place in theoretical nuclear structure physics. With the development of new concepts, the exploitation of symbiotic collaborations with scientists in diverse fields, and advances in computing technology and numerical algorithms, theorists are progressing toward understanding the nucleus in a comprehensive and unified way.

Revising the Paradigms of Nuclear Structure

Shell Structure: A Moving Target

The concept of nucleons moving in orbits within the nucleus under the influence of a common force gives rise to the ideas of shell structure and resulting magic numbers. Like an electron’s motion in an atom, nucleonic orbits bunch together in energy, forming shells, and nuclei having filled nucleonic shells (nuclear “noble gases”) are exceptionally well bound. The numbers of nucleons needed to fill each successive shell are called the magic numbers: The traditional ones are 2, 8, 20, 28, 50, 82, and 126 (some of these are exemplified in Figure 2.1). Thus a nucleus such as lead-208, with 82 protons and 126 neutrons, is doubly “magic.” The concept of magic numbers in turn introduces the idea of valence nucleons—those beyond a magic number. Thus, in considering the structure of nuclei like lead-210, one can, to some approximation, consider only the last two valence neutrons rather than all 210. When proposed in the late 1940s, this was a revolutionary concept: How could individual nucleons, which fill most of the nuclear volume, orbit so freely without generating an absolute chaos of collisions? Of course, the Pauli exclusion principle is now understood to play a key role here, and the resulting model of nucleonic orbits has become the template used for over half a century to view nuclear structure.

One experimental hallmark of nuclear structure is the behavior of the first excited state with angular momentum 2 and positive parity in even-even nuclei. This state, usually the lowest energy excitation in such nuclei, is a bellwether of structure. Its excitation energy takes on high values at magic numbers and low values as the number of valence nucleons increases and collective behavior emerges. The picture of nuclear shells leads to the beautiful regularities and simple repeated patterns, illustrated in Figure 1.2 and seen here in the energies of the 2+ states shown at the top of Figure 2.2. The concept of magic numbers was forged from data based on stable or near-stable nuclei. Recently, however, the traditional magic numbers underwent major revisions as previously unavailable species became accessible. The shell structure known from stable nuclei is no longer viewed as an immutable construct but instead is seen as an evolving moving target. Indeed the elucidation of changing shell structure is one of the triumphs of recent experiments in nuclear structure at exotic beam facilities worldwide. For example, experiments



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