arXiv subjects

N. Schunck

Publications and source records attributed to N. Schunck.

At least 19 recordsLinked to original sources

arXiv2024

Optimized nuclear energy density functionals including long-range pion contributions

Nuclear energy density functionals successfully reproduce properties of nuclei across almost the entire nuclear chart. However, nearly all available functionals are phenomenological in nature and lack a rigorous connection to systematically improvable nuclear forces. This issue might be solved with an energy density functional obtained from first principles. As an intermediate step towards this goal we construct the GUDE family of functionals that is obtained from a hybrid scheme consisting of long-range pion-exchange contributions derived from chiral effective field theory at the Hartree-Fock level and a phenomenological Skyrme part. When including pion contributions beyond next-to-leading order in the chiral expansion, we find significant improvements over a reference Skyrme functional constructed following the same protocol. We analyze the importance of different pion contributions and identify which terms drive the observed improvements. Since pions are incorporated without adding further optimization parameters to the functionals, the improvements can be attributed to the functional form of these terms. Our work therefore suggests that the considered chiral contributions constitute useful ingredients for true ab initio energy density functionals.

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arXiv2022

Microscopic Calculation of Fission Product Yields for Odd-Mass Nuclei

Fission data are essential inputs to reaction networks involved in nucleosynthesis simulations and nuclear forensics. In such applications as well as in the description of multi-chance fission, the characteristics of fission for odd-mass nuclei are just as important as those for even-even nuclei. The fission theories that aim at explicitly describing fission dynamics are typically based on some variant of the nuclear mean-field theory. In such cases, the treatment of systems with an odd number of particles is markedly more involved, both formally and computationally. In this article, we use the blocking prescription of the Hartree-Fock-Bogoliubov theory with Skyrme energy functionals to compute the deformation properties of odd-mass uranium isotopes. We show that the resulting fission fragment distributions depend quite significantly on the spin of the odd neutron. By direct calculation of the spin distribution of the fissioning nucleus, we propose a methodology to rigorously predict the charge and mass distributions in odd-mass nuclei.

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arXiv2022

Axially-deformed solution of the Skyrme-Hartree-Fock-Bogoliubov equations using the transformed harmonic oscillator basis (IV) hfbtho (v4.0): A new version of the program

We describe the new version 4.0 of the code hfbtho that solves the nuclear Hartree-Fock-Bogoliubov problem by using the deformed harmonic oscillator basis in cylindrical coordinates. In the new version, we have implemented the restoration of rotational, particle number, and reflection symmetry. The restoration of rotational symmetry does not require using bases closed under rotation. Furthermore, the SeaLL1 functional was added and the calculation of the Coulomb potential was improved. Finally, the code has been refactored to facilitate maintenance and future developments.

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arXiv2021

Two-body weak currents in heavy nuclei

In light and medium-mass nuclei, two-body weak currents from chiral effective field theory account for a significant portion of the phenomenological quenching of Gamow-Teller transition matrix elements. Here we examine the systematic effects of two-body axial currents on Gamow-Teller strength and $β$-decay rates in heavy nuclei within energy-density functional theory. Using a Skyrme functional and the charge-changing finite amplitude method, we add the contributions of two-body currents to the usual one-body linear response in the Gamow-Teller channel, both exactly and though a density-matrix expansion. The two-body currents, as expected, usually quench both summed Gamow-Teller strength and decay rates, but by an amount that decreases as the neutron excess grows. In addition, they can enhance individual low-lying transitions, leading to decay rates that are quite different from those that an energy-independent quenching would produce, particularly in neutron-rich nuclei. We show that both these unexpected effects are related to changes in the total nucleon density as the number of neutrons increases.

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arXiv2021

Fission fragments intrinsic spins and their correlations

The intrinsic spins and their correlations are the least understood characteristics of fission fragments from both theoretical and experimental points of view. In many nuclear reactions the emerging fragments are typically excited and acquire an intrinsic excitation energy and an intrinsic spin depending on the type of the reactions and interaction mechanism. Both the intrinsic excitation energies and the fragments intrinsic spins and parities are controlled by the interaction mechanism and conservations laws, which lead to their correlations and determines the character of their de-excitation mechanism. We outline here a framework for the theoretical extraction of the intrinsic spin distributions of the fragments and their correlations within the fully microscopic real-time density functional theory formalism and illustrate it on the example of induced fission of $^{236}$U and $^{240}$Pu, using two nuclear energy density functionals. These fission fragment intrinsic spin distributions display new qualitative features previously not discussed in literature. Within this fully microscopic framework we extract for the first time the intrinsic spin distributions of fission fragments of $^{236}$U and $^{240}$Pu as well as the correlations of their intrinsic spins, which have been debated in literature for more than six decades with no definite conclusions so far.

