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

This work treats few-body systems consisting of neutrons interacting with a ${}^4\mathrm{H}\mathrm{e}$ 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 ${}^6\mathrm{H}\mathrm{e}$ and ${}^7\mathrm{H}\mathrm{e}$ nuclei. A simplified central potential model for the ${}^4\mathrm{H}\mathrm{e}-n$ interaction is used in conjunction with a spin-dependent three-body interaction to reproduce ${}^6\mathrm{H}\mathrm{e}$ bound-state and resonance properties as well as properties for the ${}^8\mathrm{H}\mathrm{e}$ nucleus in its ground-state. With this Hamiltonian, the adiabatic hyperspherical representation is used to compute bound and scattering states for both ${}^6\mathrm{H}\mathrm{e}$ and ${}^7\mathrm{H}\mathrm{e}$ nuclei. For the ${}^6\mathrm{H}\mathrm{e}$ system, the electric quadrupole transition between the $0^{+}$ and $2^{+}$ state is investigated. For the ${}^7\mathrm{H}\mathrm{e}$ system, ${}^6\mathrm{H}\mathrm{e}+n$ elastic scattering is investigated along with the four-body recombination process ${}^4\mathrm{H}\mathrm{e}+n+n+n\to$${}^6\mathrm{H}\mathrm{e}+n$ and breakup process ${}^6\mathrm{H}\mathrm{e}+n\to$${}^4\mathrm{H}\mathrm{e}+n+n+n$.