Laser excitation spectra of He2

Metastable $\text{a(2sσ)}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ He₂ molecules are produced by a dc discharge in a flowing He stream. Laser excitation downstream of the discharge produces excitation spectra for a number of He₂ states. LIF spectra are observed for the $\text{(npπ)}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ series for n = 4–9, excepting 5 and the $\text{(npπ)}{}^3\text{Π}{}_{\mathrm{g}}$ series for n = 5–15.     

The spectrum and structure of the He2 molecule: Characterization of the triplet states associated with the UAO's 4pσ, 5pσ, and 6pσ

The emission spectrum of the He₂ molecule has been rephotographed in the ～3200–4100 Å region and the $\text{4pσ g}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{→ 2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, $\text{5pσ k′}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{→ 2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, and $\text{6pσ n}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{→ 2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ transitions analyzed. The g, k′, and n states, which have not been reported previously, are characterized through v = 1, 2, and 1, respectively. Several small accidental perturbations have been observed in the rotational manifolds of the k′ and n states.     

Contributions of operators of twist two and higher in large n moments of structure functions

Though high twist terms are becoming important as x→1, or equivalently, in large n moments, their detection in this regime in deep inelastic lepton scattering needs special caution. The high order terms in the twist two component are strongly dependent on n; one finds that at $\text{Q}{}^2\text{?Q}{}^2{}_7\text{?Λ}{}^2\text{a}{}_{\mathrm{k}}\text{exp}\text{[α}{}_{\mathrm{k}}\text{(}\text{log}\text{n)}{}^{\mathrm{<mtext>2?1</mtext><mtext>k</mtext>}}\text{(}\text{1+b}{}_{\mathrm{k}}\text{log}\text{n}\text{)]}$ the perturbative expansion is invalid whereas higher twist terms are important at $\text{Q}{}^2\text{?Q}{}_1{}^2\text{= Λ}{}^2\text{nC}$. Since $\text{Q}{}_7{}^2$ grows very fast with n the necessary requirement for any deep inelastic phenomenological analysis, namely $\text{Q}{}_1{}^2\text{?Q}{}_7{}^2$, cannot hold for too large moments. The scheme dependence of a_k, α_k and b_k is also discussed.     

Transverse spin correlation function of the one-dimensional spin-12 XY model

The transverse spin pair correlation function p^x_n=<S^x_mS^x_m+n>=<S^x_mS^x_m+n> is calculated exactly in the thermodynamic limit of the system described by the one-dimensional, isotropic, spin-$\text{1}\text{2}$, XY Hamiltonian

$\text{H=?2J}\text{∑}\text{l=1}\text{N}\text{(S}{}^{\mathrm{x}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{x}}{}_{\mathrm{l+1}}\text{+S}{}^{\mathrm{y}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{y}}{}_{\mathrm{l+1}}\text{)}$

. It is found that at absolute zero temperature (T = 0), the correlation function ρ^x_n for n ≥ 0 is given by

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p}}\text{=}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p}}\text{Π}\text{j=1}\text{p?1}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p?2j}}\text{if}\text{n=2p}$

,

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p+1}}\text{=±}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p+1}}\text{Π}\text{j=1}\text{p}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p+2j}}\text{if}\text{n=2p+1}$

, where the plus sign applies when J is positive and the minus sign applies when J is negative. From these the asymptotic behavior as n → ∞ of |?^x_n| at T = 0 is derived to be $\text{|ρ}{}^{\mathrm{x}}{}_{\mathrm{n}}\text{| ～}\text{a}\text{n}$ with a = 0.147088?. For finite temperatures, ρ^x_n is calculated numerically. By using the results for ?^x_n, the transverse inverse correlation length and the wavenumber dependent transverse spin pair correlation function are also calculated exactly.     

