ETD

Archivio digitale delle tesi discusse presso l'Università di Pisa

Tesi etd-03142018-092115


Tipo di tesi
Tesi di laurea magistrale
Autore
NANNINI, ALESSIA
URN
etd-03142018-092115
Titolo
Non-Symmetrized Hyperspherical Harmonics for a three-body system
Dipartimento
FISICA
Corso di studi
FISICA
Relatori
relatore Prof.ssa Marcucci, Laura Elisa
Parole chiave
  • NSHH
  • Hyperspherical Harmonics
  • HH
  • ab initio method
  • three-body system
Data inizio appello
18/04/2018
Consultabilità
Completa
Riassunto
The Hyperspherical Harmonics (HH) method has been widely applied in the study of the bound states of few-body systems, namely A=3 and A=4. Usually, the use of the HH basis is preceeded by a symmetrization procedure that takes into account the fact that protons and neutrons are fermions, and therefore the wave function has to be antisymmetric under exchange of any pair of these particles. However, this preliminary step is not strictly necessary, since after the diagonalization of the Hamiltonian, the eigenvectors turn out to have a well-defined symmetry under particle permutation.
In this case, the method is known as Non-Symmetrized Hyperspherical Harmonics (NSHH) method. In this work we present a generalization of the NSHH method for a three-body system, composed by two particles having equal masses, but different from the mass of the third particle.
In particular we focus on the triton, 3He and hyper-triton systems.
In the first part of the thesis we present a complete description of the NSHH method.
Then, we study the convergence of the method in order to estimate its accuracy. We also compare some selected cases, for the triton, treated as an equal masses three-body system, to the results present in the literature, obtained with the (symmetrized) standard HH method. The agreement has been found in general very nice.
We proceed studying the difference of binding energy between triton and 3He due to the difference between the proton and the neutron masses, and we have obtained a nice agreement with the "standard" perturbative estimate. Finally, we study the hyper-triton system with several nucleon-nucleon (NN) and hyperon-nucleon (YN) potential models. Also in this case, the results are found in nice agreement with those present in the literature.
In conclusion, in this work, we have generalized the NSHH method, developed for an equal mass system, to the case of different masses, limiting ourselves to a three-body system.
Our results, obtained with a variety of nuclear potential models, demonstrate the validity of the method, and are therefore very promising. In a near future, we plan to apply this method to other systems, which can be clustered as three-body systems, where one of the constituents is an 4He particle, as the Borromean 6He (seen as 4He+n+n) and the 6Li (seen as 4He+n+p) nuclei.
Furthermore, our method can also be generalized to the case of A=3 scattering systems, taking advantage of the already existing expertise in the case of the standard HH method.
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