Nuclear-Polarization Corrections to the Levels of Muonic Atoms

Abstract

It is shown that information about the nuclear electromagnetic-transition vertex derived from experimental inelastic-scattering cross sections for electrons may be used to evaluate the nuclear-polarization (dispersion) corrections to the levels of muonic atoms. A modelindependent result is obtained for the contributions of discrete nuclear states. The most important systematic features of nuclear-excitation spectra, the giant-dipole resonance and the quasielastic peak, are considered in detail. The Goldhaber-Teller model is used for the former, and a simple-harmonic-oscillator shell model for the latter. Numerical estimates are obtained for total level shifts of low-lying muon states in nuclei with closed (harmonic-oscillator) proton shells, using closure approximation for the muon. The muon closure energies are considered in detail. It is felt that the results obtained are probably accurate to a factor of 2. The shifts are estimated to be several keV for the Is state in heavy nuclei, and somewhat less (a few tenths to about 1 keV) for the 2s and 2p states. These shifts are significant in comparison to the present accuracy of measurement of muonic x-ray spectra, and should be considered in calculations to fit nuclear-charge distributions . H*Y RQ (Sl q )(f\\M K (q)\\i) _ K + J.-MJ J f K J i J T (qL.= £(-) f f( J 1 KQ \-M Q M. J %

Test of electron screening and vacuum polarization in heavy muonic atoms

“…Nuclear polarization. Values for this effect are taken from Ericson and Htifner [35] and Cole [36]. A detailed discussion can be found in these papers.…”

“…: vacuum polarization of order cdZ c~). c~2(Z c~) and e(Z cO 3' s, ~ [10]; c5 ELs: Lamb shift ~self energy) and vacuum polarization due to ~t ~ # pair [24]; 6 E, ~: relativistic correction of the reduced mass [22,23]; ~Eyp: nuclear polarization [35,36]; 6E~s: electron screening self-consistent calculation with Z 1 electrons [44]; E,h~or: calculated energy including all corrections:…”

Few-body model approach to the lowest bound S-state of non-symmetric exotic atoms and ions

“…It is interesting to note that muon being nearly 200 times heavier than an electron, revolves around the nucleus, in an orbit much smaller than that of an orbital electron. A 1S muon spends about one-half of its periodic life inside the nucleus in muonic atoms/ions having nuclear charge number Z ∼ 82 [14].…”

Numerical approach to the lowest bound state of muonic three-body systems

“…However the present communication we shall consider only those atoms or ions in which the positively charged nucleus is being orbited by one electron and one negatively charged muon. By far exotic muonic atoms were widely used to probe a number of atomic properties including nature and strength of eletron-muon interaction [11], these were considered an effective testing probe to study the electromagnetic properties of nuclei [12]. A number of observables like magnetic hyperfine structure by Johnson and Sorensen [13], isotopic shifts in muonic spectra of isotopes of the chemical elements like Ca, Cr, Cu, Mo etc by Macagno et al [14], perturbation calculation for hyperfine structure of muonic helium atom (µe 4 He), Lamb-shift in the muonic deuterium (µD) by Krutov and Martynenko [15] have been studied.…”