Quantum Monte Carlo calculations of nucleon systems

Project: Research project

Description

Overview: Page A The main thrust of the work is to continue to develop and use quantum Monte Carlo methods, in particular the auxiliary field diffusion Monte Carlo (AFDMC) method, to solve for the properties of nonrelativistic nucleons interacting via realistic two- and three-body potentials that have been fit to experimental scattering and other data. Intellectual Merit : The nuclear many-body problem is complicated because realistic interactions have both strong spin-isospin and nonlocal or momentum dependence. While the two-body interaction for relative energies less than about 300 MeV is well determined from scattering data, the three- or more body parts are only determined by taking forms dictated by more fundamental field theories and fitting these to calculated properties of more complicated nuclei or nuclear matter. In order to understand the abilities and limitations of using a model of nonrelativistic nucleons interacting via potentials, it is necessary to have accurate calculational methods. We have already demonstrated that AFDMC can give accurate results for both open and closed shell nuclei and nuclear matter. We have used a simplified two-body interactions (Argonne v6 and v8) that leave out weaker, but still important, contributions like the isospin dependent commutator terms in the three-body interactions. Much of the proposed work will be continuing the development and applications of the Monte Carlo methods so that the most realistic available nucleon interactions can be used, and the accuracy of the results improved by improving the trial wave functions that are used to reduce the statistical errors and control the fermion sign problem. Comparison with nuclear energy levels and response functions will allow us to assess the accuracy of our methods. Good agreement with experiment will indicate that we can accurately calculate properties of nuclei and nuclear matter in regions where there is no experimental data, such as for astrophysically important processes (e.g. neutron rich matter, r-process nucleosynthesis). We can also use our results to parameterize the nuclear density functional in regions without experimental data, and predict new phenomena. Accurate calculations of heavier nuclei should indicate the limitations of the current potential models and ultimately the limitations of using a potential model. We propose to include some explicit pion degrees of freedom to explore the consequences of their addition. Broader Impacts : This project will continue training graduate students, both Ph.D. students and students enrolled in a research rotation with the PI. Undergraduate researchers will be involved in the project. The project allows the PI and students to attend scientific meetings to disseminate the results. The methods developed in this project can be and have been applied in other areas of strongly interacting many-body problems. Previous work developed for the nuclear Hamiltonian has been applied to a variety of cold atom problems and to electronic structure. The Monte Carlo expertise developed here has contributed to work on extracting electronic densities from X-ray free electron laser diffraction data.

Description

The supplement will allow the completion of the development of improved trial wave functions nuclei and nuclear matter for auxiliary field diffusion Monte Carlo and is in the intended scope of the original proposal. These trial functions will allow accurate calculations of heavier nuclei than previously, and improve the equation of state for superfluid phases in neutron stars. The funds, will support a graduate Ph.D. student allowing a full time effort on this research, and completion of the Ph.D. dissertation.
StatusFinished
Effective start/end date8/1/147/31/19

Funding

  • National Science Foundation (NSF): $392,870.00

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students
Monte Carlo method
many body problem
nuclei
heavy nuclei
nucleons
interactions
wave functions
commutators
supplements
nuclear energy
scattering
nuclear fusion
free electron lasers
thrust
neutron stars
proposals
pions
education
equations of state