arXiv subjects

Mark A. Caprio

Publications and source records attributed to Mark A. Caprio.

At least 19 recordsLinked to original sources

arXiv2026

Intruder structure, deformation, and $E2$ strengths in $^{14}\mathrm{C}$ from an ab initio perspective

The semimagic nucleus $^{14}\mathrm{C}$ lies just above the $N=8$ island of inversion, raising the possibility of low-lying intruder states and associated deformation. Through ab initio no-core configuration interaction calculations, we shed light on the role of intruder structure, quadrupole deformation, and Elliott SU(3) symmetry in $^{14}\mathrm{C}$. The results also highlight the influence of mixing between normal and intruder states on the strengths of the $E2$ transitions from the first two $2^+$ states.

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arXiv2026

Future directions in nuclear $\beta$ decay at FRIB and beyond

Motivated by the opportunities presented for studies relevant to nuclear structure, astrophysics, and fundamental symmetries with nuclear $\beta$ decay, the Facility for Rare Isotope Beams (FRIB) Theory Alliance topical program ``Future Directions in Nuclear $\beta$ Decays at FRIB'' was held in September of 2025. This white paper summarizes the main points of discussion over the two-week program, and it aims to provide a snapshot of the current status of the field while also highlighting important questions and opportunities for future work. We provide an overview of the experimental tools and techniques that enable modern $\beta$ decay studies, discuss the current state of nuclear many-body approaches used to study $\beta$ decays, and highlight the important science questions that can be addressed by weak decays.

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arXiv2026

One-Body and Two-Body Density Matrix Elements in a Symplectic Many-Body Basis

The symplectic no-core configuration interaction (SpNCCI) framework is an ab initio many-body method for nuclear structure which makes use of the approximate symplectic symmetry of nuclei by appropriate choice of many-body basis states. In this paper we derive recurrence relations allowing for calculation of one-body and two-body density matrix elements between the SpNCCI basis states. Availability of these matrix elements allows for integration of the SpNCCI framework with other modern many-body methods and for calculation of matrix elements of any one-body or two-body operator.

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arXiv2026

Symplectic no-core configuration interaction framework for nuclear structure

We present the symplectic no-core configuration interaction (SpNCCI) framework, in which the nuclear many-body problem is solved a symmetry-adapted basis that explicitly encodes approximate symmetries associated with nuclear collectivity and deformation. In this framework, calculations are carried out in a basis organized into Sp(3,R) irreducible representations (irreps), each of which can be expressed as an infinite tower of U(3) irreps. In this framework, matrices of realistic relative two-body operators, such as the nuclear Hamiltonian, are computed directly in the Sp(3,R) many-body basis, obviating the need to expand all Sp(3,R) many-body states in, e.g., a U(3)-coupled configuration basis. Instead, many-body matrix elements are obtained via a recurrence relation that expresses a given matrix element in terms of matrix elements between basis states with fewer oscillator quanta. To use this recurrence method for computing matrix elements of relative two-body operators, we must first expand each operator into components of U(3) tensors. To this end, we present a method for decomposing arbitrary operators into U(3) tensor components.

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arXiv2026

A modern Fortran library for SU(3) coupling and recoupling coefficients

The group $\mathrm{SU}(3)$ has applications in several branches of physics. Many of these applications depend on availability of $\mathrm{SU}(3)$ coupling and recoupling coefficients. We have developed a modern Fortran library for calculation of the coupling coefficients, for both the $\mathrm{SU}(3)\supset\mathrm{U}(1)\times\mathrm{SU}(2)$ and $\mathrm{SU}(3)\supset\mathrm{SO}(3)$ group chains, and the recoupling coefficients. The library implements the algorithms of Draayer, Akiyama, and Millener, which are laid out in the paper. Performance of the library has been tested and compared to the Akiyama-Draayer (AD) library implementing the same algorithms as well as to a more recent implementation. Our library works for a larger range of $\mathrm{SU}(3)$ quantum numbers and provides more accurate coupling coefficients with large quantum numbers than the AD library.

