Carl David Anderson The Nobel Prize in Physics 1936

biography and work

work - nobel lecture

The positron is the antiparticle of the electron: it has the same mass as the electron but its charge is positive. Positrons are available e.g. from radioactive sources such as the Na-22 isotope. When positrons have entered a solid they loose rapidly their excess energy and became thermalized positrons. Then the positron is in a quantum-mechanical state in which the strong positron - positive nuclei repulsion is a prominent feature pushing the positron density away from ion core regions. If the solid is a crystal with an ideal, perfect lattice the positron density is delocalized over the whole crystal. Fig. 1 shows as an example the calculated positron wave function for the Si crystal.

1. An isosurface of the positron wave function in a perfect Si lattice. The positions of the Si atoms are denoted by blue spheres, and the electronic interatomic bonds as blue sticks.The positron lifetime in this state is according to experiments and theory about 220 ps. The positron density is concentrated as tubes along the open interstitial channels between the ions. If there is an open-volume defect, such as a vacancy, in the crystal, the reduction of the positron-nuclei repulsion may trap the positron at the defect. For example, Fig. 2 shows the density for a positron localized at a monovacancy in Si.

2. An isosurface of the positron wave function at a vacancy surrounded by one Sb impurity. The Sb atom is denoted by a yellow sphere. The positron lifetime in this state is according to theory about 230 ps.

In the solid the positron lives only a very short time. Typically, after 100 - 300 ps it annihilates with an electron resulting in two gamma rays emitted in opposite directions. These gamma rays contain the information measured in positron annihilation techniques. They give the positron lifetime (the birth of the positron can be detected by a gamma ray emitted by the radioisotope during its decay). They carry also information about the momentum of the annihilating electron-positron pair. The positron lifetime and the momentum density depend on the site where the annihilation takes place. If the positron is trapped by a vacancy-type defect in a solid its lifetime increases from that of a delocalized positron due to the reduced electron density. This causes also the peaking of the momentum density to lower values. These changes in the positron annihilation characteristics make the positron annihilation spectroscopies powerful to study the electronic and ionic structures and the associated processes of defects in solids.

The goal of our work has been to support the experimental positron research by theoretical calculations of positron annihilation characteristics (M.J. Puska and R.M. Nieminen, Reviews of Modern Physics, vol. 66, p. 841 (1994)). We have developed models (within the density functional theory) to describe positron states and annihilation in solids. These include a reliable prediction of positron lifetimes in solids (B. Barbiellini et al., Physical Review B, vol. 51, p. R7341 (1995); ibid. vol. 53, p. 16201 (1996)) and a calculation of the momentum density of annihilating positron-electron pairs (M. Alatalo et al., Physical Review B, vol. 54, p. 2397 (1996) ). For a typical example, see Fig. 3. The changes induced by a trapped positron to the ionic and electronic structure of the defect can be taken into account (Puska et al. Physical Review B, vol. 52, p. 10947 (1995); T. Korhonen et al. Physical Review B, in print (1996)). The basis of our calculations are modern electronic-structure calculation methods, such as the linear muffin-tin orbital method (B. Barbiellini et al., T. Korhonen et al., above), or the pseudo-potential plane-wave approach (M.J. Puska et al., above). We have also developed methods to calculate the positron state and annihilation characteristics by a real-space method, which treats the full three-dimensional geometry when solving the positron Schrodinger equation (Seitsonen et al., Physical Review B, vol. 51, p. 14057 (1995)). The positron densities in Figs. 1 and 2 are obtained by this method.

3. High-momentum parts of the positron-electron momentum distributions (K. Saarinen et al., Physical Review Letters 82, 1883 (1999)). The theoretical predictions (solid lines) are compared with the spectra measured by the Doppler broadening techniques (markers). The comparison identifies vacancy-P complexes in electron-irradiated P-doped Si (green circles), vacancy-As complexes in electron-irradiated As-doped Si (blue circles), and vacancy-As_3 complexes in as-grown highly As-doped Si (red circles). The annihilation of As 3d electrons raises the intensity. The study concludes that the saturation of the free electron density in in highly As-doped Si is mainly caused by the formation of vacancy-As_3 complexes.


