Investigation of double beta decay of $^{100}$Mo to excited states of $^{100}$Ru

Double beta decay of $^{100}$Mo to the excited states of daughter nuclei has been studied using a 600 cm$^3$ low-background HPGe detector and an external source consisting of 2588 g of 97.5% enriched metallic $^{100}$Mo, which was formerly inside the NEMO-3 detector and used for the NEMO-3 measurements of $^{100}$Mo. The half-life for the two-neutrino double beta decay of $^{100}$Mo to the excited 0$^+_1$ state in $^{100}$Ru is measured to be $T_{1/2}=[7.5 \pm{0.6}(stat) \pm {0.6}(syst)]\cdot 10^{20}$ yr. For other $(0\nu + 2\nu)$ transitions to the 2$^+_1$, 2$^+_2$, 0$^+_2$, 2$^+_3$ and 0$^+_3$ levels in $^{100}$Ru, limits are obtained at the level of $\sim (0.25-1.1)\cdot 10^{22}$ yr.