Linus Pauling’s Polyspheron Theory

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[Part 1 of 2]

“I consider the polyspheron theory to be a simple statement about the insight into nuclear structure that is provided by the experimental data and to some extent by the quantum mechanical calculations.” 

– Linus Pauling, 1976

In the early twentieth century, when physicists were gaining knowledge of the properties of atomic nuclei in strides, the still young field of quantum mechanical theory was being used to interpret experimental data. At the same time, chemists were beginning to explore the implications of quantum theory as it pertained to molecular structure, a trend that culminated in Linus Pauling’s groundbreaking book, The Nature of the Chemical Bond, published in 1939.

In the following forty years however, no single theory of the structure of the atomic nucleus emerged that could conceptually account for all the results that chemists and physicists were observing. Nor was there a satisfactory theory that could link the behavior of the most infinitesimal and internal parts of the atom with the much larger scale of molecular behavior and chemical reactions. In other words, there was not yet a single accepted unified theory of quantum physics and chemistry. The pursuit of just such a theory stood as a holy grail of sorts, occupying the hopes, dreams and energy of many a twentieth century scientist.

For parts of five decades, Linus Pauling strove to develop just such a theory, one that could account for the basic structural tendencies and behaviors of the atomic nucleus and prove useful not only for atomic physicists but also for chemists. His efforts resulted in what he called “close-packed spheron theory,” simplified later as “polyspheron theory.”


Though he had begun work on the topic much earlier, Pauling first revealed his theory to the world on October 11, 1965 at a meeting of the National Academy of Sciences, held at the University of Washington in Seattle. His talk that day was titled “The Close-Packed-Spheron Theory of the Structure of Nuclei and the Mechanism of Nuclear Fission,” and its contents mirrored a pair of similarly titled papers that he published that same year: “The Close-Packed-Spheron Theory and Nuclear Fission,” published in Science, and “The Close-Packed-Spheron Model of Atomic Nuclei and Its Relation to the Shell Model,” which appeared in the Proceedings of the National Academy of Sciences.

In each of these works, Pauling advanced a theoretical framework that incorporated features of three older theories – the cluster, shell and liquid-drop theories – while also accounting for several observed phenomena of atomic nuclei that were difficult to explain at the time, such as asymmetric nuclear fission. Importantly, the close-packed spheron model of the nucleus differed from past models by declaring “spherons” as its units, rather than nucleons. Pauling described his rationale for this choice as having been an outgrowth of his thinking about nuclear fission.

Twenty five years ago a phenomenon of tremendous importance was discovered, nuclear fission. In the uranium nucleus and other heavy nuclei, fissioning produces a lighter and a heavier nucleus, with mass ratio about 2/3, several hundred times as often as two nuclei with equal mass are produced.

Why is fission asymmetric in this way? Here is a simple reason why this might be: I assume that in nuclei the nucleons may, as a first approximation, be described as occupying localized 1s orbitals to form small clusters. These small clusters, called spherons, are usually helions, tritons, and dineutrons: in nuclei containing an odd number of neutrons, a (Helium-3) cluster or a deuteron may serve as a spheron.

Pauling’s basic assumption here was that, in atomic nuclei, the nucleons were in large part aggregated into clusters that are arranged as closely as allowed by the laws of physics. Nuclei with more neutrons than protons were called tritons or dineutrons by Pauling. Likewise, the clusters of neutrons and protons occupying localized 1s orbitals were called spherons.

The most important spherons in Pauling’s conception were aggregates of two neutrons and two protons, which he called helions, though they were already known to physicists as alpha particles. The localized 1s orbitals that these spherons occupied could also be described mathematically as hybrids of the central-field orbitals that are outlined in shell theory. This process of hybridization of orbitals provided a formal basis for relating the cluster model – of which Pauling’s theory was an extreme version – and the shell model.

Pauling also put forth the idea that the spherons in a nucleus were arranged in a series of concentric layers. For a large nucleus, the outer part of the cavity inside the surface layer was occupied by spherons that were in contact with the inner side of the surface layer. These spherons constituted a layer of their own, within which Pauling believed there might reside yet another layer of spherons. To avoid confusion with the “shells” of the shell model, Pauling referred to his spheron layers as follows: “the mantle” for the surface layer, and the “outer core” and “inner core” for the two additional constituents of a three-layer nucleus.

In an effort to assure the scientific rank and file that he was not seeking to upend their entire understanding of nuclear physics, Pauling promised that the quantum mechanical calculations enabled by his polyspheron theory were essentially the same as those that had been made using various other models in the past.

Perhaps unwittingly, this assurance left many colleagues within the field wondering why Pauling was bothering to develop this theory at all. For many physicists, Pauling’s work seemed redundant, or perhaps merely an attempt to change the names of existing terms to new ones that fit more elegantly into Pauling’s conceptual framework of atomic structure.

Pauling countered this skepticism by suggesting that both qualitative and rough quantitative conclusions could be drawn from his model without the aid of extensive calculations. If these conclusions agreed with the experimental evidence, Pauling argued, then detailed calculations of this sort might not always be required in the future, pushing scientists just that little bit closer to the discovery of their holy grail.