科研之友
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摘要
Background: Unbound single-particle states become important in determining the properties of a hot nucleus as its temperature increases. We present relativistic mean field (RMF) for hot nuclei considering not only the self-consistent temperature and density dependence of the self-consistent relativistic mean fields but also the vapor phase that takes into account the unbound nucleon states. Purpose: The temperature dependence of the pairing gaps, nuclear deformation, radii, binding energies, entropy, and caloric curves of spherical and deformed nuclei are obtained in self-consistent RMF calculations up to the limit of existence of the nucleus. Method: We perform Dirac-Hartree-Bogoliubov (DHB) calculations for hot nuclei using a zero-range approximation to the relativistic pairing interaction to calculate proton-proton and neutron-neutron pairing energies and gaps. A vapor subtraction procedure is used to account for unbound states and to remove long range Coulomb repulsion between the hot nucleus and the gas as well as the contribution of the external nucleon gas. Results: We show that p-p and n-n pairing gaps in the S-1(0) channel vanish for low critical temperatures in the range T-cp approximate to 0.6-1.1 MeV for spherical nuclei such as Zr-90, Sn-124, and Ce-140 and for both deformed nuclei Sm-150 and Er-168. We found that superconducting phase transition occurs at T-cp = 1.03 Delta(pp) (0) for Zr-90, T-cp = 1.16 Delta(pp) (0) for Ce-140, T-cp = 0.92 Delta(pp) (0) for Sm-150, and T-cp = 0.97 Delta(pp) (0) for Er-168. The superfluidity phase transition occurs at T-cp = 0.72 Delta(nn) (0) for Sn-124, T-cp = 1.22 Delta(nn) (0) for Sm-150, and Tcp = 1.13 Delta(nn) (0) for Er-168. Thus, the nuclear superfluidity phase-at least for this channel-can only survive at very low nuclear temperatures and this phase transition (when the neutron gap vanishes) always occurs before the superconducting one, where the proton gap is zero. For deformed nuclei the nuclear deformation disappear at temperatures of about T-cs = 2.0-4.0 MeV, well above the critical temperatures for pairing, T-cp. If we associate the melting of hot nuclei into the surrounding vapor with the liquid-gas phase transition our results indicate that it occurs at temperatures around T = 8.0-10.0 MeV, somewhat higher than observed in many experimental results. Conclusions: The change of the pairing fields with the temperature is important and must be taken into account in order to define the superfluidity and superconducting phase transitions. We obtain a Hamiltonian form of the pairing field calibrated by an overall constant c(pair) to compensate for deficiencies of the interaction parameters and of the numerical calculation. When the pairing is not zero, the states close to the Fermi energy make the principal contribution to the anomalous density that appears in the pairing field. By including temperature through the use of the Matsubara formalism, the normal and anomalous densities are multiplied by a Fermi occupation factor. This leads to a reduction in the anomalous density and in the pairing as the temperature increases. When the temperature increases (T >= 4 MeV), the effects of the vapor phase that take into account the unbound nucleon states become important, allowing the study of nuclear properties of finite nuclei from zero to high temperatures.
- 出版日期2016-2-25
