Some Weisskopf Contributions to Atomic Physics

Kurt Gottfried and David Jackson (Physics Today, February 2003, page 43) cited the width of spectral lines and the theory of resonance radiation as being Viktor Weisskopf’s first contributions to physics. Although the authors subsequently focused on more fundamental problems, two research papers related to Viki’s work have had a significant continuing impact on atomic physicists. One of those papers, based on Viki’s thesis, deals with the Hanle effect and, more generally, with radiation from atomic levels that become degenerate in magnetic fields. ¹  

In the mid-1920s, polarization of resonance radiation was studied intensively in the US and Europe. Arnold Sommerfeld, an atomic physicist widely known for the Bohr—Sommerfeld theory, went to Göttingen, Germany, and visited quantum physicist James Franck, familiar for the Franck—Hertz experiment. Sommerfeld showed Franck a letter from Robert W. Wood and Alexander Ellett, ² who had obtained some puzzling results on polarization in fluorescence that they could not explain by the Zeeman effect. Wood was well known for his work in physical optics in the early part of the 20th century. Franck called in his graduate student, Wilhelm Hanle, who worked in physical optics, and asked if he could understand Wood’s findings. Hanle immediately gave his explanation in terms of the classical precession of a radiating electron oscillator in a magnetic field—the basis of what is now called the Hanle effect.

Franck and Sommerfeld did not quite believe it, so Hanle went to the laboratory. He worked all night, took pictures of the appropriate observations, came to Franck the next day, and declared, “This is my thesis!” Hanle was invited to present his work in Innsbruck, Austria, at a joint meeting of the Austrian and German physical societies. Before the meeting, Franck received much criticism and skepticism from colleagues who tried to explain the observations by the Faraday effect. Not wishing to have his student suffer humiliation, Franck canceled the presentation. To console Hanle, Franck invited him to lunch with some other physicists, after which one of them, an older gentleman, took Hanle aside and said, “don’t worry about this, young man. We all make mistakes, and I am sure that you will do something worthwhile in the future.” Later, Hanle found out that man was Max Planck!

Viki’s paper also provided the underlying quantum mechanical theory that determines, according to the Zeeman effect, how large the magnetic field must be before the magnetic sublevels become distinct. If the radiation line width is included for the energy levels in the Zeeman diagram, the range of the magnetic field in which the overlap of the levels decreases and polarization changes occur becomes clear. Viki’s theory was included in Gregory Breit’s review paper, ³ which was rediscovered about 30 years later by Peter Franken and coworkers. ⁴ Franken’s group actually began applying Viki’s theory to spectroscopy. But they did not recognize the original author.

Another contribution Viki made to atomic physics is our understanding of the Bohr—Weisskopf effect, also known as the hyperfine-structure anomaly. ⁵ Viki and Aage Bohr’s theory accounts for the effect of the finite size of the nuclear magnetization on the hyperfine-structure interaction. Hans Kopfermann suggested the effect’s existence in the first edition of his book on nuclear moments, ⁶ but qualified the effect as much too small ever to be observed.

Francis Bitter’s experiments ⁷ at MIT stimulated the work of Bohr and Viki. Bitter observed that the interaction of the nuclear magnetization measured by nuclear magnetic resonance in a homogeneous magnetic field differs from its interaction with the slightly inhomogeneous magnetic field set up by the electron at the site of the nucleus. The interaction in the inhomogeneous field is dependent on the distribution of the nuclear magnetization. For many ordinary atoms, the effect is small; nonetheless, highly precise experiments allow extraction of nuclear wavefunction data beyond those provided by nuclear moments alone. For muonic atoms, the Bohr—Weisskopf effect can account for half of the hyperfine structure interaction. Experiments on the hyperfine structure of hydrogen-like ions of heavy elements also require knowing the Bohr—Weisskopf effect in order to extract the influence of quantum electrodynamics.

The information in this letter is based on Wilhelm Hanle’s recollections and on my remarks in 1983 at the Sixth International Conference on Laser Spectroscopy in Interlaken, Switzerland, on the occasion of the 60th anniversary of the Hanle effect (with permission of Comments in Atomic and Molecular Physics).