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In this work, we calculate magnetic moments and transition magnetic momentsof the $P^{N^{0}}_{\psi}$ states in molecular model, diquark-diquark-antiquarkmodel and diquark-triquark model, whose isospin doublet states$P^{N^{+}}_{\psi}$ have been observed in the LHCb Collaboration in recentyears. Our results show that in the diquark-diquark-antiquark model, themagnetic moments of $\lambda $ excitation state are usually larger than themagnetic moments of $\rho $ excitation state. We find some interestingproportional relationships between the expressions of transition magneticmoments. The results provide important insights for future experimentalobservation of $P^{N^{0}}_{\psi}$ states and help to distinguish their innerstructures. With these efforts, our understanding of the properties for thehidden-charm pentaquark states will become more abundant.

Analysis of the hidden-charm pentaquark states $P^{N^{0}}_{\psi}$ based on magnetic moment and transition magnetic moment