684 research outputs found
Energies of the ground state and first excited state in an exactly solvable pairing model
Several approximations are tested by calculating the ground-state energy and
the energy of the first excited state using an exactly solvable model
with two symmetric levels interacting via a pairing force. They are the BCS
approximation (BCS), Lipkin - Nogami (LN) method, random-phase approximation
(RPA), quasiparticle RPA (QRPA), the renormalized RPA (RRPA), and renormalized
QRPA (RQRPA). It is shown that, in the strong-coupling regime, the QRPA which
neglects the scattering term of the model Hamiltonian offers the best fit to
the exact solutions. A recipe is proposed using the RRPA and RQRPA in
combination with the pairing gap given by the LN method. Applying this recipe,
it is shown that the normal-superfluid phase transition is avoided, and a
reasonably good description for both of the ground-state energy and the energy
of the first excited state is achieved.Comment: 18 pages, 4 figure
Superfluid-normal phase transition in finite systems and its effect on damping of hot giant resonances
Thermal fluctuations of quasiparticle number are included making use of the
secondary Bogolyubov's transformation, which turns quasiparticles operators
into modified-quasiparticle ones. This restores the unitarity relation for the
generalized single-particle density operator, which is violated within the
Hartree-Fock-Bogolyubov (HFB) theory at finite temperature. The resulting
theory is called the modified HFB (MHFB) theory, whose limit of a constant
pairing interaction yields the modified BCS (MBCS) theory. Within the MBCS
theory, the pairing gap never collapses at finite temperature T as it does
within the BCS theory, but decreases monotonously with increasing T. It is
demonstrated that this non-vanishing thermal pairing is the reason why the
width of the giant dipole resonance (GDR) does not increase with T up to T
around 1 MeV. At higher T, when the thermal pairing is small, the GDR width
starts to increase with T. The calculations within the phonon-damping model
yield the results in good agreement with the most recent experimental
systematic for the GDR width as a function of T. A similar effect, which causes
a small GDR width at low T, is also seen after thermal pairing is included in
the thermal fluctuation model.Comment: Invited lecture at the Predeal international summer school in nuclear
physics on ``Collective motion and phase transitions in nuclear systems'', 28
August - 9 September, 2006, Predeal, Romania; 18 pages, 3 figures; to be
published by World Scientific in the proceedings of this schoo
Thermal pairing and giant dipole resonance in highly excited nuclei
Recent results are reported showing the effects of thermal pairing in highly
excited nuclei. It is demonstrated that thermal pairing included in the phonon
damping model (PDM) is responsible for the nearly constant width of the giant
dipole resonance (GDR) at low temperature 1 MeV. It is also shown that
the enhancement observed in the recent experimentally extracted nuclear level
densities in Pd at low excitation energy and various angular momenta is
the first experimental evidence of the pairing reentrance in finite (hot
rotating) nuclei. In the study of GDR in highly excited nuclei, the PDM has
been extended to include finite angular momentum. The results of calculations
within the PDM are found in excellent agreement with the latest experimental
data of GDR in the compound nucleus Mo. Finally, an exact expression is
derived to calculate the shear viscosity as a function of in finite
nuclei directly from the GDR width and energy at zero and finite . Based on
this result, the values of specific shear viscosity in several medium
and heavy nuclei were calculated and found to decrease with increasing to
reach at 5 MeV, that is almost the same
value obtained for quark-gluon-plasma at 170 MeV.Comment: 6 pages, 4 figures, invited lecture at the 11th Spring Seminar on
Nuclear Physics, Ischia May 12 - 16, 201
- âŠ