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Register a new userOn Continuum- and Bound-State l^- Decay Rates of Pionic and Kaonic Hydrogen in the Ground State
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We calculate the continuum- and bound-state l^- decay rates of pionic and kaonic hydrogen in the ground state, where l^- is either the electron or the muon.
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This paper is addressed to the analysis of the set of observables of the bound-state beta-decay, which can be used for the experimental investigation of contributions of i) interactions beyond the Standard Model (SM) and of ii) the left-handed polarisation state of antineutrinos. For this aim we calculate the branching ratio, probabilities and angular distributions of probabilities of hydrogen in the hyperfine states and of the proton-electron pair in different spinorial states, induced by left-handed and right-handed hadronic and leptonic currents. The branching ratio of the bound-state beta-decay is calculated by taking into account radiative corrections. We show that the probabilities of the bound-state beta-decay can be good observables for experimental investigations of contributions of interactions beyond the SM, whereas the angular distributions of probabilities are good observables for experimental searches of contributions of the left-handed polarisation state of antineutrinos.
In the model of low-energy bar-K N interactions near threshold (EPJA 21, 11 (2004); 25, 79 (2005)) we calculate isospin-breaking corrections to the energy level displacement of the ground state of kaonic hydrogen, investigated by Meissner, Raha and Rusetsky (EPJC 35, 349 (2004)) within the non-relativistic effective Lagrangian approach based on ChPT by Gasser and Leutwyler. Our results agree well with those by Meiss ner et al.. In addition we calculate the dispersive corrections, caused by the transition K^-p -> bar-K^0n ->K^-p with the bar-K^0n pair on-mass shell. We show also how hypothesis on the dominant role of the bar-K^0n-cusp for the S-wave amplitude of low-energy K^-p scattering near threshold, used by Meissner et al., can be realized in our approach. The result agrees fully with that by Meissner et al..
We calculate the decay rates lambda_(beta^-_c) and lambda_(beta^-_b) of the continuum- and bound-state beta^- decays for bare 205Hg80+ and 207Tl81+ ions. For the ratio of the decay rates R_(b/c) = lambda_(beta^-_b)/lambda_(beta^-_c) we obtain the values R_(b/c) = 0.161 and R_(b/c) = 0.190 for bare 205Hg80+ and 207Tl81+ ions, respectively. The theoretical value of the ratio R_(b/c) = 0.190 for the decays of 207Tl81+ agrees within 1% of accuracy with the experimental data R^exp_(b/c) = 0.188(18), obtained at GSI. The theoretical ratio R_(b/c) = 0.161 for 205Hg80+ is about 20% smaller than the experimental value R^exp_(b/c) = 0.20(2), measured recently at GSI.
The anti-kaon nucleon scattering lengths resulting from a Hamiltonian effective field theory analysis of experimental data and lattice QCD studies are presented. The same Hamiltonian is then used to compute the scattering length for the $K^- d$ system, taking careful account of the effects of recoil on the energy at which the $bar{K}N$ T-matrices are evaluated. These results are then used to estimate the shift and width of the $1S$ levels of anti-kaonic hydrogen and deuterium. The $K^- p$ result is in excellent agreement with the SIDDHARTA measurement. In the $K^- d$ case the imaginary part of the scattering length and consequently the width of the $1S$ state are considerably larger than found in earlier work. This is a consequence of the effect of recoil on the energy of the $bar{K}N$ energy, which enhances the role of the $Lambda(1405)$ resonance.
Two--photon decay of hydrogen--like ions is studied within the framework of second--order perturbation theory, based on relativistic Diracs equation. Special attention is paid to the effects arising from the summation over the negative--energy (intermediate virtual) states that occurs in such a framework. In order to investigate the role of these states, detailed calculations have been carried out for the $2s_{1/2} - 1s_{1/2}$ and $2p_{1/2} - 1s_{1/2}$ transitions in neutral hydrogen H as well as for hydrogen--like xenon Xe$^{53+}$ and uranium U$^{91+}$ ions. We found that for a correct evaluation of the total and energy--differential decay rates, summation over the negative--energy part of Diracs spectrum should be properly taken into account both for high--$Z$ and low--$Z$ atomic systems.
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