Bound state resonances in atom-solid scattering

Theoretical studies and numerical calculations of bound state resonances (selective adsorption) in the elastic scattering of low-energy light atoms from a perfect crystalline surface are made. The surface-atom potential used is the sum of Yukawa-6 pair potentials with the pair potential parameters fixed to yield the correct bound state energies for the HeLiF system. The scattering equation is numerically integrated using basis sets of open and closed channels of varying number. It is found that numerically accurate solutions are obtained only if the basis set includes the bound state in resonance, all diffracted channels coupled strongly to it by the periodic surface potential, and the specular and other low-order diffracted channels. The calculations yield specular minimum and (11) and (21) diffraction maximum under (01) selective adsorption conditions in agreement with experimental observations for the HeLiF and HeNaF systems. These results appear independent of the potential model. The atomic band structure due to the surface periodic potential is found to yield splitting of the specular minima and/or broadening of the minima. It is suggested that studying such splittings will yield information on the periodic surface potential.     

Atom-surface scattering with velocity-selected H and D atomic beams from LiF and NaF (001)

Hydrogen and deuterium atoms with an energy between 20 and 140 meV have been scattered from LiF and NaF (001) cleavage planes in UHV. The atomic beam was nearly monoenergetic by use of a slotted disk type velocity selector with a velocity resolution of $\text{Δv}\text{v}\text{=12\%}$ (FWHM). The scattering showed diffraction with a pronounced specular beam. The energies of several bound surface states have been determined by analysis of selective adsorption minima. These energies together with relative intensities of diffracted beams and specular intensity versus incident energy measurements may be represented by an interaction potential of Morse-type with additional terms which are periodic parallel to the surface. The parameters of the Morse-potential have been found to be: depth D=17.8 meV and reciprocal range $\text{κ=1.04}\text{A}\text{?}{}^{\mathrm{?1}}$ for H₁/LiF (001) and D = 17.9 meV, k = 1.15 Å^?1 for H₁/NaF (001); the additional periodic terms have relative strength β₁₀=0.04 and $\text{β}{}_{11}\text{≈}\text{β}{}_{10}\text{2}$ in the case of H ₁/LiF, but β₁₁≈β₁₀=0.03 in the case of H₁/NaF. From the observed influence of surface temperature on the position of selective adsorption minima the coefficient of thermal expansion of the topmost surface layer turns out to be approximately twice the bulk value.     

Atom-solid scattering: He + graphite basal plane

Theoretical studies of scattering of atoms by solid surfaces and calculations of atomic band structure of adsorbed atoms are presented. Inelastic effects on the intensities of diffracted beams are considered within the framework of the optical model potential. The atom-solid potential used for carrying out the numerical calculation is the sum of Lennard-Jones 12-6 pair potentials for the He-graphite system. Resonances with bound states of adsorbed atoms are shown to enhance the diffraction into some of the open channels and inelastic scattering. The degree of enhancement for a certain process depends on the coupling between that process and the resonant bound state and the coupling between the bound state and the incident beam. For first order bound state resonances, minima in the specular intensity may result from a large increase in some of the diffracted intensities or enhancement of inelastic scattering.     

The rotational spectrum of HCNO in excited bending combination states

Millimeter wave rotational transitions of HCNO have been measured and assigned for 25 different sublevels in the vibrational states v₁v₂v₃v₄v₅ = 00004, 00012, 00013, 00021, 00022, and 00101. The measurements extend to 252 GHz covering J values up to J = 11 ← 10. Accurate effective constants B_eff and D_eff were obtained for all of these levels. Each state was treated separately, because of the quasilinearity of the ν₅ mode, and the lines were analyzed in terms of an effective Hamiltonian for linear molecules. Several Coriolis-type resonances between levels with adjacent l values were found. One set of resonances, analogous to that found earlier for lower levels, could be analyzed. Fits to the effective Hamiltonian were unsatisfactory in reproducing some of the measured frequencies, indicating resonances which were not analyzed, but the constants obtained show the trend in the parameters of the effective Hamiltonian as a function of bending excitation.     

