  A variational analysis is performed within the framework of lattice QCD to
extract the masses of the spin-3/2 positive parity $ \Delta^+ $ baryons,
including radial excitations. $2+1$ flavour dynamical gauge-field
configurations provided by the PACS-CS collaboration via the ILDG are
considered. To improve our interpolator basis, we perform an iterative process
of source and sink smearing and solve a generalised eigenvalue problem using
the resulting fermion operators. We obtain a clear signal for the ground and
first excited states at a light quark mass corresponding to $ m_\pi = 413 $
MeV. Furthermore, we show that one can use the eigenvectors obtained in this
method to investigate the nature of these states, allowing us to classify our
results as $ 1s $ and $ 2s $ states for the ground and first excited states
respectively. Finally, we briefly highlight the method of Hamiltonian Effective
Field Theory which can be used to make comparison with quark model
expectations.
