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Neptunium-236 has a half-life of about 154,000 years, which is quite long for an isotope with odd numbers of both protons an neutrons, correct?

Other 'odd-odd' nuclides with longer-than-expected half-lifes can only decay by going through major changes in spin, so are considered 'high-spin stabilized'. But I cannot find a place where it specifically says this about Np-236......

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The quantity $Z^2/A$ equals 36.6 for this isotope, which makes it not have any significant probability of decay by spontaneous fission. See https://en.wikipedia.org/wiki/Spontaneous_fission .

In alpha decay, its daughter will also be odd-odd, so the alpha decay half-life doesn't get shorter just because it's odd-odd. Its $Z$ isn't very high, so it's not surprising that alpha decay is weak.

That leaves beta decay and electron capture. Its main mode of decay is electron capture.

Other 'odd-odd' nuclides with longer-than-expected half-lifes can only decay by going through major changes in spin, so are considered 'high-spin stabilized'. But I cannot find a place where it specifically says this about Np-236......

Did you try looking at ENSDF?

Jπ: High log ft′s in β−, ε decays suggest large K value. Nilsson level syst (1972El21) suggests Jπ=6−. β− and ε decays to 6+ levels in 236Pu and 236U are consistent with J=6.

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