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In this work, the radiative capture reactions 7Li(n, γ)8Li, 7Be(p, γ)8B, 3He(α, γ)7Be, and 3H(α, γ)7Li are studied using halo effective field theory (EFT). These capture reac- tions are some of the key nuclear reactions for the solar neutrino production and heavy element production in stellar and primordial nucleosyntheses. At low energy, halo EFT provides a model independent framework to describe physical observable as an expansion of a low momentum scale over a high momentum scale with well-defined error estimates. In this dissertation, electric dipole (E1) capture cross section of 7Li(n, γ)8Li reaction is calculated as a coupled channel using EFT with excited 7Li⋆ core and is compared with EFT without the excited 7Li⋆ core. Then we extend our coupled channel treatment to 7Be(p, γ)8B reaction which is the iso-spin mirror of 7Li(n, γ)8Li by adding the Coulomb force in the calculation. Similar to 7Li(n,γ)8Li calculation, we calculate the astrophys- ical Sactor for 7Be(p,γ)8B reaction using the two halo EFTs, one halo EFT without excited 7Be⋆ core and the other halo EFT with the excited 7Be⋆ core as an explicit degree of freedom. We present a formalism to compare different EFT power countings using Bayesian analysis. This is useful when the EFT couplings are poorly known, and one has competing power counting proposals. The Sactor for 3He(α,γ)7Be reaction was calculated for two competing power countings in halo EFT approach. The two power countings defer in the contribution of the two body currents. In one power counting, the two body currents contribute at the leading order and in the other power counting, the two body currents contribute at higher orders. Bayesian inference is drawn to estimate EFT parameters and calculate the posterior odds in order to do the model comparison. The posterior odds is used to propose the best power counting. We extend our calculation to the iso-spin mirror 3H(α,γ)7Li reaction using the same expressions by making the appropriate changes in masses, charges, and binding momenta. We estimate the EFT parameters and calculate the posterior odds using Bayesian analysis. The best power counting is proposed using the posterior odds.

This thesis is missing pages 152 and 194, neither of which are in the other copies of this thesis. -Digitization Centre / Restricted Hartree-Fock calculations for light even-even nuclei have been carried out using simple effective interactions. The primary emphasis is on the nature of the intrinsic states, and, in particular, on the deformation of these states. In order to find the equilibrium deformations a representation of deformed cylindrically symmetric states is used. A self-consistent technique for finding the equilibrium size and shape is proposed. There is a strong secondary emphasis on the role of the effective interaction, and four rather different interactions are used. Two of these incorporate a dependence on the density on the nuclear system, and this density dependence improves the systematic behaviour of the energies and sizes of light nuclei. / Thesis / Doctor of Philosophy (PhD)