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Register a new userSymmetric nuclear matter with chiral three-nucleon forces in the self-consistent Greens functions approach
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We present calculations for symmetric nuclear matter using chiral nuclear interactions within the Self-Consistent Greens Functions approach in the ladder approximation. Three-body forces are included via effective one-body and two-body interactions, computed from an uncorrelated average over a third particle. We discuss the effect of the three-body forces on the total energy, computed with an extended Galitskii-Migdal-Koltun sum-rule, as well as on single-particle properties. Saturation properties are substantially improved when three-body forces are included, but there is still some underlying dependence on the SRG evolution scale.
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The present thesis aims at studying the properties of symmetric nuclear and pure neutron matter from a Greens functions point of view, including two-body and three-body chiral forces. An extended self-consistent Greens function formalism is defined to consistently incorporate three-body forces in the many-body calculations. The effect of three-nucleon interactions is included via the construction of a dressed two-body density dependent force. This is obtained performing an average of the leading order three-body terms in the chiral effective field theory expansion. The dressed force corresponds to the use of an in-medium propagator in the average which takes into account the correlations characterizing the system at each stage of the many-body calculation. The total energy of the system is obtained by means of a modified Galitskii-Migdal-Koltun sumrule to correctly account for the effect of three-body forces. Microscopic as well as macroscopic properties of symmetric nuclear and pure neutron matter are analyzed in detailed.
A systematic study of the microscopic and thermodynamical properties of pure neutron matter at finite temperature within the Self-Consistent Greens Function approach is performed. The model dependence of these results is analyzed by both comparing the results obtained with two different microscopic interactions, the CD-BONN and the Argonne V18 potentials, and by analyzing the results obtained with other approaches, such as the Brueckner--Hartree--Fock approximation, the variational approach and the virial expansion.
We extend the self-consistent Greens functions formalism to take into account three-body interactions. We analyze the perturbative expansion in terms of Feynman diagrams and define effective one- and two-body interactions, which allows for a substantial reduction of the number of diagrams. The procedure can be taken as a generalization of the normal ordering of the Hamiltonian to fully correlated density matrices. We give examples up to third order in perturbation theory. To define nonperturbative approximations, we extend the equation of motion method in the presence of three-body interactions. We propose schemes that can provide nonperturbative resummation of three-body interactions. We also discuss two different extensions of the Koltun sum rule to compute the ground state of a many-body system.
We investigate the roles of chiral three-nucleon force (3NF) in nucleon-nucleus elastic scattering, using the standard framework based on the Brueckner-Hartree-Fock method for nuclear matter and the $g$-matrix folding model for the nucleon-nucleus scattering. In nuclear matter, chiral 3NF at NNLO level (mainly the 2$pi$-exchange diagram) makes the single particle potential less attractive for the singlet-even channel and more absorptive for the triplet channels. The single-particle potential calculated from chiral two-nucleon force (2NF) at N$^{3}$LO level is found to be close to that from Bonn-B 2NF. The Melbourne $g$-matrix interaction is a practical effective interaction constructed by localizing the $g$-matrices calculated from Bonn-B 2NF. We then introduce the chiral-3NF effects to the local Melbourne $g$-matrix interaction. For nucleon-nucleus elastic scattering on various targets at 65 MeV, chiral 3NF makes the folding potential less attractive and more absorptive. The novel property for the imaginary part is originated in the enhancement of tensor correlations due to chiral 3NF. The two effects are small for differential cross sections and vector analyzing powers at the forward and middle angles where the experimental data are available. If backward measurements are done, the data will reveal the effects of chiral 3NF.
Background: Modern ab initio theory combined with high-quality nucleon-nucleon (NN) and three-nucleon (3N) interactions from chiral effective field theory (EFT) can provide a predictive description of low-energy light-nuclei reactions relevant for astrophysics and fusion-energy applications. However, the high cost of computations has so far impeded a complete analysis of the uncertainty budget of such calculations. Purpose: Starting from NN potentials up to fifth order (N4LO) combined with leading-order 3N forces, we study how the order-by-order convergence of the chiral expansion and confidence intervals for the 3N contact and contact-plus-one-pion-exchange low-energy constants (cE and cD) contribute to the overall uncertainty budget of many-body calculations of neutron-He elastic scattering. Methods: We compute structure and reaction observables for three-, four- and five-nucleon systems within the ab initio frameworks of the no-core shell model an no-core shell model with continuum. Using a small set of design runs, we construct a Gaussian process model (GPM) that acts as a statistical emulator for the theory. With this, we gain insight into how uncertainties in the 3N low-energy constants propagate throughout the calculation and determine the Bayesian posterior distribution of these parameters with Markov-Chain Monte-Carlo.
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