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.     

Toward the theory of electron and positron states in dielectric clusters

Analytical expressions for the binding energy of electrons and positrons in dielectric clusters, analyzed in this work, neglect the elastic effects. Therefore, we present the density-functional theory for neutral liquid clusters that experience the spontaneous deformation. Using the 1/R-expansion, R being the cluster radius, the exact analytical expressions for the size corrections to the chemical potential, surface tension, and atomic density are derived from the condition of mechanical equilibrium. The problem of calculating these corrections is reduced to calculating the quantities for a liquid with a flat surface. The size compression and tension of density occur in the 1/R and 1/R ² orders respectively. The sizes of charged rigid and elastic critical clusters, for which the electron or positron binding energy is close to zero, are calculated for Xe _N ^? , Kr _N ^? , Ar _N ^? , Ne _N ⁺ , He _N ⁺ . The calculations show significant contribution of self-compression to the binding energy of the excess electron in contrast to the positron.     

Hyperfine structure of the atomic osmium spectrum: Superposition of configurations and the effect of nucleus volume

The contributions of the superposition of configurations ns ²5d ⁷6s+ns5d ⁷6sn′s+ns5d ⁷6s ² (n=1–5, n′=7–10) to the parameters of the hyperfine structure a _5d ⁰¹ , a _5d ¹² , a _5d ¹⁰ , a _6s ¹⁰ in the spectrum of the osmium atom Os I are calculated. Nonzero contributions are shown to be made only to the parameters a _5d ¹⁰ and a _6s ¹⁰ . This fact justifies the inclusion of the parameter a _5d ¹⁰ in the semiempirical analysis of experimental values of magnetic dipole constants of the hyperfine structure of the 5d ⁷ s configuration in the spectrum of the osmium atom. The effect of nucleus volume on the parameters of the hyperfine structure in the spectra of osmium isotopes ¹⁸⁷Os and ¹⁸⁹Os is estimated.     

Low energy π-π resonances in the Veneziano model

We attempt to impose elastic unitarity on the forward π-π scattering using the Veneziano Amplitude together with a crossing symmetric subtraction term as an input. TheN/D method is used and thep, ? mesons are interpreted as CDD poles. The self consistency requirement led to the evalutation of the low energy parameters and theS andP-wave phase shifts. The values of the scattering lengths obtained area ₀ ⁰ =0.084m _π ^?1 ,a ₂ ⁰ =?0.024m _π ^?1 ,a ₁ ¹ =0.047m _π ^?3 .     

Two-particle production inK + p interactions at 32 GeV/c

Results are presented on two-particle inclusive production inK ⁺ p interactions at 32 GeV/c. We study thex _1,2=x ₁+x ₂ dependence of invariant structure functions of (ππ)-pairs and compare them to single particle inclusive distributions in the fragmentation regions. Distributions of particles observed at Feynmanx ₂ in association with various “trigger” particles or systems atx ₁ in the same hemisphere are dicussed in terms of the reduced variable \(\tilde x_2 = x_2 /(1 - |x_1 |)\) . We further present absolute production rates and production ratios of π⁺'s and π^?'s associated with π^±,K _s ⁰ , Λ, \(\bar \Lambda \) ,K ^*+ (890), (K _s ⁰ π⁺), and (π⁺ π^?)-triggers, and compare them with qualitative predictions of the quark recombination model. Forwardbackward correlations between (K _s ⁰ π^±), (K _s ⁰ ,p), (Λ, π^?), \((\bar \Lambda \pi ^ \pm )\) , and (p, π^?) pairs are also discussed.     

Neutral strange particle production in proton-proton collisions at\sqrt s = 63 GeV

The inclusive cross section for the production ofK _s ⁰ mesons, Λ and \(\bar \Lambda\) particles in proton-proton interactions at \(\sqrt s = 63\) GeV is presented. The produced particles have been detected in the full phase space. Behaviour of the longitudinal and transversal depandences of the cross sections are discussed. The total production cross sections for _s ⁰ mesons and Λ particles was determined to \(\sigma _{{\rm K}_S^0 } = (25.5 \pm 1.4)\) mb andσ _Λ =(7.8±1.2) mb respectively. A strong energy dependence of the production cross sections is observed.     

