Rigorous evaluation of the ring diagram contribution to the ground state energy of an electron gas

The ground state energy and the correlation energy of an electron gas are evaluated rigorously without using the smallr _s expansion and the small momentum-transfer approximation in the ring diagram contribution and taking into consideration the first order and second order exchange graphs. The Fermi momentum is determined by solving the number density equation without using iteration and is compared with that obtained by iteration. The ground state energy is found to stay positive in contrast to the iterative solution which becomes negative beyond a certain value ofr _s .     

Correlation energy of 2-D electrons

The correlation energy and the Fermi momentum of an electron gas in 2-D are evaluated explicitly as functions of density. The ring diagram and first- and second-order exchange contributions are treated. In comparison with the 3-D case, the kinetic energy for the same r_s is approximately one-half and the exchange and correlation energies are somewhat larger. The ground state energy plotted against r_s shows a minimum at around r_s = 1.65 with a minimum value of ?0.9858 Ryd. If the third-order ring contribution is added, the curve is shifted upward. The correlation energy is ?0.6258 to order e⁴. The third-order ringw contribution increases this value almost linearly with r_s. The Fermi momentum decreases with r_s due to the contribution. Different from the 3-D case, no ln r_s term appears in the correlation energy within the approximation.     

Note on the correlation energy of an electron gas

The residual ring diagram contribution which is due to the use of approximate eigenvalues and a momentum cutoff is evaluated and the terms of orderr _s in the correlation energy are given explicitly. The result is exact to orderr _s within neglect of the third order exchange contribution and improves the results of Du Bois, and Carr and Maradudin. The correlation energy plotted againstr _s connects rather smoothly to the low density results obtained recently by Stevens and Pokrant based on an entirely different variational method.This work was supported by the National Science Foundation     

On the ground state energy of a two-dimensional electron fluid

A new theory of the ground state energy of a two-dimensional electron fluid is presented. It is shown that the ring diagram contribution changes its analytical behavior atr _s =2^1/2, wherer _s is the usual density parameter defined by r_S = 1/a ₀(π n)^1/2,a ₀ being the Bohr radius andn is the electron density. For smallr _s , a high density series is obtained in agreement with the previous calculation. For larger _s , a hitherto unknown low density series is obtained. In the low density region, the first order exchange energy is completely cancelled out by a term from the ring contribution so that the ground state energy decreases in proportion tor _s ^?2/3 , followed byr _s ^/?4/3 and higher order terms. The energy is found to be minimum atr _s=1.4757, the minimum value being ?0.481915 Rydbergs.     

Gradient expansion of the kinetic energy including nonlocal exchange contributions

We discuss the gradient expansion of the kinetic energy density, explicitly including nonlocal exchange contributions to ordere ². Restricting the expansion to orderh ²2 one finds that the expression obtained in the standard TFDW model is unchanged.     

Spatial correlations in the electron gas: Path integral Monte Carlo simulation

Thermally excited states of the three-dimensional electron gas in a neutralizing background are computed by path integral Monte Carlo simulation for values of the Wigner-Seitz radius within the interval 5 < r _s < 15. Coulomb and exchange interactions, permutation symmetry, and spin state are treated explicitly. Variation of electron correlation functions with density and temperature is analyzed. Quantum effects suppress and enhance spatial correlation at low and high densities, respectively. Transition between the electron-gas states characterized by these opposite trends corresponds to a density of approximately 2.5 × 10²¹ cm^?3. A transition line between liquid-like and gaslike phases is determined in the temperature-density diagram. Weak anisotropy of many-body correlations in the liquid-like state stimulates excitation of spherically symmetric collective rotational modes. The effective short-range pseudopotential exhibits strong temperature dependence due to exchange effects. For strongly correlated systems, the characteristic screening length deviates from that predicted by the Thomas-Fermi screening model ( $ \sim \sqrt {r_s } $ ), approaching a linear function of r _s. The effective short-range interaction substantially differs from the Yukawa potential in mean field theory. Coulomb interaction shifts the Fermi level up by an order of magnitude or higher, and this effect becomes stronger with decreasing density.     

