Application Of The Atomic One-Dimensional Oscillator With Quantized Impedance

In the interaction theory between light and matter,an atom is usually simplified as the one-dimensional oscillator,whether in classical or quantum situations.One of the main problems in the two models is the lack of explicit and specific mathematical expressions of the damping coefficient.Due to this deficiency,the two models cannot be used in the explanation of the characteristics of the actual atomic spectra.By introducing the new concepts of quantized impedance damping and collision cross section into the classical oscillator in November 2015,the one-dimensional oscillator with quantized impedance was proposed,in which the damping coefficient was defined as the average collision frequency of the electronic transition process impacted by other atoms.The corresponding and specific mathematical expressions are also given in the modified oscillator.The simulated emission spectrum of hydrogen atom is well in accordance with the experimental one.Based on this model,by taking hydrogen atom for instance,we have investigated the influence of the energy level width on the damping coefficient and transition frequency,the temperature characteristics of atomic spectrum,and the relationship between the atomic linear absorption and the electron transitions crossing the Bohr-Sommerfeld orbits.The main results of our effort are as following:1.The influences of the energy level lifetime on the damping coefficient and the energy level width on the transition frequency are analyzed quantitatively.Considering the atomic energy level width and lifetime of an excited atom,we have obtained the expression of the first order electric susceptibility for the isotropic dielectric on the basis of the energy transform and conservation law.Our numerical results show that the influence of the energy level lifetime on the damping coefficient can be completely neglected in the range of UV,visible and infrared light and the energy level width influence on the transition frequency of the related atom is insignificant as well.The average collision frequency of the jumping electron sufficiently represents the meaning of the damping coefficient determining the FWHM of atomic spectrum.2.According to the average collision frequency of the transition electron process,we have investigated the temperature characteristics of atomic spectral line width and intensity.Our results appear that the spectral line width broadens with the temperature rise.Moreover,FWHM of the spectral series such as Balmer and Paschen series will exceed over 1.0 nm and 20.0 nm,respectively when the temperature is higher than 1000 K.The numerical results also exhibit that the linear absorption coefficient of Balmer series increases with the temperature going up.In addition,compared with the spectrum in Balmer series,the spectrum in Lyman series appears brighter and narrower at the same temperature.Similarly,compared with the spectrum in Paschen series,the spectrum in Balmer series appears brighter and narrower.By means of the one-dimensional oscillator with quantized impedance,the well-known Sellmeier empirical formula about refractive index has been further analyzed.3.According to Bohr-Sommerfeld’s orbital theory,we have studied the relationship between the linear absorption coefficient of hydrogen atom H_αspectrum and the electron transition crossing different orbits.Taking the orbital transition from n=2、n_φ=2 to n=3、n_φ=3 as the benchmark,we have calculated the relative differences of the absorption coefficients of electron transition between different orbits.The results show that the highest relative difference of the absorption coefficient of electron transition between different orbits(also for H_αspectrum)can reach up to 351.31%.The different values for absorption coefficient of electron transition between different orbits indicate that the probability of electron transition between different orbits may be different.In another word,the absorption coefficient is clearly related to the atomic charge transfer process and its final charge-distribution.These results may be worthy of as a certain reference for the actual measurement and analysis of the spectral characteristics of hydrogen-like atom.