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arXiv2025

Deformation-driven intruder states in light island-of-inversion nuclei

Islands of inversion occur when the nuclear ground state is dominated by intruder configurations, specifically particle-hole excitations across shell gaps, rather than by the naive spherical shell-model expectation of filled shell configurations. Using the realistic and rigorous no-core shell model, we are able to confirm that deformation drives these intruder states in the light halo nuclides $^{11}$Li and $^{29}$F. In small model spaces, these deformed intruders lie high in energy with respect to spherical normal states; as the model space size increases, the intruders energetically approach, albeit slowly, the normal states. This provides further strong evidence of the connection between shape deformation/coexistence and islands of inversion, as well demonstrating as the computational challenges in rigorously modeling this phenomenon. Our results also suggest halo states can be strongly deformed and/or strongly mixed with normal spherical states.

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arXiv2025

Ab Initio Study of $^7$Li with Coupled Mass Partitions

Background: Lithium is of broad interest in nuclear astrophysics, fusion energy research, and nuclear technology. From a theoretical perspective, the nucleus $^7$Li presents a remarkable challenge, as its bound and resonant states can exhibit contributions from both the $^4$He + $^3$H cluster configuration and configurations involving a neutron or proton coupled to a $^6$Li or $^6$He core, respectively. Purpose: We aim to achieve a unified ab initio description of bound-state and continuum properties of $^7$Li by explicitly including simultaneously the coupled mass/charge partitions $^4$He + $^3$H, $^6$Li + $n$, and $^6$He + $p$. Specifically, we investigate the effect of inter-partition coupling on the spectrum of $^7$Li and calculate cross sections for the $^6$Li($n,p)^6$He, $^6$He($p,n)^6$Li, and $^6$He($p,t)^4$He reactions. Method: We employ the no-core shell model with continuum for the first time in a calculation that couples three mass/charge partitions of the aggregate nucleus $^7$Li, using a chiral nucleon-nucleon interaction as input. Results: The calculated spectrum reproduces all the experimentally observed states of $^7$Li in the correct order and predicts additional resonances. The calculation also reproduces the overall energy dependence of the $^6$Li$(n,p)^6$He cross section. Improved agreement with measured cross sections is obtained after phenomenological adjustment of resonance energies. Conclusions: The present results show that coupling the relevant mass/charge partitions is important for a consistent description of the $^7$Li spectrum and reaction cross sections, and offers a useful framework for interpreting existing data and guiding future measurements.

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arXiv2025

Robust ab initio predictions for dimensionless ratios of E2 and radius observables. I. Electric quadrupole moments and deformation

Converged results for E2 observables are notoriously challenging to obtain in ab initio no-core configuration interaction (NCCI) 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. However, we exploit systematic correlations between the calculated E2 and radius observables to yield meaningful predictions for relations among these observables. In particular, we examine ab initio predictions for dimensionless ratios of the form Q/r^2, for nuclei throughout the $p$ shell. Meaningful predictions for electric quadrupole moments may then be made by calibrating to the ground-state charge radius, if experimentally known, or vice versa. Moreover, these dimensionless ratios provide ab initio insight into the nuclear quadrupole deformation.

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arXiv2025

Robust ab initio predictions for dimensionless ratios of E2 and radius observables. II. Estimation of E2 transition strengths by calibration to the charge radius

Converged results for E2 observables are notoriously challenging to obtain in ab initio no-core configuration interaction (NCCI) 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. However, we exploit systematic correlations between the calculated E2 and radius observables to yield meaningful predictions for relations among these observables. In particular, we examine ab initio predictions for dimensionless ratios of the form B(E2)/(e^2r^4), for nuclei throughout the p shell. Meaningful predictions for E2 transition strengths may then be made by calibrating to the ground-state charge radius, if experimentally known.

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arXiv2024

Direct ab initio calculation of the $^{4}$He nuclear electric dipole polarizability

The calculation of nuclear electromagnetic sum rules by directly diagonalizing the nuclear Hamiltonian in a large basis is numerically challenging and has not been performed for $A>2$ nuclei. With the significant progress of high performance computing, we show that calculating sum rules using numerous discretized continuum states obtained by directly diagonalizing the ab initio no-core shell model Hamiltonian is achievable numerically. Specifically, we calculate the $^{4}$He electric dipole ($E1$) polarizability, that is an inverse energy weighted sum rule, employing the Daejeon16 $NN$ interaction. We demonstrate that the calculations are numerically tractable as the dimension of the basis increases and are convergent. Our results for the $^{4}$He electric dipole polarizability are consistent with the most recent experimental data and are compared with those of other theoretical studies employing different techniques and various interactions.

