Physics of Nuclei: Key Role of an Emergent Symmetry

Abstract

Exact symmetry and symmetry-breaking phenomena play a key role in providing a better understanding of the physics of many-particle systems, from quarks and atomic nuclei, to molecules and galaxies. In atomic nuclei, exact and dominant symmetries such as rotational invariance, parity, and charge independence have been clearly established. However, even when these symmetries are taken into account, the structure of nuclei remains illusive and only partially understood, with no additional symmetries immediately evident from the underlying nucleon-nucleon interaction. Here, we show through ab initio large-scale nuclear structure calculations that the special nature of the strong nuclear force determines additional highly regular patterns in nuclei that can be tied to an emergent approximate symmetry. We find that this symmetry is remarkably ubiquitous, regardless of its particular strong interaction heritage, and mathematically tracks with a symplectic group. Specifically, we show for light to intermediate-mass nuclei that the structure of a nucleus, together with its low-energy excitations, respects symplectic symmetry at about 70-80% level, unveiling the predominance of only a few equilibrium shapes, deformed or not, with associated vibrations and rotations. This establishes the symplectic symmetry as a remarkably good symmetry of the strong nuclear force, in the low-energy regime. This may have important implications to studies, e.g., in astrophysics and neutrino physics that rely on nuclear structure information, especially where experimental measurements are incomplete or not available. A very important practical advantage is that this new symmetry can be utilized to dramatically reduce computational resources required in ab initio large-scale nuclear structure modeling. This, in turn, can be used to pioneer predictions, e.g., for short-lived isotopes along various nucleosynthesis pathways. arXiv:1810.05757v1 [nucl-th]

A Guided Tour of ab initio Nuclear Many-Body Theory

“…While results for transitions that are dominated by a few nucleons, e.g., M1 transitions [230] or β decays (see reference [232] and the discussion below) can be quite good, the description of collective transitions is hampered by inherent truncations of these many-body methods, which are better suited for dynamical, few-particle correlations (see sections 2.3.3 and 2.3.4). Results from the SA-NCSM [139,140] and the IM-GCM discussed in section 2.3.3 show that the modern chiral interactions themselves adequately support the emergence of nuclear collectivity.…”

“…Another important research program is the exploration of many-body states that are constructed from the irreducible representations (irreps) of the symplectic group Sp(3,R), which describes an approximate emergent symmetry of finite nuclei [139,140]. An exact diagonalization in such a symmetry-adapted basis will offer a much more efficient description of nuclear states with intrinsic deformation than the conventional NCSM, which would need to use massive model spaces with manyparticle-many-hole excitations.…”

“…An exact diagonalization in such a symmetry-adapted basis will offer a much more efficient description of nuclear states with intrinsic deformation than the conventional NCSM, which would need to use massive model spaces with manyparticle-many-hole excitations. This reduction of the model space dimensions also allows such symmetry-adapted NCSM [139,140] and NCCI approaches [141] to reach heavier nuclei than the conventional versions.…”

“…This is illustrated for the case of 20 Ne in Figure 14. The SA-NCSM calculations [140] based on the two-nucleon NNLO opt potential [264] describe the ground-state rotational band extremely well, all the way to the J = 8 + state. It is dominated by a single SU 3irrep, associated with the axially elongated shape of the computed intrinsic density profile that is also shown in the figure.…”

“…(B) Distribution of the equilibrium shapes that contribute to the ground state and first excited 2 + state, indicated by the average deformation parameters (β, γ ). See reference [140] for additional details. addressed either by using mean-field reference states with spontaneously broken symmetries (cf.…”