Island of Stability, Magic Numbers and Kuhnian Anomalies in the Theory of the Nucleus

The International Union of Pure and Applied Chemistry has formally named four new elements previously discovered.

As reported by Physics World

The International Union of Pure and Applied Chemistry (IUPAC) has officially named four new elements: 113, 115, 117 and 118. Element 113 was discovered at the RIKEN Nishina Center for Accelerator-Based Science in Japan and will be called nihonium (Nh). Nihon is a transliteration of “land of the rising sun”, which is a Japanese name for Japan. Moscovium (Mc) is the new moniker for element 115 and was discovered at the Joint Institute for Nuclear Research (JINR) in Moscow. Element 117 will be called tennessine (Ts) after the US state of Tennessee, which is home to the Oak Ridge National Laboratory, while element 118 will be named oganesson after the Russian physicist Yuri Oganessian, who led the team at JINR that discovered the element.

The discovery of new heavy elements brings us closer and closer to the fabled “island of stability,” more of which in due course.

Those of interested in the analysis of nuclear weapons and nuclear energy matters know, or at least some of us do, about the semi empirical mass formula and the liquid drop model of nuclear fission, so named because it is based on the liquid drop model of the nucleus, due to Bohr and Wheeler, and thereupon we don’t really bother to inquire further regarding developments in the theory of the nucleus and the strong interactions.

We don’t really have to as that is a matter for fundamental theory, but I like to follow these things, mostly out of personal curiosity and enjoyment.

The semi empirical mass formula is so named because it depends partly upon theory and partly upon experimental measurements, and the liquid drop model of the nucleus, from which the semi empirical mass formula is derived, is a semi classical theory. That is it is not a purely quantum mechanical theory of the nucleus.

We would like to have a quantum mechanical theory of the nucleus, and the nuclear shell model is just such a theory. Critical to the nuclear shell model is a Pauli Exclusion Principle effect, as with electrons and electron shells, as applied to nucleons and “magic numbers” are important to the theory

Inside nuclei, protons and neutrons fill up separate buckets—called shells—with each shell characterized by a different energy level that can accommodate only a certain number of particles. A nucleus holds a magic number of protons or neutrons when the particles completely fill its shells without any room left for adding more, rendering it stable and longer-lived than other nuclei.

Nuclei with an even number of protons and neutrons are relatively more stable than those with odd numbers, and those with “magic numbers” of protons and neutrons are especially stable. The most well known magic numbers are

2,8,20,28,50,82,126

Nuclei with a magic number of nucleons are spherical, and their higher relative stability cannot be accounted for by the semi empirical mass formula hence the need for a quantum mechanical account. Other predicted magic numbers are 114, 122, 124, and 164 for protons and 184, 196, 236, and 318 for neutrons.

The interesting thing about all this is that it points to an “island of stability” in the superheavy elements beyond uranium. The transuranics tend to have very short half lives, so are unstable, but large magic numbers suggest there is an island of stability consisting of yet to be discovered stable superheavy elements. Given that these elements have yet to be discovered we might say that an empirically well verified quantum mechanical theory of the nucleus still awaits us.

Not many know this, for we assume nuclear physics to have been settled at the fundamental level long ago. This is not so.

What is interesting, also, is that of the standard elements of the periodic table that we know and love the magic numbers of their radioactive isotopes don’t play ball (from the Scientific American article linked above)

In this alternative realm of radioactive isotopes magic numbers aren’t what they seem. For example, 20 is thought to be a standard magic number for neutrons. But the isotope 32magnesium, with 12 protons and 20 neutrons, turns out to be unstable, without any of the properties expected of magic nuclei. The same is true of 28oxygen —with eight protons and 20 neutrons it was expected to be bound tight but, on further inspection, turns out not to be. “Nobody would have bet an iota some years ago that it would be this way, but it is,” says nuclear physicist Robert Janssens of Argonne National Laboratory. “That’s part of the challenge for us to understand at the moment.”

The comment by Eric Scerri is instructive

Scientists hope eventually to map the limits of stability and determine which nuclei can and can’t exist. “Scientifically, this is extremely interesting,” says Eric Scerri, a chemist and philosopher of chemistry at the University of California, Los Angeles. “The nuclear magic numbers are kind of giving way—the dogma begins to break down and the rules of the game have to be expanded. When you push things to a more extreme domain, new science comes out.”

Thomas Kuhn might consider the instability of radioisotopes with magic numbers to be an anomaly, no?