Physicist Nishina Yoshio (仁科 芳雄) was born #OTD in 1890. He spent time at Cambridge and Copenhagen in the 1920s, where he contributed to the development of quantum electrodynamics, then returned to Japan and established a national program of modern physics research.
In 1928, while visiting Copenhagen, he wrote a paper with Oscar Klein on Compton scattering: "On the Scattering of Radiation by Free Electrons According to Dirac's New Relativistic Quantum Dynamics".
When physicists describe scattering they usually talk about it in terms of a "cross section." This is just an area, usually denoted σ, that describes how big a target one particle presents to another for a particular kind of scattering.
In some scenarios, scattering in one direction may be more or less likely than another direction. In that case the differential cross section, dσ/dΩ, tells you how that target size changes for processes that scatter the particles at specific angles.
For example, a glancing interaction that doesn’t change a particle’s trajectory very much might be much more likely than one that sends it careening off at a 90 degree angle.
The former process can be thought of as presenting a larger target than the latter.
Aside: In nuclear and particle physics, cross sections are quoted in units of "barns." 1 barn is 10⁻²⁸ m², which is roughly the cross section presented by a Uranium nucleus in many processes.
The name was coined in 1942 by Manhattan Project physicists at Purdue University. They needed a name for the unit that wouldn't reveal what they were working on.
They settled on "barn." A uranium nucleus is considered a pretty big target. Scattering off one is as easy as hitting the broad side of a barn.
Klein and Nishina derived the differential cross section for Compton scattering — a photon bouncing off a charged particle like an electron — at lowest order in Quantum Electrodynamics.
Besides the various relevant constants like Planck's constant ℏ, the fine structure constant ɑ, the electron mass m, and the speed of light c, the differential cross section depends on the photons' initial and final energy and its scattering angle.
We now refer to their result as the Klein-Nishina formula:
It's a lovely calculation that has since taught generations of particle physics students the difference between a long homework assignment and a very long homework assignment. This one clocked in at around 40 pages.
After returning to Japan in the early 1930s, Nishina founded a lab focused on research in quantum mechanics, nuclear physics, and cosmic rays. They built cyclotrons, including the first one outside the US.
After WWII, Nishina had to petition the occupying US force for special permission to continue operating his research institute's cyclotrons for medical and biological research.
After the war, Nishina became the director of Japan's Institute of Physical and Chemical Research (RIKEN). It was in shambles from bombings and occupation, but he helped restore it before passing away in 1951.
@mcnees It's not Olivia Newton-John, but an update since dumping the first cyclotrons into the bay: Now RIKEN's Nishina Center has a really impressive cyclotron, used to make fast (relativistic) beams of rare isotopes. https://www.nishina.riken.jp/facility/SRC_e.html
@mcnees * I say _very_ carefully, but in reality you could never be too careful. One day I left my experiment idling and went home for dinner. While I was eating I got a call from the NIST fire department, who were in my lab because the water cooling loop for my high voltage laser failed catastrophically and flooded the lab. Good times. 😎
@mcnees Thanks for the reminder about “barns”! Spent several years developing an experiment to accurately measure cross-sections of small molecules in the infrared. Eventually got the limit of detection down to <0.1 barns, and used it to slowly and _very_ carefully(*) collect data that eventually helped resolve an 80-year old mystery in atmospheric physics.
@mcnees For those not wanting to read all 2814 posts 😉 😀, a much shorter derivation of the Klein-Nishina formula can be found in Weinberg's "The Quantum Theory of Fields" Vol I, p 362.