The relativistic motion of atoms formed by pi(+) and pi(-) mesons in m
atter is considered. Exact analytic expressions for the form factors o
f hydrogen-like atoms for discrete-discrete transitions are obtained i
n a form convenient for numerical calculations. The total and transiti
on cross sections for the interaction of pi(+)pi(-) atoms with matter
are calculated in the Born approximation. The evolution of atomic-stat
e populations is treated in terms of kinetic equations. The method of
calculation makes it possible to obtain the populations of discrete at
omic states, as well as the probability of transitions to the continuo
us spectrum (ionization). The proposed method yields the first experim
ental estimate of the lifetime of the pi(+)pi(-) atom.