Space-time symmetries and the gravitational-neutrino field equations in general relativity

We consider a neutrino field with geodesic rays in interaction with a gravitational field admitting a Killing vector field n^μ. It is found that for solutions of the Einstein-Weyl field equations the neutrino field ξ^A and the neutrino flux vector l^μ are restricted by the equations: $\text{L}{}_{\mathrm{n}}\text{ξ}{}^{\mathrm{<mtext>A\; =\; ?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{is}\text{ξ}{}^{\mathrm{A}}$ and $\text{L}{}_{\mathrm{n}}\text{l}{}^{\mathrm{\mu }}\text{= 0}$, whereas s is a real constant. In the case of pure radiation neutrino fields these equations become: $\text{L}\text{ξ}{}^{\mathrm{A}}\text{=}\text{case1}\text{2}\text{(p ? is)ξ}{}^{\mathrm{A}}$, $\text{L}{}_{\mathrm{n}}\text{l}{}^{\mathrm{\mu }}\text{= pl}{}^{\mathrm{\mu }}$, where p and s are in general real functions of the coordinates.     

Activation energy of field emission flicker noise power due to adsorbed potassium on tungsten

The temperature dependence of the field emission flicker noise spectral density functions has been investigated for potassium adsorbed on tungsten (112) planes by a probe hole technique. By integration of the spectral density functions $\text{W(?) = B}{}_{\mathrm{i}}\text{?}{}^{\mathrm{?ge}}\text{i}$ the noise power $\text{(δn}{}^2{}_{\mathrm{\Delta ?}}$ for different frequency intervals Δ? is obtained. From the exponential temperature dependence of $\text{(δn}{}^2{}_{\mathrm{\Delta ?}}$ noise power “activation energies” q_Δ? are determined. Plots of these energies versus coverage show a similar “oscillating” behaviour as recently found for $\text{W(?}{}_{\mathrm{j}}\text{)}$ or which indicates phase transitions of the adsorbed potassium submonolayers. The noise activation energies are discussed in terms of existing models and a comparison is made between the experimental q values and surface diffusion energies E_d as determined by conventional methods.     

Magnetic circular dichroism of transition metal ions in solids—II K2NaGaF6: Cr3+

The absorption and MCD spectra of the ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{a}}$ and ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{b}}$ spin-allowed transitions of Cr³⁺ in K₂NaGaF₆ are reported. It is shown that transitions to the ${}^4\text{T}{}_{\mathrm{1g}}$. states are induced by T_1u vibratio the other spin-allowed transition, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, there are three competing intensity mechanisms: electric dipole induced by T_1u vibrations, electric dipole induced by T_2u vibrations and magnetic dipole, and an estimate is made of the relative importance of these. The magnetic dipole ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^2\text{E}{}_{\mathrm{g}}$ zero-phonon line is observed to be accompanied by a vibrational sideband for which the coupling is predominantly with T_2u vibrations. Other weak transitions are observed in MCD spectra and their origin briefly discussed.     

On the mobility of very pure semiconductors at very low temperatures

The mobility μ of a very pure semiconductor at very low temperatures is investigated in terms of a model where electrons are scattered by charged impurities distributed uniformly in space, and the electron-electron interaction is taken into account by the Debye-Hueckel screening in the interaction potential. The equation for the current relaxation rate Γ, derived previously by the proper connected diagram expansion, incorporates the quasi-particle effect in a self-consistent manner. The solution of this equation at high carrier concentrations n yields the so-called Brooks-Herring formula. At lower concentrations, the solution deviates significantly from the latter. The solution is in general smaller than the standard expression for the rate based on the Boltzmann equation; and this is consistent with the existing conductivity data available. At the very low concentrations e.g. n = n₃ = 10¹³cm^?3 or lower for Ge, the mobility calculated is inversely proportional to the square-root of the impurity concentration n_s, and has a $\text{T}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$-dependence (T: temperature).

$\text{μ = 0.3597\&z.xl;h}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{k(k}{}_{\mathrm{B}}\text{T)}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{(ze)}{}^{\mathrm{?1}}\text{n}{}_{\mathrm{s}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{m}{}^1{}^{\mathrm{<mtext>?3</mtext><mtext>4</mtext>}}$

, where k is the dielectric constant. The conductivity data directly comparable with this formula are not available at present. However, the quasi-particle effect which led to this peculiar concentration-dependence should also show itself in the cyclotron resonance width; there, experiment and theory both show the ${}_{\mathrm{n}}{}_{\mathrm{s}}$-dependence for very pure semiconductors.     

