A broad variety of many-body methods exists for the investigation of ground-state properties, ranging from sophisticated ab initio approaches to traditional, phenomenological models. The description of low-lying excited states of medium-mass nuclei with ab initio methods has also become possible through recent progress in many-body theory. For collective modes at higher energies, however, these methods usually cannot be applied. Therefore, when describing collective excitations either completely phenomenological, macroscopic models are employed or microscopic models using phenomenological interactions. One of the microscopic models well suited for the calculation of collective properties is the random-phase approximation (RPA). In the past, the use of phenomenological interactions for RPA has shown promising results. However, the application of chiral NN interactions yielded transitions at significantly too high energies, far from agreement with experimental data. This thesis focuses on the description of collective modes using both RPA and its second-order extension, SRPA. In contrast to previous research endeavors, we employ chiral NN+3N interactions. The use of chiral interactions is an important first step for describing ground-state, excitation and collective properties on an equal foundation. We find that the inclusion of 3N terms is crucial for RPA calculations and the prediction for collective modes is drastically improved through the 3N terms. For SRPA we show first-ever results with chiral interactions, again leading to an improvement in the predictions. For a successful ab initio description of ground-state properties the inclusion of correlations is of paramount importance. Past RPA calculations have been performed using the quasi-boson approximation, effectively neglecting ground-state correlations. Using RPA, the next step along the path towards an ab initio description of collective properties will, therefore, be the inclusion of correlations. To that end, we extend the RPA formalism to include ground-state correlations from two different many-body methods, the in-medium similarity renormalization group (IM-SRG) and coupled-cluster theory with singles and doubles excitations (CCSD). Both methods have been applied with great success for the calculation of ground-state energies. We develop a formalism based on density matrices for CC-RPA that enables RPA based on an CCSD ground state. The use of IM-SRG transformed matrix elements gives us the possibility to include ground-state correlations even at the level of SRPA. For both methods we observe a strong upward shift in the strength distributions, and, unexpectedly, we find a good agreement between IM-RPA and CC-RPA results. The structure of the transitions remains largely unchanged. We conclude that correlations have significant impact on the energetic positions, but not on the structure of the strength distributions. Employing IM-SRPA we find a strong downward shift in energy similar to the case of SRPA. The agreement of both methods with experiment is comparable.
A broad variety of many-body methods exists for the investigation of ground-state properties, ranging from sophisticated ab initio approaches to traditional, phenomenological models. The description of low-lying excited states of medium-mass nuclei with ab initio methods has also become possible through recent progress in many-body theory. For collective modes at higher energies, however, these methods usually cannot be applied. Therefore, when describing collective excitations either completely phenomenological, macroscopic models are employed or microscopic models using phenomenological interactions. One of the microscopic models well suited for the calculation of collective properties is the random-phase approximation (RPA). In the past, the use of phenomenological interactions for RPA has shown promising results. However, the application of chiral NN interactions yielded transitions at significantly too high energies, far from agreement with experimental data. This thesis focuses on the description of collective modes using both RPA and its second-order extension, SRPA. In contrast to previous research endeavors, we employ chiral NN+3N interactions. The use of chiral interactions is an important first step for describing ground-state, excitation and collective properties on an equal foundation. We find that the inclusion of 3N terms is crucial for RPA calculations and the prediction for collective modes is drastically improved through the 3N terms. For SRPA we show first-ever results with chiral interactions, again leading to an improvement in the predictions. For a successful ab initio description of ground-state properties the inclusion of correlations is of paramount importance. Past RPA calculations have been performed using the quasi-boson approximation, effectively neglecting ground-state correlations. Using RPA, the next step along the path towards an ab initio description of collective properties will, therefore, be the inclusion of correlations. To that end, we extend the RPA formalism to include ground-state correlations from two different many-body methods, the in-medium similarity renormalization group (IM-SRG) and coupled-cluster theory with singles and doubles excitations (CCSD). Both methods have been applied with great success for the calculation of ground-state energies. We develop a formalism based on density matrices for CC-RPA that enables RPA based on an CCSD ground state. The use of IM-SRG transformed matrix elements gives us the possibility to include ground-state correlations even at the level of SRPA. For both methods we observe a strong upward shift in the strength distributions, and, unexpectedly, we find a good agreement between IM-RPA and CC-RPA results. The structure of the transitions remains largely unchanged. We conclude that correlations have significant impact on the energetic positions, but not on the structure of the strength distributions. Employing IM-SRPA we find a strong downward shift in energy similar to the case of SRPA. The agreement of both methods with experiment is comparable.
A general implementation of the equation-of-motion (EOM) formalism for correlated many-body states is presented and applied to the description of collective excitations in atomic nuclei. While EOM approaches are traditionally formulated on top of independent-particle reference states, the present work extends the method to correlated reference states generated by modern many-body solvers. This formulation enables a consistent treatment of ground-state correlations and excited-state dynamics within a unified framework. Particular emphasis is placed on collective nuclear excitations employing chiral nuclear Hamiltonians in an ab initio context. The approach is motivated by the renewed interest in EOM techniques across several fields, including quantum chemistry and quantum computing, where they provide efficient and systematically improvable descriptions of excitation spectra. The present results demonstrate that the EOM framework offers a flexible and powerful tool for the microscopic description of nuclear spectroscopy beyond the traditional mean-field paradigm.