Nuclear Structure with Unitarily Transformed Two-Body plus Phenomenological Three-Body Interactions
The importance of three-nucleon forces for a variety of nuclear structure phenomena is apparent in various investigations. This thesis provides a first step towards the inclusion of realistic three-nucleon forces by studying simple phenomenological three-body interactions. The Unitary Correlation Op...
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| Format: | Others |
| Language: | English en |
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2011
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| Online Access: | http://tuprints.ulb.tu-darmstadt.de/2422/1/AnnekeGuenther_Dissertation.pdf Günther, Anneke <http://tuprints.ulb.tu-darmstadt.de/view/person/G=FCnther=3AAnneke=3A=3A.html> : Nuclear Structure with Unitarily Transformed Two-Body plus Phenomenological Three-Body Interactions. Technische Universität, Darmstadt [Ph.D. Thesis], (2011) |
| Summary: | The importance of three-nucleon forces for a variety of nuclear structure phenomena is apparent in various investigations. This thesis provides a first step towards the inclusion of realistic three-nucleon forces by studying simple phenomenological three-body interactions. The Unitary Correlation Operator Method (UCOM) and the Similarity Renormalization Group (SRG) provide two different approaches to derive soft phase-shift equivalent nucleon-nucleon (NN) interactions via unitary transformations. Although their motivations are quite different the NN interactions obtained with the two methods exhibit some similarities. The application of the UCOM- or SRG-transformed Argonne V18 potential in the Hartree-Fock (HF) approximation and including the second-order energy corrections emerging from many-body perturbation theory (MBPT) reveals that the systematics of experimental ground-state energies can be reproduced by some of the interactions considering a series of closed-shell nuclei across the whole nuclear chart. However, charge radii are systematically underestimated, especially for intermediate and heavy nuclei. This discrepancy to experimental data is expected to result from neglected three-nucleon interactions. As first ansatz for a three-nucleon force, we consider a finite-range three-body interaction of Gaussian shape. Its influence on ground-state energies and charge radii is discussed in detail on the basis of HF plus MBPT calculations and shows a significant improvement in the description of experimental data. As the handling of the Gaussian three-body interaction is time-extensive, we show that it can be replaced by a regularized three-body contact interaction exhibiting a very similar behavior. An extensive study characterizes its properties in detail and confirms the improvements with respect to nuclear properties. To take into account information of an exact numerical solution of the nuclear eigenvalue problem, the No-Core Shell Model is applied to calculate the 4He ground-state energy. As they are of direct interest for nuclear astrophysics collective excitation modes, namely giant resonances, are investigated in the framework of the Random Phase Approximation. Including the full three-body interaction would be very time-demanding. Therefore, a density-dependent two-body interaction is used instead. This simple interaction leads to a significant improvement in the description of the isovector dipole and isoscalar quadrupole resonances while the isoscalar monopole resonances remain in good agreement with experimental data compared to the results obtained with pure unitarily transformed two-body interactions. |
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