A Limited Symmetry Found by Comparing Calculated Magnetic Dipole Spin   and Orbital Strengths in $^4\mbox{He}$
  Allowing for $2$$\hbar \omega$ admixtures in $^4\mbox{He}$ we find that the summed magnetic dipole isovector orbital and spin strengths are equal. This indicates a symmetry which is associated with interchanging the labels of the spin with those of the orbit. Where higher admixtures are included, the orbital sum becomes larger than the spin sum, but the sums over the low energy region are still nearly the same. 
M.S. Fayache and L. Zamick