$N_pN_n$ scheme and the valence proton-neutron interaction
  We examine the common belief that the $N_pN_n$ scheme is manifested as a direct consequence of the valence proton-neutron interaction which has proven to be a dominant factor in developing collectivity in nuclei. We show that the simplification of the $N_pN_n$-plot of the lowest $2^+$ excitation energy is introduced merely because the excitation energy always decreases when the valence nucleon number becomes larger. 
Youngshin Byun, Guanghao Jin, Jin-Hee Yoon, Dongwoo Cha