Energy and centrality dependence of deuteron and proton production in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mtext>Pb</mml:mtext><mml:mo>+</mml:mo><mml:mtext>Pb</mml:mtext></mml:mrow></mml:math>collisions at relativistic energies

The transverse mass ${m}_{t}$ distributions for deuterons and protons are measured in $\text{Pb}+\text{Pb}$ reactions near midrapidity and in the range $0&lt;{m}_{t}\ensuremath{-}m&lt;1.0\phantom{\rule{0.3em}{0ex}}(1.5)\phantom{\rule{0.3em}{0ex}}\text{GeV}∕{c}^{2}$ for minimum bias collisions at $158A\phantom{\rule{0.3em}{0ex}}\text{GeV}$ and for central collisions at 40 and $80\phantom{\rule{0.3em}{0ex}}A\phantom{\rule{0.3em}{0ex}}\text{GeV}$ beam energies. The rapidity density $dn∕dy$, inverse slope parameter $T$ and mean transverse mass $⟨{m}_{t}⟩$ derived from ${m}_{t}$ distributions as well as the coalescence parameter ${B}_{2}$ are studied as a function of the incident energy and the collision centrality. The deuteron ${m}_{t}$ spectra are significantly harder than those of protons, especially in central collisions. The coalescence factor ${B}_{2}$ shows three systematic trends. First, it decreases strongly with increasing centrality reflecting an enlargement of the deuteron coalescence volume in central $\text{Pb}+\text{Pb}$ collisions. Second, it increases with ${m}_{t}$. Finally, ${B}_{2}$ shows an increase with decreasing incident beam energy even within the SPS energy range. The results are discussed and compared to the predictions of models that include the collective expansion of the source created in $\text{Pb}+\text{Pb}$ collisions.