Influence of self-fields on the Vlasov equilibrium and stability properties of relativistic electron beam-plasma systems

The influence of self-fields on the equilibrium and stability properties of relativistic beam-plasma systems is studied within the framework of the Vlasov-Maxwell equations. The analysis is carried out in linear geometry, where the relativistic electron beam propagates through a background plasma (assumed nonrelativistic) along a uniform guide field $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$, It is assumed that $\text{ν}\text{γ}{}_0\text{? 1}$ for the beam electrons (ν is Budker's parameter, and γ₀mc² is the electron energy), but no a priori assumption is made that the beam density is small (or large) in comparison with the plasma density, or that conditions of charge neutrality or current neutrality prevail in equilibrium. It is shown that the equilibrium self-electric and self-magnetic fields, $\text{E}{}_{\mathrm{r}}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{r}}$ and $\text{B}{}_{\mathrm{\theta }}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{\theta }}$, can have a large effect on equilibrium and stability behavior. Equilibrium properties are calculated for beam (j = b) and plasma (j = e, i) distribution functions of the form f_b⁰(H, P_θ, P_z) = F(H ? ω_rbP_θ) × δ(P_z ? P₀)(j = b), and $\text{f}{}_{\mathrm{j}}{}^0\text{(H, P}{}_{\mathrm{\theta }}\text{, P}{}_{\mathrm{z}}\text{) = f}{}_{\mathrm{j}}{}^0\text{(H ? ω}{}_{\mathrm{rj}}\text{P}{}_{\mathrm{\theta }}\text{? V}{}_{\mathrm{j}}\text{P}{}_{\mathrm{z}}\text{?}\text{m}{}_{\mathrm{i}}\text{V}{}_{\mathrm{j}}{}^2\text{2}\text{)}$ (j = e, i), where H is the energy, P_θ is the canonical angular momentum, P_z is the axial canonical momentum, and ω_rj (the angular velocity of mean rotation for j = b, e, i), V_j (the mean axial velocity for j = e, i), and P₀ are constants. The linearized Vlasov-Maxwell equations are then used to investigate stability properties in circumstances where the equilibrium densities of the various components (j = b, e, i) are approximately constant. The corresponding electrostatic dispersion relation and ordinary-mode electromagnetic dispersion relation are derived (including self-field effects) for body-wave perturbations localized to the beam interior (r <R_b). These dispersion relations are analyzed in the limit of a cold beam and cold plasma background, to illustrate the basic effect that lack of charge neutrality and/or current neutrality can have on the two-stream and filamentation instabilities. It is shown that relative rotation (induced by self-fields) between the various components (j = b, e, i) can (a) result in modified two-stream instability for propagation nearly perpendicular to $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$, and (b) significantly extend the band of unstable k_z-values for axial two-stream instability. Moreover, in circumstances where the beam-plasma system is charge-neutralized but not current-neutralized, it is shown that the azimuthal self-magnetic field $\text{B}{}_{\mathrm{\theta }}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{\theta }}$ has a stabilizing influence on the filamentation instability for ordinary-mode propagation perpendicular to $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$.     

Structural evidence of 2kF commensurability effects in TTF-TCNQ under high pressure

We have shown that the Fermi wave vector describing the low temperature longitudinal distorsion of TTF-TCNQ moves under hydrostatic pressure from an incommensurable value ($\text{2k}{}_{\mathrm{F}}\text{= .295 b}{}^1$) at ambient pressure to a commensurable one ($\text{2k}{}_{\mathrm{F}}\text{= b}{}^1\text{/3}$) around 14.5 Kbar. This value is maintained until 17.5 Kbar at least. Between these two pressures the commensurable low temperature superstructure has a periodicity a × 3b × c.     

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.     

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.     

Electron-muon mass ratio,neutrino masses and Weinberg angle in an approximate SU(4)+ ⊗ SU(4)− symmetry for leptons

Assuming an SU(4) group for leptons together with the dynamical equation $\text{P}{}_{\mathrm{z}}\text{{z ? z} = 0}$ ($\text{P}{}_{\mathrm{z}}$ is the projection of the representation z from the direct product z ? z) for the symmetry breaking, we predict: and a Weinberg angle $\text{sin}{}^2\text{θ}{}_{\mathrm{<mtext>w</mtext>}}\text{=}\text{1}\text{4}$.     