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arXiv2020

A Bayesian Analysis of Nuclear Deformation Properties with Skyrme Energy Functionals

In spite of numerous scientific and practical applications, there is still no comprehensive theoretical description of the nuclear fission process based solely on protons, neutrons and their interactions. The most advanced simulations of fission are currently carried out within nuclear density functional theory (DFT). In spite of being fully quantum-mechanical and rooted in the theory of nuclear forces, DFT still depends on a dozen or so parameters characterizing the energy functional. Calibrating these parameters on experimental data results in uncertainties that must be quantified for applications. This task is very challenging because of the high computational cost of DFT calculations for fission. In this paper, we use Gaussian processes to build emulators of DFT models in order to quantify and propagate statistical uncertainties of theoretical predictions for a range of nuclear deformations relevant to describing the fission process.

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arXiv2020

Global Description of Beta Decay with the Axially-Deformed Skyrme Finite Amplitude Method: Extension to Odd-Mass and Odd-Odd Nuclei

We use the finite amplitude method (FAM), an efficient implementation of the quasiparticle random phase approximation, to compute beta-decay rates with Skyrme energy-density functionals for 3983 nuclei, essentially all the medium-mass and heavy isotopes on the neutron rich side of stability. We employ an extension of the FAM that treats odd-mass and odd-odd nuclear ground states in the equal filling approximation. Our rates are in reasonable agreement both with experimental data where available and with rates from other global calculations.

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arXiv2020

Calibration of Energy Density Functionals with Deformed Nuclei

Nuclear density functional theory is the prevalent theoretical framework for accurately describing nuclear properties at the scale of the entire chart of nuclides. Given an energy functional and a many-body scheme (e.g., single- or multireference level), the predictive power of the theory depends strongly on how the parameters of the energy functionals have been calibrated with experimental data. Expanded algorithms and computing power have enabled recent optimization protocols to include data in deformed nuclei in order to optimize the coupling constants of the energy functional. The primary motivation of this work is to test the robustness of such protocols with respect to some of the technical and numerical details of the underlying calculations, especially when the calibration explores a large parameter space. To this end, we quantify the effect of these uncertainties on both the optimization and statistical emulation of composite objective functions. We also emphasize that Bayesian calibration can provide better estimates of the theoretical errors used to define objective functions.

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arXiv2019

Fission in a microscopic framework: from basic science to support for applications

Recent developments, both in theoretical modeling and computational power, have allowed us to make progress on a goal not fully achieved yet in nuclear theory: a microscopic theory of nuclear fission. Even if the complete microscopic description remains a computationally demanding task, the information that can be provided by current calculations can be extremely useful to guide and constrain more phenomenological approaches, which are simpler to implement. First, a microscopic model that describes the real-time dynamics of the fissioning system can justify or rule out some of the approximations. Second, the microscopic approach can be used to obtain trends, e.g., with increasing excitation energy of the fissioning system, or even to compute observables that cannot be otherwise calculated in phenomenological approaches or that can be hindered by the limitations of the method. We briefly present in this contribution the time-dependent superfluid local density approximation (TDSLDA) approach to nuclear fission, approach that has become a very successful theoretical model in many areas of many-body research. The TDSLDA incorporates the effects of the continuum, the dynamics of the pairing field, and the numerical solution is implemented with controlled approximations and negligible numerical corrections. The main part of the current contribution will be dedicated to discussing the method, and recent results concerning the fission dynamics. In addition, we present results on the excitation energy sharing between the fragments, which are in agreement with a qualitative conclusions extracted from a limited number of experimental measurements of properties of prompt neutrons.