Hadronic contributions to (g−2) of the leptons and to the effective fine structure constant α(M Z 2 )

The new experiment planned at Brookhaven to measure the anomalous magnetic moment of the muona _μ≡(g _μ?2)/2 will improve the present accuracy of 7 ppm by about a factor of 20. This requires a careful reconsideration of the theoretical uncertainties of theg?2 predictions, which are dominated by the error of the contribution from the light quarks to the photon vacuum polarization. This issue is cruicial also for the precise determination of the running fine structure constant at theZ-peak as LEP/SLC experiments continue to increase their precision. In this paper we present an updated analysis of the hadronic vacuum polarization using all presently availablee ⁺e^? data. This seems to be justified because previous work on the subject was based to some extent on preliminary or incomplete experimental data. Contributions from different energy ranges are presented separately forg?2 of the muon and the τ-lepton and for α(M _Z ² ). We obtain the resultsa _μ ^had* =(725±16)×10^?10 anda _τ ^had* =(351±10)×10^?8, where the asterisk indicates the dressed (renormalization group improved) value. For the effective fine structure constant atM _Z=91.1888 GeV we obtainΔα _had ⁽⁵⁾ =0.0280±0.0007 and α(M _Z ² )^?1=128.896±0.090. Further improvement in the accuracy of theoretical predictions which depend on the hadronic vacuum polarization requires more precise measurements ofe ⁺e^? cross-sections at energies below about 12 GeV in future experiments.     

Observation of perturbations in the rovibronic transition probabilities for the (4d)r 3Π g − , (4d) s 3 Δ g − → (2p) c 3Π u ± band systems of the H2 molecule

The ratios of the radiative transition probabilities for the lines of the P, Q, and R branches of the (4d)r ³Π _g ^? , (4d)s ³Δ _g ^? → (2p) c ³Π _u ^± band systems of the H₂ molecule have been measured for the first time. Significant (to two orders of magnitudes) differences are found between the experimental values and the adiabatic theory predictions. It is established that the results of the nonadiabatic calculation performed by us in the pure-precession approximation taking into account the electronic-rotational interaction of the 4d ³Π_g and 4d ³Δ_g states are in agreement with the experimental data. The optimal energies of rovibronic levels of the r ³Π _g ^? , s ³Δ _g ^? , c ³Π _u ^? , and c ³Π _u ⁺ states have been found and reidentification of 11 from 54 spectral lines, assigned previously to the (0-0) and (1-1) bands, was performed.     

Correlation femtoscopy of Kaons in the SELEX experiment

Preliminary results from the correlation femtoscopy of identical kaons in the SELEX experiment (Fermilab E781) are presented. Kaons are selected in inclusive reactions of Σ^?C(Cu) interactions at an initial energy of 610 GeV. Kaon pairs are studied in all possible charged states: K _s ⁰ K _s ⁰ , K _s ⁰ K⁺, K _s ⁰ K^?, K⁺K⁺, K⁺K^? and K^?K^?. The source sizes of the hadronization region of neutral and charged kaon pairs are measured.     

Study of a random Heisenberg ferromagnet by the Molecular CPA method

The spin wave Green function of a random dilute Heisenberg ferromagnet is calculated by the Molecular CPA method for the bond model of the f.c.c. lattice. It is found that the ferromagnetic spin order atT=0 becomes unstable, if the concentration of the non-zero bondC _A decreases below the critical valueC _A ⁰ =0.1702, which is some-what larger than the percolation concentrationC _A ^P =0.125. In the regionC _A <C _A ⁰ , aδ function spectrum appears atE=0 corresponding to the free rotations of the total spins of the finite clusters. The peculiar structure of the spin wave state density near the critical concentration is analysed in detail and a speculation is made for the topological structure of the spin clusters.     

