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From Current Literature
Scattering of Positive and Negative $\pi$ Mesons by Deuterons
The paper under review¹ is a continuation of works by the same authors devoted to the study of nuclear scattering of $\pi$ mesons². In the previous papers, the scattering of positive and negative $\pi$ mesons by hydrogen was investigated. In the present work the same method is used to study the scattering of $\pi$ mesons by deuterium. In this case the difference in the attenuation of a beam of $\pi$ mesons on targets of H$_2$O and D$_2$O was considered. The scattering chambers, both in the case of H$_2$O and in the case of D$_2$O, had the same shape and dimensions and contained approximately the same number of atoms per 1 cm$^2$. This led to the fact that energy losses, Coulomb scattering, and also nuclear effects due to the presence of oxygen were approximately the same in both cases. Thus, the measured difference of the observed effective scattering cross sections on H$_2$O and on D$_2$O gives the difference of the scattering cross sections of $\pi$ mesons by deuterium and hydrogen $(\sigma_D-\sigma_H)$¹.
The difference of cross sections measured in this way had to be corrected by taking into account nuclear events leading to the scattering of particles into the last four-inch counter. This correction is of the order of magnitude of 10% in the case of scattering of $\pi$ mesons making up the beam. In order to introduce it, it was assumed that $\sigma_D-\sigma_H$ for $\pi$ mesons is equal to $\sigma_H(\pi^+)$. To calculate the correction, the results of measurements of the scattering cross section of $\pi$ mesons by hydrogen² were used, and it was also assumed that this scattering is isotropic. A justification for the assumption of the equivalence of $\sigma_D-\sigma_H$ for $\pi^\pm$ and $\sigma_H$ for $\pi^+$ may be provided by their comparison in the table.
In the region of higher energies, some deviation from such equivalence is observed.
The table presents the experimental results. The first column gives the solid angle at which the last (four-inch) counter is seen from the scattering target. This angle characterizes the quality of the “geometry” of the experiment. It is important that the values of the scattering cross section obtained with different geometries (different solid angle) agree within the experimental errors. The second column gives the energies of the $\pi$ mesons, the energy spread being due both to the spread in the primary meson beam ($\pm 3$ MeV) and to energy losses in the scattering chamber. These data were obtained partly from analysis of the beam by means of a magnetic field, partly from the range curve, and from calculation of the energy losses in the sample. The inaccuracy of the measurement $(\sigma_D-\sigma_H)'$ was due to the insufficiency of the statistics.
also by the presence in the beam of electrons and \(\mu\)-mesons, whose number reached 5%. The quoted measurement error \((\sigma_D-\sigma_H)'\) includes both this (\(\sim 2\%\)) and statistical errors, as well as errors arising in the electronic circuit for counting coincidences.
Effective scattering cross sections of negative and positive
\(\pi\)-mesons on deuterium and hydrogen
| Scattering angle in steradians | Energy in MeV | \((\sigma_D-\sigma_H)'\) in \(10^{-27}\ \mathrm{cm}^2\) | \((\sigma_D-\sigma_H)\) in \(10^{-27}\ \mathrm{cm}^2\) | \(\sigma_H\) in \(10^{-27}\ \mathrm{cm}^2\) | \(\sigma_D\) in \(10^{-27}\ \mathrm{cm}^2\) |
|---|---|---|---|---|---|
| 0.63 | \(79\pm10\) | \(\pi^-\) \(31\pm10\) | \(\pi^-\) \(34\pm10\) | \(\pi^+\) \(48\pm10\) | \(\pi^-\) \(54\pm13\) |
| 0.63 | \(109\pm15\) | \(66\pm4\) | \(72\pm5\) | \(80\pm10\) | \(103\pm10\) |
| 0.088 | \(115\pm9\) | \(87\pm7\) | \(88\pm7\) | \(95\pm15\) | \(124\pm11\) |
| 0.63 | \(115\pm9\) | \(77\pm18\) | \(84\pm18\) | ||
| 0.43 | \(127\pm15\) | \(77\pm7\) | \(84\pm8\) | \(125\pm15\) | \(129\pm11\) |
| 0.63 | \(133\pm9\) | \(66\pm13\) | \(76\pm15\) | \(135\pm15\) | \(128\pm16\) |
| 0.088 | \(164\pm9\) | \(135\pm13\) | \(139\pm13\) | \(198\pm12\) | |
| 0.63 | \(164\pm9\) | \(119\pm11\) | \(128\pm14\) | ||
| 0.088 | \(179\pm9\) | \(170\pm10\) | \(172\pm10\) | \(234\pm12\) | |
| 0.63 | \(179\pm9\) | \(146\pm9\) | \(163\pm12\) | ||
| 0.43 | \(209\pm15\) | \(109\pm24\) | \(131\pm25\) | \(192\pm26\) | |
| 0.43 | \(72\pm17\) | \(\pi^+\) \(24\pm6\) | \(\pi^+\) \(24\pm6\) | \(\pi^-\) \(15\pm8\) | \(\pi^+\) \(60\pm9\) |
| 0.63 | \(79\pm10\) | \(30\pm13\) | \(31\pm13\) | \(20\pm8\) | \(79\pm15\) |
| 0.43 | \(109\pm15\) | \(28\pm12\) | \(29\pm12\) | \(31\pm9\) | \(109\pm16\) |
| 0.43 | \(127\pm15\) | \(25\pm15\) | \(26\pm16\) | \(45\pm10\) | \(151\pm21\) |
The scattering cross section on deuterium is obtained by adding \(\sigma_H\) to \(\sigma_D-\sigma_H\). Within the experimental errors, \(\sigma_D\) proves to be the same for \(\pi\)-mesons of both signs (the same was observed for mesons with an energy of 60 MeV). Such equality is predicted on the basis of considerations of charge symmetry, according to which, for scattering on free nucleons, the relations hold:
\[ \sigma_N(\pi^+) = \sigma_H(\pi^-), \qquad \sigma_H(\pi^+) = \sigma_N(\pi^-). \]
In the figure, in addition to the scattering cross section on deuterium, the sum \(\sigma_H(\pi^+) + \sigma_H(\pi^-)\) is plotted for comparison. This sum does not differ very strongly from \(\sigma_D\), which is a confirmation of the idea of approximately independent scattering of a \(\pi\)-meson by the neutron and proton of the deuteron. Only at energies greater than 115 MeV is there some indication that \(\sigma_D\) is less than \(\sigma_H(\pi^+) + \sigma_H(\pi^-)\). Clarification of this circumstance is of undoubted interest, which
apparently, can be achieved with some increase in the accuracy of the experiment.
Thus, in addition to obtaining specific numerical data on the cross section for scattering of $\pi$ mesons by deuterons, which are of undoubted interest, and also as a result of papers$^{2}$ that cannot be understood from the point of view of ideas about a weak coupling of the nucleon and meson fields, this work confirms the symmetric coupling of the meson field with nucleons.
V. S.
References
- H. Anderson, E. Fermi, D. Nagle, and G. Yodh, Phys. Rev. 86, 413 (1952).
- Anderson, Fermi, Long, Martin, and Nagle, Phys. Rev. 85, 934 (1952); Anderson, Fermi, Long, and Nagle, Phys. Rev. 85, 936 (1952); Fermi, Anderson, Lundby, Nagle, and Yodh, Phys. Rev. 85, 935 (1952). UFN 48, 625.
- Isaacs, Sachs, and Steinberger, Phys. Rev. 85, 802 (1952).