Carl David Anderson (190591) received the Nobel Prize in 1936 for the discovery of the positron. In 1936, with Seth Neddermeyer, Anderson also discovered the positive and negative "mesotron," now called the muon. Thus he added three new fundamental particles to physics and pointed the way to the existence of antimatter. At age 31, Anderson was then the youngest person to receive the Nobel Prize. (Tsung-Dao Lee got the 1957 prize when he was 30.) Anderson wrote this autobiography during five years, beginning in his late seventies, at the request of his son and daughter-in-law, David and Melanie Anderson, who did the preliminary editing after his death. Anderson began his long career at Caltech as an undergraduate. Then came his PhD thesis on photoelectrons produced by x rays, under the nominal direction of Robert Millikan. ("For this I thanked him," Anderson wrote, "but not once during the three years of my graduate thesis work did he visit my laboratory or discuss the work with me.") Then came postdoctoral work, again, loosely supervised by Millikan, during which Anderson built and ran the Caltech Magnet Cloud Chamber. For this project, Anderson built a large vertical cloud chamber and a heavy air-core magnet that produced a field of 25 kilogauss. When he first put the unwieldy apparatus, resembling an "obese pig," into operation, Anderson obtained "dramatic and completely unexpected" results: approximately equal numbers of positive and negative particles where only electrons were expected.

Anderson continued the measurements with his first graduate student, Seth Neddermeyer. They first interpreted the thin "wrong-curvature" tracks they observed as upward-moving electrons. However, with the insertion of a lead plate in the chamber, the change in curvature above and below the plate showed the particles' direction of motion. The first track thus analyzed turned out to be an upward-moving positive electron! This event, and subsequent data, led to Anderson's Nobel Prize.

To obtain more intense, higher-energy cosmic rays, the pair transported their magnet cloud-chamber to the summit of Pikes Peak, Colorado. Analyzing the cloud-chamber photos after a summer at the Peak, they found positive and negative tracks that were different from electrons and protons and appeared to have intermediate mass. While they were still pondering their high-altitude results, Millikan ordered the cloud chamber and its team to Coco Solo, in the Panama Canal Zone, to investigate the latitude dependence of sea-level cosmic rays. After their return, toward the end of 1936, Anderson and Neddermeyer proposed that the high-altitude tracks were new, unknown particles that (on account of their mass) they called "mesotrons."

Succeeding chapters of Anderson's autobiography deal with the award of the Nobel Prize, the development of rocket launchers at Caltech during World War II, and Anderson's postwar cosmic-ray research using a B-29 bomber. An interesting (and apparently little-known) wartime episode involved Anderson's being asked by Arthur H. Compton in May 1942, "to head a project to design and build an atomic bomb." Anderson turned it down "on purely economic grounds." Five months later, General Leslie R. Groves offered the job to J. Robert Oppenheimer, who accepted. Anderson observes: "I believe my greatest contribution to the World War II effort was my inability to take part in the development of the atomic bomb. Thinking so brings me peace of mind."

Anderson's autobiography gives valuable insights into the early days of cosmic-ray and elementary-particle research in America, and especially at Caltech. He describes his barely funded research and tells of the joys and challenges of "small science," remarking: "To find the positive electron and the two muons cost about $15,000."

This small book is well worth reading, but I must say (to put it gently) that it is seriously under-edited. Thus, Anderson describes the cloud chamber as counter-controlled, but fails to mention the role played by Patrick Blackett and Giuseppe Occhialini, at the University of Cambridge, who invented the coincidence counter-triggered cloud chamber in 1932 and who observed and identified electronpositron pair production. Nor does Anderson point out that Cecil Powell, Occhialini, and Cesare Lattes, at Bristol, discovered Hideki Yukawa's nuclear-force meson in 1947. In fact, the unwary reader could easily conclude from Anderson's account that the AndersonNeddermeyer "mesotron" (now known to be the muon) was the particle predicted two years earlier by Yukawa and not a confusing look-alike. In his account of the Nobel Prize award, Anderson never mentions Viktor Hess, the discoverer of cosmic rays, with whom he shared the prize. A few editorial footnotes could have avoided these omissions and possible misconceptions.

Also, figure 4 is printed upside down, so it looks exactly like a downward-moving electron, and not an upward-moving positron as it should. The captions are exchanged on figures 25 and 26.

These criticisms aside, I am glad that the autobiography of this remarkable scientist has become generally available, and I enjoyed reading it.

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