Semiempirical determination of the atom-surface interaction

We discuss three methods of determining V(z), the lateral average (G = 0 Fourier component) of the atom-surface interaction, from the bound state spectrum found in beam scattering. One method uses the Rydberg-Klein-Rees technique, which yields the width of the potential (i.e., separation of classical turning points) as a function of energy. This method incorporates also the known asymptotic form V ～ ?C₃z^?3, whereC₃ is derived from the polarizability and dielectric function of atom and solid, respectively. The second method uses a hybrid potential, constructed from a Morse potential with shifted zero of energy connected to the asymptotic form,?C₃z^?3, requiring continuity of V and $\text{d}\text{V}\text{d}\text{z}$. The third potential is a Lennard-Jones 3–9 interaction. Results are presented for H and He scattering from LiF and NaF.     

Constraints on the short-range potential from the energy level shifts in protonium

A method of obtaining model-independent constraints on the short-range potential from the energy level shifts is discussed. It is based on the use of knowledge of the long-range potential and the two isospin scattering lengthsa ₀ anda ₁     

Improved potential energy curve and vibrational energies for the electronic ground state of the hydrogen molecule

The potential energy curve for the electronic ground state of the hydrogen molecule has been recomputed for intermediate and large internuclear separations. for 2.4 ≤ R ≤ 8.0a.u. the previous potential energy curve has been improved. The largest improvement amounts to 5.5 cm^?1, and was obtained in the vicinity of R = 4.4a.u.. Using the new potential energy curve, and the adiabatic and relativistic corrections, the vibrational and rotational energy levels have been calculated for H₂, HD, and D₂. The deviations of the calculated energy levels G(v) of H₂ and D₂ from the observed values follow very closely the nonadiabatic corrections resulting from the Van Vleck formula.     

Microscopic calculation of the repulsive core in the elastic nucleon-nucleon scattering

The resonating group method is used to study the effective potential between two nucleons, due to the confining potential between quarks taken together with the Pauli principle for quarks. The potential used has harmonic form, unitary spin factor λ(1)·λ(2), and both ordinary and spin-spin components. Its parameters are determined by appeal to experimental data, and phase shifts are calculated for the¹ S ₀ and³ S ₁ states of the nuncleon-nucleon (NN) system. The results indicate that the repulsive core in theNN potential may arise from quark antisymmetrization required if nucleons are composed of quarks.     

The electronic conductivity of lead fluoride and the D.C. Polarization theory

The electronic conduction characteristics of solid lead fluoride were investigated using the Wagner d.c. polarization technique. It was found that when the (?) Pb/PhF₂/graphite ( + ) cell was polarized at potentials much below a critical value, E_c, the steady state current, I, as a function of the polarization potential, E, behaves in accordance with the Wagner equation. The log I vs E plots gave straight lines with slopes having the theoretical value of F/2.303 RT. On the other hand, when the polarization potential was equal or higher than E_c, an anomalous behavior was observed. Slopes with values less than the theoretical were obtained from the log I vs E plots. This anomalous behavior was attributed to the high concentration of electron holes at the PbF₂/graphite interface resulting from the high polarization potential. The critical potential was defined as the applied potential where the electron hole concentration at the PbF₂/graphite interface becomes so high that the electronic conductivity is equal to the ionic conductivity which contradicts the assumptions for the Wagner equation. Consequently, the Wagner equation is not applicable under these conditions.     

On the connection between the vacuum polarization potential in muonic atoms andg-2 of the muon

A simple connection, between the vacuum polarization potential used in muonic atoms and the muon anomaly arising from the second-order vertex graph with electron vacuum polarization insertions, is established. In particular, the leading log-term and the orderm _e/m _μ term are essentially the same in the two cases. We make use of this connection to determine the vacuum polarization potential in order α³(Zα).     

Intracellular potential relief and size effects in the lattice of a LaF3 superionic conductor

The potential relief in the lattice of a LaF₃ crystal is calculated by quantum-mechanical methods for clusters containing from 24 to 1200 ions. For the dielectric phase, formation energy E _a for defects of the vacancy-interstitial fluorine ion type and potential barrier E _d preventing the motion of fluorine ions are found to grow from minimal values E _a = 0.12 eV and E _d = 0.22 eV for a cluster of 24 ions to maximal values E _a = 0.16 eV and E _d = 0.26 eV for clusters of 576 and 1200 ions. The values of E _a and E _d obtained in quasi-mechanical calculations are in good agreement with those obtained from Raman and quasi-elastic light scattering data.     

Binding effects in the optical potential of pionic atoms

We calculate the contribution from nucleon binding to the coefficient Re B₀ in the optical potential of pionic atoms. The relevant Feynman graphs are deduced for nuclear matter. They depend on off-shell values for pion-nucleon scattering lengths a_πN and for the nucleon-binding potential V_NA. Off-shell effects are found to be very important: A pole model for a_πN, extrapolated off-shell, increases binding effects by a factor of three over the use of on-shell values. Two simple models are proposed for the off-shell continuation of V_NA. One leads to attractive, the other to repulsive contributions to Re B₀.     

