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Line 25:
<math> \mid s\mid = \frac{4\pi}{\lambda}\sin (\theta / 2)
</math>, with <math> \lambda
</math> being the electron wavelength defined above and <math> \theta
</math> being the scattering angle
Line 42:
</math> , with <math> K = \frac{8 \pi ^2me^2}{h^2}
</math>, <math> R
</math> being the distance between the point of scattering and the detector, <math> I_0
</math> being the intensity of the primary electron beam and <math> f_i(s)
</math> being the scattering amplitude of the i-th atom. In essence theis is a summation over the scattering contributions of all atoms independent of the molecular structure. <math> I_a(s)
</math>is the main contribution and easily obtained if the atomic composition of the gas (sum formula) is known.
Line 52:
<math> I_m(s) = \frac{K^2}{R^2}I_0\sum_{i=1}^N \sum_{j=1,i\neq j}^N \mid f_i(s)\mid\mid f_j(s)\mid \frac{\sin [s(r_{ij}-\kappa s^2)]}{sr_{ij}}e^{-(1/2 l_{ij} s^2)} \cos [\eta _i (s) -\eta _i (s)]
</math> with <math> r_{ij}
</math> being the parameter of main interest: the atomic distance between two atoms, <math> l_{ij}
</math> being the mean square amplitude of vibration between the two atoms, <math> \kappa
</math> the anharmonicity constant (correcting the vibration description for deviations from a purely harmonic model), and <math> \eta
</math> is a phase factor which becomes important if a pair of atoms with very different nuclear charge is involved.
The first part is simlilar to the atomic scattering, but contains two scattering factors of the involved atoms. Summation is performed over all atom pairs.
Line 61:
<math> I_t(s)
</math> is negligible in most cases and not described here in more detail and <math> I_b(s)
</math> is mostly determined by fitting and subtracting smooth functions to account for the background contribution.
So it is the molecular scattering intensity that is of interest, and this is obtained by calculation all other contributions and subtracting them from the experimentally measured total scattering function.
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