Bound state vibrational spectrum of the 3–9 atom-surface interaction

The potential $\text{V(z) =}\text{C}{}_9\text{z}{}^9\text{?}\text{C}{}_3\text{z}{}^3$ is a reasonable parametrization of the atom-surface interaction. We evaluate the discrete spectrum E_n of bound states for this potential with arbitrary coefficients C₉ and C₃. The resulting form in the WKB approximation is $\text{E}{}_{\mathrm{n}}\text{= ?D [1 ?}\text{(n +}\text{l}\text{2}\text{)}\text{L}\text{]}{}^6$, where L depends on the mass and D is the well depth. We find that the exact solution of the Schrödinger equation can be written in the same form, with n shifted slightly by an amount δ_n, which we calculate. The results are applied to the case of He near a NaF surface, in which the calculated eigenvalue spectrum agrees well with experimental values.     

Exchange energy density of inhomogeneous electron gas near a metal surface

Using the first-order density matrix of an infinite barrier model of a metal surface, the exchange energy density can be evaluated exactly as a function of the distance z from the barrier. This result is compared with the local approximation $\text{?}\text{3}\text{4}\text{e}{}^2\text{(}\text{3}\text{π}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{[?(z)]}{}^{\mathrm{<mtext>4</mtext><mtext>3</mtext>}}$ where the electron density in the model. The local approximation follows the exact result quite closely at all z but leads to a large percentual error in the integrated surface exchange energy.     

Φecчet ДИLcy;н boЛн Л sИЛ osцИЛЛЯtoΦo b ДЛЯ ИЗoЭЛeКtponnoЙ ПosЛeДoBateЛЬn ostИ Li

ФeйnмanoBsкaя диaгpaмnaя teчnи кa пpимenena для pasЧeta длen Bo лn и sил osцилляtopoB osnBoг и nикoto pыч neжnич Boэбyждennыч sstoяn ий Li-пoдoбnыч иonoB. passЧиtanы Bклaды ot диaгp aмм пepBыч пopядкoB длк nepeляtи Bиstsкoй эnepгии, peляtиBиstsкич пoпpaBoк и дипoл ьnыч matpиЧnыч matpиЧnыч элeme ntoB. Для pasЧeta peляtиBиstsкич пoпpaBoк был иsпoльэoBan oпepat op Бpeйta. pяд пo $\text{1}\text{z}$ для эnepгии пpe дstaBлen B sлeдyющeem Bидe

$\text{E = E}{}_0\text{z}{}^2\text{+ΔE}{}_1\text{z+}\text{1}\text{z}\text{ΔE}{}_3\text{+}\text{α}{}^2\text{4}\text{(E}{}_0{}^{\mathrm{p}}\text{z}{}^4\text{+ ΔE}{}_1{}^{\mathrm{p}}\text{z}{}^3\text{),}$

для дипoльnoгo matpиЧoгo элe

$\text{P =}\text{a}\text{z}\text{1+}\text{τ}{}_1\text{z}\text{+}\text{τ}{}_2\text{z}{}^2\text{.}$

ПoлyЧennыe Чиsлennяe эnaЧennы e эnaЧenия кoэффициentoB пpи z^k дaли Boэmoжnostь passЧиtatь длиnы Boлn и sилы osцилляtopoB пe peчoдoB 1s²2s ? 1s²2p, 1s²2s ? 1s²3p, 1s²2p ? 1s²3s, 1s²2p ? 1s²3d, 1s²3s ? 1s²3p, 1s²3p ? 1s²3d для Li-п oдoбnыч иonoB. peэyльtatы pasЧe ta spaBnиBaюtsя s экsпepиmentaльныmи для иэoэлeкtpnnoй пoлeдoBat eльnostи Li. Чopoшee soглasиe s экsпepиment aльnыmи (0,01–0,1%) дaet Boэmoжnostь naдetьsя, Чto pяд пo $\text{1}\text{z}$ sчoдиtsя д ostatoЧno быstpo.Feynman diagram techniques have been applied to the calculation of wavelengths and oscillator strengths of the ground state and of a number of low-lying excited states for Li-like ions (1s²2l, 1s²3l). Contributions have been calculated to the first order for the nonrelativistic energy, relativistic corrections and dipole matrix elements. Relativistic corrections have been obtained by computing the active 〈H_B〉 matrix. Numerical results for the $\text{1}\text{z}$ expansion are presented in the following form: for the energy,

