A relativistic treatment of the three-body final state in the photoproduction of π on the deuteron

We study the problem of the three-body corrections in final state for particles with spin in view of applying it to the photoproduction on the deuteron: γd → NNπ. A particular attention is paid to the kinematical singularities of the problem.     

The S′ state in the trinucleon

The relative probability (P_S′) of the mixed-symmetry S-state (the S′ state) in the ground state if the trinucleon, is determined by fitting the charge form factors and the muon capture rate of the three-particle system. The spatial wave functions used in this work are of exponential form with two-body correlations in the predominant totally symmetric S-state and have been proved sufficiently flexible in our recent binding energy calculations. Our results indicate that P_S′ cannot exceed 1.5%.     

On the Mie-Grüneisen and Hildebrand approximations to the equation of state of cubic solids

An analysis is made of the conditions under which the equation of state of a cubic solid under hydrostatic pressure takes the form given by either the Mie-Grüneisen or the Hildebrand approximation. The condition of validity of the vibrational or thermal formulation of the Mie-Grüneisen approximation is reduced to the existence of a purely volume-dependent characteristic temperature for the vibrational or thermal free energy of the solid. The analysis consists then in a search for temperature ranges where these restrictions on the functional form of the free energy, and the restrictions on the form of the internal energy imposed by the Hildebrand approximation, are satisfied for a non-metal in the quasi-harmonic approximation. The main results are as follows: (1) At temperatures somewhat above the Debye characteristic temperature for the (quasi-harmonic) high-temperature heat capacity at constant volume, it is appropriate to take as equation of state the vibrational Hildebrand equation: (2) at somewhat lower temperatures, this Hildebrand equation is generally more inaccurate than the corresponding Mie-Grüneisen equation; and (3) in the low-temperature T³ region of the heat capacity, the equation of state reduces to the thermal Mie-Grüneisen equation. The explicit forms of the vibrational and thermal Mie-Gruneisen equations of state, and of their volume derivatives at constant temperature, are reported together with the corresponding Hildebrand equations. Some corollary results are obtained, within the quasi-harmonic approximation, on the temperature variation at constant volume of the Grüneisen parameters relating the explicit volume and temperature dependence of the vibrational and thermal free energy and of the entropy of a cubic solid, and (in an Appendix) on the temperature variation of the Debye temperatures appropriate to the various thermodynamic functions of any non-metal. The available experimental and theoretical evidence on the anharmonic contributions to the thermodynamic functions of solids is briefly discussed, and points to the conclusion that their weight is quite small in the region of temperature of interest for our analysis.     

A theoretical study of FeNC in the Δ electronic ground state

We report an ab initio calculation, at the MR-SDCI + Q + E_rel/[Roos ANO (Fe), aug-cc-pVQZ (C, N)] level of theory, of the potential energy surface for ⁶Δ_i FeNC. From the ab initio results, we have computed values for the standard spectroscopic parameters of FeN¹²C and FeN¹³C. Analytical representations of the potential energy surfaces have been fitted through the ab initio points, and the resulting functions have been used for directly solving the rotation-vibration Schrödinger equation by means of the MORBID program and by means of an adiabatic-separation method. For ⁶Δ_i FeNC, our ab initio calculations show that the equilibrium structure is linear with r_e (Fe-N) = 1.9354 Å and r_e (N-C) = 1.1823 Å. We find that the bending potential is very shallow, and the MORBID calculations show that the zero-point averaged structure is bent with the expectation values 〈r (Fe-N)〉 = 1.9672 Å, 〈r(N-C)〉 = 1.1866 Å, and . The experimentally derived bond length r₀ (N-C) = 1.03(8) Å reported for ⁶Δ_i FeNC by Lie and Dagdigian [J. Chem. Phys. 114 (2001) 2137-2143] is much shorter than the corresponding ab initio r_e-value and the averaged value from MORBID. Our calculations suggest that this discrepancy is caused by the inadequate treatment of the large-amplitude bending motion of ⁶Δ_i FeNC. It would appear that for floppy triatomic molecules such as FeNC, r₀-values have little physical meaning, at least when they are determined with the effects of the large-amplitude bending motion being ignored, i.e., under the assumption that the r₀ structure is linear.     