Order relations for lattice sums from order relations for theta functions

Let {τ} and {γ} denote mutually reciprocal unit Bravais lattices in an n-dimensional Euclidean space, and consider the Theta Functions (TF's) $\text{V}{}_{\mathrm{\tau }}\text{(t) = t}{}^{\mathrm{<mtext>n</mtext><mtext>4</mtext>}}\text{∑}{}_{\mathrm{\tau }}\text{exp}\text{(?πtτ}{}^2\text{)}$ for all 0 < t < ∞. By showing how to evaluate a larger class of sums $\text{Z}{}_{\mathrm{\tau }}{}^{\mathrm{(K)}}\text{(t)  π}{}^{\mathrm{k}}\text{t}{}^{\mathrm{<mtext>k\; +\; </mtext><mtext>n</mtext><mtext>4</mtext>}}\text{∑}{}_{\mathrm{\tau }}{}_{\mathrm{r}}{}^{\mathrm{2k}}\text{exp (?πtτ}{}^2\text{)}$, k a nonnegative integer, we are able to evaluate any derivative of the V-functions. With this information we find order relations for the TF's on the cubic lattices in three dimensions. Coupling these relations with Ewald's Theta Function method, we secure order relations for Lennard-Jones, Chaba-Pathria, and other lattice sums on cubic lattices. We also sketch extensions to non-Bravais lattices and give an order relation for TF's on the non-Bravais hexagonal closepacked and the Bravais facecentered cubic.     

On the mobility of a very pure semiconductor including the low impurity concentration limit

The low temperature mobility μ limited by charged impurities is calculated by solving the equation for the relaxation rate previously derived. The calculated μ behaves like $\text{μ = 2.03 κ}{}^2\text{(k}{}_{\mathrm{B}}\text{T)}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{e}{}^{\mathrm{?3}}\text{z}{}^{\mathrm{?2}}\text{n}{}_{\mathrm{s}}{}^{\mathrm{?1}}\text{m}{}^{\mathrm{<mtext>1</mtext><mtext>?1</mtext><mtext>2</mtext>}}$ In $\text{[38.2κ}{}^2\text{m}{}^{\mathrm{<mtext>1</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{(k}{}_{\mathrm{B}}\text{T)}{}^{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{/z}{}^2\text{e}{}^4\text{h}\text{?}\text{n}{}_{\mathrm{s}}\text{]}$ for lowest concentrations n_s<10¹¹cm^?3 for Ge and

$\text{μ = 0.360}\text{h}\text{?}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{κ(k}{}_{\mathrm{B}}\text{T)}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{(ze)}{}^{\mathrm{?1}}\text{n}{}_{\mathrm{s}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{m}{}^{\mathrm{<mtext>1</mtext><mtext>?3</mtext><mtext>4</mtext>}}$

for intermediate concentrations n_s ～ 10¹²?10¹⁴cm^?3.     

Spectrum and structure of the He2 molecule: Characterization of the singlet and triplet states associated with the UAO's 4s, 4dσ, 4dπ, and 4dδ

The emission spectrum of the He₂ molecule has been rephotographed in the ～4000–～5700 Å region and the $\text{4d(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$, $\text{4d(}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^1\text{Π}{}_{\mathrm{u}}\text{,}{}^1\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$, $\text{4s}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$ and $\text{4s}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$ transitions analyzed. The 4dδj³Δ_u, 4dπj³Π_u, $\text{4dσj}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and $\text{4sh}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states have been characterized through v = 2 and the 4dδJ¹Δ_u, 4dπJ¹Π_u, $\text{4dσJ}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, and $\text{4sH}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states for v = 0. The term levels for these perturbed and l-uncoupled states have been confirmed (a) by analyses of bands with common levels from Δv = 0, ±1 sequences and (b) by analyses of the transitions between the above states from 4d and 4s and the $\text{c}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ and $\text{C}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ states associated with 3pσ. Molecular constants are reported which have been partially corrected for the effects of l-uncoupling and the homogeneous perturbations between the state pairs J, H and j, h.     

