Doubly-Excited States of Beryllium-Like Ions
The resonance energies and widths for doubly-excited (1s23d2, 3p4f, 3d4d) 1Ge states of beryllium-like ions are determined by calculating the density of resonance states using the stabilization method. A model potential is used to represent the interaction between the outer electrons and the core electrons. Products of Slater Orbitals are used to represent the two-electron wave functions. We present results for some lower-lying doubly-excited states for Z = 5-10. Comparisons are made with other calculations in the literature.
Berglund-H\"ubsch duality is an example of mirror symmetry between orbifold Landau-Ginzburg models. In this paper we study a D-module-theoretic variant of Borisov's proof of Berglund-H\"ubsch duality. In the $p$-adic case, the D-module approach makes it possible to endow the orbifold chiral rings with the action of a non-trivial Frobenius endomorphism. Our main result is that the Frobenius endomorphism commutes with Berglund-H\"ubsch duality up to an explicit diagonal operator.