  At low densities, with decreasing temperatures, in symmetric nuclear matter
alpha-particles are formed, which eventually give raise to a quantum condensate
with four-nucleon alpha-like correlations (quartetting). Starting with a model
of alpha-matter, where undistorted alpha particles interact via an effective
interaction such as the Ali-Bodmer potential, the suppression of the condensate
fraction at zero temperature with increasing density is considered. Using a
Jastrow-Feenberg approach, it is found that the condensate fraction vanishes
near saturation density. Additionally, the modification of the internal state
of the alpha particle due to medium effects will further reduce the condensate.
  In finite systems, an enhancement of the S state wave function of the c.o.m.
orbital of alpha particle motion is considered as the correspondence to the
condensate. Wave functions have been constructed for self-conjugate 4n nuclei
which describe the condensate state, but are fully antisymmetrized on the
nucleonic level. These condensate-like cluster wave functions have been
successfully applied to describe properties of low-density states near the n
alpha threshold. Comparison with OCM calculations in 12C and 16O shows strong
enhancement of the occupation of the S-state c.o.m. orbital of the
alpha-particles. This enhancement is decreasing if the baryon density
increases, similar to the density-induced suppression of the condensate
fraction in alpha matter. The ground states of 12C and 16O show no enhancement
at all, thus a quartetting condensate cannot be formed at saturation densities.
