Surface Vibrations and the Pairing Interaction in Nuclei

Abstract

The induced pairing interaction arising from the exchange of low-lying collective surface vibrations among nucleons moving in time reversal states close to a Fermi energy is found to lead to values of the pairing gap which constitute a large fraction of those experimentally observed. PACS numbers: 21.30.Fe, 21.60.Jz, 27.40. + z, 27.60. + j It is well established that nucleons moving close to the Fermi energy in time reversal states have the tendency to form Cooper pairs which eventually condense [1]. This phenomenon, which parallels that which is at the basis of low-temperature superconductivity [2], modifies in an important way the nuclear properties.While in the case of low-temperature superconductivity the attraction among electrons is generated by the exchange of lattice phonons, in the nuclear case the origin of the pairing interaction is related to the 1 S 0 phase shift of the free nucleons, which is attractive at low relative momenta. Within the spirit of the BCS approximation [2] the matrix elements of the pairing interaction in nuclei are, in general, approximated by a constant inversely proportional to the mass number of the nucleus (G ഠ 25͞A MeV). The consequences of this model have been extensively studied (cf., e.g., Ref.[1] and references therein).In keeping with the fact that the free nucleon-nucleon interaction is strongly renormalized in nuclei, there exists a long tradition in the study of core polarization of the effective two-nucleon interaction (cf. Refs. [3-7] and references therein), in particular in the case of J 0, T 1 pairs (pairing correlations) where the role of exchange of high-lying quadrupole and hexadecapole modes (giant resonances) has been systematically studied (cf., e.g., Ref.[8] and references therein).In the present paper we shall show that Cooper pair formation in nuclei can particularly benefit from the exchange of low-lying collective surface vibrations (cf. Refs. [1,9,10]), a mechanism which gives rise to pairing gaps which account in most cases for 50%-70% of the experimental values. Calculations have been carried out for a number of isotopic chains: A 20 Ca, A 22 Ti, and A 50 Sn. The results provide insight into the role the induced interaction plays in neutron and proton pairing correlations in nuclei. Calculations have also been carried out for the case of 42 21 Sc and found to lead to strong proton-neutron pairing correlations.The basic ingredients needed in the calculation of the induced pairing interaction (cf. inset of Fig. 1) are the singleparticle energies e n and the corresponding wave functions f n ͑ r ! ͒, as well as the energieshv l ͑n͒ and transition probabilities B͑ ͑ ͑El; 0 ! l͑n͒͒ ͒ ͒ of the vibrational modes. The quantities e n and f n ͑ r ! ͒ were calculated assuming nucleons to move in an average field containing a spinorbit term and parametrized in terms of a Saxon-Woods potential, with values of the depth, radius, diffusivity, and spin-orbit strength taken from Ref. [11]. The vibrations were calculated by diagonalizing multipole-multipole intera...

Attractive and repulsive contributions of medium fluctuations to nuclear superfluidity

“…In particular, it has been found that medium polarization effects associated with the exchange of vibrations lead to a quenching of the bare pairing interaction in the 1 S 0 channel in the inner crust of neutron stars [7] while, at the same time, account for a sizeable fraction of the pairing gap in open shell nuclei [8,9,10]. In the present paper we present, for the first time, evidence which allows to understand these seemingly contradictory results.…”

“…2(a)) within the framework presented in ref. [10]. The matrix elements between two pairs of neutrons in timereversal states are given by…”

Pairing matrix elements and pairing gaps with bare, effective, and induced interactions

“…Conversely, a number of studies have shown that the superfluid properties of nuclear systems, ranging from infinite nuclear and neutron matter to finite atomic nuclei, are strongly influenced by polarization phenomena [7][8][9]. In these calculations one starts from a bare nucleon-nucleon potential (Argonne, Bonn, Paris, etc.)…”

Nuclear response theory with multiphonon coupling in a covariant framework

“…[23] a general concept for the quasiparticle-vibration (phonon) coupling (QVC) part of the single-nucleon self-energy has been proposed. This concept had various implementations over the years within the Quasiparticle-Phonon Model (QPM) [24][25][26], Nuclear Field Theory [27][28][29][30][31][32][33] and others [34][35][36][37][38][39][40][41][42][43][44]. In particular, the approaches [39,41,43,44] are formulated as a theory for nuclear response function.…”