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Deuteron Transcendental Equation
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[QUOTE="James_1978, post: 6855751, member: 272105"] [B]Homework Statement:[/B] I believe I solved the transcendental equation but the plot does not make sense. [B]Relevant Equations:[/B] ##k_{1} \cot{k_{1}R} = -k_{2}## ##k_{1} = \frac{\sqrt{2m(E+V_{o})}}{\hbar}## ##k_{2} = \frac{\sqrt{-2mE}}{\hbar}## ##x = -\tan{bx}## ##x = \sqrt{\frac{-(V_{o} + E)}{E}}## Dear Forum, I am trying to solve a problem (4.6) from the introductory nuclear physics textbook by Krane. The problem is as follows: Solving the deuteron using the radial equations gives the transcendental function, ##k_{1} \cot{k_{1}R} = -k_{2}## Were ##k_{1} = \frac{\sqrt{2m(E+V_{o})}}{\hbar}## And ##k_{2} = \frac{\sqrt{-2mE}}{\hbar}## That gives the relations between and R. Show that this equation can be written in the form, ##x = -\tan{bx}## Where ##x = \sqrt{\frac{-(V_{o} + E)}{E}}## Evaluate the parameter b for R = 2fm. Note that is the reduced mass. Solve the transcendental equation. When rearranging we get ##b## as. ##b = \frac{\sqrt{-2mE}}{\hbar}*R## For the reduced mass ##m = \frac{1.67x10^{-27}}{2} kg## For ##\hbar = 1.054x10^{-34} J-s## For ##E = -2.22 MeV## We are suppose to see that when solving the transcendental equation we get ##V_{o} = 36 MeV##. However we must have something wrong because the function does not clearly show how you infer the ##V_{o} = 36 MeV##. Any help is appreciated. [/QUOTE]
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Deuteron Transcendental Equation
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