A first-person account is given of the serendipitious route leading to the most accurate measurement of the gyromagnetic raio or g-factor of the electron at the University of Miochigan in the early 1950’s. In 1986 President Ronald Reagan awarded Crane the National Medal of Science for this work.

Note: The following has been scanned and converted from the original document that Crane prepared for the symposium presentation. You can see the original document here.

Alfred Hill Memorial Symposium
University of Michigan, 3/30/89
Talk by H. R. Crane

HOW g-2 GOT STARTEDI

I’m glad to be asked to recount a few interesting experiences of a period that is getting to be close to 40 years back. I had to go back and refresh my own memory.

I don’t think you want a technical talk. What you may get is one example showing that often the most interesting things don’t happen in the vel1 planned way they are portrayed in our archival journals.

In the very early 1950’s we were in the process of building what we called the “racetrack” synchrotron. It had two features that were new: a combination of curved and straight sections, and frequency modulated injection. Suffice it to say it eventually worked, and those features were adopted for much larger machines around the country and world.

The importance of that project for the story I’m telling now is that the apparatus that produced a 600,000 volt beam of electrons for injection into the race-track got finished far ahead of the main magnet. And we had a student, Bill Louisell, who was ready and hoping to do a thesis on the machine.

So naturally, we had to think hard about making do with what, we had, namely the 600,000 volt electron gun. I had been interested in the past in the polarization of electron beams, according to the well known theory of N. F. Mott, and had attempted some experiments. So the availability of this electron beam, which had plenty of energy for the purpose, was tempting.

Let me tell briefly what Mott said, for those who were not reading physics 60 years ago, when it was published. He calculated that in the encounter of a fast <a few hundred kev) electron with a heavy nucleus, say in a gold foil, the electron will scatter with a little preference to the right or the left, according as its spin happened to be up or down. If then the left ones, say, are scattered by a second foil, they will be more likely to scatter to the left again than to the right. So the first foil is the polarizer and the second the analyzer.

You would think such a thing would have been easy to show experimentally. But even up to the time we are talking about — 25 years later, there had not been a really clean cut measurement. The problem was background. For every electron that made a close encounter with a nucleus, there were thousands that did not, and bounced around and made background. For any new experiment, that was the main problem to be solved.

So that’s where a little piece of luck came our way. The room the electron gun was in had been used for X-ray apparatus in the dim past, and the room next to it, which evidently had been the observation room, was separated by a floor-to- ceiling concrete wall, 3 ft. thick. It had small tunnels going through. We thought Aha! If our polarizing scatterer were at the electron gun, and the analyzing scatterer were inside that shielded room, we would be rid of background. But they would be 30 ft. apart. How to get the electrons from the first to the second scatterer without 1oss?

Well, you know electrons can be piped like water, if the pipe has a magnetic field parallel to its axis. So we we set up a brass pipe running from the first scatterer location to inside the observation room, 6″ in diameter, wound with a layer of magnet wire.

Then the $64 question hit us. Would the magnetic field destroy the polarization, or what would it do to it? Simple-minded thinking said that the electrons would precess like little gyroscopes and end up polarized in a different plane. We hoped that would be true–it would be a way of measuring the magnetic moment–more interesting than checking the Mott theory!

The first theorist we tried that on was George Uhlenbeck, just upstairs from us. He threw up his hands—or scolded us, I don’t know which—citing a simple proof by Niels Bohr in about 1925, that the magnetic moment of the free electron is not an observable quantity. And what we were proposing to do was just that.

Our theoretical group didn’t dismiss it completely. Ken Case at the time had a thesis student, Harold Mendlowitz, working in Dirac theory. He put him to calculating whether a magnetic field would rotate the plane of polarization. I don’t know whether he did that expecting to put another nail in our coffin, but if so he got a surprise. I’ll tell his result later.

A word about Bohr’s proof. In 1922 Stern and Gerlach had sent a beam of neutral silver atoms through a magnetic field having a strong gradient, and had found that the beam split, according to the different orientations of the magnetic moments of the atoms. Three years later Goudsmit and Uhlenbeck discovered that the electron in an atom must be assigned a spin and a magnetic moment. The question immediately came up as to whether the free electron could be shown to have a magnetic moment, by an experimenent like that of Stern and Ger1ach.

Bohr disposed of the idea with an elegant proof of just a few lines. In essence, the location of the beam in the inhomogenious field is not defined to better than is allowed by the uncertainty relation, and that is just enough to smear out the expected separation due to the different magnetic moment orientations. He showed that a magnetometer experiment would be defeated in the same way.