$\text{E = E}{}_0\text{z}{}^2\text{+ΔE}{}_1\text{z+}\text{1}\text{z}\text{ΔE}{}_3\text{+}\text{α}{}^2\text{4}\text{(E}{}_0{}^{\mathrm{p}}\text{z}{}^4\text{+ ΔE}{}_1{}^{\mathrm{p}}\text{z}{}^3\text{),}$

for the dipole matrix elements,

$\text{P =}\text{a}\text{z}\text{1+}\text{τ}{}_1\text{z}\text{+}\text{τ}{}_2\text{z}{}^2\text{.}$

The results were used for calculations of the wavelengths and oscillator ofthe transitions 1s²2s ? 1s²2p, 1s²2s ? 1s²3p, 1s²2p ? 1s²3s, 1s²2p ? 1s²3d, 1s²3s ? 1s²3p, 1s²3p ? 1s²3d for Li-like ions. Results are compared with experimental data for the isoelectronic sequence of Li (Li I-SX IV). Good agreement with experimental data (0·01–0·1%) suggests that the $\text{1}\text{z}$-expansion converges rapidly.     

On the universality classes of the Henon map

Within an appropriate renormalization framework, we discuss a¹(b) and δ associated with the bifurcation road to chaos of a Hénon-like map generalized as follows: (x_t+1, y_t+1) = (1?a|x_t|^z + y_t, ?bx_t); (b?0, z?1). For fixed z, we obtained (i) only two universality classes, namely the conservative (b = 1) and non-conservative (b≠1) ones and (ii) $\text{a}{}^1\text{(}\text{1}\text{b}\text{) =}\text{a}{}^1\text{(b)}\text{b}{}^{\mathrm{z}}$. For b = 1, δ(z) presents a minimum, and diverges for z → 1 and z → ∞ (this contrasts with the b≠1 case).     

Radiative lifetimes in MoI using a novel atomic beam source

Radiative lifetimes of the 4d⁵ (a⁶S)5pz ⁷P^o levels and the 4d⁵ (a⁶S)5pz⁵P^o levels in MoI are reported as follows: $\text{τ(}\text{z}{}^7\text{P}{}_4{}^{\mathrm{<mtext>O</mtext>}}\text{) = 15.9}\text{ns}$, $\text{τ(}\text{z}{}^7\text{P}{}_3{}^{\mathrm{<mtext>O</mtext>}}\text{) = 17.0}\text{ns}$, $\text{τ(}\text{z}{}^7\text{P}{}_2{}^{\mathrm{<mtext>O</mtext>}}\text{) = 17.1}\text{ns}$, $\text{τ(}\text{z}{}^5\text{P}{}_3{}^{\mathrm{<mtext>O</mtext>}}\text{) = 22.3}\text{ns}$, $\text{τ(}\text{z}{}^5\text{P}{}_2{}^{\mathrm{<mtext>O</mtext>}}\text{) = 22.1}\text{ns}$, and $\text{τ(}\text{z}{}^5\text{P}{}_1{}^{\mathrm{<mtext>O</mtext>}}\text{) = 21.7}\text{ns}$ (±5%). The lifetimes are measured using time resolved laser induced fluorescence and a novel atomic beam source. This novel hollow cathode effusive beam source produces an intense beam of ground state Mo atoms and metastable Mo atoms. Our measurements on the z ⁷P^O levels are in agreement with earlier lifetime measurements. Our measurements on the z ⁵P^O levels are the first direct radiative lifetime measurements of these levels; the z ⁵P^O measurements are of particular interest because the a⁵S → z⁵P^O multiplet is used to determine the solar abundance of Mo.     

Phenomenological thermodynamics of mixed valence phenomenon

The fluctuation of valence in some rare-earth (RE) compounds is described in terms of the effective potential seen by the RE ion. The nearly degenerate $\text{4?}{}^{\mathrm{n+1}}\text{(5d6s)}{}^2$ and $\text{4?}{}^{\mathrm{n}}\text{(5d6s)}{}^3$ levels of the RE ion split in energy in the presence of a repulsive potential. The energy separation (ΔE) between these levels is a function of external variables such as temperature, pressure or composition, which change the effective potential seen by the ion. The variation of ΔE with temperature is obtained for four Europium compounds from ¹⁵¹Eu Mössbauer isomer shift data. The temperature dependence of susceptibility is then obtained from the same (ΔE) variation and compared with experimental results. A characteristic temperature (T_υ) is found below and above which (ΔE) behave as ΔE = αT and ΔE = βT+γ respectively.     

Strong vacuum polarization and self-damping of e+e− annihilation

If the hadronic contribution to vacuum polarization, which is proportional to the ration of e⁺e^? annihilation into hadrons to that into μ⁺μ^? rises asymptotically as a power $\text{β >}\text{1}\text{2}$ of the squared four-momentum, the ratio $\text{σ}\text{(e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→hadrons)}\text{σ}$ point $\text{(}{}^{\mathrm{\sigma }}\text{point =}\text{(4πα}{}^2\text{)}\text{(3s))}$ is bound to be less than $\text{?}\text{(3}\text{tg}\text{πβ)}\text{(8α)}$ and this limit is approached sooner for higher β. Other models of vacuum polarizations are also considered together with their possible origin and implications.     

