A Shell-model-Like APproach (SLAP) suggested to treat the pairing correlations in relativistic mean field theory is introduced, in which the occupancies thus obtained having been iterated back into the densities. The formalism and numerical techniques are given in detail. As examples, the ground state properties and low-lying excited states for Ne isotopes are studied. The results thus obtained are compared with the data available. The binding energies, the odd-even staggering, as well as the tendency for the change of the shapes in Ne isotopes are correctly reproduced.

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The pairing correlations in hot nuclei $^{162}$Dy are investigated in terms of the thermodynamical properties by covariant density functional theory. The heat capacities $C_V$ are evaluated in the canonical ensemble theory and the paring correlations are treated by a shell-model-like approach, in which the particle number is conserved exactly. A S-shaped heat capacity curve, which agrees qualitatively with the experimental data, has been obtained and analyzed in details. It is found that the one-pair-broken states play crucial roles in the appearance of the S shape of the heat capacity curve. Moreover, due to the effect of the particle-number conservation, the pairing gap varies smoothly with the temperature, which indicates a gradual transition from the superfluid to the normal state.Comment: 13 pages, 4 figure

The α-cluster structures for 12C and 16O are investigated in the framework of the covariant density functional theory, where the pairing correlation is treated with a particle number conserving shell-model-like approach. The ground states of 12C and 16O have been calculated and the density distributions demonstrate an equilateral triangle 3α clustering for 12C and a regular tetrahedron 4α clustering for 16O. The existence of linear nα chain structure of both 12C and 16O is revealed at high quadrupole deformation.

A particle number conserving BCS approach (FBCS) is formulated in the relativistic mean field (RMF) model. It is shown that the so-obtained RMF+FBCS model can describe the weak pairing limit. We calculate the ground-state properties of the calcium isotopes 32−74 Ca and compare the results with those obtained from the usual RMF+BCS model. Although the results are quite similar to each other, we observe an interesting phenomenon, i.e., for 54 Ca, the FBCS approach can enhance the occupation probability of the 2p 1/2 single particle level and slightly increases its radius, compared with the RMF+BCS model. This leads to an unusual scenario that although 54 Ca is more bound with a spherical configuration but the corresponding size is not the most compact one. We anticipate that such a phenomenon might happen for other neutron rich nuclei and should be checked by further more systematic studies. *

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Within the relativistic mean field (RMF) theory, the ground state properties of dysprosium isotopes are studied using the shell-model-like approach (SLAP), in which pairing correlations are treated with particlenumber conservation, and the Pauli blocking effects are taken into account exactly. For comparison, calculations of the Bardeen-Cooper-Schrieffer (BCS) model with the RMF are also performed. It is found that the RMF+SLAP calculation results, as well as the RMF+BCS ones, reproduce the experimental binding energies and one-and twoneutron separation energies quite well. However, the RMF+BCS calculations give larger pairing energies than those obtained by the RMF+SLAP calculations, in particular for nuclei near the proton and neutron drip lines. This deviation is discussed in terms of the BCS particle-number fluctuation, which leads to the sizable deviation of pairing energies between the RMF+BCS and RMF+SLAP models, where the fluctuation of the particle number is eliminated automatically.