  This work treats few-body systems consisting of neutrons interacting with a
$^{4}{\mathrm{He}}$ nucleus. The adiabatic hyperspherical representation is
utilized to solve the $N$-body Schr$\ddot{\mathrm{o}}$dinger 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
$^{4}{\mathrm{He}}-n$ 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, the adiabatic hyperspherical
representation is used to compute bound and scattering states for both
$^{6}{\mathrm{He}}$ and $^{7}{\mathrm{He}}$ nuclei. For the $^{6}{\mathrm{He}}$
system, the electric quadrupole transition between the $0^{+}$ and $2^{+}$
state is investigated. For the $^{7}{\mathrm{He}}$ system,
$^{6}{\mathrm{He}}+n$ elastic scattering is investigated along with the
four-body recombination process
$^{4}{\mathrm{He}}+n+n+n\rightarrow$$^{6}{\mathrm{He}}+n$ and breakup process
$^{6}{\mathrm{He}}+n\rightarrow$$^{4}{\mathrm{He}}+n+n+n$.