Millimeter wave spectrum of acetonitrile oxide,CH3CNO,in the ν10 vibrational manifold: The ground state and the state v10 = 1

The pure rotational spectrum of CH₃CNO was measured in the frequency range 75 to 230 GHz. For the ground state, transitions were measured for J between 9 and 28 and for K from 0 to 12. In the v₁₀ = 1 state the measurements range from J = 0 to 19 and from K = 0 to 11. Numerous perturbations are observed, apparently due to accidental resonances with levels in other vibrational states. The contributions due to ΔK = 2, Δl = 2 matrix elements (l-type resonance and l-type doubling) are accounted for by matrix diagonalization, and the effects due to accidental resonances are presented graphically.     

Microwave spectrum of dimethylallene excited states and strong Coriolis coupling

The rotational spectra of six excited vibrational states of dimethylallene were measured and assigned to the corresponding vibrational levels, and for three more excited state spectra at least the rotational constants could be determined. Between the two lowest excited levels of symmetry species b₂ and b₁ of group C_2v a strong a-type Coriolis coupling was found to exist. The evaluation of the resulting perturbation by a diagonalization of the energy matrix yielded ζ^(a) = 0.36 and a precise value for the vibrational energy difference 48.761 GHz (1.6 cm^?1). The state b₂ is believed to be the first excited torsional substate (01, 10)₁ of methyl internal rotation, and the rotational transitions of this state as well as those of the strongly coupled state b₁ presented very irregular multiplet splittings. On the other hand, the splittings of the next-higher excited state of species a₂ which could be identified as the partner torsional substate (01, 10)₂, followed the regular pattern, yielding an internal rotation barrier V₃ (2079 cal/mole) not unlike that derived earlier from ground state splittings.     

Optische Messung der Elektronenstoß-Anregung von Xenon und molekularem Stickstoff im Schwellenbereich mit hoher Energieauflösung

Relative optical excitation functions of Xe and N₂ have been measured in the threshold region. The inciting electron beam had a FWHM of 50 meV. The threshold behaviour of the excitation functions ofp-levels of Xenon is strongly influenced by resonances. The onset is step-like, in some cases resonance structure is to be seen just above threshold. In some excitation functions resonance structure is found immediatly above the ionization limit. This is believed to be caused by two compound states the parent states of which could be the 6d′ and the 8s′ autoionizing state of Xenon. In nitrogen, the excitation functions of two bands of the second positive group have been measured (3371 and 3755 Å), the upper levels of which are thev=0 and thev=1 levels of theC ³Π _u state. The excitation raises linear from threshold. In the 3371 Å excitation function a resonance maximum at 11.50 eV is observed, where the cross section is increased due to resonance population by about 100%, as measured with a FWHM of 50meV of the electron beam. The broad absolute maximums of the excitation functions are found to lie at 14.0±0.1 eV in the case of the 3371 Å- and at 14.3±0.1 eV in the 3755 Å-band.     

A study of the excited states of23Na from the22Ne(p, γ)23Na reaction

The gamma decays of 19²²Ne(p, γ)²³Na resonances in the range ofE _p =400?1300 keV have been investigated by means of a 38 cm³ Ge(Li) detector. Branching ratios of the resonances and bound states were determined. Gamma-ray energy measurements yield the energies of 19 bound states and the value of 8794.0±1.5 keV forQ. The existence of the 3913 keV doublet state was studied through the (p, γ) reaction. No evidence for such a doublet was found.     

Elliptic dichroism, ellipticity and the offset angle of high harmonics generated by arbitrary homonuclear diatomic molecules

The nth harmonic emission rate has contributions of the components of the T-matrix element in the direction of the laser-field polarization and in the direction perpendicular to it. Using both components of the T-matrix element we present a theoretical approach for calculation of the ellipticity and the offset angle of high harmonics. The molecular bound state is represented by HOMO or by HOMO-1. We show that high harmonics, generated by molecules oriented by an angle ??_L with respect to the major semiaxis of the laserfield polarization ellipse, are elliptically polarized even if the applied field is linearly polarized. Using examples of N₂ and O₂ molecules we show the existence of extrema and sudden changes of the harmonic ellipticity and the offset angle for particular molecular alignment. The interference between different contributions to the T-matrix element depends on the molecular symmetry. Presenting partial or total parameters of elliptic dichroism in the (??_L, n) plane clear interference minima are observed. Therefore, the measurement of the elliptic dichroism may reveal information about the molecular structure and symmetry.     

