We study the nontrivial interplay of the well known pairing and the more complex quarteting correlations in the particular case of N > Z atomic nuclei. Within the new Analytical Disentangled Condensate model, by implementing the notion of fractional degeneracy we obtain the clear physical picture of a rather weakly interacting mixture of quartet and neutron pair condensates which mainly feel each other's influence through Pauli blocking. The basic idea of our approach may be generalized in order to scrutinize the extent to which similar manifestations are present in various many-body systems.After more than 60 years the pairing correlations, so pervasive in condensed matter, nuclear [1] and particle physics [2], are still actively investigated. In nuclear physics in particular, the richness of many body effects is substantially influenced by presence of two fermion species, protons and neutrons. The existence of four spin-isospin possible combinations allows the formation of strongly correlated four-particle structures, known as quartets, due to the nuclear attractive force. As a result, the α-particle is characterized by a large binding energy. In heavy nuclear systems, this structure survives as an α-cluster, as can be seen from the binding energies. In condensed matter systems, conceptually related manifestations may be identified, for example the formation and condensation of biexcitons in semiconductors [3] or the existence of a quartet superfluid phase in a system of fermionic cold atoms trapped in a one-dimensional optical lattice (see Ref.[4] and references therein). In nuclear systems, α-particles can appear only at relative low nuclear densities [7] on the nuclear surface of α-decaying nuclei [8]. From a theoretical viewpoint, the main difficulty is connected to strong antisymmetrization effects between nucleons entering α-like structures. On the one hand, coordinate space approaches like the THSR ansatz [5] have been successfully applied only to light nuclei or to heavy nucleus+α systems, e.g. 212 Po= 208 Pb+α [6]. On the other hand, configuration space approaches based on correlated quartet structures were recently proven to describe very precisely the four body correlations induced by the residual nuclear interaction [9][10][11][12][13][14][15][16][17][18][19], in both N = Z and N > Z nuclei. A unified microscopic description of real space α clustering and configuration (shell model) space quartet correlations is an open problem in theoretical nuclear physics.Moreover, in N > Z nuclei, it is necessary to consider the interplay of quartet and neutron pair correla- * Email address: virgil.baran@theory.nipne.ro tions. In this work, we aim to provide a clearer physical picture of such systems by developing new theoretical many body methods based on recent advances in the analytical description of pairing and quarteting correlations [20]. We consider N neutrons and Z protons moving outside a self-conjugate inert core which interact through a charge-independent pairing force. The corresponding isovector pa...
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