Relativistic, QED, and finite nuclear mass corrections for low-lying states of Li and Be+^+

Accurate results for nonrelativistic energy, relativistic, QED, and finite nuclear mass corrections are obtained for $2^1S_{1/2}$, $3^1S_{1/2}$ and $2^1P_{1/2}$ states of the Li atom and Be$^+$ ion. Our computational approach uses the Hylleraas basis set with the analytic integration and recursion relations. From comparison of experimental results for the isotope shifts to theoretical predictions including nuclear polarizabilities, we obtain nuclear charge radii for Li and Be isotopes.Comment: 19 pages, 8 tables, Phys. Rev. A in prin

Nuclear Physics. A. Stationary States of Nuclei

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Equations of motion approach to the spin-1/2 Ising model on the Bethe lattice

We exactly solve the ferromagnetic spin-1/2 Ising model on the Bethe lattice in the presence of an external magnetic field by means of the equations of motion method within the Green's function formalism. In particular, such an approach is applied to an isomorphic model of localized Fermi particles interacting via an intersite Coulomb interaction. A complete set of eigenoperators is found together with the corresponding eigenvalues. The Green's functions and the correlation functions are written in terms of a finite set of parameters to be self-consistently determined. A procedure is developed, that allows us to exactly fix the unknown parameters in the case of a Bethe lattice with any coordination number z. Non-local correlation functions up to four points are also provided together with a study of the relevant thermodynamic quantities.Comment: RevTex, 29 pages, 13 figure

The Noncommutative Quadratic Stark Effect For The H-Atom

Using both the second order correction of perturbation theory and the exact computation due to Dalgarno-Lewis, we compute the second order noncommutative Stark effect,i.e., shifts in the ground state energy of the hydrogen atom in the noncommutative space in an external electric field. As a side result we also obtain a sum rule for the mean oscillator strength. The energy shift at the lowest order is quadratic in both the electric field and the noncommutative parameter $\theta$. As a result of noncommutative effects the total polarizability of the ground state is no longer diagonal.Comment: 7 pages, no figure

Trion ground state, excited states and absorption spectrum using electron-exciton basis

We solve the Schr\"{o}dinger equation for two electrons plus one hole by writing it in the electron-exciton basis. The main advantage of this basis is to eliminate the exciton contribution from the trion energy in a natural way. The interacting electron-exciton system is treated using the recently developed composite boson many-body formalism which allows an exact handling of electron exchange. We numerically solve the resulting electron-exciton Schr\"{o}dinger equation, with the exciton levels restricted to the lowest $1s, 2s$ and $3s$ states, and we derive the trion ground state energy as a function of the electron-to-hole mass ratio. While our results are in reasonable agreement with those obtained through the best variational methods using free carrier basis, this electron-exciton basis is mostly suitable to easily reach the bound and unbound trion excited states. Through their wave functions, we here calculate the optical absorption spectrum in the presence of hot carriers for 2D quantum wells. We find large peaks located at the exciton levels, which are attributed to electron-exciton (unbound) scattering states, and small peaks identified with trion bound states.Comment: 16 pages; 15 figure

Photoluminescence signature of skyrmions at \nu = 1

The photoluminescence spectrum of quantized Hall states near filling factor \nu = 1 is investigated theoretically. For \nu >= 1 the spectrum consists of a right-circularly polarized (RCP) line and a left-circularly polarized (LCP) line, whose mean energy: (1) does not depend on the electron g factor for spin-1/2 quasielectrons, (2) does depend on g for charged spin-texture excitations (skyrmions). For \nu < 1 the spectrum consists of a LCP line shifted down in energy from the LCP line at \nu >= 1. The g-factor dependence of the red shift of the LCP line determines the nature of the negatively charged excitations.Comment: 11 pages, 2 PostScript figures. Replaced with version to appear in Physical Review B Rapid Communications. Minor changes, reference adde

Theoretical energies of low-lying states of light helium-like ions

Rigorous quantum electrodynamical calculation is presented for energy levels of the 1^1S, 2^1S, 2^3S, 2^1P_1, and 2^3P_{0,1,2} states of helium-like ions with the nuclear charge Z=3...12. The calculational approach accounts for all relativistic, quantum electrodynamical, and recoil effects up to orders m\alpha^6 and m^2/M\alpha^5, thus advancing the previously reported theory of light helium-like ions by one order in \alpha.Comment: 18 pages, 9 tables, 1 figure, with several misprints correcte

Nanopillar Arrays on Semiconductor Membranes as Electron Emission Amplifiers

A new transmission-type electron multiplier was fabricated from silicon-on-insulator (SOI) material by integrating an array of one dimensional (1D) silicon nanopillars onto a two dimensional (2D) silicon membrane. Primary electrons are injected into the nanopillar-membrane system from the flat surface of the membrane, while electron emission from the other side is probed by an anode. The secondary electron yield (SEY) from nanopillars is found to be about 1.8 times that of plane silicon membrane. This gain in electron number is slightly enhanced by the electric field applied from the anode. Further optimization of the dimensions of nanopillars and membrane and application of field emission promise an even higher gain for detector applications and allow for probing of electronic/mechanical excitations in nanopillar-membrane system excited by incident particles or radiation.Comment: 4 figure

Quasiclassical calculations of BBR-induced depopulation rates and effective lifetimes of Rydberg nS, nP and nD alkali-metal atoms with n < 80

Rates of depopulation by blackbody radiation (BBR) and effective lifetimes of alkali-metal \textit{nS}, \textit{n}P and \textit{nD} Rydberg states have been calculated in a wide range of principal quantum numbers $n \le 80$ at the ambient temperatures of 77, 300 and 600 K. Quasiclassical formulas were used to calculate the radial matrix elements of the dipole transitions from Rydberg states. Good agreement of our numerical results with the available theoretical and experimental data has been found. We have also obtained simple analytical formulas for estimates of effective lifetimes and BBR-induced depopulation rates, which well agree with the numerical data.Comment: 12 pages, 6 figures, 8 tables. Typo in Eq.16 corrected in V2. Typos in Eq.5 and Eq.9 corrected in V3. Error in calculation of Rb nP_{3/2} effective lifetimes corrected in V4: see new data in Table II and Table VII, Erratum to be published in PR

Quantum mechanical sum rules for two model systems

Sum rules have played an important role in the development of many branches of physics since the earliest days of quantum mechanics. We present examples of one-dimensional quantum mechanical sum rules and apply them in two familiar systems, the infinite well and the single delta-function potential. These cases illustrate the different ways in which such sum rules can be realized, and the varying mathematical techniques by which they can be confirmed. Using the same methods, we also evaluate the second-order energy shifts arising from the introduction of a constant external field, namely the Stark effect.Comment: 23 pages, no figures, to appear in Am. J. Phy