| Summary: | <p>In this thesis, we study low energy capture reactions and neutron-deuteron elastic scattering
using halo effective field theory (EFT). At low energy, EFT provides a general
framework to analyze physical systems regarding as an expansion of short-distance over
large distance scales. We provide a model-independent calculation for neutron capture
on carbon-14, radiative capture of <sup>3</sup>He-<sup>4</sup>He, radiative capture of <sup>3</sup>H-<sup>4</sup>He, and neutrondeuteron
(<i>n-d</i>) doublet channel elastic scattering using halo EFT. These reactions play a
significant role in the carbon-nitrogen-oxygen (CNO) cycle, solar neutrino flux measurement,
lithium production, and big bang nucleosynthesis (BBN) in the early universe.</p>
<p>The cross section is calculated for radiative neutron capture in carbon-14 using halo
EFT. This reaction is slowest in the CNO cycle, and it acts as a bottleneck in the production
of heavier nuclei <i>A</i> greater than 14. The capture contribution is different from Brett-Wigner
resonance because of interference between resonant and non-resonant contribution. Also,
we calculated, electromagnetic form factors for one-neutron halo nuclei such as carbon-15,
beryllium-11, and carbon-19 using EFT. The electromagnetic form factors depend on the
nucleon separation energy, effective range, and the two-body current. The EFT expressions
are presented to leading order (LO) for <sup>15</sup>C and next-to-leading order (NLO) for <sup>11</sup>Be and
<sup>19</sup>C.</p>
<p>We also calculated astronomical <i>S</i>-factor for <sup>3</sup>He-<sup>4</sup>He and <sup>3</sup>H-<sup>4</sup>He radiative capture
reactions. The low energy <i>S</i>-factor for these reactions are important to understand the Li
problem and neutrino physics. At the LO, the capture amplitude contains the initial state swave
strong and Coulomb interactions summed to all orders. The NLO contribution comes
from non-perturbative Coulomb interaction. Our calculated astrophysical <i>S</i>-factor for <sup>3</sup>He-
<sup>4</sup>He is slightly above the average compared to the other measurement and prediction but
consistent within current error bars. The <i>S</i>-factor for <sup>3</sup>H-<sup>4</sup>He is also compatible with the
experimental extrapolation.</p> <p>
Finally, we studied doublet channel <i>n-d</i> scattering using halo EFT. A two dimer halo
EFT is developed to describe the virtual state and three-body bound state in <i>n-d</i> scattering.
We show the connection between virtual state and three-body bound state using <i>S</i>-matrix
analysis and phase shift analysis which is supported by the Efimov plots. </p>
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