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At low densities, with decreasing temperatures, in symmetric nuclear matteralpha-particles are formed, which eventually give raise to a quantum condensatewith four-nucleon alpha-like correlations (quartetting). Starting with a modelof alpha-matter, where undistorted alpha particles interact via an effectiveinteraction such as the Ali-Bodmer potential, the suppression of the condensatefraction at zero temperature with increasing density is considered. Using aJastrow-Feenberg approach, it is found that the condensate fraction vanishesnear saturation density. Additionally, the modification of the internal stateof 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 thecondensate. Wave functions have been constructed for self-conjugate 4n nucleiwhich describe the condensate state, but are fully antisymmetrized on thenucleonic level. These condensate-like cluster wave functions have beensuccessfully applied to describe properties of low-density states near the nalpha threshold. Comparison with OCM calculations in 12C and 16O shows strongenhancement of the occupation of the S-state c.o.m. orbital of thealpha-particles. This enhancement is decreasing if the baryon densityincreases, similar to the density-induced suppression of the condensatefraction in alpha matter. The ground states of 12C and 16O show no enhancementat all, thus a quartetting condensate cannot be formed at saturation densities.

Density-induced suppression of the alpha-particle condensate in nuclear matter and the structure of alpha cluster states in nuclei