The Infrared Spectrum of C2D2: The Bending States up to v4+v5=2

The vibration-rotation spectrum of ¹³C₂D₂ has been recorded in the infrared region between 420 and 1100 cm⁻¹ with an effective resolution ranging from 0.004 to 0.006 cm⁻¹, and in the millimeter-wave region between 68 and 518 GHz. A total of about 1400 rovibrational transitions (66 of which have been measured in the millimeter-wave region) have been assigned to 8 bands with 15 l-vibrational components involving the bending states up to v_t=v₄+v₅=2. The ground state and nine vibrationally excited states have been characterized. All the measured transitions have been analyzed simultaneously by adopting a model Hamiltonian which takes into account the usual vibration and rotation l-type resonances, together with the Darling-Dennison coupling between the v₄=2 and v₅=2 bending states. The derived spectroscopic parameters reproduce the transition wavenumbers with a standard deviation of the fit of the order of the experimental uncertainty.     

High-resolution infrared and microwave spectroscopy of the ν4 and 2ν2 bands of 14NH3 and 15NH3

More than two thousand Stark resonances of the ν₄ and 2ν₂ band transitions of ¹⁴NH₃ and ¹⁵NH₃ were observed at Doppler-limited resolution with a CO laser. Fourier transform infrared spectroscopy on ¹⁵NH₃ is also carried out. Thirty-six new microwave transitions including seven perturbation-enhanced transitions are observed in the v₄ = 1 excited vibrational state of ¹⁴NH₃ and ¹⁵NH₃. Accuracies of all available spectroscopic data on the v₄ = 1 and the v₂ = 2 states are evaluated and analyses of the vibration-rotation spectra are performed. The Coriolis interaction between the closely lying v₄ = 1 a (antisymmetric level) and v₂ = 2 s (symmetric level) states is explicitly included in the analysis. Smaller Coriolis interactions between the v₄ = 1 a and the v₂ = 1 s states and between the v₂ = 2 s and the v₂ = v₄ = 1 a states (i.e., (v₁, v₂, v′₃, v′₄) = (0 1 0⁰ 1¹)) are also taken into consideration. The accuracy in determination of the principal molecular constants is 10^?6. The parameters thus obtained reproduce the frequencies of the vibration-rotation transitions and inversion transitions within the accuracy of 0.0024 cm^?1.     

Self-consistent calculations of hypernuclear properties with the Skyrme interaction

An extension of the Skyrme-Hartree-Fock formalism is proposed for calculating Λ binding energies (B_Λ) in hypernuclei throughout the periodic table. The calculation includes the self-consistent nuclear polarization by the Λ hyperon. Realistic estimates for ground state B_Λ's are obtained with a simple effective ΛN force and are compared with a Λ-nucleus potential model. The Λ particle excitation spectra have also been calculated. They are discussed in the context of strangeness analog state formation and the emphasis is put on the symmetry between Λ and nuclear states.     

Fano resonance in graphene anti-dot and periodic graphene anti-dot arrays

We study the electron transport properties of graphene anti-dot and periodic graphene anti-dot arrays using the nonequilibrium Green?s function method and Landauer–Büttiker formula. Fano resonant peaks are observed in the vicinity of Fermi energy, because discrete states coexist with continuum energy states. These peaks move closer to Fermi energy with increasing the width of anti-dots, but move away from the Fermi energy with increasing the length of anti-dots. When N periodic anti-dots exist in the longitude direction, a rapid fluctuation appears in the conductance with varying resonance peaks, which is mainly from the local resonances created by quasibound state. When P periodic anti-dots exist in the transverse direction, P-fold resonant splitting peaks are observed around the Fermi energy, owing to the symmetric and antisymmetric superposition of quasibound states.     

