Accelerating many-nucleon basis generation for high performance computing enabled ab initio nuclear structure studies

Abstract

We present the problem of generating a many-nucleon basis in SUð3Þ-scheme for ab initio nuclear structure calculations in a symmetry-adapted no-core shell model framework. We first discuss and analyze the basis construction algorithm whose baseline implementation quickly becomes a significant bottleneck for large model spaces and heavier nuclei. The outcomes of this analysis are utilized to propose a new scalable version of the algorithm. Its performance is consequently studied empirically using the Blue Waters supercomputer. The measurements show significant acceleration achieved with over two orders of magnitude speedups realized for larger model spaces.

Ab initio View of Emergent Symplectic Symmetry and Its Crutial Role in Nuclear Dynamics

“…It is interesting to note that both shapes are "opposite" in their deformation, (1 0) is prolate and the other one (0 2) is oblate (we note that another common convention associates a positive value with a prolate shape, whereas a negative indicates an oblate shape). While, in general, 8 He is considered to be spherical, the present outcome points to an interplay of two shapes in the ground state, which on average may appear to have a zero deformation, but with a B(E2) strength from its 2 + rotational state that constructively adds the nonzero contributions of both shapes.…”

“…We generated the complete Sp(3, R) symmetry-adapted basis with up to 12 HO excitation quanta (i.e. model space including 14 HO major shells) of the oddodd 6 Li and even-even 8 He nuclei. For the intermediate-mass nuclei 20 Ne, we constructed symplectic basis spanning a physically relevant subspace that includes configurations with up to 8 excited HO quanta (i.e.…”

“…4). This has an important implication: complete SA-NCSM calculations are (d) plectic Spð3; RÞ irreps that make up the rotational band states of 6 Li, 8 He, and 20 Ne (in a close agreement with the h irrep is specified by its equilibrium shape, labeled by β and the corresponding SU(3) labels ðλμÞ together with the same irreps but without the predominant contribution, together with the β-γ plot for the ground state. i and 20 Ne calculated in the ab initio SA-NCSM with Spð3; RÞ basis using only a small number (specified in the nt symplectic irreps including the most dominant one, as compared to experiment ("Expt.").…”

“…The SA-NCSM adopts powerful mathematical algorithms of group theory [6,7] to decompose a given model space in terms of U(3) irreps constructed in proton-neutron formalism with the spatial part of basis classified by the SU(3) ⊃ SO(3) group-subgroup chain [8]. Thereby each many-nucleon basis state can be schematically labeled as…”

“…The multiplicity label κ reflects the fact that multiple occurrences of L are possible within a general irrep (λ µ) of SU(3). The symbol α p ( α n ) schematically denotes all the additional quantum numbers needed to uniquely determine proton and neutron irreps, see, e.g., ref [8] for details.…”