On the charged-impurity-limited mobility for a very pure semiconductor

The low temperature mobility μ limited by charged impurities in very pure semiconductors (Ge) is interpreted in terms of the Coulomb collision in medium. The theory yields a peculiar dependence in temperature T and charged impurity concentration $\text{n}{}_{\mathrm{s}}\text{: μ ∞n}{}_{\mathrm{s}}{}^{\mathrm{<mtext>-</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{T}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$.     

Surface cyclotron resonance in Si under uniaxial stress

The cyclotron resonance of inversion-layer electrons on (100)p-type Si is found to depend sensitively on an externally applied compressive stress. At low temperatures (T ? 10 K) we observe a considerable increase of the cyclotron mass m¹_c with stress S along the [001] direction. The effect is most strongly observed at low electron densities n_s. For $\text{S～1.5 × 10}{}^9\text{dyne}\text{cm}{}^2$ and n_s～2 × 10¹¹cm^-2 we obtain $\text{m}{}^1{}_{\mathrm{c}}\text{～0.4 m}{}_0$ instead of the expected 0.2m₀. Along with this change of $\text{m}{}^1{}_{\mathrm{c}}$ a strong narrowing of the resonance is noted. Raising the temperature gives an additional n_s- dependent increase of $\text{m}{}^1{}_{\mathrm{c}}$.     

Some aspects of the quark parton model

A modified Kuti-Weisskopf model which satisfies the Feynman threshold constraints is considered further. Detailed predictions for the sum of neutrino and anti-neutrino differential cross sections on nucleon (which can be readily compared with forthcoming NAL data), the shapes of the structure functions $\text{?}{}_2{}^{\mathrm{\nu p,\nu n}}$ and the ratio $\text{?}{}_2{}^{\mathrm{\nu p}}\text{/?}{}_2{}^{\mathrm{\nu n}}$, and spin-dependence of inelastic electron-nucleon scattering versus scaling variable x are delineated. We also compare in some detail the general features of our model with the “model independent” approach of Feynman for quark parton theory.     

Matthiessen's rule and its variation for cyclotron resonance width in two and three dimensions

Based on the proper connected diagram expansion, we calculated cyclotron resonance widths Γ_n associated with neighboring Landau states (n, n +1) for free electrons in interaction with more than one kind of impurities. In 3D usual Matthiessen's rule Γ_n=Γ⁽¹⁾_n+Γ⁽²⁾_n+…where Γ⁽ⁱ⁾_n represent widths calculated separately for each kind, is obtained. In 2D a new rule: is obtained.     

Nonorthogonality corrections in the method of correlated basis functions

A set of normalized linearly independent basis functions φ₁, φ₂, …, φ_j, … generates matrix representatives $\text{H}$ and $\text{N}$ of the Hamiltonian operator and the identity. An orthonormal basis $\text{φ}{}_1$, $\text{φ}{}_2$, …, $\text{φ}{}_{\mathrm{j}}$, … generated by a Löwdin transformation is characterized by the distance in Hilbert space between $\text{φ}{}_{\mathrm{j}}$ and φ_j. The choice of positive definite $\text{N}$${}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ minimizes these distances and maximizes the diagonal elements of $\text{N}$${}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. Again for positive definite $\text{N}$${}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and a finite basis, 1 ? j ? p, the analysis yields a general theorem on Trace $\text{N}$${}^{\mathrm{<mtext>?n</mtext><mtext>2</mtext>}}$ (? p for all positive and negative integral values of n except n = ?1 and ? p for n = ?1).Sufficient conditions are determined which permit the application of the binomial theorem to the evaluation of the transform of $\text{H}$. Approximate formulas for the energy eigenvalues through third order in nondiagonal matrix elements are presented in a compact form containing characteristic nonorthogonality corrections depending on the exterior or interior location of the matrix element in the perturbation formulas.     

