The energy and momentum conservation laws were regarded as being a basic hypothesis in Compton’s 1) and Breit’s 2) papers. In this section we give the energy and momentum conservation law on the Compton scattering presented by Compton, himself, and the equation of the frequency shift accompanying the scattering. Finally, in Section 8, we discuss the equivalence between Klein–Nishina’s semi-classical method and the quantum field theoretical method.Ģ. Works preceding to Klein–Nishina’s theory In Section 6 and Section 7, we look back their efforts to solve the most difficult problem for them, namely how to set the final states of the electron after scattering, and consider why they adopted the semi-classical method in treating electromagnetic waves. In Section 2 through Section 5, we survey Klein–Nishina’s theory and consider the process they undertook when deriving their formula. The following arguments in this article are based on the Sangokan Nishina Source, preserved by the Nishina Memorial Foundation. 12, that the experiments conducted to confirm the Klein–Nishina formula were to suggest the existence of then unknown phenomena, namely the pair production and annihilation of positive and negative electrons. Recalling that time, Bohr wrote to Nishina in 1934 10, 11) that “the striking confirmation which this formula has obtained became soon the main support for the correctness of Dirac’s theory when it was apparently confronted with so many grave difficulties.” Ekspong discussed in Ref. When Klein and Nishina started to attack this problem, they intended in part to confirm the validity of the Dirac equation, as stated in Introduction of Ref. The Klein–Nishina formula has been firmly accepted and widely used, even now. Nishina succeeded to derive the famous Klein–Nishina formula, 8, 9) calculating the intensity distribution of the scattered wave in the Compton scattering based on the Dirac equation. Soon after Dirac presented his relativistic electron theory, 6, 7) O. The energy and momentum relation of an electron used by Dirac 3) was equivalent to that of the Klein–Gordon equation. In 1927, Gordon 4) and Klein 5) independently developed the so-called Klein–Gordon equation to describe the behavior of an electron to include relativistic effects in Compton scattering. As for Compton scattering, he obtained energy-momentum conservation for the Compton scattering, but did not show the intensity distribution of the scattered wave. In 1927, Klein 5) discussed how the interaction between an electron and an electromagnetic field including Compton scattering should be treated quantum mechanically. They deduced the energy and momentum conservation law on the light-quantum and electron system quantum mechanically, which Compton hypothesized, and derived a formula giving the angular distribution of the intensity of the scattered wave. In 1926, Breit 2) discussed this problem using the correspondence principle in the old quantum theory, and obtained the same result as what Dirac 3) and subsequently Gordon 4) obtained independently, using quantum mechanics. In his analysis concerning the angular distribution of the intensity of the scattered wave, Compton used relativistic theory and the Doppler effect. This analysis showed that the Compton effect was one of the important experimental facts confirming the quantum theory of light. Compton 1) explained the wavelength shift upon scattering by using the conservation principle of energy and momentum of the light quantum and electron system. In 1923, using the light quantum theory for X-rays, A.H. In Compton scattering, the scattering of an X-ray by an electron, the wavelength of the scattered X-ray varies with the scattering angle.
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