Tributes to Hans Bethe continue

The October 2005 special issue of Physics Today describes the breadth of Hans Bethe’s accomplishments and interests in different fields of physics. Here are two additional contributions of his that illustrate his ability to produce new advances in areas outside those for which he was most famous.

In 1929 Bethe employed group theory to examine how the crystalline field would split the energy levels of free ions and determined the symmetry required to fully quench the orbital moment. ¹ This area became an active research field only after World War II, with the development of electron paramagnetic resonance and spin Hamiltonians.

Richard Garwin and Kurt Gottfried (Physics Today, October 2005, page 52 ) mention that Bethe invented his hole coupler between two waveguides and developed his “exhaustive theory” of the coupler while at the MIT Radiation Laboratory. A second significant contribution to microwaves and electromagnetic theory by Bethe and Julian Schwinger employed Maxwell’s equations in calculating the fractional frequency shift Δf/f when a sample is inserted in a resonant cavity. The fractional frequency shift provides a direct connection to the tensor electric permittivity and the tensor magnetic permeability of the sample. Two reports exist about this work.^2,3 However, the derivation is given by Walter Hauser, ⁴ who terms the expression for the fractional frequency shift the Bethe–Schwinger cavity perturbation formula.

This fundamental expression, although known to some microwave experts, is not mentioned in the best-known electricity and magnetism texts. It is also not mentioned in the MIT Radiation Laboratory series that appeared shortly after World War II. John Slater’s postwar text ⁵ mentions the 1943 MIT report ² but doesn’t give the Bethe–Schwinger formula. I was unaware of this expression until the early 1990s, even though I’d learned microwave techniques in the 1950s. Why wasn’t this result published in an American physics journal? The report dates may provide a clue: Bethe was already at Los Alamos in early 1943.