We have studied the chemical potential shift as a function of temperature in Nd$_{1-x}$Sr$_x$MnO$_3$ (NSMO) by measurements of core-level photoemission spectra. For ferromagnetic samples ($x=0.4$ and 0.45), we observed an unusually large upward chemi
cal potential shift with decreasing temperature in the low-temperature region of the ferromagnetic metallic (FM) phase. This can be explained by the double-exchange (DE) mechanism if the $e_g$ band is split by dynamical/local Jahn-Teller effect. The shift was suppressed near the Curie temperature ($T_C$), which we attribute to the crossover from the DE to lattice-polaron regimes.