On production of η′ mesons in pp collisions close to threshold

The near threshold behaviour of the reaction cross section for pp→ppη^′, recently measured in experiments at COSY and SATURNE, is analyzed. The interaction in the pp as well as in the η^′ p final states is taken into account. The suppression of the total cross section for this process at excess energies Q < 3 MeV observed in these experiments is interpreted as an evidence for a strong repulsive η^′ p interaction. Received: 26 May 1999 / Revised version: 8 July 1999     

Measurement of the beam asymmetry in η photoproduction off the proton

The beam asymmetry, Σ , was measured at ELSA in the reaction p → ηp using linearly polarised tagged photon beams, produced by coherent bremsstrahlung off a diamond. The crystal was oriented to provide polarised photons in the energy range E _γ = 800 to 1400MeV with the maximum polarisation of P _γ = 49 % obtained at 1305MeV. Both dominant decay modes of the η into two photons and 3π⁰ were used to extract the beam asymmetry from the azimuthal modulation of the cross-section. The measurements cover the angular range Θ_cm ≃ 50 -150 degrees. Large asymmetries up to 80% are observed, in agreement with a previous measurement. The eta-MAID model and the Bonn-Gatchina partial wave analysis describe the measurements, but the required partial waves differ significantly.     

Variational study of the ground state energy of theE−b 1,b 2 Jahn-Teller system

In this paper a variational method for the ground state energy approximation of theE−b ₁,b ₂ Jahn-Teller system is presented. This method is based on the choice of a suitable variational ground state wave function. This trial wave function — a correlated squeezed state — is used to account for the correlation and anharmonicity of the interaction between the two vibrational modes; the anharmonicity of both modes is taken into account by the squeeze effects of these modes. The ground state of mode 1 in this trial wave function is considered as a linear combination of the two displaced harmonic oscillators. The ground state energies for the linearE - e Jahn-Teller system calculated by this method are not only in good agreement with the exact diagonalization results, but they are also better than those from the previous analytical studies. Another conclusion which results from the presented model is the following one: the squeezing effect of mode 1 for the linearE - e Jahn-Teller system is substantially smaller, in contrast with the results which are presented in the previous analytical studies.     

Néel order in the ground state of spin-1/2 Heisenberg antiferromagnetic multilayer systems

We show existence of Néel order for the ground state of a system withM two-dimensional layers with spin 1/2 and Heisenberg antiferromagnetic coupling, providedM8. The method uses the infrared bounds for the ground state combined with ideas introduced by Kennedy, Lieb, and Shastry.     

Transition from the 0 state to the π state in S-FNF-S Josephson structures

The critical current I _C of S-FNF-S Josephson structures has been calculated as a function of the distance between the superconducting (S) electrodes, L, via the Usadel semiclassical equations for the case of specifying the supercurrent in the direction parallel to the interface between the ferromagnetic (F) and normal (N) films of the composite weak-link region. It has been shown that, owing to the interaction between the F and N films, both the typical decrease scale of the critical current and the period of its oscillations to lengths of the scale ξ_N can be much larger than the respective quantities for the SFS junctions. Moreover, this interaction changes both the magnitude and sign of the critical current. It has been shown that the critical current in a structure with the collinear magnetization vectors of the films can be significantly different from the critical current in a structure with the antiparallel magnetization of the F films.     

Rotational band contour analysis in the Ã1A′-[Xtilde]1A′ electronic systems of substituted naphthalenes

The 0₀ ⁰ bands of the à ¹ A′-[Xtilde] ¹ A′ systems of 1-fluoro, 1-hydroxy and 1-aminonaphthalene have been investigated by rotational band contour analysis. The 0₀ ⁰ bands in 1-fluoro and 1-hydroxynaphthalene are 70 per cent type A and 30 per cent type B, and 75 per cent type A and 25 per cent type B hybrids respectively: the electronic transition moment vector has been rotated by about 15° towards the carbon atom C₃ by the F and OH substituents compared to naphthalene (in which, in the Ã-[Xtilde] system, it is along the long in-plane axis). In 1-aminonaphthalene it seems likely that the 0₀ ⁰ band is predominantly type A, but it could not be observed with sufficient intensity to be able to obtain the excited state rotational constants with any certainty.     