Inclusive production ofK s 0 , K s 0 K s 0 andK *±(892) in\bar pp interactions at 3.0, 3.5, 4.0 and 4.5 GeV/c

InclusiveK _s ⁰ andK _s ⁰ K _s ⁰ production in \(\bar pp\) interactions at 3.0, 3.5, 4.0 and 4.5 GeV/c are studied. Cross sections ofK _s ⁰ , K _s ⁰ K _s ⁰ andK ^*±(892) are presented for each incident momentum. The production ofK _s ⁰ andK ^*±(892) through annihilation process is investigated. It is found that the annihilation process is dominant but decreases with incident momentum. The annihilation process is compared withe ⁺ e ^? interactions. Remarkable similarity between them is found in the \({{x_0 = 2E(K_s^0 )} \mathord{\left/ {\vphantom {{x_0 = 2E(K_s^0 )} {\sqrt s }}} \right. \kern-0em} {\sqrt s }}\) distribution. Events with two detectedK _s ⁰ 's are analyzed. The result shows theK _s ⁰ K _s ⁰ pairs are produced in the central region of c.m. system and there is a clearS ^* signal in theK _s ⁰ K _s ⁰ effective mass distribution.     

Off-shell effects in nucleon-deuteron polarization observables

A separable representation of theS-wave Paris potential and a phase-shift equivalent Yamaguchi-type potential significantly differing in their off-shell behaviours are used to calculate second-order polarization observables of elastic nucleon-deuteron scattering atE _D=10 and 20MeV. Off-shell effects are found that stem from differences in the nuclear interaction in the inner regionr?1.2 fm. Adding approximate Coulomb-distortion contributions to the purely nuclear Faddeev amplitudes proton-deuteron predictions are obtained. Coulomb effects are not found to be negligible. Comparison with experimental data, in particular, the spin-correlation parameterC _y,y of the reaction \({}^1\vec H(\vec d,d)^1 H\) forE _D=10MeV vector-polarized deuterons and the spin-transfer coefficientsK _y ^y′ ,K _x ^x′ andK _z ^x′ for \({}^2H(\vec p,\vec p)^2 H\) atE _p=10MeV, prefer the interaction model that contains an intermediate-range repulsion.     

A new many-body solution of the Friedel resonance problem

It is numerically shown that the groundstate of the Friedel problem (consisting of a conduction band and a dresonance), occupied with (n+ 1) electrons, can be written as Ψ = (A a ₀ ^* +Bd*) Π _v=1 ⁿ a _v ^* Φ₀, where a ₀ ^* represents a localized conduction electron state, d* is the Friedel resonance state and Π _v=1 ⁿ a _v ⁸ Φ₀ is a Slater determinant of n single electron states a _t ^* , (Φ₀ is the vacuum state). The a _i ^* together with a ₀ ^* are part of a full ortho-normalized basis of the conductions band.     

Parametrization of two-body perturbation on atomic fine and hyperfine structure. The configuration (6p)3 in the bismuth atom

A method of simultaneous parametrization of one- and two-body interactions on atomic hyperfine structure of configurationl ^N is proposed and applied for the analysis of the configuration (6p)³ in the bismuth atom. For this purpose, the hyperfine structure splittings of the levels²D ₃ ^2/0 ,²D ₅ ^2/0 and²P ₁ ^2/0 were measured. The finally obtained values of HFS parameters are: for one-body parameters (in MHz):a _p ⁰¹ =2,537(9),a _p ¹² =5,182 (12),a′¹⁰=?2,019(10),b _p ⁰² =?3,198(53),b _p ¹¹ =2,816(54); for two-body parameters (in MHz):x _pp ^′/01 ,₂=284(3),x _pp ^′/12 ,₂=581(5),x _pf ^′/12 ,₂=170(70),x _pp ^′/02 ,₂=?359(36),x _pf ^′/02 ,₂=?33(100). The value of the quadrupole moment of the nucleus ₈₃ ²⁰⁹ Bi is also discussed.     

