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Omnidirectional photoluminescence (ODPL) measurement using an integrating sphere was carried out to absolutely quantify the quantum efficiency of radiation (η) in high quality GaN single crystals. The total numbers of photons belonging to photoluminescence (PL photons) and photons belonging to an excitation source (excitation photons) were simultaneously counted in the measurement, and η was defined as a ratio of the number of PL photons to the number of absorbed excitation photons. The ODPL spectra near the band edge commonly showed a two-peak structure, which originates from the sharp absorption edge of GaN. A methodology for quantifying internal quantum efficiency (ηint) from such experimentally obtained η is derived. A record high ηint of typically 15% is obtained for a freestanding GaN crystal grown by hydride vapor phase epitaxy on a GaN seed crystal synthesized by the ammonothermal method using an acidic mineralizer, when the excitation photon energy and power density were 3.81 eV and 60 W/cm2, respectively. [ABSTRACT FROM AUTHOR]