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arXiv2019

Microscopically based energy density functionals for nuclei using the density matrix expansion

While ab initio many-body techniques have been able to successfully describe the properties of light and intermediate mass nuclei based on chiral effective field theory interactions, neutron-rich nuclei still remain out of reach for these methods. Conversely, energy density functional approaches can be used to calculate properties of heavy nuclei but rely mostly on phenomenological interactions. A usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces was presented recently. The first component of this new set of functionals corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. The exchange term, which is a functional of the non-local density, is transformed into a local functional by applying the density matrix expansion. In order to reduce the computational cost due to the direct implementation of non-separable, local interactions in the Hartree term, we use an approximation to represent the regularized Yukawa functions in terms of a sum of (separable) Gaussian functions. These proceedings analyze the accuracy of such an approximation in terms of the number of Gaussian functions and look for an optimal value that gives an acceptable level of accuracy while maintaining the computational memory requirements in a many-body calculation as low as possible.

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arXiv2019

Propagation of Statistical Uncertainties of Skyrme Mass Models to Simulations of $r$-Process Nucleosynthesis

Uncertainties in nuclear models have a major impact on simulations that aim at understanding the origin of heavy elements in the universe through the rapid neutron capture process ($r$ process) of nucleosynthesis. Within the framework of the nuclear density functional theory, we use results of Bayesian statistical analysis to propagate uncertainties in the parameters of energy density functionals to the predicted $r$-process abundance pattern, by way not only of the nuclear masses but also through the influence of the masses on $β$-decay and neutron capture rates. We additionally make the first identifications of specific parameters of Skyrme-like energy density functionals which are correlated with particular aspects of the $r$-process abundance pattern. While previous studies have explored the reduction in the abundance pattern uncertainties due to anticipated new measurements of neutron-rich nuclei, here we point out that an even larger reduction will occur when these new measurements are used to reduce the uncertainty of model predictions of masses, which are then propagated through to the abundance pattern. We make a quantitative prediction for how large this reduction will be.

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arXiv2018

From Asymmetric to Symmetric Fission in the Fermium Isotopes within the Time-Dependent GCM Formalism

Predicting the properties of neutron-rich nuclei far from the valley of stability is one of the major challenges of modern nuclear theory. In heavy and superheavy nuclei, a difference of only a few neutrons is sufficient to change the dominant fission mode. A theoretical approach capable of predicting such rapid transitions for neutron-rich systems would be a valuable tool to better understand r-process nucleosynthesis or the decay of super-heavy elements. In this work, we investigate for the first time the transition from asymmetric to symmetric fission through the calculation of primary fission yields with the time-dependent generator coordinate method (TDGCM). We choose here the transition in neutron-rich Fermium isotopes, which was the first to be observed experimentally in the late seventies and is often used as a benchmark for theoretical studies. We compute the primary fission fragment mass and charge yields for 254 Fm, 256 Fm and 258 Fm from the TDGCM under the Gaussian overlap approximation. The static part of the calculation (generation of a potential energy surface) consists in a series of constrained Hartree-Fock-Bogoliubov calculations based on the D1S, D1M or D1N parameterizations of the Gogny effective interaction in a two-center harmonic oscillator basis. The 2-dimensional dynamics in the collective space spanned by the quadrupole and octupole moments is then computed with the finite element solver FELIX-2.0. The available experimental data and the TDGCM post-dictions are consistent and agree especially on the position in the Fermium isotopic chain at which the transition occurs. The main limitation of the method lies in the presence of discontinuities in the 2-dimensional manifold of generator states.

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arXiv2018

Real time description of fission

Using the time-dependent superfluid local density approximation, the dynamics of fission is investigated in real time from just beyond the saddle to fully separated fragments. Simulations produced in this fully microscopic framework can help to assess the validity of the current approaches to fission, and to obtain estimate of fission observables. In this contribution, we concentrate on general aspects of fission dynamics.

