Hydrogen-like States Research Articles

Vertical high-resolution Bragg x-ray spectrometer for the tokamak fusion test reactor

A Bragg x-ray spectrometer of high spectral resolution (λ/Δλ=10 000–20 000) which accommodates three crystals and position-sensitive detectors in the Johann configuration has been installed in the diagnostic basement of the tokamak fusion test reactor (TFTR) for the measurement of radial ion temperature profiles. The ion temperature is derived from the Doppler broadening of Kα-resonance lines of metal impurity ions, e.g., Ti, Cr, Fe, and Ni, in the helium-like and hydrogen-like charge states. The x-ray diffraction plane is almost perpendicular to the magnetic axis, but slightly tilted by an angle of 3.8°, which makes it possible to measure poloidal and toroidal plasma rotation velocities of vΘ>5×103 m/s and vΦ>1×105 m/s, from the Doppler shift of spectral lines. Results obtained from the observation of TiXXl Kα-line spectra with a 220-silicon crystal of a 2d spacing of 3.8400 Å and a curvature radius of 11.05 m are reported.

Hydrogen and helium atoms in strong magnetic fields

The behaviour of atoms in strong magnetic fields of the order of 106–1012 G is investigated, and ground-state energies of hydrogenlike and heliumlike atoms are calculated and compared with earlier results. For the hydrogen atom, we make a variational calculation for so-called hydrogenlike states, where we assume the solution in the direction of the field corresponds to the solution of a one-dimensional Schrödinger equation with a truncated Coulomb potential. For the helium atoms we also try a variational approach where the trial wave functions are products of single-particle "orbitals," which are mainly magnetic in their spatial form.Ground-state energies and ionization energies are tabulated for field strengths ranging from 106 to 1012 G. At 1012 G, for instance, the binding energy of a hydrogen atom is changed from −13.6 eV to approximately −150 eV, which is in reasonable agreement with other calculations. The corresponding result for the ground-state energy of a helium atom is a change from −78 eV to approximately −730 eV, also in fair agreement with other calculations. Ionization energies for the outer electron are found to be approximately 50 eV for H− atoms and 350 eV for He atoms in a magnetic field of 1012 G.

Photoluminescence and stimulated emission in Si- and Ge-disordered AlxGa1−xAs-GaAs superlattices

Photoluminescence and absorption data are presented on AlxGa1−xAs-GaAs superlattices (SLs) disordered into bulk-crystal AlyGa1−yAs (0≤y≤x) by Si or Ge diffusion. The bulk-crystal AlyGa1−yAs produced by impurity-induced disordering (by Al-Ga interchange) is determined by transmission electron microscopy, absorption measurements, and photoluminescence to be homogeneous, with an alloy composition (y) that agrees with the average Al concentration of the SL. For low enough Al concentration (y≊0.23<yc =0.44, the direct-indirect crossover), in absorption the Ge- or Si-disordered SL exhibits (4.2 and 77 K) the bulk-crystal exciton, which is characteristic of homogeneous alloy (AlyGa1−yAs). Stimulated emission (4.2 and 77 K) in bulk-crystal AlyGa1−yAs is observed ΔE≤50 meV below the band edge via photopumping for both Si- and Ge-disordered SLs of Al concentration yielding y∼0.23 and y∼0.39. Shallow hydrogenlike donor or acceptor states are characteristic of AlxGa1−xAs-GaAs SLs disordered with Ge or with Si. For the Si impurity (i.e., an AlxGa1−xAs-GaAs SL disordered with Si), however, much deeper states (transitions) are observed that saturate at higher photoexcitation levels. These states are attributed to nearest-neighbor or extended Si-Si pairs since similarly disordered AlxGa1−xAs-GaAs SLs doped with Ge do not exhibit deeper states.

Hydrogen-like excited states of a deep donor in germanium

It is shown that the photoconductivity spectrum of selenium-doped germanium measured by IR Fourier spectroscopy at low temperatures exhibits sharp lines due to optical transitions from the 1 s( A 1) ground state into hydrogen-like excited states. The energy positions of the lines are in excellent agreement with effective-mass theory. Values of 268.3 meV, 9.9 meV and 3.6 meV are obtained for the binding energies of the 1 s( A 1) ground state and the 1 s( T 2) and 2 s( T 2) excited states, respectively.

Limitations of variational methods for hydrogenic systems

Theoretical methods that give good approximations of the behaviours of hydrogen-like impurity states in semiconductors in uniform external magnetic fields are by now well established. With variational methods in mind the sizes of the determinants that give sufficiently accurate energies greatly depend on the quality of the wave functions chosen as these affect the rapidity of the series convergence. The recently developed hybrid functions enable hydrogenic energies to be calculated up ton=7 using fairly small determinants. However, it has emerged that there is a restricted region of variational parameters which maintains the numerical symmetry of the hamiltonian matrix elements for each group of states. Although each such parameter regime appears to narrow as the magnetic quantum number increases, the accuracies of the calculated eigenvalues remain satisfactory.

