Theory of nonradiative multiphonon transitions in impurity centers with extremely weak electron‐phonon coupling

Abstract

The nonradiative multiphonon (NMP) electron transition rate in impurity centers in ionic crystals is calculated taking into account high-order anharmonicity terms in expansion of the electronphonon (EP) interaction in atomic displacements. In the extremely weak coupling limit the traditional potential energy surface displacement relaxational mechanism is shown to be inefficient and NMP relaxation is caused mainly by high anharmonicity of the EP interaction. For this limit a new formula is obtained, which may be applied, e.g., in analysing the NMPrelaxation of RE ions in ionic crystals.IIOJIyqeHO BbIpa&eIIHe X n H CKOPOCTH MHOrO@OHOHHOrO 6e3bI3JIysaTenbHOrO (ME) 3JIeIE-

Oxysulfide optical ceramics doped by Nd3+ for one micron lasing

“…For the single-phonon frequency model the spectral density is determined as [11] J ðpÞ ðO J 0 J Þ ¼ 2p½Kð0Þ p ½nðo eff ; TÞ þ 1 p =o max…”

“…For correct estimation the results of the nonlinear theory of MR relaxation can be used [11][12][13][14][15][16][17]. In the frame of nonlinear theory of MR the total p-phonon transition probability W J 0 !J p ð Þ between the two J manifolds can be written in a form similar to the Judd-Ofelt expression for an electro-dipole radiative transition probability between the same manifolds [18,19]:…”

Mid-IR transitions of trivalent neodymium in low phonon laser crystals

“…[9][10][11] it was theoretically predicted and in Refs. [8,12] it was experimentally observed that the MR rates depend strongly on reduced matrix elements of electronic transitions U (k) .…”

“…In the frame of nonlinear theory of multiphonon relaxation [3,[8][9][10][11][12][13] and for the single phonon frequency model of lattice vibration [14] the p-phonon transition probability W J 0 !J ðpÞ between any two J manifolds at T = 0 K can be calculated using the following equation written in a form similar to Judd-Ofelt expression for an electro-dipole radiative transition probability between the same manifolds (see below first term of Eq. (14))…”

Temperature-Dependence of Multiphonon Relaxation of Rare-Earth Ions in Solid-State Hosts

“…Using the weak coupling limit, a saddle-point approximation enabled Fong et al to show that time integration of the correlation function leads to a relaxation rate in which the energy gap is effectively modified by the addition or subtraction of Δ ν quanta of the mediating phonon mode via five contributing scattering processes. 13,24,25 The radiationless decay rate of electronically excited ions in a crystalline lattice is given by 6 …”