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Angular Distribution of $\pi$-Mesons Scattered by Hydrogen
Experiments on the scattering of $\pi$-mesons by nucleons are not accidentally attracting such close attention at the present time. In contrast to experiments on the production of $\pi$-mesons by photons, in which substantial features of the phenomenon were determined by the electromagnetic interaction of $\pi$-mesons and nucleons with photons, the process of scattering of $\pi$-mesons by nucleons is the simplest act of nuclear interaction, in which electromagnetic forces play practically no noticeable role. It is precisely for this reason that the study of this process makes it possible to reveal a number of specific features of the purely nuclear interaction of mesons with nucleons. The first group of works in this direction was devoted to ...
to measuring the dependence of the total cross section for scattering of \(\pi\)-mesons on nucleons on the energy.
The paper reviewed below\({}^{1}\), in which, with the aid of a well-collimated beam of \(\pi\)-mesons from the Chicago synchrocyclotron, the angular distribution was studied of \(\pi\)-mesons scattered by liquid hydrogen, marks the beginning of the second group of works connected with a more detailed study of the process.
The intensity of the initial beam of \(\pi\)-mesons was determined by two counters, 1 and 2 (see the figure), each 5.08 cm in diameter. The beam, passing through these counters, entered a chamber with liquid hydrogen; the scattered particles were detected by two other counters of diameter 10.16 cm, which were placed at a definite angle to the initial beam. In order for a fourfold coincidence of all four counters to occur, a particle had first to pass through the first two counters and then be scattered into the second pair. The rate of fourfold coincidences, divided by the rate of double coincidences of the first pair, which were recorded at the same time, determined the part of the beam that had been scattered. By removing the liquid hydrogen from the chamber, it was possible to isolate the scattering of \(\pi\)-mesons on the walls of the chamber and of other extraneous objects. To distinguish the scattering of negative \(\pi\)-mesons with charge exchange from elastic scattering, a lead radiator was placed in front of the second pair of counters; it increased the sensitivity of the counters to \(\gamma\)-rays formed as a result of the decay of the neutral \(\pi\)-meson.
Elastic scattering of positive \(\pi\)-mesons with energies of 110 Mev and 135 Mev, and elastic and charge-exchange scattering of negative \(\pi\)-mesons with energy 135 Mev, were measured. The results in the center-of-mass system can be expressed by the following formula:
\[ \frac{d\sigma}{d\omega}=a+b\cos\theta+c\cos^{2}\theta, \]
if it is assumed that only \(s\)- and \(p\)-states contribute to the angular distribution.
The values of the coefficients, with their statistical errors, are given in the table.
The integral cross section given in this table is in good agreement with the cross section obtained earlier\({}^{2}\).
An analysis of the phase shifts was carried out under the assumption that the scattering takes place in states characterized by isotopic spin \(1/2\) and \(3/2\) and angular momenta \(s_{1/2}\), \(p_{1/2}\), and \(p_{3/2}\). In doing so, for negative
of mesons, the contribution from exchange and non-exchange scattering was added, and it was also taken into account that about \(0.8\times 10^{-27}\ \text{cm}^2\) in the cross section was due to the inverse photoeffect \((\pi^- \to \gamma)\).
The experimental data are well satisfied by the following phase-shift angles: at \(135\ \text{MeV}\), \(\pm 1^\circ\), \(+19^\circ\), and \(\pm 1^\circ\) for isotopic spin \(1/2\); \(+25^\circ\), \(+10^\circ\), and \(+35^\circ\) for isotopic spin \(3/2\); at \(110\ \text{MeV}\), \(\pm 15^\circ\), \(0^\circ\), and \(\pm 25^\circ\) for isotopic spin \(3/2\). The angles are given in the following order: for the \(s_{1/2}\), \(p_{1/2}\), and \(p_{3/2}\) states, and have an uncertainty of \(\pm 5^\circ\). It is emphasized that isotopic spin may be regarded as
Coefficients in the differential cross section
| Initial energy in MeV | Process | \(a\cdot 10^{-27}\ \text{cm}^2/\text{steradian}\) | \(b\cdot 10^{-27}\ \text{cm}^2/\text{steradian}\) | \(c\cdot 10^{-27}\ \text{cm}^2/\text{steradian}\) | \(\displaystyle \int \frac{d\sigma}{d\omega}\,d\omega \times 10^{-27}\ \text{cm}^2\) |
|---|---|---|---|---|---|
| 110 | \(\pi^+\to\pi^+\) | \(3.5\pm0.6\) | \(-4.6\pm0.8\) | \(7.2\pm1.8\) | \(74.5\pm5.4\) |
| 135 | \(\pi^+\to\pi^+\) | \(3.8\pm2.2\) | \(-6.8\pm2.7\) | \(17.5\pm6.6\) | \(121\pm19\) |
| 135 | \(\pi^-\to\pi^-\) | \(1.2\pm0.2\) | \(-0.1\pm0.3\) | \(0.3\pm0.7\) | \(16.2\pm2.3\) |
| 135 | \(\pi^-\to\pi^0\) | \(1.1\pm0.6\) | \(-2.5\pm0.5\) | \(6.3\pm1.9\) | \(40.6\pm2.3\) |
a good quantum number, since at \(135\ \text{MeV}\) the nine experimental data can be satisfied with six phase shifts.
From these experiments it follows that the interaction of the \(\pi\)-meson with the nucleon is strong in the \(p_{3/2}\) state with isotopic spin \(3/2\). However, the interaction in the \(p_{1/2}\) state with isotopic spin \(1/2\) is comparable, and it is apparently responsible for the isotropy found in the elastic scattering of \(\pi\)-mesons.
The fact that a sufficiently strong interaction was found in the \(s\)-state with isotopic spin \(3/2\) leads one to suppose that it is responsible for the scattering in the backward direction.
V. F.
CITED LITERATURE
- H. L. Anderson, E. Fermi, D. E. Nagle and G. B. Yodh, Phys. Rev. 86, 793—794 (1952).
- H. L. Anderson, Phys. Rev. 85, 936 (1952).