Energy gaps in the fractional quantum hall effect

Based on a density-of-states N(E) ∝ (E − μ₀)² Poisson's equation is solved perpendicular to the current direction in the two-dimensional Hall-plate. By comparing the result with the structure obtained for an Ising-like chain with occupation numbers $\text{σ = 0,}\text{1}\text{2}$, 1 to account for vanishing energy gaps for filling factors $\text{v =}\text{m}\text{n}$ with n even, the energy gaps for n odd are found essentially to be proportional to $\text{B}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{n}{}^{\mathrm{-2}}$ in accordance with recent results.     

Holtzmark electric field distribution in a two-dimensional electron fluid

The Holtzmark distribution for the thermal electric field at a neutral point in a two-dimensional and uncorrelated electron fluid is given by $\text{β(1 + β}{}^2\text{)}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$, with $\text{β =}\text{E}\text{E}{}_0$, and E₀ = πnZ_pe in terms of the density n and perturber Z_pe.     

A direct method for modifying certain phase-integral approximations of arbitrary order

The approximate solution of the differential equation $\text{d}{}^2\text{ψ}\text{dz}{}^2\text{+ Q}{}^2\text{(z)ψ = 0}$ by a general modification of certain phase-integral approximations of arbitrary order is considered. A consistent modification of these higher-order phase-integral approximations is derived on the assumption that one has found a function Q_mod²(z) which makes the modified first-order approximation good at certain singular points of Q²(z), where the unmodified approximation would break down.     

The bound states of weakly coupled long-range one-dimensional quantum hamiltonians

We study the small λ behavior of the ground state energy, E(λ), of the Hamiltonian $\text{?(}\text{d}{}^2\text{dx}{}^2\text{) + λV(x)}$. In particular, if V(x) ～ ?ax^?2 at infinity and if 69-1, we prove that $\text{(?E(λ))}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= ?[}\text{1}\text{2}\text{λ + aλ}{}^2\text{lnλ] ∫ dxV(x) + O(λ}{}^2\text{)}$.     

Stark mixing spectroscopy in cesium

We present a new technique for selectively populating excited states which are inaccessible by dipole excitation from the ground state. The method uses a static electric field to introduce a component of a dipole-allowed state into the state of interest. We have applied the method to cesium to measure lifetimes and a Stark mixing coefficient. The results are $\text{τ(6}{}^2\text{D}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)=64(2) ns}$, $\text{τ(7}{}^2\text{D}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)=92.5(15) ns}$, and <6²D_{$\text{5}\text{2}$}|;ez |7²P_{$\text{3}\text{2}$}>/(E_7P?E_6D)=0.7(3)×10^?3 where is in kV/cm. 141     

The five-nucleon system above the three-particle threshold

Compound nucleus states in ${}^5\text{Li}$ and ${}^5\text{He}$ have been investigated with the ${}^3\text{He(d,p)pt}$ and ${}^3\text{H(d,n)pt}$ three-particle reactions. The observed $\text{J}{}^{\mathrm{\pi }}\text{=}\text{3}\text{2}{}^{\mathrm{?}}$ states (E_X≈20 MeV) can be understood, in analogy to the ground states of the A=5 system, by coupling a $\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ nucleon to the first 0⁺ excited state of ${}^4\text{He}$.     

Magnetic moments at backbending and spectroscopy of 134Ce

Employing the static hyperfine fields at cerium nuclei in magnetized Fe and Gd hosts, the g-factor of the ¹³⁴Ce(10⁺) state at backbending (E_{x = 3719.3 keV}) has been determined as g = ? 0.30 (25). The coexistence of this neutron-dominated state with the ($\text{v}\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{n}}\text{10}{}^{\mathrm{+}}$ isomer (E_x = 3208.5 keV, g = ?0.19(1)) is unexpected. A comprehensive spectroscopic study following the ¹²²Sn(¹⁶O, 4n) reaction, including γ-angular distributions, prompt and delayed γ coincidence and recoil-distance measurements has yielded new information on quasi-collective bands of both parities. The properties of the low-lying positive-parity states are well described by the interacting boson model.     

