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.     

1+ state and effective g-factor

The effects of nuclear field r²(Y₂σ₁)_1υ on magnetic properties of single-particle states in odd-A nuclei (^208±1Pb) are considered. The coupling constant associated with this type of field is estimated by an argument that realtes it to the coupling constant for the field (γ₀σ₁)_1υ. The effects of including the r²(Y₂σ₁)_1υ field on the M1 moments and transitions are estimated.     

The role of tensor forces in Fermi liquid theory

We study the effect of tensor forces on the Fermi liquid parameters in nuclear matter. The usual stability conditions in the σ₁ · σ₂and σ₁ · σ₂τ₁ · τ₂ channels are found to be appreciably modified by tensor forces. We present Fermi liquid parameters for the Reid soft-core potential corrected for the proper inclusion of tensor forces.     

The factors influencing solid state structure — A modern Mendeleyevian answer

It is demonstrated that the different structures adopted within three important classes of compound, the AB octets, AB₂ double octets and the AB₂x₄ spinels, can be distinguished by plotting r^A_σ against r^B_σ or X^A against X^B. Here r_σ and X are defined using quantum mechanical pseudo- potential radii, in a manner that represents the traditional concepts of “size” and “electronegativity”. Thus, these unambigously defined properties are of fundamental importance in determining solid state structures.     

On stationary convection and oscillatory motions in ferromagnetic convection in a ferrofluid layer

It is shown analytically that the ‘principle of the exchange of stabilities’ (PES), in general, is not valid in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries and hence a sufficient condition is derived for the validity of the PES. Upper bounds for the complex growth rate are then obtained. It is proved that the complex growth rate σ=σ_r+iσ_i (where σ_r and σ_i are, respectively, the real and imaginary parts of σ) of an arbitrary oscillatory motion of growing amplitude, in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries lies inside a semicircle in the right half of the σ_rσ_i-plane whose center is at the origin and ²(radius)=RM₁/P_r, where R is the Rayleigh number,M₁ is the magnetic number and P_r is the Prandtl number. Further, bounds for the case of rigid ferromagnetic boundaries are also derived separately.     

Nuclear hyperfine structure in the XΣ state of ZrC

Electronic band systems of zirconium monocarbide, ZrC, in the 16 000-19 000 cm⁻¹ region have been observed following the reaction of laser-ablated Zr atoms with methane under supersonic free-jet conditions. Rotational analyses of high-resolution spectra have shown that the ground state of ZrC is a ³Σ state, with r₀=1.8066 Å and an unexpectedly small spin-spin parameter, λ=0.5139 cm⁻¹. The spectra are dense because of the five naturally occurring isotopes of Zr. Four of these, with mass numbers 90, 92, 94, and 96, have I=0, but the fifth, ⁹¹Zr, present in 11.22% abundance, has I=5/2. Lines of ⁹¹ZrC can be assigned in some of the strongest bands, and are found to display sizeable hyperfine splittings, with widths of up to 0.2 cm⁻¹. Analysis shows that the largest hyperfine effects are in the ground state, where b=−0.03133±0.00015 cm⁻¹ and c=−0.00123±0.00037 cm⁻¹ (3σ error limits). The large Fermi contact parameter, b, indicates that an unpaired Zr 5sσ electron is present, which, taken together with the small value of λ, means that the ground state must be a ³Σ⁺ state, from the electron configuration (Zr 5sσ)¹ (C 2pσ)¹. Internal hyperfine perturbations occur between the F₁ and F₃ electron spin components of the ground state in the range N=2-4, producing extra lines in some of the branches; the perturbations are of the type ΔN=0, ΔJ=±2, and are a second-order effect arising because the F₁ (J=N+1) and F₃ (J=N−1) spin components both interact with the F₂ (J=N) component through ΔN=0, ΔJ=±1 matrix elements of the Fermi contact operator. Second-order perturbations of this type can only occur in states that are very close to case (b) coupling.     

Electronic structure characteristic of carbon nanotubules

Electronic structure near the Fermi energy of single-shell carbon nanotubules has been studied within the framework of the tight-binding approximation. The electronic density of states (DOS) of tubules shows a structure consisting of many spike-like peaks. An analytical expression in a π-electron model is derived which predicts not only the energy gap (E _g ) of semiconducting tubules, but also the energy positions of those spike-like peaks in the π-DOS near the Fermi energy in any tubule. The limitation of the π-electron model in tubules is discussed by investigating the effect of σ-πmixing. The position of σ component edge in the DOS is also investigated as a function of tubule radius (R) and chiral angle (θ). It is found that this edge energy is very sensitive to θ and largely changes with R, because the dominant contribution of θ to its change is given by g(θ)/R in contrast to f(θ)/R ² for E _g .     

