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I'm reading Wong 'Introductory Nuclear Physics' and in chapter 3-1 he writes that "For the deuteron, it is known that the parity is positive. Let us see what we can learn from this piece of experimental information."

My question is, how is it known that the parity of the deuteron is positive? He is indicating that it is measured experimentally, what observable would indicate positive or negative parity?

I know that the intrinsic parity of the quarks are positive and anti-quarks are negative, which would directly lead to the parity of the proton/neutron system to be positive, but quarks weren't discovered until some time after the deuteron. Is there a way to measure parity in an experiment without going back to some theoretical declaration?

P.S. any recommendations for good graduate level nuclear physics textbooks?

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Before quarks were discovered, the intrinsic parities of the proton and neutron were positive by convention. After quarks were discovered, the intrinsic parity of hadrons could be derived from their quark structure and the intrinsic parity of quarks. The convention that quarks have positive parity was chosen because that is the convention that keeps the proton and neutron parities positive in agreement with the earlier convention.

Since the proton and neutron have positive parity, the parity of the deuteron is $(-1)^L$, where $L$ is the proton-neutron orbital angular momentum. As Bethe calculated as far back as 1940, the deuteron ground state is mostly L=0 with a bit of L=2, so the deuteron has positive parity. (The strong interactions that bind the deuteron can only mix states with the same parity.)

Obvious experimental evidence that the deuteron is mostly S-wave (and hence has positive parity) comes from comparing the magnetic moments of the proton, neutron, and deuteron. For an S-wave deuteron, the proton and neutron spins are aligned and we expect the magnetic moment of the deuteron to be the sum of the proton and neutron magnetic moments, i.e (2.7928 and -1.913 nuclear magnetons respectively, from The Table of Isotopes). The experimentally measured deuteron magnetic moment is 0.8574 nuclear magnetons, which agrees within 2.5% of the sum of the proton and neutron magnetic moments, with the small difference due to the small D-wave contribution to the deuteron ground state. If the proton and neutron were in a P-wave, then their spins would have to be anti-aligned, so the magnetic magnetic moment of the deuteron would be different.

More direct evidence for positive parity of the deuteron comes from scattering experiments. For example, according to Landau & Smorodinsky, p. 15, as far back as the 1950s low energy scattering of neutrons by protons was consistent with the existence of a $(1^+)^3S_1+^3D_1$ positive parity deuteron, but not consistent with a $(1^-)^1P_1$ or $(1^-)^3P_1$ negative parity deuteron. More recently, there has been much theoretical and experimental work on the tiny parity-violation effects in $n d$, $p d$, $e d$, and $\gamma d$ scattering. Since the parity violation depends on the different parity states involved, they are effectively also precision measurements of the deuteron parity.

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    $\begingroup$ As someone who spent several years working on parity violation in $np\to d\gamma$, I applaud this top-notch answer. $\endgroup$
    – rob
    Nov 24, 2023 at 4:24

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