Main Quantum Number Research Articles

State-resolved measurements ofsingle-electron capture in slow Ne7+- and Ne8+-heliumcollisions

Single-electron capture in collisions of 9 keV × q Ne8+ and Ne7+ ions with He has been studied usingcold-target recoil-ion momentum spectroscopy. With an improvedapparatus a longitudinal momentum resolution of 0.07 au has beenachieved. This momentum component is directly proportional tothe difference in the binding energy of the active electronbetween the final and the initial state. For the first timestate-resolved differential cross sections have been determinedwith respect to the main quantum number, subshell level and spinstate of the captured electron. A comparison with recenttheoretical results for energy levels in Be-like Ne is given.

QSPR Modeling of Stability of Complexes of Adenosine Phosphate Derivatives with Metals Absent from the Complexes of the Teaching Access

A descriptor calculated from correlation weights of the main quantum number, orbital quantum number, number of electrons on the atomic orbital, and Morgan degrees of the second-order vertices in the graph of atomic orbitals (GAO) was proposed. Using the optimization of correlation weights (OCW) of the listed local invariants of GAO, their values were found at which the correlation coefficient between the descriptor and stability constants is maximum for teaching accesses. The quality of models of stability constants of the complexes were verified by reference accesses. The results of the series of OCW experiments show that the proposed approach allows one to predict the stability constants of the Ca2+, Cu2+, and Zn2+complexes with adenosine phosphate derivatives using teaching accesses containing no complexes of these metals.

Another bunch of superpotentials in terms of a master function

It is shown that shape invariance on the main quantum number n introduces a bunch of superpotentials, and, consequently, derives some quantum solvable systems in terms of a master function. Also, a representation of unitary parasupersymmetry algebra of order p by wavefunctions of solvable systems is derived.

Empirical Regularities in the Behavior of the Dissociation Excitation Cross Sections in Collisions of Electrons with Cesium–Halide Molecules

The behavior of the constants Ai. and αi that characterize the dependence of the dissociation excitation cross sections on the main quantum number of the upper energy level is analyzed for spectral series of the cesium atom in collisions of electrons with cesium–halide molecules. In addition to a similarity, some deviations from analogous regularities established previously for the halides of other alkali metals are also found.

Procedures for the evaluation of atomic transition matrix elements in the interaction with laser light

Analytical and numerical procedures for the calculation of atomic transition matrix elements in the interaction with linearly and circularly polarized laser light are presented. The laser—atom interaction is treated beyond the dipole approximation. The procedures are derived explicitly for hydrogen but may be readily generalized to other one-electron systems with, e.g., quantum defect type radial wavefunctions. The numerical procedure is programmed in Matlab and tested for main quantum numbers up to n = 30. The results clearly indicate when the dipole approximation breaks down in connection with laser excitation of angular Rydberg wavepackets.

Strong asymptotics of Laguerre polynomials and information entropies of two-dimensional harmonic oscillator and one-dimensional Coulomb potentials

The information entropies of the two-dimensional harmonic oscillator, V(x,y)=1/2λ(x2+y2), and the one-dimensional hydrogen atom, V(x)=−1/|x|, can be expressed by means of some entropy integrals of Laguerre polynomials whose values have not yet been analytically determined. Here, we first study the asymptotical behavior of these integrals in detail by extensive use of strong asymptotics of Laguerre polynomials. Then, this result (which is also important by itself in a context of both approximation theory and potential theory) is employed to analyze the information entropies of the aforementioned quantum-mechanical potentials for the very excited states in both position and momentum spaces. It is observed, in particular, that the sum of position and momentum entropies has a logarithmic growth with respect to the main quantum number which characterizes the corresponding physical state. Finally, the rate of convergence of the entropies is numerically examined.