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arXiv2024

Intruder band mixing in an ab initio description of 12Be

The spectrum of 12Be exhibits exotic features, e.g., an intruder ground state and shape coexistence, normally associated with the breakdown of a shell closure. While previous phenomenological treatments indicated the ground state has substantial contributions from intruder configurations, it is only with advances in computational abilities and improved interactions that this intruder mixing is observed in ab initio no-core shell model (NCSM) predictions. In this work, we extract electromagnetic observables and symmetry decompositions from the NCSM wave functions to demonstrate that the low-lying positive parity spectrum can be explained in terms of mixing of rotational bands with very different intrinsic structure coexisting within the low-lying spectrum. These observed bands exhibit an approximate SU(3) symmetry and are qualitatively consistent with Elliott model predictions.

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arXiv2023

Magnetic moments of $A = 3$ nuclei with chiral effective field theory operators

Chiral effective field theory ($χ$EFT) provides a framework for obtaining internucleon interactions in a systematically improvable fashion from first principles, while also providing for the derivation of consistent electroweak current operators. In this work, we apply consistently derived interactions and currents towards calculating the magnetic dipole moments of the $A=3$ systems Triton and Helium-3. We focus here on LENPIC interactions obtained using semilocal coordinate-space (SCS) regularization. Starting from the momentum-space representation of the LENPIC $χ$EFT vector current, we derive the SCS-regularized magnetic dipole operator up through N2LO. We then carry out no-core shell model calculations for Triton and Helium-3 systems, using the SCS LENPIC interaction at N2LO in $χ$EFT, and evaluate the magnetic dipole moments obtained using the consistently derived one-nucleon and two-nucleon electromagnetic currents. As anticipated by prior results with $χ$EFT currents, the current corrections through N2LO provide improved, but not yet complete, agreement with experiment for the Triton and Helium-3 magnetic dipole moments.

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arXiv2022

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

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 proportional. 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 be obtained by calibration to the ground-state quadrupole moment. We test this approach for well-measured low-lying $E2$ transitions in $^7$Li and $^9$Be, then provide predictions for transitions in $^8$Li and $^9$Li. In particular, we address the $2^+\rightarrow1^+$ transition in $^8$Li, for which the reported measured strength exceeds ab initio Green's function Monte Carlo (GFMC) predictions by over an order of magnitude.

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arXiv2022

Triaxiality explored by an odd quasi-particle

The triaxiality of odd-mass nuclei is investigated by coupling a quasiparticle to an even-even core through the core-quasiparticle coupling model. Both soft and rigid triaxial cores are considered. The "soft core" is described by the collective model with rotation-vibrational motion, while the "rigid core" is described by the triaxial rotor model, which is a limiting case of the collective model with only rotational motion. We show that the presence of the odd quasiparticle modifies the collective quadrupole dynamics of the core to appear more "rigid".

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arXiv2022

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

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 (NCCI) 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.

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arXiv2022

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

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 $^3\mathrm{He}$ as an illustrative testbed, we explore aspects of NCCI calculations with natural orbitals for the ground state of the $p$-shell neutron halo nucleus $^6\mathrm{He}$.

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arXiv2021

A greedy algorithm for computing eigenvalues of a symmetric matrix

We present a greedy algorithm for computing selected eigenpairs of a large sparse matrix $H$ that can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a small number of its components have large magnitudes, the proposed algorithm identifies the location of these components in a greedy manner, and obtains approximations to the desired eigenpairs of $H$ by computing eigenpairs of a submatrix extracted from the corresponding rows and columns of $H$. Even when the eigenvector is not completely localized, the approximate eigenvectors obtained by the greedy algorithm can be used as good starting guesses to accelerate the convergence of an iterative eigensolver applied to $H$. We discuss a few possibilities for selecting important rows and columns of $H$ and techniques for constructing good initial guesses for an iterative eigensolver using the approximate eigenvectors returned from the greedy algorithm. We demonstrate the effectiveness of this approach with examples from nuclear quantum many-body calculations, many-body localization studies of quantum spin chains and road network analysis.

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arXiv2020

From bound states to the continuum

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.

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