We report angle-resolved measurements on photoelectrons emitted upon near-threshold two-photon double ionization (TPDI) of Kr irradiated by free-electron laser (FEL) pulses. These photoelectron angular distributions (PADs) are compared with the results of semirelativistic $R$-matrix calculations. As reported by Augustin et al. [Phys. Rev. A 98, 033408 (2018)], it is found that the presence of autoionizing resonances within the bandwidth of the exciting FEL pulse strongly influences the PADs. In contrast to measurements on lower-$Z$ targets such as Ne and Ar, the larger spin-orbit interaction, inherent in $4p$-subshell hole states of Kr, permits us to resolve and study PADs associated with some of the fine-structure components of the ${\mathrm{Kr}}^{+}$ and ${\mathrm{Kr}}^{2+}$ ions.
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