ORTHOGONALITY AND BOUNDARY CONDITIONS IN QUANTUM MECHANICS

One-dimensional particle states are constructed according to orthogonality conditions, without requiring boundary conditions. Free particle states are constructed using Dirac’s delta function orthogonality conditions. The states (doublets) depend on two quantum numbers: energy and parity (“+” or “−”). With the aid of projection operators the particles are confined to a constrained region, in a way similar to the action of an infinite well potential. From the resulting overcomplete basis, only the mutually orthogonal states are selected. Four solutions are found, corresponding to different non-commuting Hamiltonians. Their energy eigenstates are labeled with the main quantum number n and parity “+” or “−”. The energy eigenvalues are functions of n only. The four cases correspond to different boundary conditions: (I) The wave function vanishes on the boundary (energy levels: l+,2−,3+,4−,...), (II) the derivative of the wavefunction vanishes on the boundary (energy levels 0+,l−,2+,3−,...), (III) periodic boundary conditions (energy levels: 0+,2+,2−,4+,4−6+,6−,...), (IV) periodic boundary conditions (energy levels: l+,1−,3+,3−,5+,5−,...). Among the four cases, only solution (III) forms a complete basis in the sense that any function in the constrained region, can be expanded with it. By extending the boundaries of the constrained region to infinity, only solution (III) converges uniformly to the free particle states. Orthogonality seems to be a more basic requirement than boundary conditions. By using projection operators, confinement of the particle to a definite region can be achieved in a conceptually simple and unambiguous way, and physical operators can be written so that they act only in the confined region.

Auger decay of core-excited higher Rydberg states of carbon monoxide

The de-excitation of higher core-excited Rydberg states of carbon monoxide has been studied. It is found that already with a main quantum number of 4 or higher, Rydberg states of p-symmetry can be successfully treated within the single-particle hydrogenic model for both the core-excited and the final states. From a study of the binding energy of the Rydberg electron in the final state versus the core-excited state, the importance of relaxation in the core-excited intermediate state is shown. Also, for core-excited Rydberg states with main quantum number of 5 or higher, an almost total quenching of strict spectator lines in the de-excitation spectra is observed.

Three-body recombination of ions with electrons in cooler-storage rings

Three-body recombination (TBR) of bare ions with free electrons of anisotropic velocity distribution is discussed in the context of recombination experiments in cooler-storage rings. The recombination rates are derived from the electron impact ionization rates using the modified Saha equation. Analytical expressions for the TBR rates and new scaling rules with main quantum number n, atomic number Z, and both transverse and longitudinal electron temperatures are derived for the low n-states regime probed in experiments in cooler-storage rings. In this context, the discrepancies found between measured rates and predictions for radiative recombination for the e + Ne10+ system [Gao et al., Phys. Rev. Lett. 75 (1995) 4381] are discussed. Present results show that TBR rates for the flattened electron beam velocity distribution cannot account for the recombination enhancement observed at very low relative energies.

Oscillator strengths of Ba I and Sr I Rydberg transitions

We describe a novel experimental technique which allows the determination of absolute oscillator strengths of Rydberg transitions with medium to high quantum numbers. Absolute photoionization cross sections measured with the saturation method are used for a calibration of the f-values. The technique and its limitations are described in detail. Results are given for the main quantum numbers n = 28 - 60 for the series Ba I (), Sr I () and for the Ba I principal series (). For the latter series a comparison with data from the literature is given.

Quantum-mechanical treatment of strong electron-atom collision contributions to the shift and width of hydrogen lines.

A quantum-mechanical theory based on a Green's function technique has been applied to calculate the shifts and the widths of hydrogen lines. Strong collision contributions have been treated via partial summation of the corresponding perturbation series. Therefore, the developed theory contains no arbitrary cutoff parameters. The calculated widths and shifts have been compared to those given by a close-coupling approach [K. Unnikrishnan and J. Callaway, Phys. Rev. A 44, 3001 (1991); 43, 3619 (1991)], semiclassical results of the unified theory, and Griem's cutoff procedure [H. R. Griem, Phys. Rev. A 38, 2943 (1988)] for the perturbation theory. Electronic contributions to widths and shifts of the hydrogen lines up to main quantum numbers n\ensuremath{\le}4 without arbitrary cutoff parameters have been calculated. (c) 1995 The American Physical Society

Microwave spectroscopy of S, P, and D states of sodium Rydberg atoms.

