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Betaofnu Betaofnu is a program to calculate the anisotropy paramater, ß, for a diatomic molecule and for linear polarization as a function of frequency, lifetime of the dissociative state (line broadening parameter), rotational level, and rotational constants. The program is described in the work listed below. In addition to calculating beta as a function of frequency, the program also provides a spectral simulation. The program is capable of transitions for singlets between Sigma+/-, Pi, Delta, and Phi; for doublets between Sigma+/-, Pi, and Delta; and for triplets between Sigma+/- and Sigma+/-. The program automatically interpolates between Hund's case (a) and (b) behavior. Provision is made for the addition of nuclear spin statistics. The program can calculate for a single frequency, or for a range of frequencies, for a single starting rotational level, or for a range of initial J values, for individual F systems, or for any combination of them. The program works by expanding the wavefunctions in a Hund's case (a) basis using known formulae for the expansion coefficients. The angular distribution at each spectral element is given by a sum (incoherent) over contributions from different initial states of the square amplitude of a sum (coherent) over the product of the transition amplitude to each dissociatiative state times the angular part of the scattering wavefunction. See the paper below for details. Extension to circular polarization, to other diatomic states, to symmetric top polyatomic molecules, and to two-photon transitions would be possible, depending on interest in testing the results. The program calculates the angular distribution accurately for J values up to 25 (24.5 for doublet states). It makes an approximation for higher J values that appears to be reasonable. I would be grateful for a new algorithm to calculate accurate values of the d(J,N,M,theta) rotation matrix elements with J greater than 26. The one used is based on equation 3.66 in Zare's Angular Momentum. Abstract (of the paper referenced below): Quantum mechanical calculations of photofragment angular distributions have been performed as a function of the frequency of excitation, the lifetime of the dissociative state, the rotational level and the rotational constant . In the limit of high J values and white, incoherent excitation, the general results are found to agree exactly with both those of Mukamel and Jortner and those of Jonah. Example calculations describe how the anisotropy is dependent on the degree of broadening, the rotational constant, the initial rotational level, and the frequency of excitation. Applications are also made to interpret experimental results on the photodissociation of ClO via the 11-0, 10-0 and 6-0 bands of the A 2Pi3/2 - X 2Pi3/2 transition and on the photodissociation of O2 via the 0-0 band of the E 3Sigma-(u) - X 3Sigma-(g) transition. The figure below shows a result from the paper The published work is now available: Hahkjoon Kim, Kristin S. Dooley, Simon W. North, G. E. Hall, and P. L. Houston, "Anisotropy of photofragment recoil as a function of dissociation lifetime, excitation frequency, rotational level and rotational constant," J. Chem. Phys. 125, 133316-26 (2006). pdf format Download current Betaofnu. Program Instructions Revision Sheet Installation Instructions This section of our web site is supported by The Chemistry Division of the National Science Foundation "Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation."