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Fluctuations of the baryon number in relativistic heavy-ion collisions are apromising observable to explore the structure of the QCD phase diagram. Thecumulant ratios in heavy ion collisions at intermediate energies($\sqrt{s_{\textrm{NN}}} < 7$ GeV) have not been studied to date. Weinvestigate the effects of mean field potential and clustering on the cumulantratios of baryon and proton number distributions in Au+Au collisions at beamenergy of 1.23 GeV$/$nucleon as measured by the HADES Collaboration at GSI.Ultrarelativistic Quantum Molecular Dynamics (UrQMD) and the JAM model are usedto calculate the cumulants with different mean field potentials. It is foundthat the cumulant ratios are strongly time dependent. At the early stage, theeffects of the potentials on the fluctuations of the particle multiplicity inmomentum space are relatively weak. The mean fields enhance the fluctuationsduring the expansion stage, especially for small rapidity acceptance windows.The enhancement of cumulant ratios for free protons is strongly suppressed ascompared to that for all baryons. The mean field potentials and the clusteringplay an important role for the measured cumulant ratios at intermediate energy.

The cumulants of the baryon number from central Au+Au collision at $E_{lab}$= 1.23 GeV$/$nucleon reveal the nuclear mean-field potentials