Pairing correlation in atomic nuclei under extreme conditions

Abstract: The pairing correlation has long been recognized as the dominant many-body correlation beyond the nuclear mean field. Pairing plays an essential role in many nuclear phenomena including the occurrence of a systematic odd-even staggering (OES) of the nuclear binding energy. Pairing interaction plays, in particular, a significant role in the stability of weakly bound nuclei. Therefore it has been one of the most critical topics in nuclear physics because of the weakly bound structure of all newly discovered nuclei. Beyond the line of stability, pairing interaction is not a residual interaction anymore. Its strength can be of the same order of magnitude as the mean field.  In this thesis we have focused on the pairing interaction in atomic nuclei under extreme conditions to investigate the structure of loosely bound nuclei near the dripline; to probe and globally assess different outcomes of various zero-range pairing interactions and their effect on the loosely bound low angular momentum states. How much can density-dependence in zero-range pairing interaction nuclei affect the line of stability? Calculations predict that pure density-dependent pairing interaction so-called surface interaction enhances the collectivity and gives stronger neutron pairing gap in nuclei far from stability, while, the density dependence pairing interaction does not affect the gap for bound nuclei as much. The odd-even staggering of nuclear binding energies has been investigated to estimate the empirical pairing gap. A 3-point formula Δ(3)C (1/2[B(N,Z)+B(N −2,Z)−2B(N −1,Z)]) is advocated in this thesis, which we believe it is more suitable to measure the magnitude of pairing gap in even-even nuclei. The strength of Δ(3)C can be a good indicator of the two-particle spatial correlation. One-quasiparticle energies and binding energy for those odd nuclei, which can be approximated by spherical symmetry, are calculated to obtain binding energy odd-even staggering (OES) in all known semi-magic even-even nuclei. The pairing strength is fitted globally to all available data on the OES of semi-magic nuclei with Z ≥ 8. The difference between different zero-range density-dependent pairing interactions reduces with this global fitted parameter. The difference between the mean pairing gap and the OES gets larger as we get closer to the dripline. At the end of the thesis, a simple model has been developed which shows that when the mean-field becomes shallower the odd-even staggering of charge radii is reduced.This thesis covers results that are not included in the three published papers and some complementary works on the subject.