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The Bethe-Salpeter equation


Work on low energy systems
Hans Bethe Scientist
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The work by Peierls and me had shown that the scattering of neutrons by protons up to about 10 MeV, million electron volts, was almost entirely due to interaction at zero angular momentum in the S-state. And Breit had done much more elaborate calculations for proton-proton scattering using different shapes of the interaction between two protons, either the square well, or an exponential decrease, or the form that Yukawa had proposed, and he always got the same answer, it always would fit the experiment. And, so it was very intriguing just how was it possible to always get the same answer. So we got the idea and I think the idea was had simultaneously by Schwinger and by me, that probably one could describe it much better. And Schwinger produced a very beautiful theory using variational principle, and I thought it would be better to do it in a simpler way just using the wave function of the interacting two particles. So I was able to show that there was... that the interaction of two nucleons at low energy could be described by just two quantities; namely an effective range of the nuclear forces which could be deduced from the actual shape of the nuclear forces, and the scattering length at zero energy, which is measured for instance by the cross section of neutron-proton scattering both with parallel spin and with antiparallel spin. So you got two separate scattering length, the scattering length square gives you directly the cross section at zero energy. And so it was possible to describe scattering as all energy up to about 10 MeV in terms of these two quantities, scattering length and effective range. I did this first by myself and then together with Longmire who was at Columbia University and I took a sabbatic leave to Columbia, [where] we collaborated in doing the effective range theory of nuclear forces.

The late German-American physicist Hans Bethe once described himself as the H-bomb's midwife. He left Nazi Germany in 1933, after which he helped develop the first atomic bomb, won the Nobel Prize in Physics in 1967 for his contribution to the theory of nuclear reactions, advocated tighter controls over nuclear weapons and campaigned vigorously for the peaceful use of nuclear energy.

Listeners: Sam Schweber

Silvan Sam Schweber is the Koret Professor of the History of Ideas and Professor of Physics at Brandeis University, and a Faculty Associate in the Department of the History of Science at Harvard University. He is the author of a history of the development of quantum electro mechanics, "QED and the men who made it", and has recently completed a biography of Hans Bethe and the history of nuclear weapons development, "In the Shadow of the Bomb: Oppenheimer, Bethe, and the Moral Responsibility of the Scientist" (Princeton University Press, 2000).

Tags: Gregory Breit, Rudolf Peierls, Hideki Yukawa, Julian Schwinger, Conrad Longmire

Duration: 3 minutes, 57 seconds

Date story recorded: December 1996

Date story went live: 24 January 2008