On the ground state energy of a two-dimensional electron fluid

A new theory of the ground state energy of a two-dimensional electron fluid is presented. It is shown that the ring diagram contribution changes its analytical behavior atr _s =2^1/2, wherer _s is the usual density parameter defined by r_S = 1/a ₀( n)^1/2,a ₀ being the Bohr radius andn is the electron density. For smallr _s , a high density series is obtained in agreement with the previous calculation. For larger _s , a hitherto unknown low density series is obtained. In the low density region, the first order exchange energy is completely cancelled out by a term from the ring contribution so that the ground state energy decreases in proportion tor _s ^–2/3 , followed byr _s ^/–4/3 and higher order terms. The energy is found to be minimum atr _s=1.4757, the minimum value being –0.481915 Rydbergs.     

Quantum-statistical mechanics of a system of charged particles at high temperatures

If a quantum-mechanical potential is introduced the calculation of the quantummechanical binary distribution function for a system with Coulomb interaction is reduced to the well-known mathematical formalism of classical statistical mechanics in the case ofnλ³?1 (λ being the thermal wavelength). The two-particle quantummechanical potential is determined by the two-particle Slater sum. In this paper we calculated the two-particle Slater sum using an expansion according toe ² and the resolvent formalism. From the binary distribution function the correlation energy and the free energy as well were determined up to ordere ⁶. Symmetry effects were taken into account.     

The order αs2 energy-energy correlation function at small angles

The coefficients that give the small angle (back-to-back) behavior of the energy-energy correlation function in e⁺e^? annihilation are calculated at order α_s² from previous all order, small angle formulas. The purpose is to facilitate comparison with all angle, order α_s² calculations.     

Atomic Model Calculations of Gain Saturation in the 46.9 nm Line of Ne‐like Ar

The gain saturation in the 46.9 nm line of the Ar⁺⁸ laser is analyzed using an atomic kinetics code. The dependence of the gain (G) on the electron kinetic temperature (T_e) in the region (50 ‐150 eV) is calculated in the quasi steady‐state approximation for the different values of the electron density (N_e) and the plasma radius (r_pl). The influence of radiat on trapping, ion random and mean velocities, Stark line broadening and refraction losses on the gain saturation is taken into consideration. For r_pl = 150‐600 μm, the amplplication (G > 0 cm^‐1) exists in the large temperature/density domain (T_e = 60‐150 eV, N_e = 0.5‐10 × 10¹⁸ cm^‐3). However, the value G_s ∼ 1.4 cm^‐1 required for the gain saturation at the typical plasma length L_pl ∼ 15 cm is reached in the extremely narrow density regions at the high temperatures. The saturation is reached for r_pl = 600 μm at T^s_e = 150 eV in the region N^s_e = 1.8‐2 × 10¹⁸ cm ^‐3, for r_pl = 300 μm at T^s_e = 125 eV and N^s_e = 2.5‐3 × 10¹⁸ cm^‐3, and for r_pl = 150 μm at T^s_e = 110 eV and N^s_e = 3‐4 × 10¹⁸ cm^‐3. The broadest density region (N^s_e = 2 ‐8 × 10¹⁸ cm^‐3) is predicted for the narrowest column (r_pl = 150 μm) at the highest temperature (T^s_e = 150 eV). The operation in the broadest density region N^s_e, should make easier achievement of the gain saturation in the experiments.     

Instability of layered quantum liquids: 6. Strongly correlated bosons

We calculate the local-field corrections G(q, q _z) for charged bosons at zero temperature in a superlattice with interlayer distance d. An analytical expression for the local-field correction is described. The sum-rule version of the self-consistent approach for the local-field correction is used to discuss the effects of correlation. The RPAparameter r _s and the ratio d/a* determine correlation effects. a* is the effective Bohr radius. The stability region for the Bose condensate r _s < r _sc as a function of d/a* is determined: r _sc ≈ (d/a*)^3/4. The ground-state energy of the layered Bose condensate is calculated and optical and acoustical plasmons are discussed. We predict a roton structure for optical plasmons for r _s > r _sr with r _sr ≈ 0.5 (d/a*)^3/4.     

An analysis of the charged and neutral energy flow in e+e− hadronic annihilation at 34 GeV,and a determination of the QCD effective coupling constant

Using both charged and neutral components, 2600 multihadronic e⁺e^? annihilation events, recorded at 34 GeV by the CELLO detector at PETRA, have been analysed in a calometric approach. The fraction of energy carried by gamma rays is measured to be f_γ = (26.0 ± 0.4 (stat) ± 4.0 (syst)%. The neutral energy flow is seen to follow closely the overall energy flow. From the corrected oblateness distribution, a first order determination of α_s is performed. The result is α_s = 0.16 ± 0.01 (stat) ± 0.03 (syst).     

