What does "non-normal parity" mean? Nuclear physicists seem to use the term "non-normal parity" a fair bit. Googling for the term yields some 840 results, and the same search on Google Scholar indicates that about 430 of those are research papers.
Unfortunately, those searches seem to only yield research-level papers that just state the term and roll with it, assuming the reader understands it and without stopping to explain it.
So: what does "non-normal parity" mean?
 A: Going back to A.M. Lane, Reduced Widths of Individual Nuclear Energy Levels one finds the quote:

At this stage we introduce a separation of the discussion
  which is carried through to the end of the
  section, namely, nuclear states are discussed according
  to whether they are of "normal" or "nonnormal"
  parity. The normal parity of a nucleus is the parity of
  the ground state and the nonnormal parity is simply
  the opposite parity. This division is natural on the shell
  model, where the lowest states of normal parity have
  the normal configuration, i.e., a number of close shells
  and a few "loose" particles in an unfilled orbit. Nonnormal
  parity states, on the other hand, have a more
  complicated structure since they must involve the
  excitation of a particle to a higher orbit or the disturbance
  of the closed shells.

One major difference pointed out later in the text uses C$^{18}$ as the example, where the 'normal' negative parity has one configuration that is the lowest energy, while the 'nonnormal' positive parity has some 75 different states (severely complicating the calculation of the widths of the nuclear energy levels). 
Does that help?
EDIT: 
Looking through the TUNL A=10 nuclear data sheets, they seem to use 'unnatural parity' vs 'natural parity', pointing out for several of the various reactions used that some are more selective of 'unnatural parity' states than others. Perhaps at this point 'non-normal' has morphed into 'unnatural' in the literature.
A: 
A state with parity of $(−1)^L$ is defined as a natural parity state, with $L$ being the total angular momentum of the system, and parity with value of $+1$ or $−1$ are called even or odd, respectively. A state with parity of $(−1)^{L+1}$ is called unnatural parity state.

Source: Ye Ning et al., Natural and Unnatural Parity Resonance States in the Positron-Hydrogen System with Screened Coulomb Interactions. https://doi.org/10.3390/atoms4010003
