Non-local equation for the superconducting gap parameter

The properties are considered in detail of a non-local (integral) equation for the superconducting gap parameter, which is obtained by a coarse-graining procedure applied to the Bogoliubov-deGennes (BdG) equations over the whole coupling-vs-temperature phase diagram associated with the superfluid phase. It is found that the limiting size of the coarse-graining procedure, which is dictated by the range of the kernel of this integral equation, corresponds to the size of the Cooper pairs over the whole coupling-vs-temperature phase diagram up to the critical temperature, even when Cooper pairs turn into composite bosons on the BEC side of the BCS-BEC crossover. A practical method is further implemented to solve numerically this integral equation in an efficient way, which is based on a novel algorithm for calculating the Fourier transforms. Application of this method to the case of an isolated vortex, throughout the BCS-BEC crossover and for all temperatures in the superfluid phase, helps clarifying the nature of the length scales associated with a single vortex and the kinds of details that are in practice disposed off by the coarse-graining procedure on the BdG equations

Equation for the superfluid gap obtained by coarse graining the Bogoliubov-de Gennes equations throughout the BCS-BEC crossover

We derive a nonlinear differential equation for the gap parameter of a superfluid Fermi system by performing a suitable coarse graining of the Bogoliubov-de Gennes (BdG) equations throughout the BCS-BEC crossover, with the aim of replacing the time-consuming solution of the original BdG equations by the simpler solution of this novel equation. We perform a favorable numerical test on the validity of this new equation over most of the temperature-coupling phase diagram, by an explicit comparison with the full solution of the original BdG equations for an isolated vortex. We also show that the new equation reduces both to the Ginzburg-Landau equation for Cooper pairs in weak coupling close to the critical temperature and to the Gross-Pitaevskii equation for composite bosons in strong coupling at low temperature.Comment: 12 pages, 8 figure

Temperature dependence of a vortex in a superfluid Fermi gas

The temperature dependence of an isolated quantum vortex, embedded in an otherwise homogeneous fermionic superfluid of infinite extent, is determined via the Bogoliubov-de Gennes (BdG) equations across the BCS-BEC crossover. Emphasis is given to the BCS side of this crossover, where it is physically relevant to extend this study up to the critical temperature for the loss of the superfluid phase, such that the size of the vortex increases without bound. To this end, two novel techniques are introduced. The first one solves the BdG equations with "free boundary conditions", which allows one to determine with high accuracy how the vortex profile matches its asymptotic value at a large distance from the center, thus avoiding a common practice of constraining the vortex in a cylinder with infinite walls. The second one improves on the regularization procedure of the self-consistent gap equation when the inter-particle interaction is of the contact type, and permits to considerably reduce the time needed for its numerical integration, by drawing elements from the derivation of the Gross-Pitaevskii equation for composite bosons starting from the BdG equations.Comment: 18 pgaes, 16 figure

The effects of a revised 7^7Be e−^--capture rate on solar neutrino fluxes

The electron-capture rate on $^7$Be is the main production channel for $^7$Li in several astrophysical environments. Theoretical evaluations have to account for not only the nuclear interaction, but also the processes in the plasma where $^7$Be ions and electrons interact. In the past decades several estimates were presented, pointing out that the theoretical uncertainty in the rate is in general of few percents. In the framework of fundamental solar physics, we consider here a recent evaluation for the $^7$Be+e$^-$ rate, not used up to now in the estimate of neutrino fluxes. We analysed the effects of the new assumptions on Standard Solar Models (SSMs) and compared the results obtained by adopting the revised $^7$Be+e$^-$ rate to those obtained by the one reported in a widely used compilation of reaction rates (ADE11). We found that new SSMs yield a maximum difference in the efficiency of the $^7$Be channel of about -4\% with respect to what is obtained with the previously adopted rate. This fact affects the production of neutrinos from $^8$B, increasing the relative flux up to a maximum of 2.7\%. Negligible variations are found for the physical and chemical properties of the computed solar models. The agreement with the SNO measurements of the neutral current component of the $^8$B neutrino flux is improved.Comment: 7 pages, 3 figures, 4 tables. Accepted for the publication on A&

Elastic scattering of electrons by water: An ab initio study

In this work we devise a theoretical and computational method to compute the elastic scattering of electrons from a non-spherical potential, such as in the case of molecules and molecular aggregates. Its main feature is represented by the ability of calculating accurate wave functions for continuum states of polycentric systems via the solution of the Lippmann-Schwinger equation, including both the correlation effects and multi-scattering interference terms, typically neglected in widely used approaches, such as the Mott theory. Within this framework, we calculate the purely elastic scattering matrix elements. As a test case, we apply our scheme to the modelling of electron-water elastic scattering. The Dirac-Hartree-Fock self-consistent field method is used to determine the non-spherical molecular potential projected on a functional space spanned by Gaussian basis set. By adding a number of multi-centric radially-arranged s-type Gaussian functions, whose exponents are system-dependent and optimized to reproduce the properties of the continuum electron wave function in different energy regions, we are able to achieve unprecedented access to the description of the low energy range of the spectrum (0.001 < E < 10 eV) up to keV, finding a good agreement with experimental data and previous theoretical results. To show the potential of our approach, we also compute the total elastic scattering cross section of electrons impinging on clusters of water molecules and zundel cation. Our method can be extended to deal with inelastic scattering events and heavy-charged particle

