摘要 本文采用LГ表象,考虑到不同组态间的相互作用(立方场,三角场与自旋轨道作用),计算了红宝石中锐线B,S与R线的能级及其分裂和基态的分裂。所得结果是B线与R线跟实验较符合,基态的分裂较实验值小,这可能是更高能级的三角场与自旋轨道的微扰作用所引起的。 Abstract By means of the LT representation the author calculated the energy levels and the splittings of sharp lines in ruby. The interaction between various configurations has been taken into account. The splittings of energy levels of R and B lines so obtained agree well with experimental results. But the splitting of ground state comes out too small to be compared with experiment. If may be attributed to the perturbation of the higher energy levels. . 作者及机构信息 谭维翰 1. 中国科学院 Authors and contacts TAN WEI-HAN 1. 中国科学院 参考文献 [1] 施引文献
The use of a quantitative analysis of the dominant source of relaxation in ruby spin systems to make predictions of key maser amplifier parameters is described. The spin-lattice Hamiltonian which describes the interaction of the electron spins with the thermal vibrations of the surrounding lattice is obtained from the literature. Taking into account the vibrational anisotropy of ruby, Fermi's rule is used to calculate the spin transition rates between the maser energy levels. The spin population rate equations are solved for the spin transition relaxation times, and a comparison with previous calculations is made. Predictions of ruby gain, inversion ratio, and noise temperature as a function of physical temperature are made for 8.4-GHz and 32-GHz maser pumping schemes. The theory predicts that ruby oriented at 90 deg will have approximately 50 percent higher gain in dB and slightly lower noise temperature than a 54.7-deg ruby at 32 GHz (assuming pump saturation). A specific calculation relating pump power to inversion ratio is given for a single channel of the 32-GHz reflected wave maser.
The relaxation of resonant 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons trapped in a laser-excited cylinder of submillimeter diameter is investigated under the conditions of modulated pumping in ruby of 130, 700, and 2500 at. ppm
Cr3+ at 1.5 K. The decay time
Teff of the 2\ifmmode \bar{A}\else \={A}\fi{}
(2E) population, which is a measure of the phonon relaxation time, appears to depend on the metastable population
N∗ and the cylinder diameter L as the product
N∗L only, establishing boundary-limited phonon decay. At
N∗L below 5\ifmmode\times\else\texttimes\fi{}
1015 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$, pure spatial diffusion prevails.At higher
N∗L, where the measured
Teff levels off at about 1 \ensuremath{\mu}s, dependent on the ground-state concentration, the phonon relaxation is adequately accounted for by the assumption of enhancement by mediation of frequency-shifting Orbach processes at metastable
Cr3+ subject to diagonal exchange with ground-state
Cr3+. Shifts away from resonance to the extent that the phonons escape the zone by ballistic flight are considered active, which predominantly involve distant
Cr3+ neighbors.Furthermore, a random distribution of
Cr3+ is assumed, while the exchange is calibrated with reference to pair spectra. The spin-nonflip transitions of metastable
Cr3+ that are part of the pairs remain at resonance with the phonons because the exchange splittings of \ifmmode \bar{E}\else \={E}\fi{}
(2E) and 2\ifmmode \bar{A}\else \={A}\fi{}
(2E) are comparable. This is borne out by a separate calculation based on a perturbative molecular field. In addition, experiments have been performed as a function of an external magnetic field up to 4 T parallel to the c axis to disclose the effects of successive separation of the spin-flip and spin-nonflip transitions. The resultant complex development of
Teff with field as well as similar data on the
R2 luminescent intensity taken with continuous optical pumping are consistent with exchange-invoked relaxation and, further, yield effective spectral widths of the 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ transitions of the weakly coupled metastable
Cr3+ of order 1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$.
Transition probabilities of spin-lattice relaxation (RTP) based on the Kronig-Van Vleck mechanism are calculated for ruby for the orientations θ = 90 and 54° and for magnetic fields up to 15 kG. Inversion ratios are evaluated on the basis of the RTP's for various pumping modes. Experimental measurements of the inversion ratio and pumping power at a signal frequency of fs = 22.2 GHz are carried out. The Kronig-Van Vleck mechanism is shown to be the principal mechanism of spin-lattice relaxation for high magnetic fields and low concentrations of paramagnetic ions.
摘要 本文从解析性的讨论出发,应用朗道关系改进Дзялошинский的图解法,建立了双时因果格林函数的费曼图解法,它具有正确的零温权限,并可直接用来计算各种非平衡过程的动力学性质。 Abstract Starting from the discussion of analytic properties and using the Landau relation to improve the diagrammatic technique of Dzyaloshinskii, the Feynman diagrammatic technique for double time dependent causal Green's function is established. There is a correct limit of zero temperature and may be used to calculate the various dynamical properties of nonequlibrium processes. 作者及机构信息 章思俊 1. 中国科学院 Authors and contacts CHANG SHIH-CHUN 1. 中国科学院 参考文献 [1] 施引文献
The relaxation times T1for the grouud state levels in ruby were measured in the temperature range 4.2 to 1.6°K for the various concentrations of theCr^{3+}ionsffrom 0.05 to 0.7 percent. The dependenceT_{1}(f)of the formT_{1}^{-1}(f) = T_{1}^{-1}(0) + T_{1}^{-1}(I)f ^{n}withn \simeq 2has been obtained for the different transitions. The measurements of relaxation times for\pm \frac{1}{2} \leftrightarrow \pm \frac{3}{2}transition at zero magnetic field were especially aimed at establishing a form of dependenceT_{1}(f)because of the absence of the cross relaxation effects in this case. The normal temperature dependenceT_{1} \propto T_{1}^{-1}has been obtained at all concentrations in comparison with anomalous dependences observed at high concentrations by some researchers.