribution made by processes (1) and (2) to the total effective scattering cross section indicates the relation between the inelastic and exchange forces. The authors estimated the effective cross section for process (2), making use of the fact that \(\gamma\)-quanta arise in this process. For this purpose they placed at an angle of \(90^\circ\) to the beam of \(\pi\)-mesons a third telescope of scintillation counters (5, 6), intended to register particles arising in the scattering of \(\pi^-\)-mesons (see Fig. 1). If among these particles there are \(\gamma\)-quanta in appreciable quantity, then the probability of their registration must increase strongly if a lead plate 8 mm thick is placed in front of telescope 5–6. In this way the role of process (2) in the scattering of \(\pi^-\)-mesons by protons was estimated. It turned out that for an energy of \(\pi^-\)-mesons equal to 118 MeV, the effective cross section for simple scattering is

\[ \sigma_1 = (10 \pm 4)\cdot 10^{-27}\ \text{cm}^2, \]

while the effective cross section for scattering with charge exchange exceeds this value by a factor of two, i.e.

\[ \sigma_2 = (20 \pm 5)\cdot 10^{-27}\ \text{cm}^2. \]

(These values of \(\sigma\) were obtained on the assumption that the scattering is isotropic in the system in which the center of inertia of the colliding particles is at rest.) Hence it follows that exchange scattering plays the predominant role.

The data marked in Fig. 2 by crosses refer to the effective cross section for the scattering of positive $\pi^+$ mesons. We see that $\sigma_{\pi^+}$ increases extremely rapidly with energy and at $E = 126\,M_0 c^2$ turns out to be three times larger than $\sigma_{\pi^-}$ and more than twice as large as the “geometrical” dimensions of $\pi$ mesons.

Thus, from the works considered it follows that, in the scattering of $\pi^-$ and $\pi^+$ mesons by protons, the process of $\pi^+$-meson scattering has the greatest significance; an intermediate significance belongs to the process of $\pi^-$-meson scattering accompanied by charge exchange; and the smallest contribution to the total effective scattering cross section is made by ordinary non-exchange scattering of $\pi^-$ mesons.

A. V.

References

1. Steinberger, Phys. Rev. 82, 958 (1951).
2. E. Fermi et al., Phys. Rev. 85, 934 (1952).
3. E. Fermi et al., Phys. Rev. 85, 935 (1952).
4. E. Fermi et al., Phys. Rev. 85, 936 (1952).