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Perspectives on Nuclear Structure and Scattering with the Ab Initio No-Core Shell Model

Published in JPS Conference Proceedings, 2018

Nuclear structure and reaction theory are undergoing a major renaissance with advances in many-body methods, strong interactions with greatly improved links to Quantum Chromodynamics (QCD), the advent of high performance computing, and improved computational algorithms. Predictive power, with well-quantified uncertainty, is emerging from non-perturbative approaches along with the potential for new discoveries such as predicting nuclear phenomena before they are measured. We present an overview of some recent developments and discuss challenges that lie ahead. Our focus is on explorations of alternative truncation schemes in the harmonic oscillator basis, of which our Japanese–United States collaborative work on the No-Core Monte-Carlo Shell Model is an example. Collaborations with Professor Takaharu Otsuka and his group have been instrumental in these developments.

DOI: 10.7566/JPSCP.23.012001 | arXiv: 1804.10995
Recommended citation: James P. Vary, Pieter Maris, Patrick J. Fasano, and Mark A. Caprio, JPS Conf. Proc. 23, 012001 (2018) (download)

Probing ab initio emergence of nuclear rotation

Published in The European Physical Journal A, 2020

Structural phenomena in nuclei, from shell structure and clustering to superfluidity and collective rotations and vibrations, reflect emergent degrees of freedom. Ab initio theory describes nuclei directly from a fully microscopic formulation. We can therefore look to ab initio theory as a means of exploring the emergence of effective degrees of freedom in nuclei. For the illustrative case of emergent rotational bands in the Be isotopes, we establish an understanding of the underlying oscillator space and angular momentum (orbital and spin) structure. We consider no-core configuration interaction (NCCI) calculations for 7,9,11Be with the Daejeon16 internucleon interaction. Although shell model or rotational degrees of freedom are not assumed in the ab initio theory, the NCCI results are suggestive of the emergence of effective shell model degrees of freedom ($0\hbar\omega$ and $2\hbar\omega$ excitations) and $LS$-scheme rotational degrees of freedom, consistent with an $\mathrm{SU}(3)$ Elliott–Wilsdon description. These results provide some basic insight into the connection between emergent effective collective rotational and shell model degrees of freedom in these light nuclei and the underlying ab initio microscopic description.

DOI: 10.1140/epja/s10050-020-00112-0 | arXiv: 1912.00083
Recommended citation: Caprio, M.A., Fasano, P.J., Maris, P. et al. Probing ab initio emergence of nuclear rotation. Eur. Phys. J. A 56, 120 (2020). (download)

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

Published in Physical Review Letters, 2020

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 $\mathrm{Sp}(3,\mathbb{R}) \supset \mathrm{U}(3)$ 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 $^7\mathrm{Be}$. Low-lying states form an Elliott $\mathrm{SU}(3)$ spectrum, while an $\mathrm{Sp}(3,\mathbb{R})$ excitation gives rise to an excited rotational band with strong quadrupole connections to the ground state band.

DOI: 10.1103/PhysRevLett.125.102505 | arXiv: 2008.05522
Recommended citation: A. E. McCoy et al., Phys. Rev. Lett. 125, (2020). (download)

Intrinsic operators for the translationally-invariant many-body problem

Published in Journal of Physics G: Nuclear and Particle Physics, 2020

The need to enforce fermionic antisymmetry in the nuclear many-body problem commonly requires use of single-particle coordinates, defined relative to some fixed origin. To obtain physical operators which nonetheless act on the nuclear many-body system in a Galilean-invariant fashion, thereby avoiding spurious center-of-mass contributions to observables, it is necessary to express these operators with respect to the translational intrinsic frame. Several commonly-encountered operators in nuclear many-body calculations, including the magnetic dipole and electric quadrupole operators (in the impulse approximation) and generators of U(3) and Sp(3,R) symmetry groups, are bilinear in the coordinates and momenta of the nucleons and, when expressed in intrinsic form, become two-body operators. To work with such operators in a second-quantized many-body calculation, it is necessary to relate three distinct forms: the defining intrinsic-frame expression, an explicitly two-body expression in terms of two-particle relative coordinates, and a decomposition into one-body and separable two-body parts. We establish the relations between these forms, for general (non-scalar and non-isoscalar) operators bilinear in coordinates and momenta.

DOI: 10.1088/1361-6471/ab9d38 | arXiv: 2004.1202
Recommended citation: Mark A Caprio et al 2020 J. Phys. G: Nucl. Part. Phys. 47 122001 (download)

Rotational bands beyond the Elliott model

Published in Submitted to Journal of Physics G: Nuclear and Particle Physics, 2020

Rotational bands are commonplace in the spectra of atomic nuclei. Inspired by early descriptions of these bands by quadrupole deformations of a liquid drop, Elliott constructed discrete nucleon representations of $\mathrm{SU}(3)$ from fermionic creation and annihilation operators. Ever since, Elliott’s model has been foundational to descriptions of rotation in nuclei. Later work, however, suggested the symplectic extension $\mathrm{Sp}(3,R)$ provides a more unified picture. We decompose no-core shell-model nuclear wave functions into symmetry-defined subspaces for several beryllium isotopes, as well as $^{20}$Ne, using the quadratic Casimirs of both Elliott’s $\mathrm{SU}(3)$ and $\mathrm{Sp}(3,R)$. The band structure, delineated by strong $B(E2)$ values, has a more consistent description in $\mathrm{Sp}(3,R)$ rather than $\mathrm{SU}(3)$. In particular, we confirm previous work finding in some nuclides strongly connected upper and lower bands with the same underlying symplectic structure.

arXiv: 2011.08307
Recommended citation: Ryan Zbikowski, et al 2020, submitted to J. Phys. G: Nucl. Part. Phys. arXiv:2011.08307

talks

teaching

Computational Methods in Physics

Undergraduate course, University of Notre Dame, Department of Physics, 2017

Grader/in-class TA for undergraduate computational physics course.