MUONIC ATOMS AND RADIAL SHAPE OF NUCLEAR CHARGE DISTRIBUTION

We find, for a rather broad set of two-, three-, and four-parameter charge-density functions, that a particular muonic-atom transition energy determines a particular moment of the nuclear charge density. The exponent k depends on the atomic number Z and on the quantum numbers of the pair of states in question, but it depends only very weakly on the mathematical form of the charge-density function. Consequently, an almost model-independent analysis of muonic-atom energies is possible. This analysis is facilitated by introduction of the equivalent radius Rk, defined by Rk=[13(k+3)rk]1k. For Z=82, a range of moments from k=0.08 to k=4.80 is provided by available data. The 2p12-1s12 transition in lead, for example, measures the k=0.80 moment and determines R0.87.013-1.49(E-5.788) F, where E is the transition energy in MeV. For this transition, as well a for several others, k is approximately a linear function of Z. © 1969 The American Physical Society.