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

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

Excitation of the electric pygmy dipole resonance by inelastic electron scattering

To complete earlier studies of the properties of the electric pygmy dipole resonance (PDR) obtained in various nuclear reactions, the excitation of the 1$^-$ states in $^{140}$Ce by $(e,e')$ scattering for momentum transfers $q=0.1-1.2$~fm$^{-1}$ is calculated within the plane-wave and distorted-wave Born approximations. The excited states of the nucleus are described within the Quasiparticle Random Phase Approximation (QRPA), but also within the Quasiparticle-Phonon Model (QPM) by accounting for the coupling to complex configurations. It is demonstrated that the excitation mechanism of the PDR states in $(e,e')$ reactions is predominantly of transversal nature for scattering angles $\theta_e \approx 90^o-180^o$. Being thus mediated by the convection and spin nuclear currents, the $(e,e')$ like the $(\gamma,\gamma')$ reaction, may provide additional information to the one obtained from Coulomb- and hadronic excitations of the PDR in $(p,p')$, $(\alpha,\alpha')$, and heavy-ion scattering reactions. The calculations predict that the $(e,e')$ cross sections for the strongest individual PDR states are in general about three orders of magnitude smaller as compared to the one of the lowest $2^+_1$ state for the studied kinematics, but that they may become dominant at extreme backward angles.Comment: Prepared for the special issue of EPJA on the topic "Giant, Pygmy, Pairing Resonances and related topics" dedicated to the memory of Pier Francesco Bortigno

Description of Double Giant Dipole Resonance within the Phonon Damping Model

In a recent Letter [1] an overall agreement with the experimental data for the excitation of the single and double giant dipole resonances in relativistic heavy ion collision in 136Xe and 208Pb nuclei has been reported. We point out that this agreement is achieved by a wrong calculation of the DGDR excitation mechanism. We also argue that the agreement with the data for the widths of resonances is achieved by an unrealistically large value of a model parameter. [1] Nguyen Dinh Dang, Vuong Kim Au, and Akito Arima, Phys. Rev. Lett. 85 (2000) 1827.Comment: Comment for Phys. Rev. Let

Damping width of double resonances

Damping width of the double giant dipole resonance of 136Xe excited in relativistic heavy ion collisions is calculated by diagonalizing a microscopic Hamiltonian in a basis containing one-, two- and three-phonon states. The coupling between these states is determined making use of the fermion structure of the phonons. The resulting width of the double giant dipole resonance is close to $\left( {3_1^ + } \right)$ times the width of the single giant dipole resonance