Rydberg atoms in crossed electric and magnetic fields. Experimental evidence for the Pauli quantization

The experimental evidence for the Pauli quantization obeyed by the Rydberg spectrum of rubidium, in crossed electric and magnetic fields, is reported. When the external field perturbation associated with Zeeman and linear Stark effects are of the same order but small compared to the Coulomb binding energy, the energy levels of the system are given by $\text{E}{}_{\mathrm{n,k}}\text{= -R/n}{}^2\text{+ ɡK (ω}{}^2{}_{\mathrm{L}}\text{+ ω}{}^2{}_{\mathrm{E}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, where K is an integer ω_L, ω_E the Larmor and linear Stark frequencies respectively.     

Polarization and polarization transfer in the 2H(d,n)3He reaction at 10 MeV

Angular distributions of six polarization transfer coefficients $\text{K}{}_{\mathrm{x}}{}^{\mathrm{x\prime }}\text{(θ), k}{}_{\mathrm{x}}{}^{\mathrm{z\prime }}\text{(θ), K}{}_{\mathrm{z}}{}^{\mathrm{<mtext>x</mtext><mtext>?</mtext>}}\text{(θ), K}{}_{\mathrm{z}}{}^{\mathrm{<mtext>z</mtext><mtext>?</mtext>}}\text{(θ),}\text{and}\text{K}{}_{\mathrm{yy}}{}^{\mathrm{<mtext>y</mtext><mtext>?</mtext>}}\text{(θ)}$; of the four analyzing powers A_y(θ), A_xx(θ), A_yy(θ), and A_zz(θ); and of the polarization function P^ý(θ), have been measured atE_d = 10.00 MeV for the reaction ²H(d, n)³He. Measurements were made for neutron lab angles between 0° and 80° in 10° steps. Additionally the y-axis associated quantities were measured at θ_1ab = 99°. Most of the measured coefficients are large at some angles and all show considerable variation with angle.     

Quantum theory of longitudinal dielectric response properties of a two-dimensional plasma in a magnetic field

An analysis of dynamic and nonlocal longitudinal dielectric response properties of a two-dimensional Landau-quantized plasma is carried out, using a thermodynamic Green's function formulation of the RPA with a two-dimensional thermal Green's function for electron propagation in a magnetic field developed in closed form. The longitudinal-electrostatic plasmon dispersion relation is discussed in the low wavenumber regime with nonlocal corrections, and Bernstein mode structure is studied for arbitrary wavenumber. All regimes of magnetic field strength and statistics are investigated. The class of integrals treated here should have broad applicability in other two-dimensional and finite slab plasma studies.The two-dimensional static shielding law in a magnetic field is analyzed for low wavenumber, and for large distances we find $\text{V(}\text{r}\text{) ～}\text{Q}\text{k}{}_0{}^2\text{r}{}^3$. The inverse screening length $\text{k}{}_0\text{=}\text{2πe}{}^2\text{??}\text{?ξ}$ (? = density, ξ = chemical potential) is evaluated in all regimes of magnetic field strength and all statistical regimes. k₀ exhibits violent DHVA oscillatory behavior in the degenerate zero-temperature case at higher field strengths, and the shielding is complete when $\text{ξ = r′}\text{l}\text{z.shtsls;}\text{ω}$, but there is no shielding when $\text{ξ ≠ r′}\text{l}\text{z.shtsls;}\text{ω}{}_{\mathrm{c}}$. A careful analysis confirms that there is no shielding at large distances in the degenerate quantum strong field limit $\text{l}\text{z.shtsls;}\text{ω}{}_{\mathrm{c}}\text{> ξ}$. Since shielding does persist in the nondegenerate quantum strong field limit $\text{l}\text{z.shtsls;}\text{ω}{}_{\mathrm{c}}\text{> KT}$, there should be a pronounced change in physical properties that depend on shielding if the system is driven through a high field statistical transition. (It should be noted that the static shielding law of semiclassical and classical models has no dependence on magnetic field in two dimensions, as in three dimensions.) Finally, we find that the zero field two-dimensional Freidel-Kohn “wiggle” static shielding phenomenon is destroyed by the dispersal of the zero field continuum of electron states into the discrete set of Landau-quantized orbitals due to the imposition of the magnetic field.     

Optical and electrical energy gaps of the n-type impure silicon at 300 K

The band-gap narrowing ΔE_{g, opt} and ΔE_{g, elec} (or ΔE_{g, eff}) for optical and electrical energy gaps of the n-type impure silicon at 300 K, are investigated based on simplified models of heavily doped semiconductors. It is suggested that, for $\text{4 × 10}{}^{19}\text{cm}{}^{-3}\text{? n}{}_0\text{? 3 × 10}{}^{20}\text{cm-3}\text{, ΔE}{}_{\mathrm{g,\; elec}}\text{(or ΔE}{}_{\mathrm{g,\; eff}}\text{)}$ is significantly larger than ΔE_{g, opt}, in good agreement with observed results. This difference is caused especially by the effect of the polaron.