Theoretical Study On The Nonlinear Force Constants Of One-dimensional Oscillator Based On Atomic Elliptic Orbit And Its Application

In the interaction theory between light and matter,an atom is usually regarded as the one-dimensional classical or quantum oscillator.The classical oscillator is only a qualitative approach in explaining the linear and nonlinear spectral properties of many media for lack of the relationship between its intrinsic frequency and the energy level structure of the related atom and the damping coefficient expression in detail.In November2015,the one-dimensional oscillator with quantized impedance was proposed to quantize the classical vibrator successfully.The damping coefficient is defined as the average collision frequency acting on the transition electron collided by other atoms,and its concrete mathematical expression is also given in the new oscillator model.The theoretical simulation of this model is in good agreement with the linear absorption spectrum of hydrogen atom.The main purpose of this dissertation is to find out a way to calculate the nonlinear force constants of the oscillator on the basis of the idea that,relative to nucleus,the sub-motion in the long-axis direction of electronic elliptical motion is deemed as the one-dimensional an-harmonic oscillator under the resilience resulting from the component in the long-axis of Coulomb force.Some results have been obtained as follows.1.The expressions of the second-and third-order nonlinear force constants of the an-harmonic oscillator are derived out by the taylor expansion of the resilience by means of Bohr-Sommerfeld orbits.In unit of the international system?SI?,our results appear that when the hydrogen atom is in the state with energy quantum number n=2 and the angular quantum number n_?=1,the second-and third-order nonlinear force constants are 1.18×10¹²and 2.41×10²¹,respectively.When the hydrogen atom is in the state of n=3 and n_?=1,the second-and third-order nonlinear force constants are respectively 5.80×10¹00 and 5.03×10¹⁹.2.The two-photon absorption?2PA?characteristics of the two spectrum lines in Lyman series of hydrogen atom have been investigated with the help of the damping coefficient of the modified oscillator.Our results show that,in the standard state,the 2PA cross section of the hydrogen atom transition from the ground state to the first excited state?n=2?n_?=1?is about 2.81×10^-4747 cm⁴?s?photon^-1.For the transition from the ground state to the second excited state?n=3?n_?=1?,the 2PA cross section is round about 5.97×10^-51cm⁴?s?photon^-1.3.We have theoretically simulated the Kerr coefficient of the hydrogen atom medium and the second-and third-order nonlinear susceptibility in the standard state.The detailed results in SI units exhibit that when the hydrogen atom jumps from the ground state to n=2?n_?=1 and n=3?n_?=1,the maximum values of the Kerr coefficient can respectively reach to 4.80×10^-2323 and 7.00×10^-2727 in near 2PA resonance.The two maximum values of the second-order susceptibility corresponding to the second harmonic is about 1.90×10^-77 and4.30×10^-10.The two maximum values of the third order susceptibility corresponding to the third harmonic can reach to 1.36×10^-1414 and 3.40×10^-1818 respectively.The above results may be significant for the study of the nonlinear optical properties of the media composed of hydrogen-like atoms.Our method dealing with the nonlinear force constants of the one-dimensional an-harmonic oscillator can also be further applied to study the fourth or higher order nonlinear force constants.