Calculations of the rotational lines and their strength for the swan band of C{sub}2 molecules: a study on the degenerate four wave mixing spectrum

摘要

The C{sub}2 molecule is an important in astrophysics and diamond synthesis and this molecule can be generated abundantly, using an oxy-acetylene torch, for research. Recently, Kaminski et al. assigned the DFWM rotational energy level for the (0,0) Swan band (d 3{sup left}∏{sub}g <→ a 3{sup left}∏{sub}u) of a C{sub}2 molecule using molecular constants for Brown et al.'s effective Harniltoman. The Hamiltonian formalism developed by Brown et al. diagonalizes upper- and lower-state Hamiltonianmatrices of the transition using a basis set of the Hund's case (a) representation, and it is very useful for empirical fitting of the data. The Hamiltonian formalism proposed by Zare et al. also uses a basis set of Hund's case (a) and the second-orderperturbations are based on a unique perturbing model, in which the submatrix connecting the electronic states of interest to a single perturbing state is diagonalized. This formalism is better for understanding the physically meaningful values of themolecular parameters rather than the empirical fitting of the data because the electronic state of interest may be perturbed by many nearby electronic states of the different symmetries. However, the molecular constants that must be used in any particular effective molecular Hamiltonian are more or less unique to that Hamiltonian.