Paul Moskowitz - The Moskowitz-Lombardi Rule

The Moskowitz-Lombardi Rule

While working at the University of Grenoble in France, Paul Moskowitz and French Physicist Maurice Lombardi published an empirical relation that has come to be called the Moskowitz-Lombardi rule or ML rule. The rule helps give nuclear physicists insight into the complex structure of the atomic nucleus which may contain two hundred or more individual protons and neutrons.

A charged atomic nucleus with non-zero spin produces a magnetic field whose strength may be expressed by the size of its magnetic moment µ. The magnetization may be distributed over the volume of the nucleus. The distribution of nuclear magnetization is its deviation from that of a point nucleus, and is expressed by the parameter ε. Moskowitz and Lombardi observed that for a series of ten mercury isotopes, a simple relation existed between the magnetic distribution ε and the magnetic moment µ, namely ε = α/µ, where α is a constant, "Distribution of Nuclear Magnetization in Mercury Isotopes" (Phys. Lett. 1973).

An investigation by T. Fujita and A. Arima (Nucl. Phys. 1975) found the M-L rule to yield results closer to the measured values than did calculations based upon nuclear theory. The rule has been applied to isotopes of elements including mercury, iridium, gold, thallium, platinum, tungsten, osmium, and barium. T. Asaga, et al. have proposed measuring the systematics of the nuclear properties of a series of europium isotopes to test the universality of the rule (Z. Phys. 1997). Researchers at Mainz, S. Trapp et al. (Hyperfine Interactions, 2000) have indicated that they plan to pursue experimental europium measurements. Author Clifford A. Pickover has granted permission to use information which is in his recent book, Archimedes to Hawking: Laws of Science and the Great Minds Behind Them, Oxford University Press, 2008, ISBN 978-0-19-533611-5