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Register a new userOn the asymptotic methods for nuclear collective models
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Contractions of orthogonal groups to Euclidean groups are applied to analytic descriptions of nuclear quantum phase transitions. The semiclassical asymptotic of multipole collective Hamiltonians are also investigated.
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We discuss advanced statistical methods to improve parameter estimation of nuclear models. In particular, using the Liquid Drop Model for nuclear binding energies, we show that the area around the global $chi^2$ minimum can be efficiently identified using Gaussian Process Emulation. We also demonstrate how Markov-chain Monte-Carlo sampling is a valuable tool for visualising and analysing the associated multidimensional likelihood surface.
The status of the macroscopic and microscopic description of the collective quadrupole modes is reviewed, where limits due to non-adiabaticity and decoherence are exposed. The microscopic description of the yrast states in vibrator-like nuclei in the framework of the rotating mean field is presented.
The application of renormalization group methods to microscopic nuclear many-body calculations is discussed. We present the solution of the renormalization group equations in the particle-hole channels for neutron matter and the application to S-wave pairing. Furthermore, we point out that the inclusion of tensor and spin-orbit forces leads to spin non-conserving effective interactions in nuclear matter.
A remarkably simple regularity in the energies of 0+ states in a broad class of collective models is discussed. A single formula for all 0+ states in flat-bottomed infinite potentials that depends only on the number of dimensions and a simpler expression applicable to all three IBA symmetries in the large boson number limit are presented. Finally, a connection between the energy expression for 0+ states given by the X(5) model and the predictions of the IBA near the critical point is explored.
We discuss, in an investigation based on Vlasov equation, the properties of the isovector modes in nuclear matter and atomic nuclei in relation with the symmetry energy. We obtain numerically the dipole response and determine the strength function for various systems, including a chain of Sn isotopes. We consider for the symmetry energy three parametrizations with density providing similar values at saturation but which manifest very different slopes around this point. In this way we can explore how the slope affects the collective response of finite nuclear systems. We focus first on the dipole polarizability and show that while the model is able to describe the expected mass dependence, A^{5/3}, it also demonstrates that this quantity is sensitive to the slope parameter of the symmetry energy. Then, by considering the Sn isotopic chain, we investigate the emergence of a collective mode, the Pygmy Dipole Resonance (PDR), when the number of neutrons in excess increases. We show that the total energy-weighted sum rule exhausted by this mode has a linear dependence with the square of isospin I=(N-Z)/A, again sensitive to the slope of the symmetry energy with density. Therefore the polarization effects in the isovector density have to play an important role in the dynamics of PDR. These results provide additional hints in the investigations aiming to extract the properties of symmetry energy below saturation.
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