The Energy Transfer Between Two Diatomic Molecules In Collinear Collisions

In this paper, the vibration-vibration and translation-vibration energy transfer in collinear collisions between two diatomic molecules are studied by employing dynamical algebraic approach.In the theoretical study of molecular scattering, three kinds of theoretical methods are used widely. One is the close coupling method, whose approximate methods containing CS, ESandIOS methods. The close coupling method is a kind of totally quantum calculating method. It starts from the SchrOdinger equation, strictly solve a set of coupling equations. But when using it to study the scatter problem, the coupling equations need to solve is a large number, so that the potential integrate becomes very complicated. The results of the approximate method mentioned above can be the standards that other theoretical method compared with. The second one is called classical S— matrix method introduced by Miller and Marcus. In this method, both of the relative motion and the molecular inside motion is treated classically, the quantum effect of the system is imported through statical adding theory and uncertainty theory. The third one is semiclassical method, where the relative motion of the incidence particle is treated classically, and the molecular inside motion is dealt by quantum mechanics. The Lie group and Lie algebra method is based on symmetrical theory. In the paper, using the third method plus the Interactive Picture, also referring to the algebraic model of anharmonic Morse oscillator which is introduced by Levineetal. in 1983, and considering the two diatomic molecular head-to-head collinear collision, the author studied the vibration-vibration and translation-vibration energy transfer of the system and also discussed the revolution of the expectation value of molecular dynamical operators during the collision.Lie algebraic method of molecules which is also called vibron mode, was introduced by Iachello, Levineetal. in 1980s from nuclear physics to molecular physics. Its advantages lies at that it not only in principle provide the exact solution of the system, but also is effective when usual methods is in difficulty. The models are based on the idea of dynamic symmetry, which is expressed through the language of Lie algebra. Applying second quantization method, one can construct algebraic Hamiltonian operator of physical system. However, in the general case, it is difficult to solve. If one takes dynamic symmetry into account, the Hamiltonian operator of system can be indeed simplified greatly and easily get its revolution operator. For different physical systems, one can describe them with the same algebra, which is the merit of this method. For studying the simple diatomic molecules, SU(2) Lie group and the direct sum of it is usually enough and there are also complicated Lie group such as SU(A)etal. for the complicated molecules.The paper discuss the vibration-to-vibration (V-V) and translation-to-vibration (T-V) energy transfer in scatter system AB+CD. The model discussed in the paper is collinear collision. Although it is simple, it's very useful in the actual theoretical researches. It can be used to check up the earlier approximated methods and some numerical value studies. When dealing with the scattering problems, a theoretical method can be extended to be used in studying the three dimensional model when it is successfully used in dealing with the collinear model. This paper successfully use Lie group and Lie algebra to discuss the collinear collision between two diatomic molecule. The energy transfer after the collision is discussed, and the result is compared with other numerical results.There are four chapters in the paper:In chapter 1, first of all we introduce background of the molecular scatter containing the general use and models of scattering system, the widely used theoretical methods for molecular scatter and the developing degree in discussing in the field and also the basic theoretical found which is used in the paper. The application of the dynamical of Lie group and Lie algebraic method is discussed in section 2. The an-harmonic oscillator algebraic model is discussed in section 3 containing the derivation of the model and the constructed of the second quantization process Hamiltonian of the model .Chapter 2 is the main part in the paper. The Lie group and Lie algebraic method is used to study the collision between two diatomic molecules. The exact theoretical approach is put in practice. From the construction of the Hamiltonian to the work out of the transition probabilities. The fist part is the theoretical process, including the formulae of time revolution operator, the use of SU(2) lie group, and the analytical expression of the transition probabilities. The second part mainly discuss the calculation results of the transition probabilities. A lot of pictures have been listed in this part to demonstrate the collision process. A few of collision systems have been studied in this part.In chapter 3, we have calculated the expectation value of the dynamical operators in Hamiltonian. The maximal entropy process in information theory is used in this part. The expression of the density operator of the system is worked out to study the expectation value of the mechanical operators. This part is the second part we have studied in molecular scatter and it is the advantage of lie algebraic method because that usual theoretical method can not do this. In this part, when comes to calculate the expectation value of the dynamical operator, the twice number of the bonding state of system is numbered by TV = 1/x₀, where x₀ is the anharmonic parameter of molecule.Chapter 4 concludes, we show the main conclusions of this paper. The application vistas of Lie algebraic method are prospected. Several assumptions are listed to prepare for the work to be done in molecular scattering field.