Emergent symplectic symmetry in atomic nuclei
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part of Springer Nature, 2020 https://doi.org/10.1140/epjst/e2020-000178-3
THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
Regular Article
Emergent symplectic symmetry in atomic nuclei Ab initio symmetry-adapted no-core shell model Kristina D. Launey1,a , Tom´ aˇs Dytrych1,2 , Grigor H. Sargsyan1 , Robert B. Baker3 , 1 and Jerry P. Draayer 1
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Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA ˘ z, Nuclear Physics Institute, Academy of Sciences of the Czech Republic, 250 68 Re˘ Czech Republic Institute of Nuclear and Particle Physics, and Department of Physics and Astronomy, Ohio University, Athens, OH 45701, USA Received 29 July 2020 / Accepted 28 August 2020 Published online 23 October 2020 Abstract. Exact symmetry and symmetry-breaking phenomena play a key role in gaining a better understanding of the physics of manyparticle systems, from quarks and atomic nuclei, through molecules and galaxies. In nuclei, exact and dominant symmetries such as rotational invariance, parity, and charge independence have been clearly established. Beyond such symmetries, the nature of nuclear dynamics appears to exhibit a high degree of complexity, and only now, we show the fundamental role of an emergent approximate symmetry in nuclei, the symplectic Sp(3, R) symmetry, as clearly unveiled from ab initio studies that start from realistic interactions. In this article, we detail and enhance our recent findings presented in [T. Dytrych, K.D. Launey, J.P. Draayer, D.J. Rowe, J.L. Wood, G. Rosensteel, C. Bahri, D. Langr, R.B. Baker, Phys. Rev. Lett. 124, 042501 (2020)], that establish Sp(3, R) as a remarkably good symmetry of the strong interaction, and point to the predominance of a few equilibrium nuclear shapes (deformed or not) with associated vibrations and rotations that preserve the symplectic Sp(3, R) symmetry. Specifically, we find that the structure of nuclei below the calcium region in their ground state, as well as in their low-lying excited states and giant resonances, respects this symmetry at the 60–80% level.
1 Introduction We have recently shown through first-principle large-scale nuclear structure calculations that the special nature of the strong nuclear force determines highly regular patterns in nuclei that can be tied to an emergent approximate symmetry [1]. We find that this symmetry is remarkably ubiquitous, regardless of the type of the nucleus a
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The European Physical Journal Special Topics
and the particular strong interaction heritage, and mathematically tracks with a symplectic group. For a set of A particles, the symplectic symmetry Sp(3, R) is based on a very basic concept: linear canonical transformations of particle coordinates and momenta that preserve the fundamental Heisenberg commutation relation, as detailed in Section 2. The most interesting insight, however, arises from a complementary perspective: the symplectic symmetry has been recognized to preserve an equilibrium shape under transformations, such as rotations, orie
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