Collins Russian Dictionary 2nd Edition © HarperCollins Publishers 2000, 1997:
deepen [ˈdiːpn] vt (hole etc) углубля́ть (углуби́ть*perf)
vi (crisis, mystery) углубля́ться (углуби́ться*perf)
* is used to mark translations which have irregular inflections. The Russian-English side of the dictionary gives inflectional information.
Русский: