The pervasive ubiquity of shell effects and the vexing necessity of their conceptual companions

David Verney (IJCLab, Orsay, France)

The idea that the atomic nucleus, an N-body system bound by a complicated interaction that ultimately descends from the strong force and is highly correlated, can nonetheless be discussed, and usefully approximated, in terms of “single-particle” degrees of freedom is one of the most fertile in nuclear structure. The single-particle concept sits at the heart of essentially every microscopic description of nuclei and, more broadly, it has become one of the most constitutive notions not only of our models, but also of our intimate mental picture of what a nucleus is.

And yet, the intellectual journey of this concept is not widely known, nor is the winding path that brought it to its current status. Its origins reach back almost a century, to the late 1920s, amid heated debates about the very constituents of the nucleus (protons, electrons, α particles?). It first emerged by analogy with atomic physics, but it was soon propelled, in a far more decisive way, by the “pervasive ubiquity” of shell effects, visible at essentially every scale of nuclear phenomenology and imprinted across a wide range of data and observables.

From the outset, however, the single-particle viewpoint stood in sharp tension with a competing, more “macroscopic” vision of the nucleus: that of a droplet of nuclear matter, culminating in the triumph of Niels Bohr’s compound-nucleus picture. For much of the 1930s and 1940s, single-particle approaches survived in a kind of intellectual semi-clandestinity, until the decisive breakthrough of the shell model in the following decade, through the work of Mayer, Jensen and many others.

The questions raised by this concept, and by the ideas that must accompany it if it is to remain physically meaningful, are very much alive today, and have recently been sharpened again, notably by the Saclay group in the contexte of the emergence of ab initio approaches. This theme was the focus of an ESNT workshop held in Saclay last November, entitled Effective yet elusive: exploring single particles, for which the present talk originally served as an introduction and a broader contextual framing.