Rotational band contour analysis in the à 1 A′-[Xtilde] 1 A′ electronic systems of substituted naphthalenes

The 0₀ ⁰ bands of the à ¹ A′-[Xtilde] ¹ A′ electronic systems of 2-fluoro, 2-hydroxy- and 2-aminonaphthalene have been identified and then rotationally analysed by the method of rotational band contour analysis. The effect of 2-substitution on the direction of the electronic transition moment vector in naphthalene is found to be drastic: the vector is oriented by about 70–80° (anti-clockwise in figure 1) by the substituent. However, the orientation is almost unaffected by the nature of the substituent.

The 0₀ ⁰ bands are all type A, B hybrids but predominantly type B. Significant differences in the 0₀ ⁰ band rotational contours in the three molecules are reflected in the different values of ΔA, ΔB and ΔC found from the contour analyses. An attempt to interpret the changes of rotational constants in terms of changes in geometry from the ground to the excited state suggest very strongly that the geometry change of the naphthalene rings in all the molecules is similar to that in naphthalene itself but that the carbon-substituent bonds contract in the excited state. The contraction increases from F to OH to NH₂ and is probably quantitatively similar to that suggested previously for the corresponding monosubstituted benzenes.     

Can one determine the underlying fermi surface in the superconducting state of strongly correlated systems?

The question of determining the underlying Fermi surface (FS) that is gapped by superconductivity (SC) is of central importance in strongly correlated systems, particularly in view of angle-resolved photoemission experiments. Here we explore various definitions of the FS in the superconducting state using the zero-energy Green's function, the excitation spectrum, and the momentum distribution. We examine (a) d-wave SC in high-Tc cuprates, and (b) the s-wave superfluid in the BCS-Bose-Einstein condensation (BEC) crossover. In each case we show that the various definitions agree, to a large extent, but all of them violate the Luttinger count and do not enclose the total electron density. We discuss the important role of chemical potential renormalization and incoherent spectral weight in this violation.     

Mössbauer study of the iron atom state in modified chromium dioxide

Powders of modified chromium dioxide produced by the hydrothermal method were studied using ⁵⁷Fe Mössbauer spectroscopy at a temperature of 298 K. The content of the modifier, i.e., ⁵⁷Fe compound, was varied from 2 to 10 mmol/mol Cr at a Sb content of 2.2 and 10 mmol/mol Cr. It was shown that, independently of concentrations, Fe³⁺ ions are distributed between three magnetic solid solutions (sextets): based on CrO₂ (bulk material and iron-enriched surface layer), based on Cr₂O₃, and surface β-CrOOH (doublet). In this case, chromium atoms were not substituted in the CrSbO₄ nucleation (12 nm in size) phase with an accuracy up to the Mössbauer factor. It was assumed that the powder coercivity, in addition to the size factor, is controlled by the iron concentration in the CrO₂ surface layer.     

On experimental tests of D-states in the 3He3H ground state

Recent experiments relevant for D-state components in the ground state of the A = 3 systems are discussed in a simple scheme. This displays the close connection between the tensor force and the D-state components and allows one to interpret the experimental results in a transparent way. Suggestions for a complete experimental test of the D-state are given.     

On Takahashi's study of the thermodynamics of the Heisenberg-Ising ring for | Δ | < 1

We use the equations recently proposed by Takahashi for the free energy of the Heizenberg-Ising ring for | Δ | < 1 to derive the first two terms in the high temperature expansion when Δ ∼ 0. The second term disagrees with the known high temperature series. We conclude that the assumptions used by Takahashi are incorrect.     

Signature of the ηNN configurations in coherent πphotoproduction on the deuteron

The photoproduction of a neutral pion on the deuteron is considered in the energy region around the η threshold, where a bump-like structure was observed at very backward pion angles. Different dynamical aspects which may be responsible for this phenomenon are analysed within a theoretical frame which includes intermediate ηNN configurations. The results show, in particular, that a three-body treatment of the ηNN interaction is of special importance.     

Contribution of the lowest 1+ intermediate state to the 2νββ-decay amplitude

The half-life with respect to two-neutrino double-beta (2νββ) decay to the final ground state is calculated under the assumption of single-state dominance. To the best of our knowledge, the energy denominators of perturbation theory are considered for the first time without invoking any approximation. The results obtained for the experimentally interesting A=100, 110, 114, 116, and 128 nuclear systems are presented.