The energy of the fragments in the laboratory frame
of a moving molecule that dissociates can be calculated using a Galilei
Assuming a uniform distribution of orientations of the molecules in space and a constant value of , the broadening of the energy distribution in the forward direction of the dissociated molecules can be estimated:
Using spherical coordinates with the particle moving in +z direction and an angle of the molecule axis to the z-axis, the energy of the particle in +z direction is given by Equation 5.34. With a uniform distribution of the molecule axis every direction has the same probability
the solid angle may be expressed in terms of :
The probability for a particle to get the energy after dissociation is
By substituting Equation 5.40 in Equation 5.39 and simplifying the energy distribution yields
This simple model assuming an uniform distribution of the molecule
axis yields a rectangular energy distribution in forward direction.
By extending Equation 5.20 a new fit function
was constructed consisting of a exponentional, a gaussian, and a rectangular
part (Equations 5.43 to 5.46).
is the Heaviside step function and
denotes the full width of the rectangular part.
March 2001 - Martin Wieser, Physikalisches Institut, University of Berne, Switzerland