Advocating for Polyspheron Theory Over Two Decades

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[Part 2 of 2]

In the mid-1960s, as he continued to develop his close-packed spheron theory of atomic nuclei, Linus Pauling sought to use the techniques of creative visualization that had served him so well in his past theoretical work. The situation was trickier this time however, as the discipline of nuclear physics had not yet put forth a single agreed-upon understanding of molecular structure on which a visual model might be built. Rather, as Pauling put it:

There are now two ways of considering the structure of a molecule. One of these ways is by application of a highly refined set of ideas about chemical bonds that was largely developed during the period from 1860 to 1900, and was then significantly extended between 1925 and 1935 through consideration of the empirical information about molecular structure in light of basic principles that were introduced by quantum mechanics.

The second way of considering the structure of a molecule is by solving the wave equation for the molecule, describing the state of the various electrons interacting with one another and with the nuclei.

Both methods had been used since quantum mechanics entered the mainstream in the 1920s and began being applied to topics in chemistry. But according to Pauling, very little effort had been made to develop an empirical theory of the structure of atomic nuclei that corresponded nicely with contemporary ideas on chemical structure. The wave equation approach was further complicated by the fact that, by the mid-1960s, reliable quantum mechanical calculations could be carried out for only a small number of molecules.

In Pauling’s estimation, the most useful attempt to date to develop a workable theory was folded into a discussion that conceptualized light nuclei as aggregates of alpha particles – particles that Pauling renamed “helions” and made a centerpiece of his theory. To address the perceived need to move forward with this mode of thinking, Pauling developed his own conceptual framework and promoted it throughout the 1960s.


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Notes from Pauling’s second Robbins Lecture, February 25, 1966

In 1966 Pauling used his platform as Pomona College’s first Robbins Lecturer to begin spreading a more popular word of this theory — he gave five lectures on the subject in February and March of that year. In 1967 he delivered three more talks on the theory, this time at Princeton University under the auspices of the Plaut Lectureship, an honorific which Pauling was again the first person to occupy. Finally, in 1971, he offered a free public lecture at the University of Colorado, Boulder, promoting his theory as the E.U. Condon Chemical-Physics Lecturer.

Throughout all of this public outreach, Pauling continued to draw up new manuscripts for publication on the topic. In these, he began considering how nuclear wave functions and magnetic-moment values could all be accounted for using polyspheron theory. He also continued to emphasize the compatibility of his ideas with the shell and cluster theories that had gained traction within the discipline.


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A figure included with Pauling’s 1976 manuscript submission to Physical Review

Pauling’s fight to push polyspheron theory into the physics mainstream continued in 1976, by which time the term “helion” was generally being used by nuclear physicists to refer to a Helium-3 nucleus. This common understanding proved disadvantageous to Pauling, as he had defined the term as referring instead to alpha particles (although, interestingly, Pauling had earlier pointed out that “his” helions were notably present in Helium-3).

But there was also good news for Pauling: by now, scientists using electron scattering techniques to investigate the electromagnetic properties of atomic nuclei with prolate deformation were publishing data that seemed to support his point of view. In particular, these experiments had derived information about the shapes of the deformed nuclei that showed what appeared to be the formation of spherons out of the objects defined by polyspheron theory as “helions” and “tritons.”

Pauling almost immediately pounced on this encouraging data, writing a paper initially titled “Comment on the Shapes of Deformed Nuclei,” and then later more forcefully retitled as “The Predication of the Shapes of Deformed Nuclei by the Polyspheron Theory.” He submitted his manuscript to Physical Review in Spring 1976, arguing that reports from current nuclear physicists had confirmed many of his model’s assumptions and that, accordingly, polyspheron theory merited wider acceptance within the field.

The referee overseeing Pauling’s manuscript asked that he make several revisions prior to publication. One major request was that Pauling reshape some of the terminology that was so specific to his theory, due to its confusing nature with respect to broader accepted nomenclature. The journal also asked that Pauling support his claims with clearer and more substantial calculations.

Pauling responded that the journal’s editors had apparently misunderstood the purpose and the importance of his work, and then appended a more substantive introduction to the beginning of the paper to clarify some of the specifics that had been requested of him. When the journal later asked Pauling to remove the extended introduction he refused and his submission was withdrawn. In 1982, some six years later, a paper with the same title finally made it into print by way of the Proceedings of the National Academy of Sciences, a journal that had historically published most submissions authored by distinguished Academy members, among whom Pauling could certainly count himself.

In 1987 Pauling again attempted to advocate on behalf of his theory, writing a new paper titled “Properties of the High-Spin Superprolate Structure of 15266Dy86 are Explained by the Polyspheron Theory.” This paper once more claimed that his now thirty-year-old theory was being steadily confirmed by contemporary laboratory research.

As in 1976, the 1987 manuscript was also rejected, this time by Physical Review and by Nature alike. Seven years later, right around Pauling’s ninety-third birthday, an article with a far less forthright title did appear, once again in PNAS: “Analysis of a Hyperdeformed Band of 152 66 Dy86 on the Basis of a Structure with Two Revolving Clusters, Each with a Previously Unrecognized Two-Tiered Structure.”


Despite his periodic appeals to the practicality of his theory over the course of several decades, and disregarding his insistence that the theory had been vindicated by its prediction of novel discoveries, Linus Pauling’s ideas on polyspherons were never generally accepted by his peers in either physics or chemistry.

