We report a study of a spin-down impurity strongly coupled to a spin-up Fermi sea (a so-called Fermi polaron) with the diagrammatic Monte Carlo (DiagMC) technique. Conditions of zero temperature and three dimensions are considered for an ultracold atomic gas with resonant interactions in the zero-range limit. A Feynman diagrammatic series is developed for the one-body and two-body propagators providing information about the polaron and molecule channel, respectively. The DiagMC technique allows us to reach diagram orders that are high enough for extrapolation to infinite order. The robustness of the extracted results is examined by checking various resummation techniques and by running the simulations with various choices for the propagators and vertex functions. It turns out that dressing the lines in the diagrams as much as possible is not always the optimal choice. We also identify classes of dominant diagrams for the one-body and two-body self-energy in the region of strong interaction. These dominant diagrams turn out to be the leading processes of the strong-coupling limit. The quasiparticle energies and $Z$ factor are obtained as a function of the interaction strength. We find that the DiagMC results for the molecule and polaron properties are very similar to those obtained with a variational ansatz. Surprisingly, this variational ansatz gives very good predictions for the quasiparticle residue even when this residue is significantly less than 1.

We present a detailed study of a continuum random-phase approximation approach to quasielastic electron-nucleus and neutrino-nucleus scattering. We compare the $\left(e,e\prime \right)$ cross-section predictions with electron scattering data for the nuclear targets ${}^{12}\mathrm{C}$, ${}^{16}\mathrm{O}$, and ${}^{40}\mathrm{Ca}$, in the kinematic region where quasielastic scattering is expected to dominate. We examine the longitudinal and transverse contributions to ${}^{12}\mathrm{C}\left(e,e\prime \right)$ and compare them with the available data. We find an overall satisfactory description of the $\left(e,e\prime \right)$ data. Further, we study the ${}^{12}\mathrm{C}\left({\nu }_{\mu },{\mu }^{-}\right)$ cross sections relevant for accelerator-based neutrino-oscillation experiments. We pay special attention to low-energy excitations which can account for non-negligible contributions in measurements, and require a beyond-Fermi-gas formalism.

The photoproduction $p\left(\gamma {,K}^{+}\right)\Lambda$ process is studied within a field-theoretic approach. It is shown that the background contributions constitute an important part of the reaction dynamics. We compare predictions obtained with three plausible techniques for dealing with these background contributions. It appears that the extracted resonance parameters drastically depend on the applied technique. We investigate the implications of the corrections to the functional form of the hadronic form factor in the contact term, recently suggested by Davidson and Workman [Phys. Rev. C 63, 025210 (2001)]. The role of background contributions and hadronic form factors for the identification of the quantum numbers of “missing” resonances is discussed.

We study ($p,2p$) and ($p,pn$) reactions at proton energies in the range of 100 MeV\char21{}1 GeV. Our purpose is to explore the most sensitive observables in unpolarized reactions with inverse kinematics involving radioactive nuclei. We formulate a model based on the eikonal theory to describe total cross sections and momentum distributions of the recoiled residual nucleus. The model is similar to the one adopted for knockout reactions with heavy ions. We show that momentum distributions are sensitive to the angular momentum of the ejected nucleon which can be used as an spectroscopic tool. The total cross sections are sensitive to the nucleon separation energies and to multiple scattering effects. Our calculations also indicate that a beam energy around 500 MeV/nucleon has a smaller dependence on the anisotropy of the nucleon-nucleon elastic scattering.