  The intermediate neutron capture process (i-process) operates at neutron
densities between those of the slow and rapid neutron-capture processes. It can
be triggered by the ingestion of protons in a convective helium-burning region.
One possible astrophysical site is low-mass low-metallicity asymptotic giant
branch (AGB) stars. We study here the possibility that actinides (particularly
Th and U) may be significantly synthesized through i-process nucleosynthesis in
AGB stars. We computed a 1 $M_{\odot}$ model at [Fe/H] $= -2.5$ with the
stellar evolution code STAREVOL. We used a nuclear network of 1160 species from
H to Cf coupled to the transport processes. During the proton ingestion event,
the neutron density goes up to $\sim 10^{15}$ cm$^{-3}$. While most of the
nuclear flow cycles in the neutron-rich Pb-Bi-Po region, a non-negligible
fraction leaks towards heavier elements and eventually synthesizes actinides.
The surface enrichment in Th and U is subject to nuclear and astrophysical
model uncertainties that could be lowered in the future, in particular by a
detailed analysis of the nuclear inputs that affect the neutron capture rates
of neutron-rich isotopes between Pb and Pa. One stellar candidate that may
confirm the production of actinides by the i-process is the carbon-enhanced
metal-poor r/s star J0949-1617, which shows Th lines in its spectrum. Its
surface abundance is shown to be reasonably well reproduced by our AGB model.
Combined with cosmochronometry, this finding opens the way to dating the
i-process event and thus obtaining a lower limit for the age of CEMP-r/s stars.
Such a dating is expected to be accurate only if surface abundances of Th and U
can be extracted simultaneously. This work shows that actinides can be
synthesized in AGB stars through the i-process. As a consequence, the r-process
may not be the sole mechanism for the production of U and Th.