Josephson effect at finite temperature along the BCS-BEC crossover

The Josephson current-phase characteristics, that arise when a supercurrent flows across two fermionic superfluids separated by a potential barrier, can be controlled by varying either the interparticle coupling or the temperature. While the coupling dependence has been addressed in detail both theoretically and experimentally for an attractive Fermi gas undergoing the BCS-BEC crossover, a corresponding study of the temperature dependence of the Josephson characteristics is still lacking in this context. Here, we investigate the combined coupling and temperature dependence of the Josephson characteristics in a systematic way for a wide set of barriers, within ranges of height and width that can be experimentally explored. Our study smoothly connects the two limiting cases, of nonoverlapping composite bosons at low temperature described by the Gross-Piatevskii equation, and of strongly overlapping Cooper pairs near the critical temperature described by the Ginzburg-Landau equation. In this way, we are able to explore several interesting effects related to how the current-phase characteristics evolve along the BCS-BEC crossover as a function of temperature and of barrier shape. These effects include the coherence length outside the barrier and the pair penetration length inside the barrier (which is related to the proximity effect), as well as the temperature evolution of the Landau criterion in the limit of a vanishingly small barrier. A comparison is also presented between the available experimental data for the critical current and our theoretical results over a wide range of couplings along the BCS-BEC crossover

Modeling the Li abundances of RGB and AGB stars with a new estimate for the 7Be half-life time

Stars with M≤2:3M⊙ are considered Li depletion sites during their early and late evolutionary stages. Indeed 7Li, synthesized through electron-captures on 7Be, is burnt into two alpha particles, when the H-shell burns below convective envelopes of Red Giant Branch (RGB) and Asymptotic Giant Branch (AGB) stars. Furthermore, Li abundances observed in the spectra of these stars cover a wide range of values, which is difficult to be explained by stellar models, both Li-rich and Li-poor objects being observed. Difficulties arise in measuring very low Li abundances in O-rich AGBs and the lack of knowledge about the physical causes of extra-mixing, but the main source of uncertainty in investigating Li nucleosynthesis concerns the 7 Be life-time, as the avail- able estimations actually are valid only for the Sun [1]. Since in RGB and AGB H-shell burning temperatures and densities might be respectively up to five times higher and five orders of mag- nitudes lower than in the solar core, using for giants a 7Be life-time, extrapolated from the one valid in solar condition is at least hazardous. We present the consequence on Li nucleosynthesis of a new 7Be life-time estimation computed by a theoretical approach inherited from quantum chemistry. Extra-mixing models integrated with this new datum well reproduce the trends of Li destruction observed in RGBs and are suitable to account for Li observations in AGBs, explaining also the amount of nuclei from C to A

Theoretical estimate of the half-life for the radioactive 134^{134}Cs and 135^{135}Cs in astrophysical scenarios

We analyze the $^{134}_{55}$Cs$\rightarrow^{134}_{56}$Ba and $^{135}_{55}$Cs$\rightarrow^{135}_{56}$Ba $\beta^-$ decays, which are crucial production channels for Ba isotopes in Asymptotic Giant Branch (AGB) stars. We reckon, from relativistic quantum mechanis, the effects of multichannel scattering onto weak decays, including nuclear and electronic excited states (ES) populated above $\simeq$ 10 keV, for both parent and daughter nuclei. We find increases in the half-lives for $T>10^8$ K (by more than a factor 3 for $^{134}$Cs) as compared to previous works based on systematics. We also discuss our method in view of these previous calculations. An important impact on half-lives comes from nuclear ES decays, while including electronic temperatures yields further increases of about 20\% at energies 10-30 keV, typical of AGB stars of moderate mass ($M \lesssim 8~M_{\odot}$). Despite properly considering these effects, the new rates remain sensitively lower than the TY values, implying longer half-lives at least above 8-9 keV. Our rate predictions are in substantial accord with recent results based on the shell model, and strongly modify branching ratios along the $s$-process path previously adopted. With our new rate, nucleosynthesis models well account for the isotopic admixtures of Ba in presolar SiC grains and in the Sun.Comment: 15 pages, 3 figures, 5 tables. Accepted for publication in Ap

Vortex arrays in neutral trapped Fermi gases through the BCS–BEC crossover

Vortex arrays in type-II superconductors reflect the translational symmetry of an infinite system. There are cases, however, such as ultracold trapped Fermi gases and the crust of neutron stars, where finite-size effects make it complex to account for the geometrical arrangement of vortices. Here, we self-consistently generate these arrays of vortices at zero and finite temperature through a microscopic description of the non-homogeneous superfluid based on a differential equation for the local order parameter, obtained by coarse graining the Bogoliubov–de Gennes (BdG) equations. In this way, the strength of the inter-particle interaction is varied along the BCS–BEC crossover, from largely overlapping Cooper pairs in the Bardeen–Cooper–Schrieffer (BCS) limit to dilute composite bosons in the Bose–Einstein condensed (BEC) limit. Detailed comparison with two landmark experiments on ultracold Fermi gases, aimed at revealing the presence of the superfluid phase, brings out several features that make them relevant for other systems in nature as well

Lithium abundances in AGB stars and a new estimate for the7Be life-time

In most cases RGB and AGB stars with M< 2M⊙ destroy Li (which is instead synthesized trough electron-captures on 7Be). This occurs through the combined operation of mixing processes and proton captures, when H-burning operates close to the envelope. Observed Li abundances are however difficult to explain, as they cover a wide spread. Various uncertainties affect model attempts, but so far the largest one concerns the processes of bound and free e- captures on 7Be, hence its life-time, whose known estimates are valid only for solar conditions. RGB and AGB stages have temperatures and densities below the envelope covering a wide range and differing from solar by up to a factor of five for T and up to five orders of magnitudes for ρ, hence extrapolations are unreliable. Recently, we presented an estimate of the 7Be half-life based on a fully quantistic method that goes beyond the Debye-Huckel approximation. Here we discuss its consequences on Li nucleosynthesis in low mass AGB stars