Morse potential momentum

The dissociation of a diatom differs from that of polyatomic molecules in two ways. First, the dissociation has no real barrier and is given by a simple one-dimensional interaction potential which is often expressed as a Lennard-Jones or a Morse potential. Secondly, the product atoms have no angular momentum. Thus, the initial angular momentum of the diatom is converted exclusively into orbital angular momentum (which is relative translational energy) of the products. For this reason, the diatom dissociation is not an appropriate model for the much more complex dissociation of polyatomic molecules. Nevertheless, there are certain features that carry over. 

This corresponds to an anharmonic sequence of levels labeled by m (the total number of states being once more equal to N-l-1). This quantum number, m, should not be confused with the quantum number associated with the projection of the angular momentum operator. The most interesting situations occurs with the particular choice >li=0, A = A2 (i in (2.64) and (2.65). In this case it is possible to put the spectrum (2.65) in a one-to-one correspondence with the bound-state spectrum of the one-dimensional Morse potential. This can be done by choosing in Eq. (2.65) only the nonnegative branch of the quantum... 

Figure 3 Plot of effective potentials derived using the Morse potential for several values of angular momentum, L, as marked on each curve. See text for the parameters used for the Morse potential. Reproduced with permission of John Wiley from Shirts RB (1986) In Futrell JH (eds) Gaseous Ion Chemistry and Mass Spectrometry.

In this way one can extend previous kinematical models of molecular collisions based on sequences of hard-sphere collisions. Realistic potentials may be included, as well as the role of diatomic momentum distributions of reactants and products.Recent results with this approach include probabilities of T-V transfer and dissociation in collinear H + D collisions with a Morse potential for D2 and exponential or hard-core repulsion for some of which are shown in... 

If the energy and angular momentum of the diatomic are not too large and the potential energy function for the diatomic is either the harmonic or Morse function, n can be determined from the following second-order perturbation theory expression for Ed( ,7) ... 

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