Finite–size effects on two–particle production in continuous and discrete spectrum

The effect of a finite space–time extent of particle production region on the lifetime measurement of hadronic atoms produced by a high energy beam in a thin target is discussed. Particularly, it is found that the neglect of this effect on the pionium lifetime measurement in the experiment DIRAC at CERN could lead to the lifetime overestimation on the level of the expected 10% statistical error. It is argued that the data on correlations of identical particles obtained in the same experimental conditions, together with transport code simulation, allow to diminish the systematic error in the extracted lifetime to an acceptable level. The theoretical systematic errors arising in the calculation of the finite–size effect due to the neglect of non-equal emission times in the pair c.m.s., the space–time coherence and the residual charge are shown to be negligible.