Progress of Monte Carlo methods in nuclear physics using EFT-based NN interaction and in hypernuclear systems.

Introduction In this thesis I report the work of my PhD; it treated two different topics, both related by a third one, that is the computational method that I use to solve them. I worked on EFT-theories for nuclear systems and on Hypernuclei. I tried to compute the ground state properties of both systems using Monte Carlo methods. In the first part of my thesis I briefly describe the Monte Carlo methods that I used: VMC (Variational Monte Carlo), DMC (Diffusion Monte Carlo), AFDMC (Auxiliary Field Diffusion Monte Carlo) and AFQMC (Auxiliary Field Quantum Monte Carlo) algorithms. I also report some new improvements relative to these methods that I tried or suggested: I remember the fixed hypernode extension (§ 2.6.2) for the DMC algorithm, the inclusion of the L2 term (§ 3.10) and of the exchange term (§ 3.11) into the AFDMC propagator. These last two are based on the same idea used by K. Schmidt to include the spin-orbit term in the AFDMC propagator (§ 3.9). We mainly use the AFDMC algorithm but at the end of the first part I describe also the AFQMC method. This is quite similar in principle to AFDMC, but it was newer used for nuclear systems. Moreover, there are some details that let us hope to be able to overcome with AFQMC some limitations that we find in AFDMC algorithm. However we do not report any result relative to AFQMC algorithm, because we start to implement it in the last months and our code still requires many tests and debug. In the second part I report our attempt of describing the nucleon-nucleon interaction using EFT-theory within AFDMC method. I explain all our tests to solve the ground state of a nucleus within this method; hence I show also the problems that we found and the attempts that we tried to overcome them before to leave this project. In the third part I report our work about Hypernuclei; we tried to fit part of the ΛN interaction and to compute the Hypernuclei Λ-hyperon separation energy. Nevertheless we found some good and encouraging results, we noticed that the fixed-phase approximation used in AFDMC algorithm was not so small like assumed. Because of that, in order to obtain interesting results, we need to improve this approximations or to use a better method; hence we looked at AFQMC algorithm aiming to quickly reach good results.