A theory for shifts of energy spectra due to electron-phonon interaction (EPI) has been developed. Both the temperature-independent contributions and the temperature-dependent ones of acoustic branches and optical bra...A theory for shifts of energy spectra due to electron-phonon interaction (EPI) has been developed. Both the temperature-independent contributions and the temperature-dependent ones of acoustic branches and optical branches have been derived. It is found that the temperature-independent contributions are very important, especially at low temperature. The total pressure-induced shift (PS) of a level (or spectral line or band) is the algebraic sum of its PS without EPI and its PS due to EPI. By means of both the theory for shifts of energy spectra due to EPI and the theory for PS of energy spectra, the total PS of R<SUB>1</SUB> line of tunable laser crystal GSGG:Cr<SUP>3+</SUP> at 70 K as well as the ones of its R<SUB>1</SUB> line, R<SUB>2</SUB> line and U band at 300 K will be successfully calculated and explained in this series of papers.展开更多
With the strong-field scheme and trigonal bases, the complete d<SUP>3</SUP> energy matrix in a trigonally distorted cubic-field has been constructed. By diagonalizing this matrix, the normal-pressure energ...With the strong-field scheme and trigonal bases, the complete d<SUP>3</SUP> energy matrix in a trigonally distorted cubic-field has been constructed. By diagonalizing this matrix, the normal-pressure energy spectra and wavefunctions of GSGG:Cr<SUP>3+</SUP> at 70 K and 300 K have been calculated without the electron-phonon interaction (EPI), respectively. Further, the contributions to energy spectra from EPI at two temperatures have also been calculated, where temperature-independent terms of EPI are found to be dominant. The sum of aforementioned two parts gives rise to the total energy spectrum. The calculated results are in good agreement with all the optical-spectral experimental data and the experimental results of and . It is found that the contribution from EPI to R<SUB>1</SUB> line of GSGG:Cr<SUP>3+</SUP> with taking into account spin-orbit interaction (H<SUB>so</SUB>) and trigonal field (V<SUB>trig</SUB>) is much larger than the one with neglecting H<SUB>so</SUB> and V<SUB>trig</SUB>, and accordingly it is essential for the calculation of the EPI effect to take first into account H<SUB>so</SUB> and V<SUB>trig</SUB>. The admixture of base-wavefunctions,and , the average energy separation and their variations with temperature have been calculated and discussed.展开更多
文摘A theory for shifts of energy spectra due to electron-phonon interaction (EPI) has been developed. Both the temperature-independent contributions and the temperature-dependent ones of acoustic branches and optical branches have been derived. It is found that the temperature-independent contributions are very important, especially at low temperature. The total pressure-induced shift (PS) of a level (or spectral line or band) is the algebraic sum of its PS without EPI and its PS due to EPI. By means of both the theory for shifts of energy spectra due to EPI and the theory for PS of energy spectra, the total PS of R<SUB>1</SUB> line of tunable laser crystal GSGG:Cr<SUP>3+</SUP> at 70 K as well as the ones of its R<SUB>1</SUB> line, R<SUB>2</SUB> line and U band at 300 K will be successfully calculated and explained in this series of papers.
文摘With the strong-field scheme and trigonal bases, the complete d<SUP>3</SUP> energy matrix in a trigonally distorted cubic-field has been constructed. By diagonalizing this matrix, the normal-pressure energy spectra and wavefunctions of GSGG:Cr<SUP>3+</SUP> at 70 K and 300 K have been calculated without the electron-phonon interaction (EPI), respectively. Further, the contributions to energy spectra from EPI at two temperatures have also been calculated, where temperature-independent terms of EPI are found to be dominant. The sum of aforementioned two parts gives rise to the total energy spectrum. The calculated results are in good agreement with all the optical-spectral experimental data and the experimental results of and . It is found that the contribution from EPI to R<SUB>1</SUB> line of GSGG:Cr<SUP>3+</SUP> with taking into account spin-orbit interaction (H<SUB>so</SUB>) and trigonal field (V<SUB>trig</SUB>) is much larger than the one with neglecting H<SUB>so</SUB> and V<SUB>trig</SUB>, and accordingly it is essential for the calculation of the EPI effect to take first into account H<SUB>so</SUB> and V<SUB>trig</SUB>. The admixture of base-wavefunctions,and , the average energy separation and their variations with temperature have been calculated and discussed.
