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Many Fermion Dynamics - nuclear (MFDn)

MFDn is a configuration interaction code for performing no-core configuration interaction (NCCI) calculations for light nuclei using realistic 2-and 3-body interactions. It is an MPI/OpenMP hybrid code with Lanczos and LOBPCG eigensolvers. It has been extensively optimized for Cori KNL, and is undergoing reimplementation for Permutter GPU.

Symplectic No-Core Configuration Interaction (spncci) Permalink

spncci is a code for ab initio calculations in an $\mathrm{Sp}(3,\mathbb{R})$ symmetry-adapted basis, via the symplectic no-core configuration interaction (SpNCCI) approach. Many-body Hamiltonian matrix elements are evaluated through a laddering procedure, involving $\mathrm{Sp}(3,\mathbb{R})$ and $\mathrm{SU}(3)$ group theoretical coefficients, leading to a dense Hamiltonian matrix, which is then diagonalized via the Lanczos algorithm. Algorithms are structured for efficient parallelization, in collaboration with Lawrence Berkeley National Laboratory (LBNL) Scalable Solvers group. Currently the code is OpenMP parallelized, with exploratory work on MPI/OpenMP implementation. Full MPI/OpenMP parallelization and integration with a distributed, iterative eigensolver for dense matrices with block structure is anticipated by early in the new allocation year.


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: J. P. Vary, P. Maris, P. J. Fasano, and M. A. Caprio, JPS Conf. Proc. 23, 012001 (2018) (download)

First Measurement of the B(E2;3/2→1/2) Transition Strength in 7Be: Testing Ab Initio Predictions for A=7 Nuclei

Published in Physical Review C, 2019

Electromagnetic observables are able to give insight into collective and emergent features in nuclei, including nuclear clustering. These observables also provide strong constraints for ab initio theory, but comparison of these observables between theory and experiment can be difficult due to the lack of convergence for relevant calculated values, such as $E2$ transition strengths. By comparing the ratios of $E2$ transition strengths for mirror transitions, we find that a wide range of ab initio calculations give robust and consistent predictions for this ratio. To experimentally test the validity of these ab initio predictions, we performed a Coulomb excitation experiment to measure the $B(E2;3/2^− \rightarrow 1/2^−)$ transition strength in 7Be for the first time. A $B(E2;3/2^− \rightarrow 1/2^−)$ value of 26(6)stat(3)syst e2 fm4 was deduced from the measured Coulomb excitation cross section. This result is used with the experimentally known 7Li $B(E2;3/2^− \rightarrow 1/2^−)$ value to provide an experimental ratio to compare with the ab initio predictions. Our experimental value is consistent with the theoretical ratios within $1\sigma$ uncertainty, giving experimental support for the value of these ratios. Further work in both theory and experiment can give insight into the robustness of these ratios and their physical meaning.

DOI: 10.1103/PhysRevC.99.064320 | arXiv: 2109.07312
Recommended citation: S. L. Henderson, T. Ahn, M. A. Caprio, P. J. Fasano, et al., Phys. Rev. C 99, 064320 (2019). (download)

Ab initio rotation in 10Be

Published in Bulgarian Journal of Physics, 2019

Ab initio theory describes nuclei from a fully microscopic formulation, with no presupposition of collective degrees of freedom, yet signatures of clustering and rotation nonetheless arise. We can therefore look to ab initio theory for an understanding of the nature of these emergent phenomena. To probe the nature of rotation in 10Be, we examine the predicted rotational spectroscopy from no-core configuration interaction (NCCI) calculations with the Daejeon16 internucleon interaction, and find spectra suggestive of coexisting rotational structures having qualitatively different intrinsic deformations: one triaxial and the other with large axial deformation arising primarily from the neutrons.

arXiv: 1912.06082
Recommended citation: M. A. Caprio, P. J. Fasano, A. E. McCoy, P. Maris, and J. P. Vary, Bulg. J. Phys. 46, 445 (2019). (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: M. A. Caprio, P. J. Fasano, P. Maris, A. E. McCoy, and J. P. Vary, 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 7Be. 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, M. A. Caprio, T. Dytrych, and P. J. Fasano, Phys. Rev. Lett. 125, 102505 (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 $\mathrm{U}(3)$ and $\mathrm{Sp}(3,\mathbb{R})$ 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: M. A. Caprio, A. E. McCoy, and P. J. Fasano, J. Phys. G: Nucl. Part. Phys. 47, 122001 (2020). (download)

