On hall’s formula for the relativistic photoeffect

H. Hall:Rev. Mod. Phys.,8, 358 (1936), the formula forτ _k=N ₀ σ _k on p. 395.ADSCrossRefGoogle Scholar

H. Hall:Phys. Rev.,84, 167 (1951).ADSCrossRefGoogle Scholar

A recent, more simple demonstration of this result was given byR. Prange andR. Pratt:Phys. Rev.,108, 139 (1957).MathSciNetADSCrossRefMATHGoogle Scholar

The explanation of these approximations is given in ref. (1), p. 396.CrossRefGoogle Scholar

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.Google Scholar

Ref. (1);J ₀ is the integral of Eq. (44) multiplied by 3/S.ADSCrossRefGoogle Scholar

Prange andPratt [ref. (3)] succeeded in evaluatingJ(ΔZ) exactly, in the special case (not realized physically) ΔZ=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 ΔZ.MathSciNetADSCrossRefMATHGoogle Scholar

The curves ofHulme et al. (Proc. Roy. Soc. A149, 131, (1935); Fig. 2), representing 5 · 10³² σ_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.ADSCrossRefGoogle Scholar