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arXiv2018

Microscopically-based energy density functionals for nuclei using the density matrix expansion: Full optimization and validation

We seek to obtain a usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces. We thus consider a functional obtained from the density matrix expansion of local nuclear potentials from chiral effective field theory. We propose a parametrization of this functional carefully calibrated and validated on selected ground-state properties that is suitable for large-scale calculations of nuclear properties. The first component of this functional is a non-local functional of the density and corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. A second component is a local functional of the density and is obtained by applying the density matrix expansion to the exchange part (Fock term) of the expectation value of the local chiral potential. We apply the UNEDF2 optimization protocol to determine the coupling constants of this energy functional. We obtain a set of microscopically-constrained functionals for local chiral potentials from leading-order up to next-to-next-to-leading order with and without three-body forces and contributions from $Δ$ excitations. These functionals are validated on the calculation of nuclear and neutron matter, nuclear mass tables, single-particle shell structure in closed-shell nuclei and the fission barrier of $^{240}$Pu. Quantitatively, they perform noticeable better than the more phenomenological Skyrme functionals. The inclusion of higher-order terms in the chiral perturbation expansion seems to produce a systematic improvement in predicting nuclear binding energies. This result is especially promising since all the fits have been performed at the single reference level of the energy density functional approach, where important collective correlations such as center-of-mass correction have not been taken into account yet.

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arXiv2017

FELIX-2.0: New version of the finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

The time-dependent generator coordinate method (TDGCM) is a powerful method to study the large amplitude collective motion of quantum many-body systems such as atomic nuclei. Under the Gaussian Overlap Approximation (GOA), the TDGCM leads to a local, time-dependent Schrödinger equation in a multi-dimensional collective space. In this paper, we present the version 2.0 of the code FELIX that solves the collective Schrödinger equation in a finite element basis. This new version features: (i) the ability to solve a generalized TDGCM+GOA equation with a metric term in the collective Hamiltonian, (ii) support for new kinds of finite elements and different types of quadrature to compute the discretized Hamiltonian and overlap matrices, (iii) the possibility to leverage the spectral element scheme, (iv) an explicit Krylov approximation of the time propagator for time integration instead of the implicit Crank-Nicolson method implemented in the first version, (v) an entirely redesigned workflow. We benchmark this release on an analytic problem as well as on realistic two-dimensional calculations of the low-energy fission of Pu240 and Fm256. Low to moderate numerical precision calculations are most efficiently performed with simplex elements with a degree 2 polynomial basis. Higher precision calculations should instead use the spectral element method with a degree 4 polynomial basis. We emphasize that in a realistic calculation of fission mass distributions of Pu240, FELIX-2.0 is about 20 times faster than its previous release (within a numerical precision of a few percents).

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arXiv2017

Nuclear Fission: from more phenomenology and adjusted parameters to more fundamental theory and increased predictive power

Two major recent developments in theory and computational resources created the favorable conditions for achieving a microscopic description of nuclear fission almost eighty years after its discovery in 1939 by Hahn and Strassmann (1930). The first major development was in theory, the extension of the Time-Dependent Density Functional Theory (TDDFT) to superfluid fermion systems. The second development was in computing, the emergence of powerful enough supercomputers capable of solving the complex systems of equations describing the time evolution in three dimensions without any restrictions of hundreds of strongly interacting nucleons. Even though the available nuclear energy density functionals (NEDFs) are phenomenological still, their accuracy is improving steadily and the prospects of being able to perform calculations of the nuclear fission dynamics and to predict many properties of the fission fragments, otherwise not possible to extract from experiments, are within reach, all without making recourse anymore to uncontrollable assumptions and simplified phenomenological models.

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arXiv2017

Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (III) hfbtho (v3.00): a new version of the program

We describe the new version 3.00 of the code HFBTHO that solves the nuclear Hartree-Fock (HF) or Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle-hole and particle-particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck (iv) the regularization of zero-range pairing forces (v) the calculation of localization functions (vi)MPI interface for large-scale mass table calculations.

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arXiv2016

Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VIII) hfodd (v2.73y): a new version of the program

We describe the new version (v2.73y) of the code HFODD which solves the nuclear Skyrme Hartree-Fock or Skyrme Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton-neutron mixing in the particle-hole channel for Skyrme functionals, (ii) the Gogny force in both particle-hole and particle-particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy of each fragment, (v) the new version 200d of the code HFBTHO, together with an enhanced interface between HFBTHO and HFODD, (vi) parallel capabilities, significantly extended by adding several restart options for large-scale jobs, (vii) the Lipkin translational energy correction method with pairing, (viii) higher-order Lipkin particle-number corrections, (ix) interface to a program plotting single-particle energies or Routhians, (x) strong-force isospin-symmetry-breaking terms, and (xi) the Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin. Finally, an important bug related to the calculation of the entropy at finite temperature and several other little significant errors of the previous published version were corrected.

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