White paper: from bound states to the continuum

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

This white paper reports on the discussions of the 2018 Facility for Rare Isotope Beams Theory Alliance (FRIB-TA) topical program “From bound states to the continuum: Connecting bound state calculations with scattering and reaction theory”. One of the biggest and most important frontiers in nuclear theory today is to construct better and stronger bridges between bound state calculations and calculations in the continuum, especially scattering and reaction theory, as well as teasing out the influence of the continuum on states near threshold. This is particularly challenging as many-body structure calculations typically use a bound state basis, while reaction calculations more commonly utilize few-body continuum approaches. The many-body bound state and few-body continuum methods use different language and emphasize different properties. To build better foundations for these bridges, we present an overview of several bound state and continuum methods and, where possible, point to current and possible future connections.

DOI: 10.1088/1361-6471/abb129 | arXiv: 1912.00451
Recommended citation: C. W. Johnson, K. D. Launey, et al., J. Phys. G: Nucl. Part. Phys. 47, 123001 (2020). (download)

Rotational bands beyond the Elliott model

Published in Journal of Physics G: Nuclear and Particle Physics, 2021

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 $\mathrm{Sp}(3,\mathbb{R})$ 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 20Ne, using the quadratic Casimirs of both Elliott’s $\mathrm{SU}(3)$ and $\mathrm{Sp}(3,\mathbb{R})$. The band structure, delineated by strong $B(E2)$ values, has a more consistent description in $\mathrm{Sp}(3,\mathbb{R})$ 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.

DOI: 10.1088/1361-6471/abdd8e | arXiv: 2011.08307
Recommended citation: R. Zbikowski, C. W. Johnson, A. E. McCoy, M. A. Caprio, and P. J. Fasano, J. Phys. G: Nucl. Part. Phys. 48, 075102 (2021). (download)

Quadrupole moments and proton-neutron structure in p-shell mirror nuclei

Published in Physical Review C, 2021

Electric quadrupole (E2) matrix elements provide a measure of nuclear deformation and related collective structure. Ground-state quadrupole moments in particular are known to high precision in many p-shell nuclei. While the experimental electric quadrupole moment only measures the proton distribution, both proton and neutron quadrupole moments are needed to probe proton-neutron asymmetry in the nuclear deformation. We seek insight into the relation between these moments through the ab initio no-core configuration interaction (NCCI), or no-core shell model (NCSM), approach. Converged ab initio calculations for quadrupole moments are particularly challenging, due to sensitivity to long-range behavior of the wave functions. We therefore study more robustly-converged ratios of quadrupole moments: across mirror nuclides, or of proton and neutron quadrupole moments within the same nuclide. In calculations for mirror pairs in the p-shell, we explore how well the predictions for mirror quadrupole moments agree with experiment and how well isospin (mirror) symmetry holds for quadrupole moments across a mirror pair.

DOI: 10.1103/PhysRevC.104.034319 | arXiv: 2106.12128
Recommended citation: M. A. Caprio, P. J. Fasano, P. Maris, and A. E. McCoy, Phys. Rev. C 104, 034319 (2021). (download)

Symmetry and shape coexistence in 10Be

Published in Bulgarian Journal of Physics, 2022

Within the low-lying spectrum of 10Be, multiple rotational bands are found, with strikingly different moments of inertia. A proposed interpretation has been that these bands variously represent triaxial rotation and prolate axially-deformed rotation. The bands are well-reproduced in ab initio no-core configuration interaction (NCCI) calculations. We use the calculated wave functions to elucidate the nuclear shapes underlying these bands, by examining the Elliott $\mathrm{SU}(3)$ symmetry content of these wave functions. The ab initio results support an interpretation in which the ground-state band, along with an accompanying $K=2$ side band, represent a triaxial rotor, arising from an $\mathrm{SU}(3)$ irreducible representation in the $0\hbar\omega$ space. Then, the lowest excited $K=0$ band represents a prolate rotor, arising from an $\mathrm{SU}(3)$ irreducible representation in the $2\hbar\omega$ space.

