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Register a new userDirect calculation of the probability of pionium ionization in the target
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Authors
M. V. Zhabitsky
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We performed the first direct calculation of the probability of pionium (pi+pi- atom) ionization in the target. The dependence of the probability of pionium ionization in the target as a function of the pionium lifetime is established. These calculations are of interest of the DIRAC experiment at CERN, which aims to measure the pionium lifetime with high precision.
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Chiral Perturbation Theory predicts the lifetime of pionium, a hydrogen-like $pi^+ pi^-$ atom, to better than 3% precision. The goal of the DIRAC experiment at CERN is to obtain and check this value experimentally by measuring the break-up probability of pionium in a target. In order to accurately measure the lifetime one needs to know the relationship between the break-up probability and lifetime to a 1% accuracy. We have obtained this dependence by modeling the evolution of pionic atoms in the target using Monte Carlo methods. The model relies on the computation of the pionium--target atom interaction cross sections. Three different sets of pionium--target cross sections with varying degrees of complexity were used: from the simplest first order Born approximation involving only the electrostatic interaction to a more advanced approach taking into account multi-photon exchanges and relativistic effects. We conclude that in order to obtain the pionium lifetime to 1% accuracy from the break-up probability, the pionium--target cross sections must be known with the same accuracy for the low excited bound states of the pionic atom. This result has been achieved, for low $Z$ targets, with the two most precise cross section sets. For large $Z$ targets only the set accounting for multiphoton exchange satisfies the condition.
We report the progress in the measurement of the pionium lifetime by the DIRAC Collaboration at CERN (PS212). Based on data collected in 2001-2003 on Ni targets we have achieved the precision of 11% in the measurement of the pionium lifetime, which corresponds to the measurement of S-wave pion-pion scattering lengths difference |a0-a2| with the accuracy of 6%.
Recently, much work has been devoted to the calculation of order $alpha$ corrections to the decay rate of pionium, the $pi^+ pi^-$ bound state. In previous calculations, nonrelativistic QED corrections were neglected since they start at order $alpha^2$ in hydrogen and positronium. In this note, we point out that there is one correction which is actually of order $alpha$ times a function of the ratio $mu_r alpha / m_e$, where $mu_r$ is the reduced mass of the system. When $mu_r alpha ll m_e$, this function can be Taylor expanded and leads to higher order corrections. When $mu_r alpha approx m_e$, as is the case in pionium, the function is of order one and the correction is of order $alpha$. We use an effective field theory approach to calculate this correction and find it equal to $0.4298 alpha Gamma_0$. We also calculate the corresponding correction to the dimuonium ($mu^+ mu^-$ bound state) decay rate and obtained a result in agreement with Jentschura et al.
The degree of elliptical polarization of intense short laser pulses is shown to be related to the timing of strong-field non-sequential double ionization. Higher ellipticity is predicted to force the initiation of double ionization into a narrower time window, and this pins the ionizing field strength in an unexpected way, leading to the first experimentally testable formula for double ionization probability as a function of ellipticity.
The evolution of pionium, the $pi^+ pi^-$ hydrogen-like atom, while passing through matter is solved within the density matrix formalism in the first Born approximation. We compare the influence on the pionium break-up probability between the standard probabilistic calculations and the more precise picture of the density matrix formalism accounting for interference effects. We focus our general result in the particular conditions of the DIRAC experiment at CERN.
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