Since this institute, not part of a university, had no right to award a doctorate, Mössbauer remained under the auspices of Maier-Leibnitz, his official thesis advisor, when he passed his PhD exam in Munich in 1958.

In his PhD, he discovered the recoilless nuclear fluorescence of gamma rays in 191 iridium, the Mössbauer effect.

His fame grew immensely in 1960 when Robert Pound and Glen Rebka used this effect to prove the red shift of gamma radiation in the gravitational field of the Earth; this Pound–Rebka experiment was one of the first experimental precision tests of Albert Einstein's general theory of relativity.

In 1964, his alma mater, the Technical University of Munich (TUM), convinced him to go back as a full professor.

[citation needed] In 1972, Rudolf Mössbauer went to Grenoble to succeed Heinz Maier-Leibnitz as the director of the Institut Laue-Langevin just when its newly built high-flux research reactor went into operation.

After serving a five-year term, Mössbauer returned to Munich, where he found his institutional reforms reversed by overarching legislation.