Difference between revisions of "Talk:Neutron scattering lengths"

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-==Origin of the scattering lengths==
-The following description is adapted from [www.ncnr.nist.gov/programs/sans/pdf/polymer_tut.pdf Boualem Hammouda's (NCNR) SANS tutorial].
-Consider a neutron of energy <math>E_i</math> interacting with a nucleus, which exhibits an attractive square well of depth <math>-V_0</math> and width <math>2R</math>; where <math>V_0 \gg E_i</math>. The [http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation Schrödinger equation] is:
-:<math>
-\left[ - \frac{h^2}{8 \pi^2 m}\nabla^2  + V(r) \right] \psi = E \psi
-</math>
-Outside of the square-well (<math>r>R</math>), <math>V(r)=0</math>, and so the equation is solved as simply:
-:<math>
-\psi_{s,\mathrm{out}} = \frac{\sin(kr)}{kr} - b \frac{e^{ikr}}{r}
-</math>
-where <math>k=\sqrt{2mE_i} 2 \pi/h.

Latest revision as of 11:41, 6 June 2014