Nitrogen trap bound states in In1−xGaxP

Photoluminescence and absorption data are reported for nitrogen-doped In_1?xGa_xP (0.64 ? x ? 1.0) demonstrating the existence of a shallow N-trap bound state, N_Γ, in the direct-gap composition region. The N_Γ state, which is derived from the Γ conduction band minimum, exists along with a deeper bound state, N_X, derived from the X minima. These states, which are not observed in N-doped GaP, exhibit non-crossing behavior in the composition region of strong coupling between the N_Γ and N_X states. This observation is in accord with recent experimental and theoretical work indicating that the N-trap bound states in the related alloy GaAs_1-xP_x are produced by a combination of long and short range potentials which should also exist in In_1-xGa_xP.     

Calculations of inelastic cross sections for rotational excitation

Cross sections for scattering of N₂ (j=0) molecules on He atoms are calculated for relative energies below the excitation threshold for the N₂ (j=2) rotational state. The close coupling method is used and the coupled differential equations are solved numerically. Very sharp resonances (corresponding to a lifetime of 10^?10 sec) caused by quasistable states of the N₂He system are found in the calculated cross section, when the closed channels corresponding to the N₂ (j=2) states were included in the coupled equations. The position of the resonances is compared with the calculated energy eigenvalues of the corresponding two body potential. Furthermore the equilibrium concentration of the N₂He quasistable and orbiting states is calculated at 80 °K andp _{N 2}=1 Atm. Both concentrations are found to be 1%.     

Theoretical study on the Cope rearrangement mechanisms and the homoaromaticity of semibullvalene,barbaralane, and 1,5‐methanosemibullvalene

Cope rearrangement mechanisms and the homoaromaticity of semibullvalene, barbaralane, and 1,5‐methanosemibullvalene in the ground and lowest excited states were studied by ab initio methods. In the ground state, the rearrangement reactions of semibullvalene and barbaralane occurred concertedly through the transition states with C_2v symmetry, and the transition states had a homoaromatic nature. In particular, the transition state of barbaralane exhibited the strongest homoaromaticity among the three systems treated here. On the other hand, for 7,8‐methanosemibullvalene, the structure with C_2v symmetry was not a transition state but one with a stable energy minimum. The energy minimum structure with C_2v symmetry had a biradical character. The lowest excited states of semibullvalene and barbaralane were the excitation to the σ* anti‐orbital, ¹B₂ and ¹B₁ states, and led to near di‐allyl states. The lowest excitation state of 1,5‐methanosemibullvalene had C_s symmetry and was the A″ state excitation in one side of two allyl parts. Copyright © 2011 John Wiley & Sons, Ltd.     

The microwave spectrum of trifluoroacetonitrile in excited vibrational states

The microwave transitions J → J + 1 have been observed in the symmetric top molecule trifluoroacetonitrile, CF₃CN, for molecules excited into several of the low-lying vibrational states. Measurements made in the degenerate states v₇ = 1 v₈ = 1 have been fitted to the formula derived by Grenier-Besson and Amat (1) for transitions J → J + 1 in degenerate vibrational states of molecules with C_3v symmetry. The measurements for the state v₈ = 1 have been extended to 150 GHz where it is shown that the above formula becomes inadequate to describe accurately the observed spectrum.     

Stretching vibrational overtone and combination states in silicon tetrafluoride

A simple three-parameter model is shown to account for the observed SiF stretching vibrational states of silicon tetrafluoride. A symmetrized anharmonic bond oscillator basis set is used to calculate stretching overtone and combination eigen values, all of which are given up to v₁ + v₃ = 5. The results show that the highest levels of the nν₃ manifold move gradually out of resonances with n quanta of ν₃ as n increases, which indicates that anharmonic resonances between the ν₃ ladder and some other vibrational ladders and (or) multiphoton resonances are needed to explain the observed multiphoton processes.     

The a-type rotational spectrum of HNCS in the excited bending states

The microwave and millimeter wave spectra of HNCS in the three bending excited states, v₄ = 1, v₅ = 1, and v₆ = 1, have been measured. The ^qR₀, ^qR₁, and ^qR₂ branches for each of these three states and the ^qR₃ branch for the lowest excited state have been assigned. Effective rotational and centrifugal distortion constants have been determined for each vibrational and K_a-rotational sub-state. Two local resonances, caused by the Coriolis induced asymmetry interaction and a b-type Coriolis resonance, allow unambiguous confirmation of the assignment of the state v₆ = 1, the first excited state of the out-of-plane vibration.