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Register a new userHyperfine structure of excited state of muonic helium atom
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Added by
Alexei P. Martynenko
Publication date
2012
fields
Physics
and research's language is
English
Authors
A.A. Krutov
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The recoil, vacuum polarization and electron vertex corrections of first and second orders in the fine structure constant $alpha$ and the ratio of electron to muon and electron to alpha-particle masses are calculated in the hyperfine splitting of the $1s^{(e)}_{1/2}2s^{(mu)}_{1/2}$ state of muonic helium atom (mu e ^4_2He) on the basis of a perturbation theory. We obtain total result for the muonically excited state hyperfine splitting $Delta u^{hfs}=4295.66$ MHz which improves previous calculations due to the account of new corrections and more accurate treatment of the electron vertex contribution.
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On the basis of the perturbation theory in the fine structure constant $alpha$ and the ratio of the electron to muon masses we calculate one-loop vacuum polarization and electron vertex corrections and the nuclear structure corrections to the hyperfine splitting of the ground state of muonic helium atom $(mu e ^3_2He)$. We obtain total result for the ground state hyperfine splitting $Delta u^{hfs}=4166.471$ MHz which improves the previous calculation of Lakdawala and Mohr due to the account of new corrections of orders $alpha^5$ and $alpha^6$. The remaining difference between our theoretical result and experimental value of the hyperfine splitting lies in the range of theoretical and experimental errors and requires the subsequent investigation of higher order corrections.
We make precise calculation of hyperfine structure of $S$-states in muonic ions of lithium, beryllium and boron in quantum electrodynamics. Corrections of orders $alpha^5$ and $alpha^6$ due to the vacuum polarization, nuclear structure and recoil in first and second orders of perturbation theory are taken into account. We obtain estimates of the total values of hyperfine splittings which can be used for a comparison with future experimental data.
We find the threshold structure of the two- and three-nucleon systems, with the deuteron and 3H/3He as the only bound nuclei, sufficient to predict a pair of four-nucleon states: a deeply bound state which is identified with the helium-4 ground state, and a shallow, unstable state at an energy 0.38(25) MeV above the triton-proton threshold which is consistent with data on the first excited state of helium-4. The analysis employs the framework of Pionless EFT at leading order with a generalized regulator prescription which probes renormalization-group invariance of the two states with respect to higher-order perturbations including asymmetrical disturbances of the short-distance structure of the interaction. In addition to this invariance of the bound-state spectrum and the diagonal triton-proton 1S0 phase shifts in the helium-4 channel with respect to the short-distance structure of the nuclear interaction, our multi-channel calculations with a resonating-group method demonstrate the increasing sensitivity of nuclei to the neutron-proton P-wave interaction. We show that two-nucleon phase shifts, the triton channel, and three-nucleon negative-parity channels are less sensitive with respect to enhanced two-nucleon P-wave attraction than the four-nucleon triton-proton 1S0 phase shifts.
We present new investigation of the Lamb shift (2P_{1/2}-2S_{1/2}) in muonic deuterium (mu d) atom using the three-dimensional quasipotential method in quantum electrodynamics. The vacuum polarization, nuclear structure and recoil effects are calculated with the account of contributions of orders alpha^3, alpha^4, alpha^5 and alpha^6. The results are compared with earlier performed calculations. The obtained numerical value of the Lamb shift 202.4139 meV can be considered as a reliable estimate for the comparison with forthcoming experimental data.
Precision calculations of the fine and hyperfine structure of muonic atoms are performed in a relativistic approach and results for muonic 205 Bi, 147 Sm, and 89 Zr are presented. The hyperfine structure due to magnetic dipole and electric quadrupole splitting is calculated in first order perturbation theory, using extended nuclear charge and current distributions. The leading correction from quantum electrodynamics, namely vacuum polarization in Uehling approximation, is included as a potential directly in the Dirac equation. Also, an effective screening potential due to the surrounding electrons is calculated, and the leading relativistic recoil correction is estimated.
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