Discovering unexplored high-spin states in neutron-rich nuclei can open up a new direction to study band structure and the associated shell structure in isospin-asymmetric many-body systems. However, experimental reach has so far been limited to neutron-deficient or stable nuclei which are preferentially produced in fusion reactions used in such studies. By using neutron-rich rare-isotope beams, this limitation can be effectively removed, exposing previously inaccessible nuclei to this proven approach.This dissertation reports an experiment designed to kick off a spectroscopy program to study nuclear structure by means of low-energy nuclear reactions with reaccelerated rare-isotope beams available from the ReA3 facility at National Superconducting Cyclotron Laboratory. A 40Ar stable beam and a 45K rare-isotope beam impinged on a self-supporting lithium target to produce products ranging from argon to titanium via both direct and compound nucleus reactions. These mechanisms provide complementary tools to study the single-particle and collective natures of the states being probed. Using particle and gamma-ray coincidence relations between a silicon charged-particle detector and the Segmented Germanium Array, reaction channels were distinguished, and new properties were revealed, including for the nuclei 46Ca and 47K. For 46Ca, three new higher-lying states around 6 MeV and five new gamma-ray transitions were identified, suggesting three independent band structures formed from different particle-hole configurations. The rotational-like band built on the 0+2 state is established up to the tentatively assigned 6+2 state. New results are compared to large-scale shell model calculations, confirming the validity of the effective interaction describing particle-hole excitations across the Z=20 and N=28 shell gaps in the vicinity of doubly-magic 48Ca. Shape coexistence observed in lighter-mass calcium isotopes is suggested to persist in 46Ca, albeit as part of a transition from neutron to proton cross-shell excitations. For 47K, differential cross sections were extracted for the two-neutron transfer channel related to the present intruder configuration. Comparisons to Coupled Reaction Channels calculations indicate strong single-particle character for the states and a direct one-step process for the reaction itself. This work successfully developed the experimental techniques to use reaccelerated beams for spectroscopy of hitherto unexplored nuclei and demonstrated the ability of this approach to expand the experimental reach of nuclear structure studies.
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