Today the utility of Pauling’s model of the atomic nucleus remains in doubt. What does seem to be clear is that he did not succeed in grasping one of the scientific world’s most elusive holy grails: a unified theory of quantum physics and chemistry.

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.

A Return to Scientific Theory

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[Part 6 of 6 in a series examining Pauling’s association with the Center for the Study of Democratic Institutions]

One of Linus Pauling’s hopes during his time at the Center for the Study of Democratic Institutions (CSDI) was to collaborate with neighboring institutions, such as branches of the University of California, and perform scientific research while contributing to the Center’s discussions on world peace. Pauling joined the Center because he believed that science should be used to address social issues and to offer solutions to the problems facing society. Pauling was optimistic of the support and independence that he would enjoy at the Center in support of his ambitions. Upon their arrival to Santa Barbara, however, Ava Helen Pauling expressed the fear that her husband might find the CSDI “too superficial.”

Ava Helen’s prediction, as it turned out, was basically correct, and more and more her husband found himself disappointed by his inability to progress his scientific research. Originally he had hoped to use the scientific method to tackle world affairs but, as he soon realized, the Center preferred to focus on appeals to the public rather than programs of research. His options for joining neighboring institutions to perform scientific work were also quite limited. Importantly, the University of California rejected Pauling’s application for an adjunct position at UC Santa Barbara because of his controversial politics. By August 1965, only two years after being hired by the CSDI and just one year after moving to Santa Barbara, Pauling was writing letters to the Center’s president, Robert Hutchins, asking to spend less time at CSDI headquarters so that he might advance his scientific work from a new base – the Pauling ranch at Big Sur.


Figure from "The close-packed-spheron theory and nuclear fission," Science, October 1965.

Figure from “The close-packed-spheron theory and nuclear fission,” Science, October 1965.

Pauling spent much of his time away from Santa Barbara developing a new model of the atom, which he called the close-packed-spheron model of atomic nuclei. This theory of nuclear structure was published in four different articles (“Structural significance of the principal quantum number of nucleonic orbital wave functions,” Phys. Rev. Lett., September 1965; “Structural basis of neutron and proton magic numbers in atomic nuclei,” Nature, October 1965; “The close-packed-spheron model of atomic nuclei and its relation to the shell model,” Proc. Natl. Acad. Sci., October 1965; and “The close-packed-spheron theory and nuclear fission,” Science, October 1965) each of which addressed different implications of the theory.

Pauling’s work dealt with “magic numbers” and nuclear subshells. Previously it was known that magic numbers describe the quantity of protons and neutrons that make an atom particularly stable. Pauling’s theory, however, suggests that the “magic” qualities associated with these numbers of nuclear components corresponds to the filling of nuclear “spherons,” or nuclear sub-units where protons and neutrons are arranged. (These spherons or sub-units were also referred to as shells in previous theories.) The close-packed theory therefore suggests that nuclear components form clusters rather than arranging as independent particles.

The close-packed-spheron model was based on the earlier nuclear shell theory. Pauling took the nuclear shell theory a step further by attempting to explain why specific numbers of protons and neutrons cause greater nuclear stability. The close-packed-spheron model states that the lower magic numbers represent atoms in which the first or second nuclear shells are filled, and that higher magic numbers correspond to a special “mantle” shell; that is, a hybridized shell that can form if greater amounts of nuclear components arrange into spheres.

In developing his model, Pauling was trying to explain the arrangement of nuclear components by simplifying previous theories and applying the principles of electron orbitals to protons and neutrons in the atomic nucleus. Pauling’s past work had helped to establish the principles of electron orbital hybridization, and he hoped that this new work would yield similar fruit for the atomic nucleus. If such were the case, it would then be possible to explain the stability of atoms with magic numbers and the geometric arrangement of protons and neutrons.

Pauling’s close-packed theory was interesting and relatively simple; however, it failed to spark interest among many other scientists. For the next several years, Pauling continued to advocate for the theory and, in June 1974, he applied for a National Science Foundation grant to support further theoretical research on the structure of atomic nuclei. The application was denied and Pauling turned his attentions elsewhere.


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The development of the close-packed-spheron theory and the lack of attention that it received from the scientific community are emblematic of the difficulties that Pauling experienced during his affiliation with the CSDI. The limited resources available to Pauling during this time enabled only theoretical investigations on subjects with which he was already at least somewhat familiar. And his official connection with an institution that existed well out of the scientific mainstream stifled his ability to engage with his scientific peers on a regular basis.

Pauling was only at the CSDI until 1967, and towards the end of his tenure there his eagerness to return to the sciences only grew. Other publications from the period focused on molecular protein structure and the chemical bond. As with the structure of atomic nuclei, these topics were, again, among those that he had researched prior to moving to Santa Barbara.  Once he found a new scientific home, the University of California at San Diego, Pauling began new investigations in medical chemistry which ultimately led to his famous fascination with vitamin C.

Pauling’s switch to a scientific focus could be interpreted as stemming from a waning interest in world affairs, but his papers show that it was the limitations that he encountered at the CSDI that led him to return to more scientific pursuits. World affairs remained central to Pauling’s activities and continued to lay claim to large pieces of his time, especially as the war in Vietnam escalated throughout the late 1960s and early 1970s. Pauling was interested in developing ideas that could lead the world towards peace, while the Center was primarily a think tank that often focused more on discussion rather than reaching conclusions. In the end, superficial or not, the CSDI simply was not the institution for Linus Pauling.