Calculation of the thermal broadening of the A phononless line in the 4F3/2→4I11/2 band of the Nd3 + ion in yttrium aluminum garnet

A detailed calculation is made of the width of one of the luminescence lines of Nd^{3 +} in Y₃Al₅O₁₂ in a band corresponding to the transitions from ⁴F_3/2 to ⁴I_11/2. The calculation is made on the assumption that the phonon spectrum of the crystal is of the Debye form. Allowance is made for the influence of the noncubic nature of the crystal field and for the interaction of the 4f electrons with totally symmetric, tetragonal, and trigonal vibrations in the immediate environment. The results indicate that the real profile of the impurityactive vibration spectrum of the crystal has to be allowed for in considering the broadening and shift of the phononless lines of Nd^{3 +} in Y₃Al₅O₁₂.