Bose-Einstein correlations of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mi>π</mml:mi><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>pairs in central Pb+Pb collisions at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>20</mml:mn><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mn>30</mml:mn><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mn>40</mml:mn><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mn>80</mml:mn><mml:mi>A</mml:mi></mml:mrow></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>158</mml:mn><mml:mi>A</mml:mi></mml:mrow></mml:math>GeV

Measurements of Bose-Einstein correlations of ${\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}$ pairs in central Pb+Pb collisions were performed with the NA49 detector at the CERN Super Proton Synchroton for beam energies of $20A,30A,40A,80A$, and $158A$ GeV. Correlation functions were measured in the longitudinally comoving ``out-side-long'' reference frame as a function of rapidity and transverse momentum in the forward hemisphere of the reaction. Radius and correlation strength parameters were obtained from fits of a Gaussian parametrization. The results show a decrease of the radius parameters with increasing transverse-momentum characteristic of strong radial flow in the pion source. No striking dependence on pion-pair rapidity or beam energy is observed. Static and dynamic properties of the pion source are obtained from simultaneous fits with a blast-wave model to radius parameters and midrapidity transverse-momentum spectra. Predictions of hydrodynamic and microscopic models of Pb+Pb collisions are discussed.