Commuting conformal and dual conformal symmetries in the Regge limit

In this paper we continue our study of the dual SL(2,C)$\mathit{SL}(2,C)$ symmetry of the BFKL equation, analogous to the dual conformal symmetry of N=4$N=4$ super-Yang–Mills. We find that the ordinary and dual SL(2,C)$\mathit{SL}(2,C)$ symmetries do not generate a Yangian, in contrast to the ordinary and dual conformal symmetries in the four-dimensional gauge theory. The algebraic structure is still reminiscent of that of N=4$N=4$ SYM, however, and one can extract a generator from the dual SL(2,C)$\mathit{SL}(2,C)$ close to the bi-local form associated with Yangian algebras. We also discuss the issue of whether the dual SL(2,C)$\mathit{SL}(2,C)$ symmetry, which in its original form is broken by IR effects, is broken in a controlled way, similar to the way the dual conformal symmetry of N=4$N=4$ satisfies an anomalous Ward identity. At least for the lowest orders it seems possible to recover the dual SL(2,C)$\mathit{SL}(2,C)$ by deforming its representation, keeping open the possibility that it is an exact symmetry of BFKL. Independently of a possible relation to N=4$N=4$ scattering amplitudes, this opens an avenue for explaining the integrability of BFKL in terms of two finite-dimensional subalgebras.     

Study of Be + C elastic scattering at energies near the Coulomb barrier

In this work, angular distribution measurements for the elastic channel were performed for the ⁹Be + ¹²C reaction at the energies ELab=13.0$E_{\mathit{Lab}}=13.0$, 14.5, 17.3, 19.0 and 21.0 MeV, near the Coulomb barrier. The data have been analyzed in the framework of the double folding São Paulo potential. The experimental elastic scattering angular distributions were well described by the optical potential at forward angles for all measured energies. However, for the three highest energies, an enhancement was observed for intermediate and backward angles. This can be explained by the elastic transfer mechanism.     

The H2+ molecular ion: Low-lying states

Matching for a wavefunction the WKB expansion at large distances and Taylor expansion at small distances leads to a compact, few-parametric uniform approximation found in Turbiner and Olivares-Pilon (2011). The ten low-lying eigenstates of H₂⁺ of the quantum numbers (n,m,Λ,±)$(n,m,\Lambda ,\pm )$  with n=m=0$n=m=0$ at Λ=0,1,2$\Lambda =0,1,2$, with n=1$n=1$, m=0$m=0$ and n=0$n=0$, m=1$m=1$ at Λ=0$\Lambda =0$ of both parities are explored for all interproton distances R$R$. For all these states this approximation provides the relative accuracy ?10⁻⁵$?10^{-5}$ (not less than 5 s.d.) locally, for any real coordinate x$x$ in eigenfunctions, when for total energy E(R)$E\left(R\right)$ it gives 10-11 s.d. for R∈[0,50]$R\in [0,50]$  a.u. Corrections to the approximation are evaluated in the specially-designed, convergent perturbation theory. Separation constants are found with not less than 8 s.d. The oscillator strength for the electric dipole transitions E1$E1$ is calculated with not less than 6 s.d. A dramatic dip in the E1$E1$ oscillator strength f_{1sσg−3pσu}$f_{1s{\sigma }_g-3p{\sigma }_u}$ at R∼R_eq$R\sim R_{eq}$ is observed. The magnetic dipole and electric quadrupole transitions are calculated for the first time with not less than 6 s.d. in oscillator strength. For two lowest states (0,0,0,±)$(0,0,0,\pm )$ (or, equivalently, 1sσ_g$1s{\sigma }_g$ and 2pσ_u$2p{\sigma }_u$ states) the potential curves are checked and confirmed in the Lagrange mesh method within 12 s.d. Based on them the Energy Gap between 1sσ_g$1s{\sigma }_g$ and 2pσ_u$2p{\sigma }_u$ potential curves is approximated with modified Pade Re^−R[Pade(8/7)](R)$R{e}^{-R}\left[Pade(8/7)\right]\left(R\right)$ with not less than 4-5 figures at R∈[0,40]$R\in [0,40]$ a.u. Sum of potential curves E_1sσg+E_2pσu$E_{1s{\sigma }_g}+E_{2p{\sigma }_u}$ is approximated by Pade 1/R[Pade(5/8)](R)$1/R\left[Pade(5/8)\right]\left(R\right)$ in R∈[0,40]$R\in [0,40]$ a.u. with not less than 3-4 figures.     

First-principles materials design of CuInSe2-based high-efficiency photovoltaic solar cells

Based on ab initio   electronic structure calculations by self-interaction-corrected local-density-approximation (SIC-LDA) with the Korringa–Kohn–Rostoker coherent potential approximation (KKR-CPA), we propose a materials design for high efficiency photovoltaic solar cells (PVSCs). It is shown that (i) the concentration dependence of the mixing energy of CuIn_1−xGa_xSe₂${\mathrm{CuIn}}_{1-x}{\mathrm{Ga}}_x{\mathrm{Se}}_2$ shows upward convexity, thus this system favors phase separation. Due to the type II band alignment between CuInSe₂${\mathrm{CuInSe}}_2$ and CuGaSe₂${\mathrm{CuGaSe}}_2$, efficient electron–hole separation is realized in decomposed phase of this system. (ii) CuIn_1−xZn_0.5xSn_0.5xSe₂${\mathrm{CuIn}}_{1-x}{\mathrm{Zn}}_{0.5x}{\mathrm{Sn}}_{0.5x}{\mathrm{Se}}_2$ has a direct band gap and no impurity state appears in the gap. Therefore, cost reduction is possible by using Zn and Sn instead of In. (iii) n-type CuAl_1−xSn_xS₂${\mathrm{CuAl}}_{1-x}{\mathrm{Sn}}_x{\mathrm{S}}_2$ and p-type Cu_1−xV_CuxAlS₂${\mathrm{Cu}}_{1-x}{\mathrm{V}}_{\mathrm{Cu}x}{\mathrm{AlS}}_2$ have negative activation energy for doped impurities and are expected to be low-resistive transparent conducting sulfides, which should be useful for CuInSe₂${\mathrm{CuInSe}}_2$-based PVSCs.