DOI: 10.55318/bgjp.2022.49.1.057 | arXiv: 2112.04056
Recommended citation: M. A. Caprio, A.E. McCoy, P. J. Fasano, and T. Dytrych, Bulg. J. Phys. 49, 057066 (2022) (download)

Natural orbitals for the ab initio no-core configuration interaction approach

Published in Physical Review C, 2022

Ab initio no-core configuration interaction (NCCI) calculations for the nuclear many-body problem have traditionally relied upon an antisymmetrized product (Slater determinant) basis built from harmonic oscillator orbitals. The accuracy of such calculations is limited by the finite dimensions which are computationally feasible for the truncated many-body space. We therefore seek to improve the accuracy obtained for a given basis size by optimizing the choice of single-particle orbitals. Natural orbitals, which diagonalize the one-body density matrix, provide a basis which maximizes the occupation of low-lying orbitals, thus accelerating convergence in a configuration-interaction basis, while also possibly providing physical insight into the single-particle structure of the many-body wave function. We describe the implementation of natural orbitals in the NCCI framework, and examine the nature of the natural orbitals thus obtained, the properties of the resulting many-body wave functions, and the convergence of observables. After taking 3He as an illustrative testbed, we explore aspects of NCCI calculations with natural orbitals for the ground state of the p-shell neutron halo nucleus 6He.

DOI: 10.1103/PhysRevC.105.054301 | arXiv: 2112.04027
Recommended citation: P. J. Fasano, Ch. Constantinou, M. A. Caprio, P. Maris, and J. P. Vary, Phys. Rev. C 105, 054301 (2022). (download)

Accelerating quantum many-body configuration interaction with directives

Published in Lecture Notes in Computer Science, 2022

Many-Fermion Dynamics-nuclear, or MFDn, is a configuration interaction (CI) code for nuclear structure calculations. It is a platform-independent Fortran 90 code using a hybrid MPI+X programming model. For CPU platforms the application has a robust and optimized OpenMP implementation for shared memory parallelism. As part of the NESAP application readiness program for NERSC’s latest Perlmutter system, MFDn has been updated to take advantage of accelerators. The current mainline GPU port is based on OpenACC. In this work we describe some of the key challenges of creating an efficient GPU implementation. Additionally, we compare the support of OpenMP and OpenACC on AMD and NVIDIA GPUs.

DOI: 10.1007/978-3-030-97759-7_6 | arXiv: 2110.10765
Recommended citation: B. G. Cook, P. J. Fasano, P. Maris, C. Yang, and D. Oryspayev, Accelerator Programming with Directives, Lect. Notes Comput. Sci. 13194 (2022). (download)

Ab initio prediction of E2 strengths in 8Li and its neighbors by normalization to the measured quadrupole moment

Submitted to Physical Review C

For electric quadrupole ($E2$) observables, which depend on the large-distance tails of the nuclear wave function, ab initio no-core configuration interaction (NCCI) calculations converge slowly, making meaningful predictions challenging to obtain. Nonetheless, the calculated values for different $E2$ matrix elements, particularly those involving levels with closely-related structure (e.g., within the same rotational band) are found to be robustly proportinal. This observation suggests that a known value for one observable may be used to determine the overall scale of $E2$ strengths, and thereby provide predictions for others. In particular, we demonstrate that meaningful predictions for $E2$ transitions may obtained by calibration to the ground-state quadrupole moment. We test this approach for well-measured low-lying $E2$ transitions in 7Li and 9Be, then provide predictions for transitions in 8,9Li. In particular, we address the $2^+\rightarrow1^+$ transition in 8Li, for which the reported measured strength exceeds ab initio Green’s function Monte Carlo (GFMC) predictions by over an order of magnitude.

arXiv: 2206.05628
Recommended citation: M. A. Caprio and P. J. Fasano, arXiv:2206.05628 [nucl-th]. (download)

Robust ab initio prediction of nuclear electric quadrupole observables by scaling to the charge radius

Published in Physical Review C, 2022

Meaningful predictions for electric quadrupole ($E2$) observables from ab initio nuclear theory are necessary, if the ab initio description of collective correlations is to be confronted with experiment, as well as to provide predictive power for unknown $E2$ observables. However, converged results for $E2$ observables are notoriously challenging to obtain in ab initio no-core configuration interaction approaches. Matrix elements of the $E2$ operator are sensitive to the large-distance tails of the nuclear wave function, which converge slowly in an oscillator basis expansion. Similar convergence challenges beset ab initio prediction of the nuclear charge radius. We demonstrate that the convergence patterns of the $E2$ and radius observables are strongly correlated, and that meaningful predictions for the absolute scale of $E2$ observables may be made by calibrating to the experimentally known ground-state charge radius. We illustrate by providing robust ab initio predictions for several $E2$ transition strengths and quadrupole moments in p-shell nuclei, in cases where experimental results are available for comparison.

DOI: 10.1103/PhysRevC.105.L061302 | arXiv: 2206.09307
Recommended citation: M. A. Caprio, P. J. Fasano, and P. Maris, Phys. Rev. C 105, L061302 (2022). (download)



Computational Methods in Physics

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

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