The transition frequencies of the nS\ensuremath{\rightarrow}nP and nD\ensuremath{\rightarrow}(n+1)P sodium atom series were measured within the 53--350-GHz range for the main quantum number n=22--32. More precise values of ls splitting and quantum defects for ${\mathit{P}}_{1/2,3/2}$ and ${\mathit{D}}_{3/2,5/2}$ terms were determined. The frequencies were measured with an accuracy of better than 50 kHz. The results were treated using the Rydberg formula E(n,l,j)=-${\mathit{R}}_{\mathrm{Na}}$/(n-${\mathrm{\ensuremath{\delta}}}_{\mathit{n}\mathit{l}\mathit{j}}$${)}^{2}$. The quantum defect was calculated by using the expression ${\mathrm{\ensuremath{\delta}}}_{\mathit{n}\mathit{j}}$=${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{l}\mathit{j}}$+${\mathrm{\ensuremath{\alpha}}}_{\mathit{l}\mathit{j}}$/${\mathit{n}}^{\mathrm{*}2}$. The constants ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{l}\mathit{j}}$ and ${\mathrm{\ensuremath{\alpha}}}_{\mathit{l}\mathit{j}}$ that result from this work are ${\mathrm{\ensuremath{\varepsilon}}}_{1/2}$=0.855 444 58(14), ${\mathrm{\ensuremath{\alpha}}}_{1/2}$=0.112 668 (90), ${\mathrm{\ensuremath{\varepsilon}}}_{3/2}$=0.854 625 83(12), and ${\mathit{a}}_{3/2}$=0.112 878(81) for the P term and ${\mathrm{\ensuremath{\varepsilon}}}_{3/2}$=0.014 909 19(38), ${\mathit{a}}_{3/2}$=-0.042 19(25), ${\mathrm{\ensuremath{\varepsilon}}}_{5/2}$=0.014 925 82(55), and ${\mathit{a}}_{5/2}$=-0.043 33(35) for the D term. The ls-splitting constants determined from the expression \ensuremath{\Delta}${\ensuremath{\nu}}_{\mathit{l}}$=${\mathit{A}}_{\mathit{l}}$/${\mathit{n}}^{\mathrm{*}3}$ are ${\mathit{A}}_{\mathit{p}}$=5 384 790(420) MHz for the P term and ${\mathit{A}}_{\mathit{d}}$=97 340(680) MHz for the D term.

A study of the white light flare of 1974 September 10

We have made a detailed analysis of the spectral data of the white light flare of 1974 September 10. Using a non-LTE theory we have calculated a semi-empirical atmosphere model and its radiation loss. From the spectra we found (1) a Balmer jump amounting to 11% at the flare maximum, (2) strong and broad Balmer line emission, the width of the higher order terms reaching a minimum between main quantum number 8 and 9, and (3) the continuum emission peaking at about the same time as the microwave emission, a few minutes before the H α flare maximum. These features may be common to all white light flares. Analysis shows that the heating in the photosphere and lower chromosphere is probably produced by backwarming of the enhanced emission in the upper chromosphere, while the heating of the upper chromosphere is probably due to bombardment by high-energy electron beams.

The distribution of proton-hole strengths in the (2s, 1d)-shell of 35Cl, 37Cl and 39Cl

A vector-polarized deuteron beam of 52 MeV was used to excite proton-hole states via the ( d , 3He) reaction on 36Ar, 38Ar and 40Ar. From the measured angular distributions of differential cross sections σ(θ) and analyzing powers iT 11( θ) we determined spins and parities J π = 1 2 + , 3 2 + 5 2 + and 1 2 − of a number of isolated levels in 36Cl, 37Cl and 39Cl and the complete 1d hole strength distribution in the continuum region. Relative proton occupancies, single-particle energies, the shape of the Fermi surface and spreading widths were obtained from a combined analysis with proton stripping reactions on even argon isotopes. The deduced Id spin-orbit splitting is found to be consistent with the recently observed dependence on main quantum number n and mass number A. The mass excess of 39Cl was determined to be (−29798 ± 2.8) keV compared to a value of (−29804 ± 19) keV as given in the mass tables.