Phenomenological predictions of the SO(10) supersymmetric grand unified model

The phenomenological predictions of the SO(10) supersymmetric grand unified model (SO(10) SGUM) for the mass scales M₁, M₂, weak angle ifsin²θ_w, quark-leptons mass ratios $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, $\text{m}{}_{\mathrm{t}}\text{m}{}_{\mathrm{<mtext>b</mtext>}}$, $\text{m}{}_{\mathrm{\tau }}\text{m}{}_{\mathrm{\nu }}{}_{\mathrm{\tau }}$ and proton lifetime τ_p are estimated by using renormalization group analysis at one-loop level. In contrast with SU(5) SGUM, we find that the SO(10) SGUM still has problems with τ_p but not with sin²θ_w and $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, which may suggest that supersymmetry would be bro at a mass scale $\text{?10}{}^7\text{GeV}$.     

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.     

The ′T Hooft-Polyakov monopole near the Prasad-Sommerfield limit

A perturbative classical monopole solution for the SO(3) gauge theory is constructed in the limit of small but non-vanishing Higgs potential. This corresponds to the limit $\text{μ}{}^2\text{2M}{}_{\mathrm{W}}{}^2\text{=}\text{λ}\text{? 1}$, where μ equals the mass of the scalar particle and M_W equals the mass of the intermediate vector particles. The monopole solution and mass are found to involve non-analytic functions of λ: $\text{γ}$ and λ ln λ. The monopole mass M_m is calculated to order $\text{μ}{}^2\text{M}{}_{\mathrm{W}}$ as

$\text{M}{}_{\mathrm{m}}\text{=}\text{4π}\text{e}{}^2\text{M}{}_{\mathrm{w}}\text{1+}\text{1}\text{2}\text{μ}\text{M}{}_{\mathrm{w}}\text{+}\text{1}\text{2}\text{μ}{}^2\text{M}{}^2{}_{\mathrm{w}}\text{ln}\text{μ}\text{M}{}_{\mathrm{w}}\text{+0.7071}\text{μ}{}^2\text{M}{}^2{}_{\mathrm{w}}$

.     

Elastoresistivity of TTF-TCNQ and related compounds

Elastoresistances of TCNQ high conducting salts have been measured at room temperature by an original strain gauge technique. The effects, on the longitudinal and transverse resistivities ?, of an elementary uniaxial strain ? applied along one of the three axes, a, b or c¹ respectively, have been estimated.For TTF-TCNQ, they are:

$\text{K}{}^{\mathrm{b}}{}_{\mathrm{a}}\text{=? ln ?}{}^{\mathrm{b}}\text{/??}{}_{\mathrm{a}}\text{= 16±3}$

;

$\text{K}{}^{\mathrm{b}}{}_{\mathrm{b}}\text{= ? ln α}{}^{\mathrm{b}}\text{/??}{}_{\mathrm{b}}\text{= 34±4}$

;

(5% risk).So, in an hydrostatic pressure experiment, the fraction of piezoresistivity attributable to transverse effects is 43± 10% of the total value χ^b (K^b_a and K^b_c effects accumulated).Low values have been found for the anisotropy (?^a/?^b) variations due to strains. So one may write:

$\text{K}{}^{\mathrm{a}}{}_{\mathrm{a}}\text{= ? ln ?}{}^{\mathrm{a}}\text{/??}{}_{\mathrm{a}}\text{≌K}{}^{\mathrm{a}}{}_{\mathrm{b}}$

;

$\text{K}{}^{\mathrm{a}}{}_{\mathrm{b}}\text{= ? ln ?}{}^{\mathrm{a}}\text{/??}{}_{\mathrm{b}}\text{≌ K}{}^{\mathrm{b}}{}_{\mathrm{b}}$

;

.The TTF-, HMTTF-, TSF-, HMTSF-TCNQ elastoresistance values are coherent with the previously measured hydrostatic pressure piezoresistivity values.All these experimental results are in good agreement with a model where the longitudinal but also the transverse elastoresistivities are essentially due to variations with strains of the longitudinal scattering time τ_ν defined by σ^b = ne²τ_ν/m¹.     

