Reply to comment ``On the test of the modified BCS at finite temperature''

This is our formal Reply to revised version (v2) of arXiv: nucl-th/0510004v2.Comment: accepted in Physical Review

Test of modified BCS model at finite temperature

A recently suggested modified BCS (MBCS) model has been studied at finite temperature. We show that this approach does not allow the existence of the normal (non-superfluid) phase at any finite temperature. Other MBCS predictions such as a negative pairing gap, pairing induced by heating in closed-shell nuclei, and ``superfluid -- super-superfluid'' phase transition are discussed also. The MBCS model is tested by comparing with exact solutions for the picket fence model. Here, severe violation of the internal symmetry of the problem is detected. The MBCS equations are found to be inconsistent. The limit of the MBCS applicability has been determined to be far below the ``superfluid -- normal'' phase transition of the conventional FT-BCS, where the model performs worse than the FT-BCS.Comment: 8 pages, 9 figures, to appear in PR

Self-consistent calculations of quadrupole moments of the first 2+ states in Sn and Pb isotopes

A method of calculating static moments of excited states and transitions between excited states is formulated for non-magic nuclei within the Green function formalism. For these characteristics, it leads to a noticeable difference from the standard QRPA approach. Quadrupole moments of the first 2+ states in Sn and Pb isotopes are calculated using the self-consistent TFFS based on the Energy Density Functional by Fayans et al. with the set of parameters DF3-a fixed previously. A reasonable agreement with available experimental data is obtained.Comment: 5 pages, 6 figure

Inelastic neutrino scattering off hot nuclei in supernova environments

We study inelastic neutrino scattering off hot nuclei for temperatures relevant under supernova conditions. The method we use is based on the quasiparticle random phase approximation extended to finite temperatures within the thermo field dynamics (TQRPA). The method allows a transparent treatment of upward and downward transitions in hot nuclei, avoiding the application of Brink's hypothesis. For the sample nuclei $^{56}$Fe and $^{82}$Ge we perform a detailed analysis of thermal effects on the strength distributions of allowed Gamow-Teller (GT) transitions which dominate the scattering process at low neutrino energies. For $^{56}$Fe and $^{82}$Ge the finite temperature cross-sections are calculated by taking into account the contribution of allowed and forbidden transitions. The observed enhancement of the cross-section at low neutrino energies is explained by considering thermal effects on the GT strength. For $^{56}$Fe we compare the calculated cross-sections to those obtained earlier from a hybrid approach that combines large-scale shell-model and RPA calculations.Comment: 12 pages, 9 figure

Low-energy Dipole Excitations in Nuclei at the N=50,82 and Z=50 Shell Closures as Signatures for a Neutron Skin

Low-energy dipole excitations have been investigated theoretically in N=50, several N=82 isotones and the Z=50 Sn isotopes. For this purpose a method incorporating both HFB and multi-phonon QPM theory is applied. A concentration of one-phonon dipole strength located below the neutron emission threshold has been calculated in these nuclei. The analysis of the corresponding neutron and proton dipole transition densities allows to assign a genuine pattern to the low-energy excitations and making them distinct from the conventional GDR modes. Analyzing also the QRPA wave functions of the states we can identify these excitations as Pygmy Dipole Resonance (PDR) modes, recently studied also in Sn and N=82 nuclei. The results for N=50 are exploratory for an experimental project designed for the bremsstrahlung facility at the ELBE accelerator.Comment: Nuclear Physics in Astrophysics III Conference, 26 - 31 March 2007, Forschungszentrum Dresden-Rossendorf, German

Ground state correlations and structure of odd spherical nuclei

It is well known that the Pauli principle plays a substantial role at low energies because the phonon operators are not ideal boson operators. Calculating the exact commutators between the quasiparticle and phonon operators one can take into account the Pauli principle corrections. Besides the ground state correlations due to the quasiparticle interaction in the ground state influence the single particle fragmentation as well. In this paper, we generalize the basic QPM equations to account for both mentioned effects. As an illustration of our approach, calculations on the structure of the low-lying states in $^{131}$Ba have been performed.Comment: 12 pages, 1 figur

Population of isomers in decay of the giant dipole resonance

The value of an isomeric ratio (IR) in N=81 isotones ($^{137}$Ba, $^{139}$Ce, $^{141}$Nd and $^{143}$Sm) is studied by means of the ($\gamma, n)$ reaction. This quantity measures a probability to populate the isomeric state in respect to the ground state population. In ($\gamma, n)$ reactions, the giant dipole resonance (GDR) is excited and after its decay by a neutron emission, the nucleus has an excitation energy of a few MeV. The forthcoming $\gamma$ decay by direct or cascade transitions deexcites the nucleus into an isomeric or ground state. It has been observed experimentally that the IR for $^{137}$Ba and $^{139}$Ce equals about 0.13 while in two heavier isotones it is even less than half the size. To explain this effect, the structure of the excited states in the energy region up to 6.5 MeV has been calculated within the Quasiparticle Phonon Model. Many states are found connected to the ground and isomeric states by $E1$, $E2$ and $M1$ transitions. The single-particle component of the wave function is responsible for the large values of the transitions. The calculated value of the isomeric ratio is in very good agreement with the experimental data for all isotones. A slightly different value of maximum energy with which the nuclei rest after neutron decay of the GDR is responsible for the reported effect of the A-dependence of the IR.Comment: 16 pages, 4 Fig