The spectrum and structure of the He2 molecule: Multichannel quantum defect analyses of the triplet levels associated with (1σg)2(1σu)npλ

Emission spectra for the electronic transitions $\text{6–17pπ}{}^3\text{Π}{}_{\mathrm{g}}\text{-2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and $\text{7–16pσ}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{-2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ of He₂ are reported and the electronic structures of $\text{npπ}{}^3\text{Π}{}_{\mathrm{g}}{}^{\mathrm{?}}$ and $\text{np(}{}^2\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{)}$ characterized. The energy levels associated with $\text{(1σ}{}_{\mathrm{g}}\text{)}{}^2\text{(1σ}{}_{\mathrm{u}}\text{)np(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{)}$ exhibit extensive channel mixing, which leads to a breakdown of conventional band models for the higher n¹-members of these Rydberg “series.” However, a model based on multichannel quantum defect theory quantitatively correlates the observed level structures. The higher-energy ($\text{n}{}^1\text{> ～5}$) portions of the $\text{np(}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{)}$ channels can be represented by two eigen-quantum defects μ₁ = 0.225 and μ₂ = 0.930 and the close- to loose-coupling matrix elements $\text{U}{}_{11}\text{= U}{}_{22}\text{= [N(2N + 1)}{}^{\mathrm{?1}}\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{U}{}_{12}\text{= ?U}{}_{21}\text{= [(N + 1)(2N + 1)}{}^{\mathrm{?1}}\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. The inclusion of energy dependence in the μ_α's leads to quantitative correlations for all n¹-values.     

Paзлoжeниe пo 1Z для чapтpи-фoкoвcкoй и кoppeляциoннoй энepгии, peлятивиcтcкич пoпpaвoк, дипoльнoгo мaтpичнoгo элeмeнтa

Energies and dipole matrix elements have been calculated for He, Li, Be, B, C, N, O, F, and Ne-like ions (configurations 1s²2sⁿ¹2pⁿ²?1s²2s^n1?12pⁿ²⁺¹). The Hartree-Fock energy, the correlation energy, and relativistic corrections were taken into account. Relativistic corrections were obtained by computing the entire quantity H_B. Numerical results are presented for energies of the terms in the form

$\text{E=E}{}_0\text{Z}{}^2\text{+ ΔE}{}_1\text{Z + ΔE}{}_2\text{+}\text{1}\text{Z}\text{ΔE}{}_3\text{+}\text{α}{}^2\text{4}\text{(E}{}_0{}^{\mathrm{p}}\text{Z}{}^4\text{+ ΔE}{}_1{}^{\mathrm{p}}\text{Z}{}^3\text{)}$

, and for the fine structure of the terms in the form

$\text{〈1s}{}^2\text{2s}{}^{\mathrm{n1}}\text{2p}{}^{\mathrm{n2}}\text{LSJ|H}{}_{\mathrm{Б}}\text{|1s}{}^2\text{2s}{}^{\mathrm{n1\prime }}\text{2p}{}^{\mathrm{n2\prime }}\text{L′S′J〉=(?1)}{}^{\mathrm{L+S\prime +J}}\text{LSJ}\text{S′L′1}\text{×}\text{α}{}^2\text{4}\text{(Z?A)}{}^3\text{[E}{}^{\mathrm{(0)}}\text{(Z ? B)+}\text{E}{}_{\mathrm{c0}}\text{]+(?1)}{}^{\mathrm{L\; +\; S\prime \; +\; J}}\text{LSJ}\text{S′L′2}\text{α}{}^2\text{4}\text{(Z?A)}{}^3\text{E}{}_{\mathrm{cc}}$

. Dipole matrix elements are required for calculation of oscillator strengths or transition probabilities. For the dipole matrix elements, two terms of the expansion in $\text{1}\text{Z}$ have been obtained. Numerical results are presented in the form P(a, a′) = (a/Z)[1 + (τ/Z)].