First direct search for $2\epsilon$ and $\epsilon\beta^+$ decay of $^{144}$Sm and $2\beta^-$ decay of $^{154}$Sm

The first direct search for the double electron capture ($2\epsilon$) and the electron capture with positron emission ($\epsilon\beta^+$) in $^{144}$Sm to the ground state and to the excited levels of $^{144}$Nd was realized by measuring - over 1899 h - a 342 g sample of highly purified samarium oxide (Sm$_2$O$_3$) with the ultra-low background HP-Ge $\gamma$ spectrometer GeCris (465 cm$^3$) at the STELLA facility of the Gran Sasso National Laboratory (LNGS). No effect was observed and half-life limits were estimated at the level of $T_{1/2} \sim (0.1-1.3) \times 10^{20}$ yr (90% C.L.). Moreover, for the first time half-life limits of the double beta ($2\beta^-$) decay of $^{154}$Sm to several excited levels of $^{154}$Gd have been set; they are at the level of $T_{1/2} \sim (0.06-8) \times 10^{20}$ yr (90% C.L.).