Experimentally favoured potential for mesons

We show first that a natural potential to be used in a semirelativistic wave equation for theS=1,J=J _max light and heavy mesons is, forr?1 Fermi,V(r)=ar+b/r withb??π/2, forr?1 Fermi,V(r)=cln(r/r ₀). Next we show that this particularb value favours in fact a QCD-like potential forr?1 Fermi so that a logarithmic potential is only an effective one in a smallr region.     

Electronic properties of metals at low temperatures

A many body theory of an electron gas is developed to find the internal and correlation energies at low but finite temperatures. The contribution from the first order exchange, second order (regular and anomalous) exchange, and ring diagrams are treated. The Fermi momentum and the correlation energy are determined as functions of the density by two different methods, one being based on iteration and the other a direct solution of the number density relation. It was found that the iterative solutions which are correct to ordere ² ore ⁴ become negative forr _s of order 5 while the direct solutions do not, indicating the invalidity of the former. Hence, the correlation energy evaluated to the same orders by iteration will not be satisfactory in the same range. The highest order iterative solution which includes terms of ordere ⁶ does not show such a breakdown. These terms which give the contribution of orderr _s to the correlation energy are therefore important and tend to reduce the magnitude of the correlation energy. The corresponding curve is indeed close to that determined by the direct method for smallr _s but a significant deviation takes place at largerr _s . The Coulomb interaction seems less effective at higher temperatures. The internal energy is also determined as a function of density and temperature.     

The impact parameter dependence of the K MO X-ray emission in208Pb +208Pb collisions

The emission probabilities for quasimolecular K-x-radiation (K-MOR) have been measured in²⁰⁸Pb +²⁰⁸Pb collisions at 4.3 MeV/u and 4.8 MeV/u as a function of the scattering angle using the particle-photon-coincidence technique. The probabilities exhibit a superposition of two exponential slopes with different fall-off constants. We identify the sharp fall off at very small impact parameters (<60 fm) with the K-MOR contribution from the decay of 1sσ-vacancies. The flatter slope for impact parameters larger than 60 fm is attributed to the radiative decay of holes in 2p _1/2 σ molecular states. In this way, experimental “1sσ-MOR-emission probabilities” could be extracted and compared with theory. For 4.3 MeV/u the1sσ- and 2p _1/2 σ-excitation probabilities could also be determined and have been compared to coupled-channel calculations and to a scaling law for 1sσ excitation.     

Nuclear matter approach to the heavy-ion optical potential: (II). Imaginary part

The heavy-ion optical potentials are constructed in a nuclear matter approach, for the ¹⁶O + ¹⁶O, ⁴⁰Ca + ¹⁶O and ⁴⁰Ca + ⁴⁰Ca elastic scattering at the incident energies per nucleon E^lab/A ? 45 MeV. The energy density formalism is employed assuming that the complex energy density of colliding heavy ions is a functional of the nucleon density ?(r), the intrinsic kinetic energy density τ⁽²⁾(r) and the average momentum of relative motion per nucleon K_r(≦ 1.5 fm^?1). The complex energy density is numerically evaluated for the two units of colliding nuclear matter with the same values of ρ, τ⁽²⁾ and K_r. The Bethe-Goldstone equation is solved for the corresponding Fermi distribution in momentum space using the Reid soft-core interaction. The “self-consistent” single-particle potential for unoccupied states which is continuous at the Fermi surface plays a crucial role to produce the imaginary part. It is found that the calculated optical potentials become more attractive and absorptive with increasing incident energy. The elastic scattering and the reaction cross sections are in fair agreement with the experimental data.     

Robust weighting in least-squares fits

Spectroscopic data sets often contain a significant number of outliers due to effects such as misassignments, trial assignments, or local perturbations. Standard fitting routines can be made robust to such outliers by the method of iteratively reweighted least squares. It is proposed here that the weight of datum i in a give iteration is given by w_i=1/(σ_i²+αr_i²), where σ_i is the standard deviation for the idealized distribution without outliers, and r_i is the residual from the previous iteration. The value of α should depend on the fractional number of outliers and the size of their residuals, but a standard value of α=1/3 is suggested for spectroscopic applications.     