Far infrared light emitters and detectors

Hydrogen-like impurity states and Landau level transitions are used for tunable photoconductivity in GaAs and InSb.Resolutions down to 0.25 cm −1 have been achieved with impurity transitions in high purity GaAs and spin flip transitions in uniaxially stressed InSb. Tunable emission in the far infrared generated by electrical current heating has been first generated by cyclotron emission. Detailed studies of the emission linewidth and electronic lifetime have been performed for several semiconductors (InSb, GaAs, InP, CdHgTc). The application of stress enhances radiative spin flip transition leading to extremely narrow emission linewidths down to 0.2 cm −1 . New types of emission mechanisms have been found in two-dimensional carrier systems including electrical subband emission and the radiative decay of two-dimensional plasmons via grating structures.

Hydrogen and Helium Atoms in Superstrong Magnetic Fields

The behaviour of atoms in superstrong magnetic fields of the order of 1012 G is investigated. As a first step, ground-state energies of hydrogen-like and helium-like atoms are calculated and compared with earlier results. Two different approaches are tried for the hydrogen atom; a variational calculation for so-called tightly-bound states and a perturbation-theory approach for so-called hydrogen-like states. In the first case, we make an adiabatic approximation where we neglect effects of the Coulomb interaction in the plane perpendicular to the magnetic field, and in the second case we assume the solution in the direction of the field to correspond to the solution of a one-dimensional Schrödinger equation with a truncated Coulomb potential. For the helium atoms we also try a variational approach where the trial wave functions are products of single-particle "orbitals" which are mainly "magnetic" in their spatial form.Ground-state energies and ionization energies are tabulated for field strengths ranging from 1010 G to 5 × 1013 G. At 1012 G, for instance, the binding energy of a hydrogen atom is changed from - 13.6 eV to approximately - 150 eV, which is in reasonable agreement with other calculations. The corresponding result for the ground-state energy of a helium atom is a change from - 79 eV to approximately - 610 eV, also in reasonable agreement with other calculations. Ionization energies for the "outer" electron are found to be approximately 27 eV for H--atoms and 220 eV for He-atoms in a magnetic field of 1012 G.

New hydrogen-like states due to Ni in ZnS

In addition to the narrow zero-phonon line at the photoionisation band edge at 2.4377 eV reported in absorption measurements of Ni-doped ZnS, another two sharp lines at 2.4268 and 2.4325 eV in the electroabsorption spectrum have been detected for the first time. At the bottom of the photoinization band a new structure has also been observed, which consists of a zero-phonon line at 3.3897 eV and its LO-phonon sidebands. The zero-phonon lines in the photoionization band are attributed to transitions into hydrogen-like states of a hole, loosely bound to a Ni 1+ ion which is either in the ground 2T 2 or high-lying excited 2E states.

Validity of the Conservation Rule of Nodal Surface Numbers in the Wave Function of Hydrogenic Exciton in Magnetic Field

Magnetoabsorption experiments on the $A$ exciton in InSe have been performed in search of a unified correspondence relation between low and high magnetic field levels of a hydrogenlike state. Results show that the nodal-surface conservation rule of Shinada et al. is a more appropriate representation of this relationship than the so-called noncrossing rule.

Tunnel ionization of highly-excited hydrogenic atoms in a variable field

The relations are obtained, which describe the probability of tunnel ionization from highly-excited hydrogen-like states in a variable field. The effect of initial state splitting into quasi-energy states in an external variable field is taken into account. The parameter γ 2 n is examined, whose value determines the character of the tunnel ionization process.

Hubbard model for disordered systems: Application to the specific heat of the phosphorus-doped silicon

A self-consistent many-body theory of disordered systems, described by the Hubbard Hamiltonian with random transfer integrals, is developed. The random nature of the system is taken into account by the Matsubara-Toyozawa theory of impurities in semiconductors. By considering the hydrogenlike impurity states, the electronic specific heat of uncompensated phosphorus-doped silicon is calculated and compared with experimental results. It is found that it agrees well with experiment in the entire semiconductor-to-dilute-metallic region.

Some asymptotic (n → ∞) properties of hydrogen-like states | n l m > and on the use of the correspondence principle

Some results obtained with the quantal wavefunctions are compared, as n to infinity , with those obtained from the Bohr-Sommerfeld picture. In particular, it is shown that the probability to find the electron in the classically forbidden domain may not be negligible even when all the quantum numbers go to infinity, a fact which leads one to analyse the conditions for using the correspondence principle.

Excitons in thallous halides in a magnetic field

The electronic state of excitons and their phonon coupling in high magnetic field are investigated by optical means in thallous halides. By the study of an 1s exciton in a magnetic field, inter-as well as intra-valley scatterings are found to play an important role in the internal structure of the exciton. For the hydrogen-like exciton envelope state, it is demonstrated that the energy shift by magnetic field differs considerably from what is expected from available theories. Experimental evidence of the polaron-induced anomaly of exciton is given and its peculiar behavior is discussed.

