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Vibration excitation

  1. Jul 11, 2009 #1
    When we have vibration excitation then the radius of nucleus is define like:

    where [tex]\alpha_{\lambda,\mu}=\alpha_{\lambda,-\mu}[/tex] and [tex]\alpha_{\lambda,\mu}=\alpha_{\lambda,\mu}(t)[/tex]

    How you measure this [tex]\alpha[/tex] parametar?


    And more:
    Kinetic energy of system is define like:

    [tex]T=\frac{1}{2}\sum_{\lambda,\mu}B_{\lambda}|\frac{d \alpha_{\lambda,\mu}}{d t}|^2[/tex]

    Rayleight use [tex]\rho=\frac{3M}{4R^3_0\pi}[/tex], and get [tex]B_{\lambda}=\frac{3MR^2_0}{4\pi\lambda}[/tex]. How?

    Thanks for answers
  2. jcsd
  3. Jul 11, 2009 #2


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    Which book, what have you tried? ..
  4. Jul 11, 2009 #3
    Well this is from book "Osnovi nuklearne fizike" - Lazar Marinkov. I tried Burcham and some book of Gamov. From the Marinkov's book I think that this is given in reference P. Ring and P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, New York, Heidelberg, Berlin, 1980) but I don't have this book.
  5. Jul 14, 2009 #4
    The first equation is just a decomposition of a generic function defined on a sphere in terms of spherical harmonics Y. Like a Fourier transform, but on a sphere. [tex]\alpha[/tex]'s are decomposition coefficients.

    Y's, though scary looking, are normalized so that the integral of [tex]|Y|^2[/tex] over the entire sphere is something simple (there are a few different definitions, one common definition is that [tex]\int |Y|^2 d\Omega = 1[/tex]. I can't tell right away which one is used by your book.) If you assume that only one of [tex]\alpha[/tex]'s is nonzero and make certain assumptions about the nuclear matter, perhaps that non-excited nucleus is a homogeneous sphere of density [tex]\rho[/tex], deformed according to the formula above, and make assumptions about velocity distribution, and you compute kinetic energy by integrating over the entire volume, you'll get an equation that expresses B in terms of [tex]\rho[/tex].
  6. Jul 17, 2009 #5
    Thanks for answering.
    In that series is [tex]\alpha[/tex] perhaps complex functions in general?
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