Exchange effect on the electronic specific heat

By improving the evaluation of the contribution from the first order exchange graphs reported recently by Tsai and Isihara, the electronic specific heat of an electron gas is evaluated to ordere ². It is shown that the specific heat contains a logarithmic term.     

Measurement of cross-section of excitation transfer from 3s2 to 4s1 and 5s1 energy levels of neon

Collision induced non-radiative transitions in neon plasma have been studied using high intra-cavity radiation field of a 633 nm He-Ne laser. The transitions, induced from 3s ₂ energy level to 4s₁ and 5s₁ groups of energy levels, have been detected as changes in intensities of the spectral lines originating from these energy levels. From these intensity measurements, the quantities governing the transitions i.e. (i)S ₃ ^e /S _3RT , the ratio of the probabilities of electronic deexcitation to the total radiative deexcitation of energy level 3 (ii) 〈r ₂₃ ^e v _e〉, rate of excitation transfer per particle and (iii)S ₂₃ ^e , the total probability for excitation transfer from level 2 to level 3 at a certain value of electron density have been calculated.     

Theoretical investigation of the molecular structure and transition dipole moments of the NaK low lying electronic states

The electronic structure and the spectroscopic constants of the low lying electronic states of the NaK⁺ ionic molecule have been determined through using an ab initio approach involving a non-empirical pseudopotential for the Na and K cores and core valence correlation correction. The potential energy of nearly 26 electronic states of ²Σ⁺, ²Π, and ²Δ symmetries has been calculated up to their dissociation limit Na(4d) + K⁺ and Na⁺ + K(6s). Their spectroscopic constants (R_e, D_e, T_e, ω_e, ω_eχ_e, and B_e) are derived and compared with the few available theoretical studies. A good agreement has been found for the ground state and few excited states with previous works. New potential energy curves were presented, for the first time, for the higher excited states. Numerous avoided crossing between electronic states of ²Σ⁺, ²Π symmetries have been localized and analyzed. Their existences are related to the charge transfer between the two ionic molecules Na⁺K and NaK⁺. Furthermore, we have determined the transition dipole moments for several states and analyzed the avoided crossings related to charge transfer between alkaline atoms.     

Exchange and correlation energy of an inhomogeneous electron gas

A convenient expression is derived for the coefficient, B_xc(n), which determines the first gradient corrections to the exchange and correlation energy of an inhomogeneous electron gas. The result is exact to all orders in $\text{e}$² and is expressed in terms of the single particle progagator. A method of approximation, which is exact at high density, is given for the explicit evaluation of B_xc. Numerical results are given for B_xc in the metallic density range.     

The energy dependence of σ(e+e− → hadrons) in the total centre-of-mass energy range 1.2 to 3.0 GeV

We have observed 1085 events of the type e⁺e^? → hadrons, in the total centre-of-mass energy range √s = 1.2 to 3.0 GeV. The energy dependence of the total annihilation cross-section, parametrized in the form σ(e⁺e^? → hadrons) = A·sⁿ, is measured to be n = -(1.54_?0.29^+0.17) in the above energy range.     

Determination of nonneutral plasma microstate from synchrotron radiation measurements

The spectrum of the synchrotron radiation emitted from the University of Maryland mirror confined nonneutral plasma is measured during the decay of the pulsed magnetic field and used to obtain the energy distribution ?(γ) and electron density profile n_e⁰(r). One result is that the electron density profile evolves from a relatively thin E-layer to a broad profile with density build-up on axis.     

The effect of Cu substitution on the A1g mode of La0.7Sr0.3MnO3 manganites

We report on the first Raman data of Cu substituted La_1−ySr_yMn_1−xCu_xO₃ (0≤x≤0.10 and 0.17≤y≤0.3, accordingly in order to have the same Mn⁴⁺/[Mn⁴⁺+Mn³⁺] ratio), collected in the frequency range 100-900 cm⁻¹ and at room temperature, with parallel (e_i∥e_s) and crossed (e_i⊥e_s) polarizations of the incident (e_i) and scattered (e_s) light. Spectra were fitted with a Drude-Lorentz model, and peaks at 190-220 and 430 cm⁻¹, together with two broad structures centered at near 500 and 670 cm⁻¹, have been found. We also have observed that the A_1g mode is substantially shifted with increasing Cu substitution. The A_1g phonon shift is a linear function of the tolerance factor t and the rhombohedral angle α_r, thus following the structural changes of the MnO₆ octahedra in the system.