Dissociative excitation of lithium atoms in collisions of electrons with LiCl molecules

Inelastic collisions of electrons having energies of up to 100 eV with LiCl molecules have been studied by the method of extended crossing molecular and electron beams. It is found that the process of dissociative excitation takes place, resulting in the appearance of an emission spectrum of lithium atoms within the wavelength range from 240 to 820 nm. Optical excitation functions have been measured for ten lines of the spectrum. For three spectral series investigated, the cross sections vary with the increase of the main quantum number, n, according to the formula Q i = A in −α i , where A i and α i are constants characteristic for each of the series.

Search for regularities in the melting points of AB compounds

The melting behaviour of metallic alloys and compounds differs drastically from that of molecular as well as polyanionic and polycationic valence compounds. In correlating melting temperatures with atomic properties, one has to discuss these groups separately. Additional d-electron bonding characteristically changes the trend in the dependence of the melting temperature on the main quantum number of the participating valence electrons. The appropriate atomic parameters which permit an optimal uniform description of the melting temperatures of all AB phases are yet to be found.

Scaling of measured nuclear spin-orbit splittings

The spin-orbit splittings deduced from 58 measured single-particle energies of bound protons and neutrons in closed shell nuclei show besides the trivial (2 l + 1)-proportionality a simple dependence on the number of node of the radial wavefunction (main quantum number n) and on the mass number A of the respective core.

PROFILES OF H BALMER LINES EMITTING FROM A LASER-INDUCED SILANE PLASMA

Profiles of Hα,Hβ and Hγ lines, cmited from a TEA CO2 laser induced silane plasma, are measured with an optical multichannel analizer (OMA Ⅲ) The experimental results show that FWHM (full width of half maximum) of the three lines increases with the main quantum number of the corresponding upper level of the transiti ons, i.e. △λ1/2(Hα)1/2(Hβ)1/2(Hγ), this suggests that the dominant broadening mechanism of the lines is Stark broadening. Fitting the measured Hα profile to theretical data of Stark broadening, two parameters of the plasma are obtained: average electron density N = 1017cm-3 and electron temperature T = 40 000 K. From time tesolved measurements of Hβ profile, a curve of electron density versus time is derived.

An approach to distinguish different channels for the population of fast heavy ion Rydberg states by beam-foil interaction

Rydberg states of fast hydrogenic O7+ ions have been formed by passing 13-24 MeV oxygen ions of different initial charge states (qi=3,.,5) through a carbon foil. The Rydberg ions were detected by field ionization using RYDFISS, a method offering spatial separation of the Rydberg ions of interest from the rest of the ion beam. The yield of hydrogenic O7+ Rydberg states in the range 50<or=n<or=80 of main quantum numbers has been measured as a function of carbon foil thickness in the range between 5 and 36 mu g cm-2. By taking into account the development of charge fractions during foil passage, an analysis of the Rydberg yield in terms of a rate equation has been possible in order to extract Rydberg state production and destruction cross-sections from the measured data. At the energies investigated electron capture by the bare oxygen nucleus and bound-bound excitation within the O7+ system seem to contribute roughly equally to hydrogenic Rydberg state production.

An absorption spectrum of He 2 in the VUV

Absorption profiles of He 2 molecular bands blue-shifted to the corresponding atomic resonance lines are reported. The absorption profiles are obtained from fluorescence excitation spectra of dense He gas. The strongest band is assigned to the transitions X 1Σ g +—D 1Σ u + and F 1Π u. The characteristic line shape allows the determination of the height of the barriers in the potential curves. The height of the barriers shows a simple dependence on the main quantum number which is discussed from the viewpoint of two limiting cases.