Nuclear charge-exchange excitations in a self-consistent covariant approach

Abstract : Nowadays, charge-exchange excitations in nuclei become one of the central topics in nuclear physics and astrophysics. Basically, a systematic pattern of the energy and collectivity of these excitations could provide direct information on the spin and isospin properties of the in-medium nuclear interaction, and the equation of state of asymmetric nuclear matter. Furthermore, a basic and critical quantity in nuclear structure, neutron skin thickness, can be determined indirectly by the sum rule of spin-dipole resonances (SDR) or the excitation energy spacing between the isobaric analog states (IAS) and Gamow-Teller resonances (GTR). More generally, charge-exchange excitations allow one to attack other kinds of problems outside the realm of nuclear structure, like the description of neutron star and supernova evolutions, the β-decay of nuclei which lie on the r-process path of stellar nucleosynthesis, and the neutrino-nucleus cross sections. They also play an essential role in extracting the value of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element Vud via the nuclear 0+ → 0+ superallowed Fermi β decays. For all these reasons, it is important to develop the microscopic theories of charge-exchange excitations and it is the main motivation of the present work. In this work, a fully self-consistent charge-exchange relativistic random phase approximation (RPA) based on the relativistic Hartree-Fock (RHF) approach is established. Its self-consistency is verified by the so-called IAS check. This approach is then applied to investigate the nuclear spin-isospin resonances, isospin symmetry-breaking corrections for the superallowed β decays, and the charged-current neutrino-nucleus cross sections. For two important spin-isospin resonances, GTR and SDR, it is shown that a very satisfactory agreement with the experimental data can be obtained without any readjustment of the energy functional. Furthermore, the isoscalar mesons are found to play an essential role in spin-isospin resonances via the exchange terms, which leads to a profound effect in the nuclear isovector properties, e.g., the density dependence of the symmetry energy in nuclear matter. In the investigation of the isospin symmetry-breaking corrections for the superallowed β decays, it is found that the corrections δc are sensitive to the proper treatments of the Coulomb mean field, but not so much to specific effective interactions. With these corrections δc, the nucleusindependent Ft values are obtained in combination with the experimental ft values in the most recent survey and the improved radiative corrections. The values of Cabibbo-Kobayashi-Maskawa matrix element |Vud| thus obtained well agree with those obtained in neutron decay, pion decay, and nuclear mirror transitions, while the sum of squared top-row elements somehow deviates from the unitarity condition. Expressing the weak lepton-hadron interaction in the standard current-current form, the relevant transitions from the nuclear ground state to the excited states are calculated with RHF+RPA approach. In this way, the semileptonic weak interaction processes, e.g., neutrino reactions, chargedlepton capture, β-decays, can be investigated microscopically and self-consistently. First illustrative calculations of the inclusive neutrino-nucleus cross section are performed for the 16O(νe,e−)16F reaction, and a good agreement with the previous theoretical studies is obtained. The main effort is dedicated to discussing the substantial influence of different recipes for the axial vector coupling strength and the theoretical low-lying excited states of the daughter nucleus.
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H. Liang. Nuclear charge-exchange excitations in a self-consistent covariant approach. Physique Nucléaire Théorique [nucl-th]. Université Paris Sud - Paris XI, 2010. Français. ⟨tel-00506913⟩

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