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Collective Excitations with Chiral NN+3N Interactions from Coupled-Cluster and In-Medium SRG

Richard Trippel

Published Jan 1, 2016• 2 citations
Publisher

Abstract

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.

DOI
10.26083/tuprints-00005883

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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.
Collective excitations are one of the most common and interesting features of many-body systems. Of particular interest are those collective modes which can be interpreted in terms of vibrations. Nuclei show a large variety of such modes, both low-lying and high-lying. In particular the giant dipole resonance is due to the coherent motion of protons against neutrons. Its analogue in metal clusters is the dipole plasmon excitation, due to the oscillation of electrons against the positive ions. The Random Phase Approximation (RPA) is extensively used as a microscopic theory to study the basic properties of these collective excitations. In the derivation of RPA use is made of the Quasi Boson Approximation (QBA). It consists in replacing the expectation values in the correlated ground state with those in the uncorrelated (Hartree-Fock) one. Strictly related to QBA is the feature of RPA of predicting a harmonic spectrum. On the other hand, the existence of anharmonicities in the multiphonon spectra of nuclei and their relevance in various physical processes are well established. Overcoming QBA has represented the starting point of many attempts aiming at improving RPA. A recently developed approach in this line will be presented and discussed. A very nice property of RPA is to satisfy Energy Weighted Sum Rules (EWSR). However, some violations are present in several extensions of RPA. We will show how to cure this shortcoming.
The second random-phase approximation (SRPA) is the simplest and most natural extension of the RPA. It enlarges the space of the elementary modes introduced to describe the collective states by adding 2 particle -2 hole excitations to the 1 particle -1 hole ones of the RPA. In deriving the SRPA equations, use is made, as in the RPA, of the so-called quasi-boson approximation (QBA) where expectation values in the ground state of the system are approximated by their values in the uncorrelated reference state. This, however, has been shown to imply a degree of approximation worse than that in the RPA. It is, therefore, necessary to improve the QBA by considering a reference state which contains some correlations. Having in mind to perform such calculations for realistic systems, we consider a simple extension of the SRPA in which the reference state contains 2 particle - 2 hole correlations. The quality of such an extension is tested by applying it to a solvable three-level model and found to be good.
We present a new ab initio method that uses similarity renormalization group (SRG) techniques to continuously diagonalize nuclear many-body Hamiltonians. In contrast with applications of the SRG to two- and three-nucleon interactions in free space, we perform the SRG evolution "in medium" directly in the A-body system of interest. The in-medium approach has the advantage that one can approximately evolve 3,…,A-body operators using only two-body machinery based on normal-ordering techniques. The method is nonperturbative and can be tailored to problems ranging from the diagonalization of closed-shell nuclei to the construction of effective valence-shell Hamiltonians and operators. We present first results for the energies of 4He, 16O, and 40Ca, which have accuracies comparable to coupled-cluster calculations.
The solution of the quantum many-body problem for medium-mass nuclei using realistic nuclear interactions poses a superbe challenge for nuclear structure research. Because an exact solution can only be provided for the lightest nuclei, one has to rely on approximate solutions when proceeding to heavier systems. Over the past years, tremendous progress has been made in the development and application of systematically improvable expansion methods and an accurate description of nuclear observables has become viable up to mass number A≈100A \approx 100A≈100. While closed-shell systems are consistently described via a plethora of different many-body methods, the extension to genuine open-shell systems still remains a major challenge and up to now there is no \textit{ab initio} many-body method which applies equally well to systems with even and odd mass numbers. The goal of this thesis is the development and implementation of innovative perturbative approaches with genuine open-shell capabilities. This requires the extension of well-known single-reference approaches to more general vacua. In this work we choose two complementary routes for the usage of generalized reference states. First, we derive a new \emph{ab initio} approach based on multi-configurational reference states that are conveniently derived from a prior no-core shell model calculation. Perturbative corrections are derived via second-order many-body perturbation theory, thus, merging configuration interaction and many-body perturbation theory. The generality of this ansatz enables for a treatment of medium-mass systems with arbitrary mass number, as well as the extension to low-lying excited states such that ground and excited states are treated on an equal footing. In a complementary approach, we use reference states that break a symmetry of the underlying Hamiltonian. In the simplest case this corresponds to the expansion around a particle-number-broken Hartree-Fock-Bogoliubov vacuum which is obtained from a mean-field calculation. Pairing correlations are already absorbed in the reference state. The mild scaling allows for investigations up to tin isotopic chains. All benchmarks were performed using state-of-the-art chiral two- plus three-nucleon interactions thus allowing for a universal description of nuclear observables in the medium-mass regime.
We merge two successful ab initio nuclear-structure methods, the no-core shell model (NCSM) and the multireference in-medium similarity renormalization group (IM-SRG) to define a new many-body approach for the comprehensive description of ground and excited states of closed and open-shell nuclei. Building on the key advantages of the two methods-the decoupling of excitations at the many-body level in the IM-SRG and the access to arbitrary nuclei, eigenstates, and observables in the NCSM-their combination enables fully converged no-core calculations for an unprecedented range of nuclei and observables at moderate computational cost. We present applications in the carbon and oxygen isotopic chains, where conventional NCSM calculations are still feasible and provide an important benchmark. The efficiency and rapid convergence of the new approach make it ideally suited for ab initio studies of the complete spectroscopy of nuclei up into the medium-mass regime.