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A method of calculating giant resonance strength functions using Time-Dependent Hartree-Fock techniques is described. An application to isoscalar giant monopole resonances in spherical nuclei is made, thus allowing a comparison between independent 1-, 2- and 3-Dimensional computer codes.
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The direct $gamma$-decays of the giant dipole resonance (GDR) and the giant quadrupole resonance (GQR) of $^{208}$Pb to low-lying states are investigated by means of a microscopic self-consistent model. The model considers effects beyond the linear response approximation. The strong sensitivity of $gamma$-decay to the isospin of the involved states is proven. By comparing their decay widths, a much larger weight of the $3_{1}^{-}$ component in the GQR wave function of $^{208}$Pb is deduced, with respect to the weight of the $2_{1}^{+}$ component in the GDR wave function. Thus, we have shown that $gamma$-decay is a unique probe of the resonance wave functions, and a testground for nuclear structure models.
We combine the coupled-cluster method and the Lorentz integral transform for the computation of inelastic reactions into the continuum. We show that the bound-state-like equation characterizing the Lorentz integral transform method can be reformulated based on extensions of the coupled-cluster equation-of-motion method, and we discuss strategies for viable numerical solutions. Starting from a chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order, we compute the giant dipole resonances of 4He, 16,22O and 40Ca, truncating the coupled-cluster equation-of-motion method at the two-particle-two-hole excitation level. Within this scheme, we find a low-lying E1 strength in the neutron-rich 22O nucleus, which compares fairly well with data from [Leistenschneider et al. Phys. Rev. Lett. 86, 5442 (2001)]. We also compute the electric dipole polariziability in 40Ca. Deficiencies of the employed Hamiltonian lead to overbinding, too small charge radii and a too small electric dipole polarizability in 40Ca.
Gamow-Teller (GT) and spin-dipole (SD) strength distributions of four doubly magic nuclei $^{48}$Ca, $^{90}$Zr, $^{132}$Sn and $^{208}$Pb are studied by the self-consistent Hartree-Fock plus random phase approximation (RPA) method. The Skyrme forces SAMi and SAMi-T without/with tensor interactions are adopted in our calculations. The calculated strengths are compared with available experimental data. The RPA results of GT and SD strengths of all four nuclei show fine agreement with observed GT and SD resonances in energy. A small GT peak below the main GT resonance is better described by the Skyrme interaction SAMi-T with the tensor terms. The quenching factors for GT and SD are extracted from the comparisons between RPA results and experimental strengths. It is pointed out that the quenching effect on experimental SD peaks is somewhat modest compared with that on GT peaks in the four nuclei.
The cross sections for neutrino scattering off the 12C and 16O nuclei are calculated within the framework of the continuum Random Phase Approximation. A model to consider also the final state interactions is developed. Total charge-conserving and charge-exchange cross sections for both electron neutrinos and antineutrinos have been calculated up to projectile energies of 100 MeV. The sensitivity of the cross sections to the residual interaction and to the final state interactions is investigated. A direct comparison between neutrino and electron scattering cross sections calculated under the same kinematic conditions is presented. We found remarkable differences between electromagnetic and weak nuclear responses. The model is applied to describe cross sections of neutrinos produced by muon decay at rest and in supernovae explosions.
A completely microscopic beyond mean-field approach has been elaborated to overcome some intrinsic limitations of self-consistent mean-field schemes applied to nuclear systems, such as the incapability to produce some properties of single-particle states (e.g. spectroscopic factors), as well as of collective states (e.g. their damping width and their gamma decay to the ground state or to low lying states). Since commonly used effective interactions are fitted at the mean-field level, one should aim at refitting them including the desired beyond mean-field contributions in the refitting procedure. If zero-range interactions are used, divergences arise. We present some steps towards the refitting of Skyrme interactions, for its application in finite nuclei.
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