  Motivated by the standard form of string-theory amplitude, we calculate the
field-theory amplitude to complete the higher-derivative terms in type II
supergravity theories in their conventional form. We derive explicitly the $
O(\alpha'^3) $ interactions for the RR (Ramond-Ramond) fields with graviton,
B-field and dilaton in the low-energy effective action of type II superstrings.
We check our results by comparison with previous works that have been done by
the other methods, and find an exact agreement.
