Evidence That the Deuteron Is Not an Elementary Particle

Abstract

If the deuteron were an elementary particle then the triplet $n-p$ effective range would be approximately $-\frac{\mathrm{ZR}}{\mathrm{}(I-Z)\mathrm{}}$, where $R=4.31\mathrm{}$ F is the usual deuteron radius and $Z$ is the probability of finding the deuteron in a bare elementary-particle state. This formula is model-independent, but has an error of the order of the range ${m_{\pi }}^{-1\mathrm{}}=1.41\mathrm{}$ F of the $n-p$ force, so it becomes exact only in the limit of small deuteron binding energy, i.e., $R\gg {m_{\pi }}^{-1\mathrm{}}$. The experimental value of the effective range is not of order $R$ and negative, but rather of order ${m_{\pi }}^{-1\mathrm{}}$ and positive, so $Z$ is small or zero and the deuteron is mostly or wholly composite.