The energy of the fragments in the laboratory frame
of a moving molecule that dissociates can be calculated using a Galilei
transformation [14]
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
(5.35) |
the solid angle may be expressed in terms of :
(5.36) |
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
(5.41) | |||
(5.42) |
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