A conserving T-matrix approximation is applied to the two-dimensional
attractive Hubbard model in the low-density regime. A set of self-cons
istent equations is solved in the real-frequency domain to avoid the a
nalytic continuation procedure. By tuning the chemical potential the p
article density was varied in the limits 0.01 < n < 0.18. For the valu
e of the attractive potential Ci = 8t the binding energy of pairs mono
tonically decreases with increasing n, from its zero-density limit 2.3
t, and vanishes at a critical density n(cr) = 0.19. A pairing-induced
pseudogap in the single-particle density of states is found at low den
sities and temperatures.