Many-body correlations in nuclear superfluidity

Abstract

The two-fermion two-point correlation function in the pairing channel is discussed in the equation of motion framework. Starting from the bare two-fermion interaction, we derive the equation of motion for the two-fermion pair propagator in a strongly-correlated medium. The resulting equation is of the Dyson type with the kernel having a static and a one frequency dependent components and, thus, can be regarded as Dyson Bethe-Salpeter equation (Dyson-BSE). The many-body hierarchy generated by the dynamical interaction kernel is truncated on the level of two-body correlation functions, thus neglecting the explicit three-body and higher-rank correlations. The truncation is performed via a cluster expansion of the intermediate three-particle-one-hole correlation function irreducible in the particle-particle channel, that leads to the coupling between single fermions and emergent collective modes of excitation. The latter couplings are, thus, derived in terms of the exact mapping of the in-medium two-fermion correlation functions onto the domain of bosonic quasibound states (phonons) without introducing new parameters. The approach is applied to calculations of the pairing gaps in medium-mass nuclear systems, that include calcium, nickel and tin isotopic chains.

Equation of Motion Method to strongly correlated Fermi systems and Extended RPA approaches

“…( 58). Similar studies were performed for the pp-channel [130], where analogous treatments of the static and dynamical kernels were suggested. Considering together the EOM's for both ph and pp correlation functions and the factorizations discussed above allows for a truncation of the EOM series on the two-body level.…”

“…In Ref. [75] this procedure is applied for several 2νββ emitters like 76 Ge, 78 Kr, 82 Se, 96 Zr, 106 Cd and 130 Te to ground states as well as to excited one-and two-phonon states in daughter nuclei. Later on, 76 Ge, 82 Se and 128−130 Te emitters were investigated in [76].…”

“…It is shown that the spectrum does not contain spurious low-lying states and Ikeda sum rule is analytically fulfilled. A numerical application of the model to 2νββ emitters 76 Ge, 82 Se, 100 Mo, 116 Cd, 128 Te and 130 Xe is performed in [91]. This model was called by its authors also fully renormalised pnQRPA (fr-pnQRPA).…”