Candidate chiral doublet bands in Pm138

High-spin states of $^{138}\mathrm{Pm}$ have been populated using the $^{124}\mathrm{Te}(^{19}\mathrm{F},\phantom{\rule{0.28em}{0ex}}5\mathrm{n})^{138}\mathrm{Pm}$ reaction at a beam energy of 105 MeV. A new positive-parity side band with the same $\ensuremath{\pi}{h}_{11/2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}$ configuration as that of the yrast band is observed in $^{138}\mathrm{Pm}$. The properties of the two positive-parity bands show general agreement with the fingerprints of chiral rotation and thus these two bands are suggested to be candidates for near degenerate chiral doublet bands. Besides, odd-even spin staggering of the $\ensuremath{\pi}{h}_{11/2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}$ bands is studied systematically in odd-odd Cs, La, Pr, and Pm isotopes. As a result of this study we suggest that the spin value of lowest observed state of the yrast band be reassigned as 9 in $^{138}\mathrm{Pm}$. This new spin assignment is also supported by the argument of alignment additivity.