Impurity bands in inversion layers

Impurity bands have been created and observed in inversion layers on silicon by drifting Na + ions close to the SiSiO 2 interface. The resulting hydrogen-like states can be made dense enough so that a peak in the conductivity can be observed at gate fields below the threshold for conduction in the conduction band. Three modes of conduction were observed: activation to the mobility edge, nearest neighbor hopping, and variable range hopping. From these measurements and by varying the density of ions information about binding energy, impurity band width, and the extent of the bound wave functions as a function of the electron density, ion concentration and substrate bias may be inferred.

Investigation of the fast decay of the green fluorescence in ZnO(Cu) crystals

The decay time of the green band-emission in ZnO(Cu) below 70K, excited by u.v. or i.r., is measured in delayed coincidence. The dependence on the way of excitation, temperature and doping suggests the assumption of a shallow hydrogen-like intermediate state in the recombination process.

Composite nucleon approach to the deuteron problem

A composite model is suggested for the nucleons by assuming a longrange strong gluon force between a diquark boson B and a quark A. In the proton, A is trapped inside B in an oscillator potential and, in the neutron, A is on the surface of B in a hydrogenlike state. Nucleon form factors are obtained in agreement with experiments. The model contains a mechanism for a large effective mass of the quark A. When B is identified with π and A with μ, one can fix the gluon charge value and obtain the magnetic moments of the proton and neutron. The (πμ) atomic model for the nucleon can be used to construct the deuteron on a hydrogen molecule model. It leads to values for the binding energy, electric quadrupole moment, and form factors of the deuteron that are in agreement with experiments.

Far-Infrared Magneto-Spectroscopy of Shallow Impurities and Excitons in Germanium by Using Lasers

Optical transitions between excited states of impurities in germanium, Sb or As, in a magnetic field have been investigated using HCN, DCN and H20 lasers. The energy levels of states with even parity and M= +1, i.e., 3D+l, (113) and (115), are determined experimentally and are compared with the values obtained by the variational calculation. In pure germanium under photo-excitation, the Zeeman effect of the far-infrared absorption of an indirect exciton has been. observed. An attempt is presented to interpret the origin of the strong absorption peaks of the exciton on the basis of the adiabatic approximation for the Coulomb potential. The present work is concerned with optical transitions between the excited states of group V impurities in germanium and with transitions of an exciton from its ground state to an excited state in undoped germanium. Both the impurity and exciton in germanium have a series of hydrogen-like states; the optical transitions occur in the far-infrared region. The s- and d-like excited states can be observed only by the transitions starting from some excited states. On excitons, we have little information on their excited states, though the photo-luminescence experiments reveal the nature of the ground state. Since the densities of excited impurities and of excitons are rather small, certain intense light sources are required for the spectroscopic observation of these weak absorption. Such light sources are provided by backward tubes and far-infrared lasers.

Impact Ionisation Theory for Traps in Semiconductors

AbstractEstimates are obtained for the impact ionisation probability per unit time (Pk) that an electron of wave vector k and energy Ek will impact ionise an electron from a hydrogenlike donor state specified by quantum numbers n and 1 and an ionisation energy Et. Bloch functions, hydrogen‐like wave functions, first order perturbation theory, and a non‐degenerate material with a parabolic conduction band indicate the basis of the calculation. The work goes beyond the authors' previous (1967) treatment in the extension of the theory to shallow impurities and more energetic electrons. The analytical part of the earlier work could handle only the limit Ek ≈ Et. The difficulty of going beyond this limit arises from the fact that the square of a Gegenbauer polynomial, involving wave vectors to be integrated, occurs in a matrix element which has the square of a Fourier coefficient of a hydrogen‐like function as a factor. By overcoming this difficulty, one can find expressions for the cases when Et/Ek < 1. The earlier treatment, which yielded Pk = 0 for n − l even when Et ≈ Ek is sharpened by finding numerical estimates for Pk (> 0) for a range of values of Et/Ek when n − l is even. These transitions can therefore not strictly speaking be regarded as forbidden. Results which are more reliable than the earlier ones are also obtained when n − l is odd. Results are obtained for the l‐dependence when n is fixed.

Observation of Stark beats in the H-like K X rays of oxygen and fluorine

K X rays of highly ionized oxygen and fluorine ions exhibit intensity oscillations as a function of electric field parallel to the beam. The nearly periodic behavior of the oscillations and the linear variation of the beat frequency with projectile velocity suggest a Stark beating between high n hydrogen-like states.

Absolute beam-foil excitation probabilities of hydrogen-like states in iron

By measuring the absolute intensities of hydrogen-like spectral lines, we have deduced absolute foil-excitation probabilities for several levels of high principal quantum number ( n) and several emerging charge states of a 1.5-MeV iron beam. Core polarization allows the partial resolution of transitions involving different l-values for the same initial and final n. The probability that an iron ion emerging from the foil with charge state g is in a state characterized by n is found to be of order 10 −3 for n = 6–9 and q = 4 +−7 +. For a given n, population of high l appears to be favored. A discussion of the overall state population distribution among high n states following foil excitation will be presented.