Ab Initio Nuclear Thermodynamics

Structure Factors for Hot Neutron Matter from Ab Initio Lattice Simulations with High-Fidelity Chiral Interactions

We present the first ab initio lattice calculations of spin and density correlations in hot neutron matter using high-fidelity interactions at next-to-next-to-next-to-leading order in chiral effective field theory. These correlations have a large impact on neutrino heating and shock revival in core-collapse supernovae and are encapsulated in functions called structure factors. Unfortunately, calculations of structure factors using high-fidelity chiral interactions were well out of reach using existing computational methods. In this Letter, we solve the problem using a computational approach called the rank-one operator (RO) method. The RO method is a general technique with broad applications to simulations of fermionic many-body systems. It solves the problem of exponential scaling of computational effort when using perturbation theory for higher-body operators and higher-order corrections. Using the RO method, we compute the vector and axial static structure factors for hot neutron matter as a function of temperature and density. The ab initio lattice results are in good agreement with virial expansion calculations at low densities but are more reliable at higher densities. Random phase approximation codes used to estimate neutrino opacity in core-collapse supernovae simulations can now be calibrated with ab initio lattice calculations.

Wavefunction matching for solving quantum many-body problems

Ab initio calculations have an essential role in our fundamental understanding of quantum many-body systems across many subfields, from strongly correlated fermions1-3 to quantum chemistry4-6 and from atomic and molecular systems7-9 to nuclear physics10-14. One of the primary challenges is to perform accurate calculations for systems where the interactions may be complicated and difficult for the chosen computational method to handle. Here we address the problem by introducing an approach called wavefunction matching. Wavefunction matching transforms the interaction between particles so that the wavefunctions up to some finite range match that of an easily computable interaction. This allows for calculations of systems that would otherwise be impossible owing to problems such as Monte Carlo sign cancellations. We apply the method to lattice Monte Carlo simulations15,16 of light nuclei, medium-mass nuclei, neutron matter and nuclear matter. We use high-fidelity chiral effective field theory interactions17,18 and find good agreement with empirical data. These results are accompanied by insights on the nuclear interactions that may help to resolve long-standing challenges in accurately reproducing nuclear binding energies, charge radii and nuclear-matter saturation in ab initio calculations19,20.

Nuclear Charge Radii of Silicon Isotopes

The nuclear charge radius of ^{32}Si was determined using collinear laser spectroscopy. The experimental result was confronted with ab initio nuclear lattice effective field theory, valence-space in-medium similarity renormalization group, and mean field calculations, highlighting important achievements and challenges of modern many-body methods. The charge radius of ^{32}Si completes the radii of the mirror pair ^{32}Ar-^{32}Si, whose difference was correlated to the slope L of the symmetry energy in the nuclear equation of state. Our result suggests L≤60  MeV, which agrees with complementary observables.

Ab Initio Calculation of the Alpha-Particle Monopole Transition Form Factor

We present a parameter-free ab initio calculation of the α-particle monopole transition form factor in the framework of nuclear lattice effective field theory. We use a minimal nuclear interaction that was previously used to reproduce the ground state properties of light nuclei, medium-mass nuclei, and neutron matter simultaneously with no more than a few percent error in the energies and charge radii. The results for the monopole transition form factor are in good agreement with recent precision data from Mainz.

Floating Block Method for Quantum Monte Carlo Simulations

Quantum Monte Carlo simulations are powerful and versatile tools for the quantum many-body problem. In addition to the usual calculations of energies and eigenstate observables, quantum Monte Carlo simulations can in principle be used to build fast and accurate many-body emulators using eigenvector continuation or design time-dependent Hamiltonians for adiabatic quantum computing. These new applications require something that is missing from the published literature, an efficient quantum Monte Carlo scheme for computing the inner product of ground state eigenvectors corresponding to different Hamiltonians. In this work, we introduce an algorithm called the floating block method, which solves the problem by performing Euclidean time evolution with two different Hamiltonians and interleaving the corresponding time blocks. We use the floating block method and nuclear lattice simulations to build eigenvector continuation emulators for energies of ^{4}He, ^{8}Be, ^{12}C, and ^{16}O nuclei over a range of local and nonlocal interaction couplings. From the emulator data, we identify the quantum phase transition line from a Bose gas of alpha particles to a nuclear liquid.

Emergent geometry and duality in the carbon nucleus

The carbon atom provides the backbone for the complex organic chemistry composing the building blocks of life. The physics of the carbon nucleus in its predominant isotope, ¹²C, is similarly full of multifaceted complexity. Here we provide a model-independent density map of the geometry of the nuclear states of ¹²C using the ab initio framework of nuclear lattice effective field theory. We find that the well-known but enigmatic Hoyle state is composed of a "bent-arm" or obtuse triangular arrangement of alpha clusters. We identify all of the low-lying nuclear states of ¹²C as having an intrinsic shape composed of three alpha clusters forming either an equilateral triangle or an obtuse triangle. The states with the equilateral triangle formation also have a dual description in terms of particle-hole excitations in the mean-field picture.

Nuclear Equation of State for Arbitrary Proton Fraction and Temperature Based on Chiral Effective Field Theory and a Gaussian Process Emulator

We calculate the equation of state of asymmetric nuclear matter at finite temperature based on chiral effective field theory interactions to next-to-next-to-next-to-leading order. Our results assess the theoretical uncertainties from the many-body calculation and the chiral expansion. Using a Gaussian process emulator for the free energy, we derive the thermodynamic properties of matter through consistent derivatives and use the Gaussian process to access arbitrary proton fraction and temperature. This enables a first nonparametric calculation of the equation of state in beta equilibrium, and of the speed of sound and the symmetry energy at finite temperature. Moreover, our results show that the thermal part of the pressure decreases with increasing densities.

Spontaneity of nuclear fusion: a qualitative analysis via classical thermodynamics

Background: So far the feasibility of nuclear reactions has been studied only through the evaluation of the reaction rate, which gives us information about the kinetics, while the thermodynamic analysis has been limited to evaluations of the change in enthalpy without any consideration of the change in entropy. Methods: This work examines the thermodynamics of nuclear fusion reactions through a simplified approach. The analysis introduces the thermodynamic study of fission and fusion reactions through their comparison with a chemical process. Results: The main result is that fission reactions are always spontaneous (ΔG < 0) since a lot of energy is released in the form of heat and the system moves spontaneously towards a more disordered state. In contrast, fusion reactions are spontaneous only when the enthalpic contribution of the change in Gibbs energy overcomes the entropic contribution. This condition is verified when the temperature of the process is below a characteristic value T*, calculated as the ratio between the energy corresponding to the mass defect and the change of entropy of the fusion reaction. Conclusions: Due to the unavailability of data related to entropy changes in fusion reactions, only a qualitative thermodynamic analysis has been carried out. Through such analysis, the influence of the operating conditions over the spontaneity of fusion processes has been discussed. The final considerations emphasize the role of the thermodynamics analysis that should be implemented in the current studies that, so far, have been mainly based on the assessment of the reaction rate and exothermicity of fusion reactions.