Amplitudes of multichannel scattering on the barrier with a constant height in the scattering direction

The immersing method is applied to solve the N-channel scattering problem. In particular, we consider the particle scattering on a multidimensional potential barrier, which is constant in the scattering direction and arbitrary in the lateral direction. For this case the scattering amplitudes t _m and r _m (m = 1, 2, …, N) are determined. Transition from the obtained formulas to the case of thin potential is performed. For this case analytical expressions of transmission amplitudes t _m and reflection amplitudes r _m are obtained. We show that the product of transmission and reflection amplitudes in the channel m does not depend on the scattering channel. It is assumed that the scattering particle falls on the potential with the longitudinal wave vector k _l corresponding to the channel l.     

Measurements of the spatially resolved electron temperature and plasma potential in ferrite-core side type Ar/He inductively-coupled plasmas

Spatial distributions of the effective electron temperature (T_eff) and plasma potential were studied from the measurement of an electron energy probability function in a side type ferrite-core inductively coupled plasma with an argon–helium mixture. As the helium gas was diluted at the fixed total gas pressure of 5 mTorr in an argon discharge, the distribution of the plasma density and plasma potential changed from a concave to a flat profile, and finally became a convex profile, while all spatial profiles of T_eff were hollow shapes with helium dilution in the argon discharge. This evolution of the plasma potential with helium gas could be explained by the increased energy relaxation length (λ_ε), indicating the transition of electron kinetics from local to non-local kinetics.     

The ν7 vibrational states of C3O2: A least-squares fit of the rigid-bender model to the v7ν7l7 energies and rotational constants

The rigid-bender model is used to treat the large-amplitude, low-frequency, bending vibration ν₇ of C₃O₂. Different parameterizations of the bending potential function are considered, and a simple two-term power series is found to give the best fit. With this parameterization, using a least-squares fit to energies and B values, the ν₇ potential function is determined for the ground state as well as for the states in which ν₂, ν₃, ν₄, ν₆, 2ν₆, ν₁ + ν₃, ν₁ + ν₄, ν₂ + ν₃, and 2ν₂ + ν₄ are excited. The excitation of other vibrations has in some cases a drastic effect on the ν₇ potential. In the ground state the potential has a 29 cm^?1 barrier at the linear position, in ν₁ + ν₃ the barrier increases to 79 cm^?1, while in 2ν₂ + ν₄ the barrier vanishes. An equilibrium potential is determined by correcting the ground state potential for the effects of zero-point motion of the normal vibrations ν₁, …, ν₆. This potential has a 35.6-cm^?1 barrier with a minimum at α = 11.14°, where 2α is the angular deviation from linearity. The model accurately predicts the quartic and sextic centrifugal distortion terms for the low-lying v₇ν₇^l₇ states. Second-order l-type coupling is included in the calculations of the quartic terms. The effects of this coupling, which are most pronounced for the ν₇ ≥ 2 states, adequately explain the negative D term recently reported for the ν₂ + 4ν₇⁰ state.     

Calculation of the wave functions of the ground and weakly excited states of helium II

The wave functions of the ground (Ψ₀) and the first excited (Ψ_k) states of He II in the second-order approximation, i.e., up to the first two corrections to the corresponding solutions for a weakly nonideal Bose gas, are determined by the collective variable method, which was proposed by Bogolyubov and Zubarev and developed in the studies by Yukhnovskii and Vakarchuk. The functions Ψ₀ and Ψ_k = ψ_kΨ₀ are determined as the eigenfunctions of the N-particle Schrödinger equation from a system of coupled equations for Ψ₀, Ψ_k, and the quasiparticle spectrum E(k) of helium II. The results consist in the following: (1) these equations are solved numerically for a higher order approximation compared with those investigated earlier (the first-order approximation), and (2) Ψ₀ and ψ_k are derived from a model potential of interaction between He⁴ atoms (rather than from the structure factor as earlier) in which the potential barrier is joined with the attractive potential found from experiment. The height V ₀ of the potential barrier is a free parameter. Except for V ₀, the model does not have any free parameters or functions. The calculated values of the structure factor, the ground-state energy E ₀, and the quasiparticle spectrum E(k) of He II are in agreement with the experimental values for V ₀ ≈ 100 K. The second-order correction to the logarithm of Ψ₀ significantly affects the value of E ₀ and provides the asymptotics E(k → 0) = ck, while the second-order correction to ψ_k slightly affects the E(k). The second-order corrections to Ψ₀ and ψ_k have a smaller effect on the results compared with the first-order corrections, whereby the theory is in agreement with experiment; therefore, one may assume that the truncated Ψ₀ and ψ_k well describe the microstructure of He II. Thus, the series for Ψ₀ and Ψ_k can be truncated in spite of the fact that the expansion parameter is not very small (～1/2).     

