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Register a new userA Monte Carlo Calculation of the Pionium Break-up Probability with Different Sets of Pionium Target Cross Sections
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C. Santamarina
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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.
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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.
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.
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.
Several total and partial photoionization cross section calculations, based on both theoretical and empirical approaches, are quantitatively evaluated with statistical analyses using a large collection of experimental data retrieved from the literature to identify the state of the art for modeling the photoelectric effect in Monte Carlo particle transport. Some of the examined cross section models are available in general purpose Monte Carlo systems, while others have been implemented and subjected to validation tests for the first time to estimate whether they could improve the accuracy of particle transport codes. The validation process identifies Scofields 1973 non-relativistic calculations, tabulated in the Evaluated Photon Data Library(EPDL), as the one best reproducing experimental measurements of total cross sections. Specialized total cross section models, some of which derive from more recent calculations, do not provide significant improvements. Scofields non-relativistic calculations are not surpassed regarding the compatibility with experiment of K and L shell photoionization cross sections either, although in a few test cases Ebels parameterization produces more accurate results close to absorption edges. Modifications to Biggs and Lighthills parameterization implemented in Geant4 significantly reduce the accuracy of total cross sections at low energies with respect to its original formulation. The scarcity of suitable experimental data hinders a similar extensive analysis for the simulation of the photoelectron angular distribution, which is limited to a qualitative appraisal.
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