Density functional theory based calculations within the framework of the plane-wave pseudopotential approach are carried out to define the phonon spectrum of hydroxyapatite Ca 10 (PO 4 ) 6 (OH) 2 (HAp). It allows to describe the temperature dependence of the electronic spin-lattice relaxation time T 1e of the radiation-induced stable radical NO 3 2-in Hap, which was measured in X-band (9 GHz, magnetic field strength of 0.34 T) in the temperature range T = (10-300) K. It is shown that the temperature behavior of T 1e at T > 20 K can be fitted via two phonon Raman type processes with the Debye temperature D 280 K evaluated from the phonon spectrum.