Torsion of the nitro group in nitroethylene

Eight NO₂-torsional transition frequencies obtained from interferometric far infrared measurements are reported. These data provide accurate information on the potential function for torsional angles up to 50°. The potential parameters are V₂ = 1642.7 ± 3.9 cm^?1 and V₄ = ?88.0 ± 1.7 cm^?1 for a rigid frame/rigid top model and V₂ = 1690.6 ± 4.2 cm^?1 and V₄ = ?90.8 ± 1.8 cm^?1 for a refined model allowing for distortions of the NO₂-group upon torsion. V₆ and V₈ terms are not significant.     

Scattering length and effective range in closed form for the Coulomb plus Yamaguchi potential

From the known expression for the off-shell T-matrix corresponding to the potential consisting of the sum of the Coulomb potential and the Yamaguchi potential, the physical scattering amplitude can be derived in a satisfactory way. We derive simple exact closed formulae for the scattering length a_cs and the effective range r_cs from this amplitude. These are compared with approximate formulae derived by Harrington. Also a few numerical calculations are reported and compared with results obtained by Harrington and by Ali et al.     

The proton optical-model potential near the Coulomb barrier

Proton elastic scattering data from ¹⁹⁷Au, ²⁰⁸Pb and ²⁰⁹Bi at energies near the Coulomb barrier are analyzed. The energy dependences of the real volume and imaginary surface-derivative potential depths V_R and W_SF of a local optical-model potential with fixed geometric parameters are found to be much more rapid than at higher energies. The strong energy dependence of V_Rnear the Coulomb barrier is explained in terms of the non-locality of the nucleon-nucleus interaction.     

On the second rotational isomeric form of butadiene-1,3

Eleven lines of the “hot” band progression of the torsional overtone 2ν₁₃ have been measured in the Raman spectra of cis,cis-1,4-d₂-butadiene-1,3 and d₆-butadiene-1,3. The potential of Carreira (J. Chem. Phys.62, 3851–3854 (1975)) (V₁ = 600, V₂ = 2068, V₃ = 273, and V₄ = ?49 cm^?1) and that of Bock et al. (J. Chem. Soc. Perkin II, 26–34 (1979)) (V₁ = 347.3, V₂ = 1790.0, V₃ = 612.8, and V₄ = 179.8 cm^?1) have been used to interpret the results obtained. For the accepted expansion of the Pitzer function F(φ), it is shown that the potential of Bock et al. reproduces the frequencies of the torsional overtones of these two molecules and h₆-butadiene-1,3 more closely. The improtance of data on isotopic molecules in the calculation of potential curves from spectroscopic information is emphasized.     

The three-nucleon system near the N-d threshold

The three-nucleon system is studied at energies a few hundred keV above the N-d threshold. Measurements of the tensor analyzing powers T₂₀ and T₂₁ for p-d elastic scattering at E_c.m. = 432 keV are presented together with the corresponding theoretical predictions. The calculations are extended to very low energies since they are useful for extracting the p-d scattering lengths from the experimental data. The interaction considered here is the Argonne V18 potential plus the Urbana three-nucleon potential. The calculation of the asymptotic D- to S-state ratio for ³H and ³He, for which recent experimental results are available, is also presented.     

The deformation of the ground and excited states in the Ag and Sn nuclei

The microscopic calculation of the potential energies in the ground and excited states of Ag and Sn nuclei has been performed. The single particle Nilsson potential and the shell correction Strutinski method have been used. The weak sensitivness to nonaxial deformation has been found for even neighbours of these nuclei. The small tendency towards prolate deformation of the ground and excited one-quasiparticle states originating from theg _9/2 proton subshell in^101–105Ag odd isotopes has been noticed. The behaviour with quadrupole e and hexadecapole ε₄ deformation of the ground and two-quasiparticle excited 0⁺ states originating from thed _5/2,g _9/2 andg _7/2 proton subshells andh _11/2 neutron subshell in^112–118Sn has been investigated. The small quadrupole deformation of the excited 0⁺ states has been found what is in agreement with the experimental data concerning the rotational bands build on the first excited 0⁺ states in Sn isotopes.     

On the use of a noncentral velocity dependent potential for the interpretation of the nucleon-nucleon scattering data

A phenomenological nucleon-nucleon potential containing a noncentral velocity dependent term of the form (σ ₁ ·p)(σ ₂ ·p) is used to fit the solutions YLAM and YLAN 3 M of the phaseshift analysis ofBreit et al. andHull et al. for protonproton and neutron-proton scattering respectively. The potential contains altogether 20 parameters. The fit is carried through in the range from 10 to 300 MeV laboratory energy. While the results for thep-p phase parameters are useful only in some cases the results for then-p phase parameters are in general quite satisfactory.