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Parquet theory in nuclear structure calculations

Elise Bergli

The thesis concerns a numerical implementation of the Parquet summation of diagrams within Green's functions theory applied to calculations of nuclear systems. The main motivation has been to investigate whether it is possible to develop this approach to a level comparable in accuracy and reliability to other ab initio nuclear structure methods. \n\nThe Green's functions approach is theoretically well-established in many-body theory, but to our knowledge, no actual application to nuclear systemshas been previously published. It has a number of desirable properties, foremostthe gently scaling with system size compared to direct diagonalization and the closeness to experimentally accessible quantities. The main drawback is the\nnumerical instabilities due to the pole structure of the one-particle propagator, leading to convergence difficulties. This issue is one of the main focal points of the work presented in this thesis, and strategies to improve the convergence properties are described and investigated. \n\nWe have applied the method both to a simple model which can be solved by exact diagonalization and to the more realistic 4He system. The results shows that our implementation is close to the exact solution in the simple model as long as the interaction strengths are small. As the number of particles increases,\nconvergence is increasingly hard to obtain. In the 4He case, we obtain results in the vicinity of the results from comparable approaches. The numerical in-stabilities in the current implementation still prevents the desired accuracy and\nstability necessary to achieve the current benchmark standards.The thesis concerns a numerical implementation of the Parquet summation of diagrams within Green's functions theory applied to calculations of nuclear systems. The main motivation has been to investigate whether it is possible to develop this approach to a level comparable in accuracy and reliability to other ab initio nuclear structure methods. \n\nThe Green's functions approach is theoretically well-established in many-body theory, but to our knowledge, no actual application to nuclear systemshas been previously published. It has a number of desirable properties, foremostthe gently scaling with system size compared to direct diagonalization and the closeness to experimentally accessible quantities. The main drawback is the\nnumerical instabilities due to the pole structure of the one-particle propagator, leading to convergence difficulties. This issue is one of the main focal points of the work presented in this thesis, and strategies to improve the convergence properties are described and investigated. \n\nWe have applied the method both to a simple model which can be solved by exact diagonalization and to the more realistic 4He system. The results shows that our implementation is close to the exact solution in the simple model as long as the interaction strengths are small. As the number of particles increases,\nconvergence is increasingly hard to obtain. In the 4He case, we obtain results in the vicinity of the results from comparable approaches. The numerical in-stabilities in the current implementation still prevents the desired accuracy and\nstability necessary to achieve the current benchmark standards.

Jan 1, 20101 citation

Summation of Parquet diagrams as an ab initio method in nuclear structure calculations

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