New limits on $2 \varepsilon$, $\varepsilon \beta^{+}$ɛβ+ and $2 \beta^{+}$2β+ decay of 136Ce and 138Ce with deeply purified cerium sample

A search for double electron capture (\(2\varepsilon\)), electron capture with positron emission (\(\varepsilon\beta^{+}\)), and double positron emission (\(2\beta^{+}\)) in 136Ce and 138Ce was realized with a 465 cm3 ultra-low background HP Ge \( \gamma\) spectrometer over 2299 h at the Gran Sasso underground laboratory. A 627 g sample of cerium oxide deeply purified by liquid-liquid extraction method was used as a source of \(\gamma\) quanta expected in double \(\beta\) decay of the cerium isotopes. New improved half-life limits were set on different modes and channels of double \(\beta\) decay of 136Ce and 138Ce at the level of \(T_{1/2} > 10^{17} - 10^{18}\) yr.