He began his higher education at the Gheorghe Lazăr High School in Sibiu, and completed his studies at the Seminarul Pedagogic Universitar of the University of Cluj.

He completed successfully his doctoral studies with a Ph.D. thesis entitled The Relativistic Theory of the Photoelectric Effect, building on work of Albert Einstein and Alexandru Proca.

He also studied as a visiting scholar at several major physics centers around the world: the Joint Institute for Nuclear Research in Dubna, Soviet Union, the Joint Institute for Laboratory Astrophysics in Boulder, Colorado, the International Centre for Theoretical Physics in Trieste, Italy, and the University of Pittsburgh, in Pittsburgh, Pennsylvania.

However, in spite of his election to the Academy, he refused to become entangled in any political affairs under the increasingly dictatorial communist regime, and finally he had to leave his country for Norway in the autumn of 1974.

Since 1992 he has worked as a Senior Scientist at the Institute for Theoretical Atomic, Molecular and Optical Physics (ITAMP) based at the Harvard–Smithsonian Center for Astrophysics, in Cambridge, Massachusetts.

Gavrilă completed in 1977 his previous work on the relativistic theory of the photoelectric effect in the inner atomic orbitals that he had begun in his Ph.D. thesis in 1958; thus, he applied radiative corrections to his previous calculations[4] He also investigated two-photon excitations and the elastic photon scattering amplitude in the hydrogen ground state,.

[9][10] He began this research in 1976 in connection with experimental studies carried out at AMOLF by the group of Marnix van der Wiel.