Emergent Sp(3,R) Dynamical Symmetry in the Nuclear Many-Body System from an Ab Initio Description.

Ab initio nuclear theory provides not only a microscopic framework for quantitative description of the nuclear many-body system, but also a foundation for deeper understanding of emergent collective correlations. A symplectic Sp(3,R)⊃U(3) dynamical symmetry is identified in ab initio predictions, from a no-core configuration interaction approach, and found to provide a qualitative understanding of the spectrum of ^{7}Be. Low-lying states form an Elliott SU(3) spectrum, while an Sp(3,R) excitation gives rise to an excited rotational band with strong quadrupole connections to the ground state band.

A study of the bending motion in tetratomic molecules by the algebraic operator expansion method.

We study the bending motion in the tetratomic molecules C2H2 (X̃ (1)Σg (+)), C2H2 (à (1)Au) trans-S1, C2H2 (à (1)A2) cis-S1, and X̃ (1)A1 H2CO. We show that the algebraic operator expansion method with only linear terms comprised of the basic operators is able to describe the main features of the level energies in these molecules in terms of two (linear) or three (trans-bent, cis-bent, and branched) parameters. By including quadratic terms, the rms deviation in comparison with experiment goes down to typically ∼10 cm(-1) over the entire range of energy 0-6000 cm(-1). We determine the parameters by fitting the available data, and from these parameters we construct the algebraic potential functions. Our results are of particular interest in high-energy regions where spectra are very congested and conventional methods, force-field expansions or Dunham-expansions plus perturbations, are difficult to apply.