Low-energy dilation

We study consequences of scale symmetry breaking in the QCD effective SU(2)×SU(2) chiral model. The mass of a pseudo-Goldstone boson dilation is estimated to be M_σ≅1 GeV and the upper bound to its lifetime τ_σ⩽4×10⁻²⁸ s. We also show that the dilation gives a considerable contribution to the pion scalar radius.     

Barrett moments and rms charge radii

An empirical relation is established between Barrett equivalent radii R _k,α and rms charge radii < r ² >^1/2 based on the results of model-independent and Fermi model analyses of 2p → 1s transitions in muonic atoms. This relation follows simple Z dependence, and can be usefully applied to derive rms radii < r ² >^1/2 or differences δ ^AA ′ < r ² >^1/2 in cases where only R _k,α data or isotope shifts δ ^AA ′ R _k,α are published. The atomic number dependence of the Barrett parameters k(Z) and α(Z) is also given by empirical formulae. It is shown that the Barrett moment can be expanded in a sum of integer moments < r ^m > (m ≥ 2) using an effective exponential parameter α _eff(Z). The moments < r ^m > and isotopic differences δ < r ^m > of the two-parameter Fermi distribution expressed in terms of the parameters c and a are given in the Appendix for m = 1 – 10.     

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.     

On asymptotical behaviour of the total γp- and γγ- cross sections off the mass shell

It is shown that the Regge type behaviour and the scaling law Sσ_γp ∼ f(−S/q₂) give for Sσ_γγ the asymptotics f (SS₀/q₁²q₂²) at large S, q₁² and q₂². This result is confirmed by the summation of the diagrams in ?³-theory. It is announced also that the introduction of the spin (γ⁵-theory) results in a slight breaking of the scaling law and in the suppression of the scalar photon contribution to these processes compared with the contribution of the transversal photon.     

Multicomponent dense electron gas as a model of Si MOSFET

We solve a 2D model of N-component dense electron gas in the limit N→∞ and in the range of the Coulomb interaction parameter N ^?3/2?r _s ?1. The quasiparticle interaction on the Fermi circle vanishes as ?²/Nm. The ground-state energy and the effective mass are found as series in powers of r _s ^2/3 . In the quantum Hall state on the lowest Landau level at integer filling 1?ν<N, the charge-activation-energy gap and the exchange constant are Δ=log(r _s N^3/2)?ω_H/ν and J=0.66?ω_H/ν.     

Gamow-Teller β transition from the 2− ground state of88Rb to the 3− excited state of88Sr

The Gamow-Tellerβ-transition from the ground state 2^? of⁸⁸Rb to the 3^? level at 2.734 MeV of⁸⁸Sr is studied. The nuclear matrix element 〈σ〉 and the lofft value are calculated using complete nuclear wave functions for the initial and final states. It is shown that, contrary to the normal assumption, the component ¦π2p ₃ ^2/?1 π1g _9/2〉 of the final state does give a very important contribution to 〈σ〉 due to the presence of strong cancellation effects. Although our calculations favour a wave function for the 3^? level⁸⁸Sr where neutron 1h—1p configurations are not included, there are still some facts which make that our results cannot be taken as conclusive. Nuclear Structure⁸⁸Rb,⁸⁸Sr, calculated the Gamow-Teller nuclear matrix element 〈σ〉 and the logft value using a shell model.     

Rise of proton proton total cross section and inclusive spectra

The origin of the rise of p-p total cross section (σ_t(pp)) is investigated by making use of the inclusive sum rule. The contribution to the rise of σ_t(pp) from the development of sharp peak near the kinematical boundary in the process p+p→p+ “anything” is almost completely canceled out by the decrease of the cross section in other x-region between s=45 (GeV/c)² and s=2820 (GeV/c)². Then the net contribution to the rise of σ_t(pp) from the process p+p→p+ “anything” is very likely to be zero. The true origin of the rise of σ_t(pp) is found to be the increase of inclusive cross sections at x ? 0 between PS and ISR energies. The contribution from the process p+p→π+ “anything” at x ? 0 to the rise of σ_t(pp) is estimated to be 3.2 mb, that from the process p+p→K + “anything”, 0.71 mb and that from the process p+p→$\text{p}$ “anything”, 0.62 mb. According to our conclusion we expect that all total cross sections will rise with energy at high energy.