Whether it was Bohr or others who generalized that proof to say that the magnetic moment of the free electron is unobservable in any experiment, I do not know. And we may never find out, because he did not publish it. Many other authors gave the proof, and generalized it to the hilt. One example will suffice. It’s from Mott and Massey’s well know Theory of Atomic Col 1i si ons. 1933, 2nd Ed., 1949. After giving Bohr’s proof they say: “From these arguments we must conclude that it is meaningless to assign to the free electron a magnetic moment.” That was the gospel for nearly three decades.

Before returning to our own problems I should mention that there were, in the few years prior, some ideas, and even some experiments, for getting around the Bohr restriction. They may have been suggested by the Rabi experiments, in which spins of atoms in a magnetic field were flipped by the application of a radio frequency <RF) field. The thought was, for electrons, that the flip would be a guanturn process and therefore “legitimate”. The RF frequency at which it happened would tell the g- factor.

One of the schemes was to use the Mott double scattering. A magnetic field and RF field were to be applied between the polarising and analyzing foils. At a certain frequency the polarization would destroyed, telling the g-factor. Another way employed a leaky magnetic bottle. Orbiting electrons having their magnetic moments in a certain orientation would be able to escape. Then an RF field would be applied to those remaining, to re-mix the spins. That would provide new ones that would be able to escape. Again the frequency would tell the g factor. So far as I know none of these ideas came to fruition.

Mow to return to our problem: there was no reason for Louise 11 not to go on. At the least he would have a background-free experiment on the Mott polarization. Unless, of course the magnetic pipe were to destroy the polarization; an unlikely thing, we thought. Anyway, in our optimism we right away made one change toward placing a bet on the little gyroscope idea. We built a rotating head at the analyzer end, so we could find the new plane of polarization, should it be rotated.

Of course you know the answer. The electrons did precess, in fact five times around in the 30 feet. So with results that convinced us, but which perhaps wouldn’t have just hit somebody else between the eyes, we put in abstracts for the spring 1953 meeting in Washington. Mendlowitz too, for by that time he had found that the polarization rotated.

Interesting things happened in Washington. We peeked into the meeting room where our talks were scheduled and saw very few listeners. But as time for our papers approached, quite a clump of people gathered outside the entrance. Included were a number of the “elder statesmen”. Had they come to see the bloodshed? During our papers they listened politely. At the end the first to rise was Felix Bloch–not unfamiliar with the problem, because he had instigated a “leaky bottle” experiment, then going on at Stanford. He quoted the Bohr gospel, and not saying we had imagined our results, made it clear there had to be a mistake somewhere. Other expressions of doubt followed, but not that vehemently. Later, I got word that Bloch, when half way back to Stanford, had decided there might be something to our findings.

Granted we had shown that under the right conditions electrons precess like little gyroscopes, we were at a sort of dead end. Our results for the g-factor were to about 2%–far from being useful in testing the radiative correction, which was 0.1%. To do that the electron pipe would have had to be a mile long more or less. So we got lucky again and found a way around that. Also, we dismantled the Louisel1 apparatus, moved 6 floors higher in the building, and started from scratch.

Quite simply—although not easy to do—after the polarizing scattering we caught the electrons in a magnetic bottle, or “trap” where they could spend an arbitrarily long time in orbit, processing, before being let out to undergo the analyzing scattering. At the same time the background problem was licked. We put the electrons into the trap in short bursts. While they were in there, we turned off the source gun, so when they were let out to the second scatterer there was complete peace and quiet.

Now the final thing to say about the new method is that for electrons in orbit, and a g- factor of 2 exactly, the precession would stay exactly in phase with the orbital motion. With a g- factor a part in a thousand different from 2, the spin orientation would drift in phase, a cycle in a thousand revolutions. The drift in phase was what we measured, through hundreds of cycles. So we were measuring the anomaly directly, not the whole g-factor. That gave us, you might say, three decimal places free before we started. Since it was the difference from 2 that we were measuring, the quantity—and the project—came to be called g-2. I think it was Val Telegdi who thought up that name.

I’11 re-cap here as to why, as I said in the beginning, things don’t always happen the way they are supposed to; sometimes for the better. The delay in the synchrotron magnet forced us to turn to electron polarization; the 30 ft. distance between gun and observation room plunged us into the Bohr controversy, and finally, there was lucky timing. The latter because quantum electrodynamics had come on the scene within the prior few years, and our experiment was in the unique position of being able to test it for the free electron. Talk about lucky accidents!

The g-2 project lived on for about 20 years, serving a series of thesis students and others, producing ever more precise values for g-2. About half way along I pulled out, and Art Rich took over. He and his students did many fine things with it. Our basic experimental method was not superseded until Hans Dehmelt, of the University of Washington, came along with his beautiful measurements on single electrons held for hours in a miniature trap. But that’s another whole story.

Related experiments, following on our success with the electron, were the measurement of g-2 for the mu meson, at CERN. Also, earlier in our own lab Art Rich did a beautiful job of measuring g-2 for positrons.