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Elastic collisions of mesons with electrons and protons

Published online by Cambridge University Press:  24 October 2008

H. S. W. Massey  and
H. C. Corben
H. S. W. Massey
Affiliation:
University CollegeLondon
H. C. Corben
Affiliation:
Trinity CollegeCambridge
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Extract

The cross-sections for the elastic scattering of mesons by protons and electrons are calculated by analogy with Møller's theory of collisions between electrons, and the results are compared with those of Bhabha for the collisions with protons and electrons of Fermi-Dirac particles with the same mass as the meson. For collisions with electrons, the difference is inappreciable for energies of the meson less than 100 times its rest energy, but for collisions with protons the difference is important at much lower energies. The ratio of the corresponding cross-sections for scattering by a Coulomb field is found to tend to infinity as the square of the energy of the incident particle, giving a finite cross-section for the scattering of a meson of infinite energy by such a field. It is pointed out that, if an exact solution of this problem is possible for the meson case, the question of the validity of meson theory for high energies would be considerably clarified.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 35 , Issue 3 , July 1939 , pp. 463 - 473
Copyright
Copyright © Cambridge Philosophical Society 1939

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References

† Bhabha, , Proc. Roy. Soc. A, 166 (1938), 501.CrossRefGoogle Scholar

‡ Heitler, , Proc. Roy. Soc. A, 166 (1938), 529.CrossRefGoogle Scholar

§ Møller, , Ann. Phys., Lpz., (5), 14 (1932), 531.CrossRefGoogle Scholar

† Heitler, loc. cit.

‡ Terms of order A2 and higher are neglected.

† Heitler, loc. cit.

† Bhabha, , Proc. Roy. Soc. A, 164, 257 (1938), equation (2·1).CrossRefGoogle Scholar

† The same result follows by an approximate solution of the equations for the meson field vectors in the presence of a scalar electromagnetic field by the usual Born method, and without explicit use of emission and absorption matrix elements. It then becomes clear that the difference between the formulae for electrons and mesons arises from the fact that the spin perturbation term in the second order wave equation involves the first derivatives of the scalar potential in the electron case and the second derivatives in the meson case.

† Fröhlich, , Heitler, and Kemmer, , Proc. Roy. Soc. A, 166 (1938), 154.CrossRefGoogle Scholar

‡ Bhabha, , Nature, 143 (1939), 276.CrossRefGoogle Scholar