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On Hall’s formula for the relativistic photoeffect. (English) Zbl 0084.44701

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quantum theory
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[1] H. Hall:Rev. Mod. Phys.,8, 358 (1936), the formula for{\(\tau\)} k =N 0 {\(\sigma\)} k on p. 395. · Zbl 0015.28207 · doi:10.1103/RevModPhys.8.358
[2] H. Hall:Phys. Rev.,84, 167 (1951). · doi:10.1103/PhysRev.84.167.2
[3] A recent, more simple demonstration of this result was given byR. Prange andR. Pratt:Phys. Rev.,108, 139 (1957). · Zbl 0079.43601 · doi:10.1103/PhysRev.108.139
[4] The explanation of these approximations is given in ref. (1), p. 396. · Zbl 0015.28207 · doi:10.1103/RevModPhys.8.358
[5] H. Bethe andE. Salpeter:Eneyelopedia of Physics.35, Part I (Berlin, 1957), Sect.73;W. Heitler:The Quantum Theory of Radiation (Oxford, 1954), p. 210, etc.
[6] Ref. (1);J 0 is the integral of Eq. (44) multiplied by 3/S. · Zbl 0015.28207 · doi:10.1103/RevModPhys.8.358
[7] Prange andPratt [ref. (3)] succeeded in evaluatingJ({\(\Delta\)}Z) exactly, in the special case (not realized physically) {\(\Delta\)}Z=1, findingJ(1)=0,24. Our approximation (10) gives in this ease (falling far out of its range of validity) the value 0.17. This good agreement could eventually suggest that the restO 2. of Eq. (10), is indeed negligible for ordinary {\(\Delta\)}Z. · Zbl 0079.43601 · doi:10.1103/PhysRev.108.139
[8] The curves ofHulme et al. (Proc. Roy. Soc. A149, 131, (1935); Fig. 2), representing 5 {\(\cdot\)} 1032 {\(\sigma\)} K hr/4Z 5 mc 2 as function ofmc 2/hv for differentZ, are based in the extreme relativistic limit on the formula ofHall (4), which, as shown, is in error by excess. These curves should be therefore adeguately lowered in the energy range: 0<(mc 2/hv)<0,45.
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