Pairing phase transition: A Finite-Temperature Relativistic Hartree-Fock-Bogoliubov study

Background: The relativistic Hartree-Fock-Bogoliubov (RHFB) theory has recently been developed and it provides a unified and highly predictive description of both nuclear mean field and pairing correlations. Ground state properties of finite nuclei can accurately be reproduced without neglecting exchange (Fock) contributions. Purpose: Finite-temperature RHFB (FT-RHFB) theory has not yet been developed, leaving yet unknown its predictions for phase transitions and thermal excitations in both stable and weakly bound nuclei. Method: FT-RHFB equations are solved in a Dirac Woods-Saxon (DWS) basis considering two kinds of pairing interactions: finite or zero range. Such a model is appropriate for describing stable as well as loosely bound nuclei since the basis states have correct asymptotic behaviour for large spatial distributions. Results: Systematic FT-RH(F)B calculations are performed for several semi-magic isotopic/isotonic chains comparing the predictions of a large number of Lagrangians, among which are PKA1, PKO1 and DD-ME2. It is found that the critical temperature for a pairing transition generally follows the rule $T_c = 0.60\Delta(0)$ for a finite-range pairing force and $T_c = 0.57\Delta(0)$ for a contact pairing force, where $\Delta(0)$ is the pairing gap at zero temperature. Two types of pairing persistence are analysed: type I pairing persistence occurs in closed subshell nuclei while type II pairing persistence can occur in loosely bound nuclei strongly coupled to the continuum states. Conclusions: This first FT-RHFB calculation shows very interesting features of the pairing correlations at finite temperature and in finite systems such as pairing re-entrance and pairing persistence.Comment: 13 pages, 11 figures, accepted version in Phys. Rev.

Superheavy magic structures in the relativistic Hartree-Fock-Bogoliubov approach

We have explored the occurrence of the spherical shell closures for superheavy nuclei in the framework of the relativistic Hartree-Fock-Bogoliubov (RHFB) theory. Shell effects are characterized in terms of two-nucleon gaps $\delta_{2n(p)}$. Although the results depend slightly on the effective Lagrangians used, the general set of magic numbers beyond $^{208}$Pb are predicted to be $Z = 120$, $138$ for protons and $N = 172$, 184, 228 and 258 for neutrons, respectively. Specifically the RHFB calculations favor the nuclide $^{304}$120 as the next spherical doubly magic one beyond $^{208}$Pb. Shell effects are sensitive to various terms of the mean-field, such as the spin-orbit coupling, the scalar and effective masses.Comment: 3 figures, 1 table, and 5 page

Magicity of neutron-rich isotopes within relativistic self-consistent approaches

The formation of new shell gaps in intermediate mass neutron-rich nuclei is investigated within the relativistic Hartree-Fock-Bogoliubov theory, and the role of the Lorentz pseudo-vector and tensor interactions is analyzed. Based on the Foldy-Wouthuysen transformation, we discuss in detail the role played by the different terms of the Lorentz pseudo-vector and tensor interactions in the appearing of the $N=16$, 32 and 34 shell gaps. The nuclei $^{24}$O, $^{48}$Si and $^{52,54}$Ca are predicted with a large shell gap and zero ($^{24}$O, $^{52}$Ca) or almost zero ($^{48}$Si, $^{54}$Ca) pairing gap, making them candidates for new magic numbers in exotic nuclei. We find from our analysis that the Lorentz pseudo-vector and tensor interactions induce very specific evolutions of single-particle energies, which could clearly sign their presence and reveal the need for relativistic approaches with exchange interactions.Comment: 7 pages, 5 figures, 1 tabl

Flight loads analysis of a maneuvering transport aircraft

The paper provides a method applicable for the determination of flight loads for maneuvering aircraft, in which aerodynamic loads are calculated based on doublet lattice method, which contains three primary steps. Firstly, non-dimensional stability and control derivative coefficients are obtained through solving unsteady aerodynamics in subsonic flow based on a doublet lattice technical. These stability and control derivative coefficients are used in second step. Secondly, the simulation of aircraft dynamic maneuvers is completed utilizing fourth order Runge-Kutta method to solve motion equations in different maneuvers to gain response parameters of aircraft due to the motion of control surfaces. Finally, the response results calculated in the second step are introduced to the calculation of aerodynamic loads. Thus, total loads and loads distribution on different components of aircraft are obtained. According to the above method, abrupt pitching maneuvers, rolling maneuvers and yawing maneuvers are investigated respectively

Temporal Evolution of the Magnetic Topology of the NOAA Active Region 11158

We studied the temporal evolution of the magnetic topology of the active region (AR) 11158 based on the reconstructed three-dimensional magnetic fields in the corona. The \nlfff\ extrapolation method was applied to the 12 minutes cadence data obtained with the \hmi\ (HMI) onboard the \sdo\ (SDO) during five days. By calculating the squashing degree factor Q in the volume, the derived quasi-separatrix layers (QSLs) show that this AR has an overall topology, resulting from a magnetic quadrupole, including an hyperbolic flux tube (HFT) configuration which is relatively stable at the time scale of the flare ($\sim 1-2$ hours). A strong QSL, which corresponds to some highly sheared arcades that might be related to the formation of a flux rope, is prominent just before the M6.6 and X2.2 flares, respectively. These facts indicate the close relationship between the strong QSL and the high flare productivity of AR 11158. In addition, with a close inspection of the topology, we found a small-scale HFT which has an inverse tear-drop structure above the aforementioned QSL before the X2.2 flare. It indicates the existence of magnetic flux rope at this place. Even though a global configuration (HFT) is recognized in this AR, it turns out that the large-scale HFT only plays a secondary role during the eruption. In final, we dismiss a trigger based on the breakout model and highlight the central role of the flux rope in the related eruption.Comment: Accepted by Ap

Hooked flare ribbons and flux-rope related QSL footprints

We studied the magnetic topology of active region 12158 on 2014 September 10 and compared it with the observations before and early in the flare which begins at 17:21 UT (SOL2014-09-10T17:45:00). Our results show that the sigmoidal structure and flare ribbons of this active region observed by SDO/AIA can be well reproduced from a Grad-Rubin non linear force free field extrapolation method. Various inverse-S and -J shaped magnetic field lines, that surround a coronal flux rope, coincide with the sigmoid as observed in different extreme ultraviolet wavelengths, including its multi-threaded curved ends. Also, the observed distribution of surface currents in the magnetic polarity where it was not prescribed is well reproduced. This validates our numerical implementation and set-up of the Grad-Rubin method. The modeled double inverse-J shaped Quasi-Separatrix Layer (QSL) footprints match the observed flare ribbons during the rising phase of the flare, including their hooked parts. The spiral-like shape of the latter may be related to a complex pre-eruptive flux rope with more than one turn of twist, as obtained in the model. These ribbon-associated flux-rope QSL-footprints are consistent with the new standard flare model in 3D, with the presence of a hyperbolic flux tube located below an inverse tear drop shaped coronal QSL. This is a new step forward forecasting the locations of reconnection and ribbons in solar flares, and the geometrical properties of eruptive flux ropes.Comment: Accepted for publication in Ap