Studies of X-Rays from Mu-Mesonic Atoms

A new technique of x-ray spectroscopy of $\mu$-mesonic atoms has been developed. The x-rays are produced when a ${\mu }^{-}$ meson undergoes transitions between Bohr orbits about nuclei of various $Z$. The mesons are produced by the Columbia University 164-in. Nevis cyclotron. The x-rays are detected, and their energies are measured to better than 1 percent accuracy (for $Z\ge 22$) using a NaI crystal scintillation spectrometer. The $2p\to 1s$ transition energies were measured to be 0.35, 0.41, 0.955, 1.55, 1.60, 3.50, 5.80, 6.02, and 6.02 Mev for $Z=13, 14, 22, 29, 30, 51, 80, 82, \mathrm{and} 83$. Special attention was paid to the Pb spectrum, and it is believed that an 0.2-Mev fine structure splitting has been observed. This is the expected splitting if the ${\mu }^{-}$ meson is a spin ½ Dirac "heavy electron" of 210 electron masses, having the expected Dirac magnetic moment and having no strong nonelectromagnetic interaction with nuclear matter.

Since the ${\mu }^{-}$ meson Bohr orbits are 210 times closer to the nucleus than the equivalent electron orbits, the x-ray energies are quite sensitive to nuclear size for medium and large $Z$. In the case of Pb, a 1 percent change in nuclear radius gives a 1 percent change in the calculated x-ray energy. Assuming constant proton density inside a spherical nucleus of radius $R_0=r_0{A}^{\frac{1}{3}}$ and the above properties for the $\mu$ meson, we obtain $r_0=1.17, 1.21, 1.22, \mathrm{and} 1.17\times {10}^{-13\mathrm{}}$ cm for $Z=22, 29, 51, \mathrm{and} 82$. The significance of these results in relation to other nuclear size measurements is discussed.