Evidence for a 3.6 minute isomeric 12− state of the πh 11 2/−1 vi 13 2/−1 configuration in206Tl and effective two-particle interactions

Using the²⁰⁴Hg(α, pn)-reaction andα-particles of energies 39–55 MeV, we have found an isomeric 3.6 min 12^? state in²⁰⁶Tl at 2,642.9 keV which has the two-hole configurationπh ₁₁ ^2/?1 vi ₁₃ ^2/?1 The 12^? state decays mainly by anE5 transition of energy 1,021.4 keV to a 7⁺ state at 1,621.5 keV whose main configuration isπs ₁ ^2/?1 vi ₁₃ ^2/?1 There is, in addition, evidence for a weak 565 keVM 4 branch to an 8⁺ state at 2,078 keV whose main configuration should beπh ₁₁ ^2/?1 vf ₅ ^2/?1 . The 7⁺ state decays by a stretched cascade ofγ-rays to states of the following values ofJ ^π and excitation energy: 5 _? ⁺ , 1,405.4 keV; 4^?, 952.1 keV; 2^?, 265.8 keV and 0^?, 0 keV. The main configurations of these states areπh ₁₁ ^2/?1 vp ₁ ^2/?1 ,πd ₃ ^2/?1 vf ₅ ^2/?1 ,πd ₃ ^2/?1 vp ₁ ^2/?1 andπs ₁ ^2/?1 vp ₁ ^2/?1 respectively. From the nuclear masses of²⁰⁸Pb,²⁰⁷Pb,²⁰⁷Tl, and²⁰⁶Tl and the experimental excitation energies it is possible to obtain the proton hole-neutron hole interaction in²⁰⁶Tl. This interaction is compared with the calculations of Kuo and Herling and the discrepancies are discussed. The 12^?→8⁺ M4 transition rate is reduced because of destructive interference between the protonh _11/2→d _3/2 and the neutroni _13/2→f _5/2 contributions. The magnitude of the reduction is accurately reproduced by the wave functions of Kuo and Herling. The 12^?→7⁺ E5 transition rate is about twice as large as the single-holeπh ₁₁ ^2/?1 πs ₁ ^2/?1 transition rate. This deviation is fully explained by the configuration admixtures in the 7⁺ state, given by Kuo and Herling.     

Comparative study of the semiempirical three-parameter potential energy functions for diatomic molecules

A comparative study is made of four three-parameter semiempirical potential energy functions for 32 electronic states of diatomic molecules and their ions:n ₂:X¹gS _g ⁺ ,B ³π_g,A ³ gS_u,C ³ _u,B′ ³ gS_u.a ¹ π_g, a′gS _u ^? ,Ω ¹δ_u N ₂ ⁺ :X ² gS _g ^gS +A ² π,C ² gS _u ⁺ ,B ² gS _u ⁺ CO:X¹gS⁺,a ³ π, a′³ gS_u,e ³ gS^?,d ³gD₁,A ¹π CO⁺:X²gS⁺,A ² π,B ²gS⁺ O₂:X³gS _g ^? ,B ³ gS_u,c ¹ gS _u ^? ,b ¹gS _g ^s ,a ¹ δ_g,c ³ δ_u O ₂ ⁺ :X ²π_g,A ² π_g, a¹ π_g,b ⁴ gS _g ^? A program for numerically integrating the radial Schrödinger equation by the Cooley method is worked out. Certain additional units are introduced to conserve computer time. The resulting vibrational levels are compared with the experimental levels for all the electronic states studied. It is concluded on the basis of this analysis that it is not possible to describe equally well all the electronic states of various molecules on the basis of any single three-parameter potential function. A method for choosing a potential function for describing some particular electronic state of a diatomic molecule is proposed.     

Determination of the CP violating phase γ by a sum over common decay modes toB s and\bar B_s

