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Evidence for the first empirical example of a transitional dynamical symmetry at a critical point is discussed in the spectrum of 134Ba. The role of such classes of symmetries in nuclear structural evolution is also discussed.

This textbook on nuclear structure takes a unique and complementary approach compared to existing texts on the topic. Avoiding complicated calculations and complex mathematical formalism, it explains nuclear structure by building on a few elementary physical ideas. Even such apparently intricate topics as shell model residual interactions, the Nilsson model, and the random phase approximation analysis of collective vibrations are explained in a simple, intuitive way so that predictions can usually be made without calculations, essentially by inspection. Frequent comparison with data allows the relevance of theoretical approaches to be immediately evident. This edition includes new chapters on exotic nuclei and radioactive beams, and on correlations of collective observables. Completely new discussions are given of isospin, the shell model, nature of collective vibrations, multi-phonon states, superdeformation, bandmixing, geometric collective model, Fermi gas model, basic properties of simple nuclear potentials, the deuteron, and low energy nuclear structure, as well as other topics.

Background: Microscopic calculations of heavy nuclei face considerable difficulties due to the sizes of the matrices that need to be solved. Various approximation schemes have been invoked, for example by truncating the spaces, imposing seniority limits, or appealing to various symmetry schemes such as pseudo-SU(3). This paper proposes a new symmetry scheme also based on SU(3). This proxy-SU(3) can be applied to well-deformed nuclei, is simple to use, and can yield analytic predictions. Purpose: To present the new scheme and its microscopic motivation, and to test it using a Nilsson model calculation with the original shell model orbits and with the new proxy set. Method: We invoke an approximate, analytic, treatment of the Nilsson model, that allows the above vetting and yet is also transparent in understanding the approximations involved in the new proxy-SU(3). Results: It is found that the new scheme yields a Nilsson diagram for well-deformed nuclei that is very close to the original Nilsson diagram. The specific levels of approximation in the new scheme are also shown, for each major shell. Conclusions:The new proxy-SU(3) scheme is a good approximation to the full set of orbits in a major shell. Being able to replace a complex shell model calculation with a symmetry-based description now opens up the possibility to predict many properties of nuclei analytically and often in a parameter-free way. The new scheme works best for heavier nuclei, precisely where full microscopic calculations are most challenged. Some cases in which the new scheme can be used, often analytically, to make specific predictions, are shown in a subsequent paper.

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