Is the Moment of Inertia Formula for a Fluid Nucleus Accurate?

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SUMMARY

The forum discussion centers on the accuracy of the moment of inertia formula for a fluid nucleus as presented by K.S. Krane in "Introductory Nuclear Physics," specifically equation 5.19. The formula is defined as \(\mathscr{I}_{\text{fluid}} = \frac{9}{8\pi}MR^2_{avg}\beta\), where \(\beta\) is the deformation parameter calculated using \(\beta = \frac{4}{3}\sqrt{\frac{\pi}{5}}\frac{\Delta R}{R_{avg}}\). The user is conducting a project in nuclear physics to compare experimental and theoretical moment of inertia values, noting discrepancies in Krane's earlier formulas. The discussion seeks validation and justification for equation 5.19.

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malawi_glenn
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Hi!

I was wondering if some here can confirm this formula given by K.S Krane in his book "Introductory Nuclear Physics", page 145, eq # 5.19

[tex]\mathscr{I} _{\text{fluid}} = \dfrac{9}{8\pi}MR^2_{avg}\beta[/tex] (5.19)

Moment of inertia for a ellipsodial fluid. Where [itex]\beta[/itex] is the deformation parameter, defined as:

[tex]\beta = \dfrac{4}{3}\sqrt{\dfrac{\pi}{5}}\dfrac{\Delta R}{R_{avg}}[/tex]

And Delta_R is the difference between semimajor and semiminor axix of the ellipse.

I am doing a small project in nuclear physics about comparing moment of intertia obtained from experiemt and theoretical ones. formula # 5.16 in Krane, I can show that Kranes is not correct (how you obtain beta from intrinsic quadroploe moment). But formula 5.18 are correct up to first order.

So can someone help me justify eq 5.19 ?
 
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