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Register a new userStructure of A=3 Nuclear Systems Using Realistic Hamiltonians
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The structure of A=3 low-energy scattering states is described using the hyperspherical harmonics method with realistic Hamiltonian models, consisting of two- and three-nucleon interactions. Both coordinate and momentum space two-nucleon potential models are considered.
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Background: The energy weighted sum rules of the single-particle spectral functions provide a quantitative understanding of the fragmentation of nuclear states due to short-range and tensor correlations. Purpose: The aim of this paper is to compare on a quantitative basis the single-particle spectral function generated by different nuclear hamiltonians in symmetric nuclear matter using the first three energy-weighted moments. Method: The spectral functions are calculated in the framework of the self-consistent Greens function approach at finite temperature within a ladder resummation scheme. We analyze the first three moments of the spectral function and connect these to the correlations induced by the interactions between the nucleons. In particular, the variance of the spectral function is directly linked to the dispersive contribution of the self-energy. The discussion is centred around two- and three-body chiral nuclear interactions, with and without renormalization, but we also provide results obtained with the traditional phase-shift-equivalent CD-Bonn and Av18 potentials. Results: The variance of the spectral function is particularly sensitive to the short-range structure of the force, with hard-core interactions providing large variances. Chiral forces yield variances which are an order of magnitude smaller and, when tamed using the similarity renormalization group, the variance reduces significantly and in proportion to the renormalization scale. The presence of three-body forces does not substantially affect the results. Conclusions: The first three moments of the spectral function are useful tools in analysing the importance of correlations in nuclear ground states. In particular, the second-order moment provides a direct insight into dispersive contributions to the self-energy and its value is indicative of the fragmentation of single-particle states.
We discuss the building blocks for a consistent inclusion of chiral three-nucleon (3N) interactions into ab initio nuclear structure calculations beyond the lower p-shell. We highlight important technical developments, such as the similarity renormalization group (SRG) evolution in the 3N sector, a JT-coupled storage scheme for 3N matrix elements with efficient on-the-fly decoupling, and the importance truncated no-core shell model with 3N interactions. Together, these developments make converged ab initio calculations with explicit 3N interactions possible also beyond the lower p-shell. We analyze in detail the impact of various truncations of the SRG-evolved Hamiltonian, in particular the truncation of the harmonic-oscillator model space used for solving the SRG flow equations and the omission of the induced beyond-3N contributions of the evolved Hamiltonian. Both truncations lead to sizable effects in the upper p-shell and beyond and we present options to remedy these truncation effects. The analysis of the different truncations is a first step towards a systematic uncertainty quantification of all stages of the calculation.
The advent of nucleon-nucleon potentials derived from chiral perturbation theory, as well as the so-called V-low-k approach to the renormalization of the strong short-range repulsion contained in the potentials, have brought renewed interest in realistic shell-model calculations. Here we focus on calculations where a fully microscopic approach is adopted. No phenomenological input is needed in these calculations, because single-particle energies, matrix elements of the two-body interaction, and matrix elements of the electromagnetic multipole operators are derived theoretically. This has been done within the framework of the time-dependent degenerate linked-diagram perturbation theory. We present results for some nuclei in different mass regions. These evidence the ability of realistic effective hamiltonians to provide an accurate description of nuclear structure properties.
The 4He total photoabsorption cross section is calculated with the realistic nucleon-nucleon potential Argonne V18 and the three-nucleon force (3NF) Urbana IX. Final state interaction is included rigorously via the Lorentz Integral Transform method. A rather pronounced giant resonance with peak cross sections of 3 (3.2) mb is obtained with (without) 3NF. Above 50 MeV strong 3NF effects, up to 35%, are present. Good agreement with experiment is found close to threshold. A comparison in the giant resonance region is inconclusive, since present data do not show a unique picture.
This paper discusses the derivation of an effective shell-model hamiltonian starting from a realistic nucleon-nucleon potential by way of perturbation theory. More precisely, we present the state of the art of this approach when the starting point is the perturbative expansion of the Q-box vertex function. Questions arising from diagrammatics, intermediate-states and order-by-order convergences, and their dependence on the chosen nucleon-nucleon potential, are discussed in detail, and the results of numerical applications for the p-shell model space starting from chiral next-to-next-to-next-to-leading order potentials are shown. Moreover, an alternative graphical method to derive the effective hamiltonian, based on the Z-box vertex function recently introduced by Suzuki et al., is applied to the case of a non-degenerate (0+2) hbaromega model space. Finally, our shell-model results are compared with the exact ones obtained from no-core shell-model calculations.
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