Moments of two-time spin-pair correlation functions for a one-dimensional anisotropic Heisenberg model at infinite temperature

The first ten moments of the infinite-temperature space and frequency dependent two-spin correlation functions, $\text{?}{}^{\mathrm{x}}{}_{\mathrm{r}}\text{(ω)}$ and $\text{?}{}^{\mathrm{z}}{}_{\mathrm{r}}\text{(ω)}$ are obtained for the one-dimensional anisotropic Heisenberg model for r = 0 and r = 1. These are compared with those previously known.     

Gravitational collapse in quantum mechanics with relativistic kinetic energy

It is proved that the quantum mechanical Hamiltonian $\text{H = Σ}{}_{\mathrm{i=1}}{}^{\mathrm{N}}\text{(p}{}^2\text{+ m}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? κ Σ}{}_{\mathrm{i>j}}\text{|x}{}_{\mathrm{i}}\text{? x}{}_{\mathrm{j}}\text{|}{}^{\mathrm{?1}}$ for bosons (resp, fermions) is bounded from below if N ≤ c_bκ^?1 (resp. $\text{N ≤ c}{}_{\mathrm{f}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). H is unbounded from below if N ≥ c_b^lκ^?1 (resp. $\text{N ≥ c}{}_{\mathrm{f}}{}^{\mathrm{l}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). The constants c_b and c_b^l (resp. c_f and c_f^l) differ by about a factor 2 (resp. 4).     

Prediction of strong magnetic quantum oscillations of the nuclear spin relaxation in a quasi-two-dimensional metal

The nuclear spin lattice relaxation rate in a quasi-two-dimensional (2-D) metal under strong magnetic fields is studied in a special case where the electronic cyclotron mass is small compared with the free electron mass. In the pure limit (ω_cτ ? 1) and for sufficiently low temperatures ($\text{h}\text{?}\text{ω}{}_{\mathrm{c}}\text{> 2π}{}^2\text{k}{}_{\mathrm{B}}\text{T}$) we find remarkable quantum oscillations of the relaxation rate as a function of the magnetic field. The period of these oscillations is identical to that of the de Haas-van Alphen oscillations and their amplitude grows linearly with the magnetic field. The possibility of observing such oscillations experimentally in the quasi-2-D mercury chain compound Hg_3?δAsF₆ is discussed.     

A theorem for dissociation energy and binding energy of biexcitons in the isotropic model of a semiconductor

A theorem is proved for the dissociation energy W and the binding energy E_b of biexcitons in the isotropic model of a semiconductor. The theorem determines the upper limits of the values W and E_b for the given mass ratio $\text{m}{}^1{}_{\mathrm{e}}\text{m}{}^1{}_{\mathrm{h}}$.     

On the relativistic Thomas-Fermi model

The relativistic generalization of the Thomas-Fermi model of the atom is derived. It approaches the usual nonrelativistic equation in the limit Z ? Z_crit, where Z is the total number of electrons of the atom and $\text{Z}{}_{\mathrm{<mtext>crit</mtext>}}\text{=(}\text{3π}\text{4}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{α}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ and α is the fine structure constant. The new equation leads to the breakdown of scaling laws and to the appearance of a critical charge, purely as a consequence of relativistic effects. These results are compared and contrasted with those corresponding to N self-gravitating degenerate relativistic fermions, which for $\text{N ≈ N}{}_{\mathrm{<mtext>crit</mtext>}}\text{=(}\text{3π}\text{4}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(m/m}{}_{\mathrm{<mtext>p</mtext>}}\text{)}{}^3$ give rise to the concept of a critical mass against gravitational collapse. Here m is the mass of the fermion and $\text{m}{}_{\mathrm{<mtext>p</mtext>}}\text{=(?c/G)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ is the Planck mass.     