To help the difficult determination of the angle γ of the unitarity triangle, Aleksan, Dunietz and Kayser have proposed the modes of the typeK ^? D _s ⁺ , common toB _s and $\bar B_s $ . We point out that it is possible to gain in statistics by a sum over all modes with ground state mesons in the final state, i.e.K ^? D _s ⁺ ,K ^*? D _s ⁺ ,K ^? D _s ^*+ ,K ^* D _s ^* . The delicate point is the relative phase of these different contributions to the dilution factorD of the time dependent asymmetry. Each contribution toD is proportional to a product $F^{cb} F^{ub} f_{D_s } f_K $ whereF denotes form factors andf decay constants. Within a definite phase convention (i.e. for example the one defined by the heavy quark symmetry in the limit of heavy quarks), lattice calculations do not show any change in sign when extrapolating to light quarks the form factors and decay constants. Then, we can show that all modes contribute constructively to the dilution factor, except theP-waveK ^* D _s ^*+ , which is small. Quark model arguments based on wave function overlaps also confirm this stability in sign. By summing over all these models we find a gain of a factor 6 in statistics relatively toK ^? D _s ⁺ . The dilution factor for the sumD _tot is remarkably stable for theoretical schemes that are not in very strong conflict with data onB→ψK(K ^*) or extrapolated from semileptonic charm form factors, givingD _tot≥0.6, always close toD(K ^? D _s ⁺ ).     

Hyperfine anomaly in the spectrum of the osmium atom. effect of the spatial distribution of nuclear charge

Contributions of the superposition of configurations ns ²5d ⁸+ns5d ⁸ n′s (n=1–5, n′=6–10) and ns ²5d ⁶+ns5d ⁶ n′s (n=1–6, n′=7–10) to parameters a _5d ⁰¹ , a _5d ¹² , and a _5d ¹⁰ of the hyperfine structure in the spectrum of the osmium atom OsI are calculated. It is shown that the nonzero contribution is made only to a _5d ¹⁰ . The effect of the spatial distribution of nuclear charge on the parameters of the hyperfine structure in the spectra of ¹⁸⁷Os and ¹⁸⁹Os isotopes and on the hyperfine anomaly for the 5d ⁷6s levels in the spectrum of these isotopes is estimated.     

Microscopic foundation of the interacting boson model in thes d-shell nuclei

Starting from an isospin invariant shell-model hamiltonian, we describe a method for deriving microscopically the IBM-hamiltonian appropriate to lights d-shell nuclei. The key ingredients of our approach are:a) the Belyaev-Zelevinsky-Marshalek (BZM) bosonization procedure;b) two successive unitary transformations that extract the “maximally decoupled” collective bosons with angular momentaJ=0(s _ππ ⁺ ,s _νν ⁺ ,s _πν ⁺ ) andJ =2(d _ππ ⁺ ,d _νν ⁺ ,d _πν ⁺ (T=0),d _πν ⁺ (T=1)). The method is applied to obtain the low-energy spectra and the electron scattering form factors for the 0 ₁ ⁺ →2 ₁ ⁺ transitions in²⁰Ne and²⁴Mg. Good agreement with the exact shell-model results is achieved. The inclusion of proton-neutron bosons (s _πν ⁺ ,d _πν ⁺ (T=1),d _πν ⁺ (T=0)), as well as the renormalization of boson parameters due to the non-collective degrees of freedom, are shown to play a crucial role.     

Experimental study of the energy dependence of the reaction rate coefficients of the reaction CH 3 + with N2O and NH3

The kinetics of the reaction of CH ₃ ⁺ ions with N₂O and NH₃ has been investigated in He and Ar buffers using Selected Ion Flow Drift Tube technique (SIFDT). Both studied reactions proceed with nearly collisional rate at near thermal energies. The rate coefficient of the reaction of CH ₃ ⁺ with N₂O is decreasing more than one order of magnitude (from 1.2×10^?9cm³s^?1 up to 8×10^?11cm³s^?1) with reactant ion/reactant neutral average centre-of-mass kinetic energy (E _r) increasing from near thermal up to 2 eV. The dominant product of this reaction is the isomer HCO⁺ (≥94%) and the minor product is CH₃O⁺. The reaction of CH ₃ ⁺ with NH₃ has two binary channels with the dominant product ion CH₂NH ₂ ⁺ (>70%) and the minor product ion NH ₄ ⁺ (≈10%) and three body association channel with product CH₃NH ₃ ⁺ (≈20% at 0.32 Torr). The rate coefficient of this reaction is decreasing nearly by one order of magnitude with increasingE _r from near thermal up to 0.8eV, forE _r>0.8 eV the rate coefficient increases with increasingE _r. The experimental results are interpreted in terms of a simple model assuming the reactions to proceed via the formation of long-lived collision complexes.