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3.5.5 Neutron Spin: Intrinsic Angular Momentum

Assuming that radius of the core zone, \(r_0\), is the square root of displacement constant, \(A\), and the angular momentum density, \(\alpha_0=0.94432\ 10^8\) Joule-seconds per cubic meter, it is possible to calculate the intrinsic angular momentum missing from the core zone of the neutrino. We proceed as follows.
\begin{align}
assuming\ radius\ of\ core\ zone,\ r_0 =&\ \sqrt{A} \nonumber \\
r_0 = \sqrt{1.4104729\ 10^{-28}} =&\ 1.1876333\ 10^{-14} \nonumber \\
so\ that\ volume\ of\ core\ zone,\ \frac{4}{3} \pi r_0^3 \ =&\ 7.0167456 \ 10^{-42} \nonumber \\
hence\ angular\ momentum\ missing\ from\ core\ zone\ is\ \nonumber \\
(angular\ momentum\ density)\ \times\ (volume\ of\ core\ zone) \nonumber \\
= (0.94432\ 10^8) \times\ ( 7.0167456 \ 10^{42}) =&\ 6.6260532\ 10^{-34} \nonumber
\end{align}
This is the standard value of Planck's constant, \(h\), to within five decimal places.

The accepted value of intrinsic angular momentum of a neutron is given as \(h/2\), and its not clear why this calculation gives exactly twice that value. However, the above calculation is based on other constants which are substantially correct, whereas, the intrinsic angular momentum of a neutron is not actually measured.

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