A note on the momentum distribution function for an electron gas

The one-electron momentum distribution function $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉}$ for an electron gas is investigated by a diagrammatic analysis of perturbation theory. It is shown that $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉}$ has the following exact asymptotic form for large k (k ? p_F; p_F, the Fermi momentum): $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉 =}\text{4}\text{9}\text{(}\text{αr}{}_{\mathrm{s}}\text{π}\text{)}{}^2\text{×(}\text{p}{}_{\mathrm{<mtext>F</mtext>}}{}^8\text{k}{}^8\text{) g?(0) + ?}$, where g?(0) is the zero-distance value of the spin-up-spin-down pair correlation function. The physical implications of the above asymptotic form are discussed.     

The asymptotics of the gap in the Mathieu equation

We provide a simple proof that the kth gap, Δ_k, for the Mathieu operator $\text{?d}{}^2\text{dx}{}^2\text{+ 2κ}\text{cos}\text{(2x)}$ is $\text{Δ}{}_{\mathrm{k}}\text{= 8(}\text{κ}\text{4}\text{)}{}^{\mathrm{k}}\text{[(k ? 1)!]}{}^{\mathrm{?2}}\text{(1 + o(k}{}^{\mathrm{?2}}\text{))}$, a result obtained (up to the value of an integral) by Harrell. The key observation is that what is involved is tunneling in momentum space.     

Necessary and sufficient conditions for the existence of a lagrangian. The case of quasi-linear field equations

Necessary and sufficient conditions for the existence of the Lagrangian associated with given field equations of motion are investigated. For the quasi-linear equations A_ab^μν(x^λ, φ^c, φ_?^c)φ_μν^b + B_a(x^μ, φ^b, φ_ν^b) = 0, the complete necessary and sufficient conditions are obtained, resorting to the formalism of an exterior derivative. It is emphasized that, to find expressions of these conditions, the anti-symmetric parts of the second derivatives of a Lagrangian, $\text{R}{}_{\mathrm{\mu \nu }}{}^{\mathrm{ab}}\text{= (}\text{?}{}^2\text{L}\text{?φ}{}_{\mathrm{\mu }}{}^{\mathrm{a}}\text{?φ}{}_{\mathrm{\nu }}{}^{\mathrm{b}}\text{?}\text{?}{}^2\text{L}\text{?φ}{}_{\mathrm{\nu }}{}^{\mathrm{a}}\text{?φ}{}_{\mathrm{\mu }}{}^{\mathrm{b}}\text{)/2}$, which disappear in the field equations, take an important role. The procedure to construct the Lagrandian associated with the field equations is also presented.     

Can the optical excitations of surface plasmons be used to study (liquid) metal surfaces?

The surface plasmon dispersion relation is obtained for a metal with a free electron density given by N(z) = N_b + (N_s ? N_b) exp $\text{(}\text{?z}\text{a}\text{)}$ for z ? 0 and N = 0 for z < 0. We have used a local theory which includes the effects of retarded fields and found the dispersion relation to be sensitive to the parameters $\text{(N}{}_{\mathrm{s}}\text{? N}{}_{\mathrm{b}}\text{)}\text{N}{}_{\mathrm{b}}$ and a, which characterize our density profile.     

Teopия acиммeтpии штaкoвcкиx пpoфилeй вoдopoдныx линий в плoтнoй плaзмe

The asymmetric Stark profile for spectral lines of hydrogen has been calculated in first approximation in terms of the expansion parameter $\text{n}{}^2\text{a}{}_0\text{R}{}_0$ [a₀=Bohr radius, n= principal quantum numberm $\text{R}{}_0\text{=(}\text{3}\text{4πN}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$=mean distance between charged particles]. Additional terms, which determine the asymmetry, are expressed through the universal functions Λ(β) and χ(β), which are connected with the first moments of the components of the ion-electric field inhomogeneity tensor. Comparison is made with results based on a nearest neighbour approximation. It is shown that the shift of the symmetry centre of the profiles may be the ion-electric field inhomogeneity.     

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.