A microscopic particle-vibration coupling approach for atomic nuclei. Giant resonance properties and the renormalization of the effective interaction
Marco Brenna
备注：
PhD Thesis 2014. Tutor: Gianluca Colò. arXiv admin note: text overlap with arXiv:0804.3580, arXiv:1308.1008, arXiv:nucl-th/0701081, arXiv:nucl-th/0402034 by other authors
The self-consistent mean-field (SCMF) theory describes many properties of the ground state and excited states of the atomic nucleus, such as masses, radii, deformations and giant resonance energies. SCMF models are based on the independent particle picture where nucleons are assumed to move in a self-generated average potential. In the first part of this work, we apply a state-of-the-art SCMF approach, based on the Skyrme effective interaction, to two different excitations (viz. the pygmy dipole resonance and the isovector giant quadrupole resonance), investigating their relation with the nuclear matter symmetry energy, which corresponds to the energy cost for changing protons into neutrons and is a key parameter for the nuclear equation of state. However, SCMF models present well known limitations which require the inclusion of further dynamical correlations, e.g. the ones coming from the interweaving between single-particle and collective degrees of freedom (particle-vibration coupling - PVC). In the second part of this work, we report on the application to inclusive (namely, the strength function of giant resonances) and exclusive (the gamma decay of giant resonances) observables of a new self-consistent model based on the PVC idea in the Skyrme framework. In our model we use an effective interaction fitted at mean-field level to some selected experimental data. In principle, when these interactions are used in beyond mean-field theories, one would need to re-determine the parameters of the interaction at the same level of approximation. Moreover, due to the zero-range nature of the employed interaction, divergences arise. In the last and most innovative part of this thesis, we develop, for the first time in finite nuclei, a possible way to cure the divergences, paving the way to the possibility of producing an effective interaction fitted at PVC level.
Microscopic investigation of $γ~$ vibrational band structures in odd-mass nuclei
Islamic University of Science and Technology（伊斯兰科学与技术大学）；Government Degree College Kulgam, Jammu and Kashmir Higher Education Department（古尔加姆政府学位学院，查谟和克什米尔高等教育部）；Government Degree College Shopian, Jammu and Kashmir Higher Education Department（肖皮安政府学位学院，查谟和克什米尔高等教育部）；University of Kashmir（克什米尔大学）
Quasi-particle random phase approximation with quasi-particle-vibration coupling: application to the Gamow-Teller response of the superfluid nucleus $^{120}$Sn
Towards a Renormalization Group Approach to Density Functional Theory - General Formalism and Case Studies -
讨论了一种基于重整化群流方程的两点粒子不可约（2 PPI）方法。特别地，详细分析了RG流方程的一般结构和性质。此外，我们讨论了我们的2 PPI RG方法与密度泛函理论的关系，并认为它原则上可以用于研究微观相互作用的非相对论多体系统的基态性质，如（重）核。为了说明的目的，我们使用我们的形式来计算两个玩具模型的基态性质。
