Resonances and collisional properties of neutron-rich helium isotopes in the adiabatic hyperspherical representation

The goal of this work is to treat few-body nuclear systems using the adiabatic hyperspherical representation, to test an alternative approach to treat both bound and continuum states and compare the results to other techniques often used in nuclear calculations. This method is utilized to solve the $N$-body Schr"odinger equation for the three- and four-body systems, treating both $^{6}\mathrm{He}$ and $^{7}\mathrm{He}$ nuclei. A simplified central potential model for the $^{4}\mathrm{He}\ensuremath{-}n$ interaction is used in conjunction with a spin-dependent three-body interaction to reproduce $^{6}\mathrm{He}$ bound-state and resonance properties as well as properties for the $^{8}\mathrm{He}$ nucleus in its ground state. With this Hamiltonian, bound and scattering states for both $^{6}\mathrm{He}$ and $^{7}\mathrm{He}$ nuclei are computed. For the $^{6}\mathrm{He}$ system, the electric quadrupole transition between the ${0}^{+}$ and ${2}^{+}$ state is investigated. For the $^{7}\mathrm{He}$ system, $^{6}\mathrm{He}+\phantom{\rule{0.16em}{0ex}}n$ elastic scattering is investigated along with the four-body recombination process $^{4}\mathrm{He}+\phantom{\rule{0.16em}{0ex}}n+n+n\ensuremath{\rightarrow}^{6}\mathrm{He}+\phantom{\rule{0.16em}{0ex}}n$ and breakup process $^{6}\mathrm{He}+\phantom{\rule{0.16em}{0ex}}n\ensuremath{\rightarrow}^{4}\mathrm{He}+\phantom{\rule{0.16em}{0ex}}n+n+n$. An application of the adiabatic hyperspherical representation to a five-body description of $^{8}\mathrm{He}$ is also presented with the prospects of studying four neutrons in the scattering continuum that interact with a core nucleus.