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- All Subjects: Nuclear Physics
- All Subjects: Nuclear spin
- Creators: Schmidt, Kevin E
Description
Monte Carlo methods often used in nuclear physics, such as auxiliary field diffusion Monte Carlo and Green's function Monte Carlo, have typically relied on phenomenological local real-space potentials containing as few derivatives as possible, such as the Argonne-Urbana family of interactions, to make sampling simple and efficient. Basis set methods such as no-core shell model or coupled-cluster techniques typically use softer non-local potentials because of their more rapid convergence with basis set size. These non-local potentials are typically defined in momentum space and are often based on effective field theory. Comparisons of the results of the two types of methods are complicated by the use of different potentials. This thesis discusses progress made in using such non-local potentials in quantum Monte Carlo calculations of light nuclei. In particular, it shows methods for evaluating the real-space, imaginary-time propagators needed to perform quantum Monte Carlo calculations using non-local potentials and universality properties of these propagators, how to formulate a good trial wave function for non-local potentials, and how to perform a "one-step" Green's function Monte Carlo calculation for non-local potentials.
ContributorsLynn, Joel E (Author) / Schmidt, Kevin E (Thesis advisor) / Alarcon, Ricardo (Committee member) / Lebed, Richard (Committee member) / Shovkovy, Igor (Committee member) / Shumway, John (Committee member) / Arizona State University (Publisher)
Created2013
Description
Spin-orbit interactions are important in determining nuclear structure. They lead to a shift in the energy levels in the nuclear shell model, which could explain the sequence of magic numbers in nuclei. Also in nucleon-nucleon scattering, the large nucleon polarization observed perpendicular to the plane of scattering needs to be explained by adding the spin-orbit interactions in the potential. Their effects change the equation of state and other properties of nuclear matter. Therefore, the simulation of spin-orbit interactions is necessary in nuclear matter.
The auxiliary field diffusion Monte Carlo is an effective and accurate method for calculating the ground state and low-lying exited states in nuclei and nuclear matter. It has successfully employed the Argonne v6' two-body potential to calculate the equation of state in nuclear matter, and has been applied to light nuclei with reasonable agreement with experimental results. However, the spin-orbit interactions were not included in the previous simulations, because the isospin-dependent spin-orbit potential is difficult in the quantum Monte Carlo method. This work develops a new method using extra auxiliary fields to break up the interactions between nucleons, so that the spin-orbit interaction with isospin can be included in the Hamiltonian, and ground-state energy and other properties can be obtained.
The auxiliary field diffusion Monte Carlo is an effective and accurate method for calculating the ground state and low-lying exited states in nuclei and nuclear matter. It has successfully employed the Argonne v6' two-body potential to calculate the equation of state in nuclear matter, and has been applied to light nuclei with reasonable agreement with experimental results. However, the spin-orbit interactions were not included in the previous simulations, because the isospin-dependent spin-orbit potential is difficult in the quantum Monte Carlo method. This work develops a new method using extra auxiliary fields to break up the interactions between nucleons, so that the spin-orbit interaction with isospin can be included in the Hamiltonian, and ground-state energy and other properties can be obtained.
ContributorsZhang, Jie (Author) / Schmidt, Kevin E (Thesis advisor) / Alarcon, Ricardo (Committee member) / Lebed, Richard (Committee member) / Shumway, John (Committee member) / Arizona State University (Publisher)
Created2014
Description
Quantum Monte Carlo is one of the most accurate ab initio methods used to study nuclear physics. The accuracy and efficiency depend heavily on the trial wave function, especially in Auxiliary Field Diffusion Monte Carlo (AFDMC), where a simplified wave function is often used to allow calculations of larger systems. The simple wave functions used with AFDMC contain short range correlations that come from an expansion of the full correlations truncated to linear order. I have extended that expansion to quadratic order in the pair correlations. I have investigated this expansion by keeping the full set of quadratic correlations as well an expansion that keeps only independent pair quadratic correlations. To test these new wave functions I have calculated ground state energies of 4He, 16O, 40Ca and symmetric nuclear matter at saturation density ρ = 0.16 fm−3 with 28 particles in a periodic box. The ground state energies calculated with both wave functions decrease with respect to the simpler wave function with linear correlations only for all systems except 4He for both variational and AFDMC calculations. It was not expected that the ground state energy of 4He would decrease due to the simplicity of the alpha particle wave function. These correlations have also been applied to study alpha particle formation in neutron rich matter, with applications to neutron star crusts and neutron rich nuclei. I have been able to show that this method can be used to study small clusters as well as the effect of external nucleons on these clusters.
ContributorsPetrie, Cody L (Author) / Schmidt, Kevin E (Thesis advisor) / Shovkovy, Igor A. (Committee member) / Beckstein, Oliver (Committee member) / Alarcon, Ricardo O (Committee member) / Arizona State University (Publisher)
Created2019