Electron screening in thed+3He fusion reaction

Cross section measurements of thed(³He,p)⁴He reaction have been extended to an energy as low asE _cm =5.4 keV. The data have an improved accuracy compared with previous work and confirm the existence of electron screening. The combined analysis of the present and previous data leads to an electron screening potential ofU _e =123 ± 9 eV. A similar analysis of previous data for³He(d, p)⁴He leads toU _e =186 ± 9 eV. Both screening potentials differ due to the molecular and atomic aggregate state of the targets involved in these investigations and are significantly larger than expected from available atomic physics models, supporting the general trend in studies of electron screening.     

Beta-gamma-gamma directional correlation in103Rh

β-γ-γ directional correlation studies for the cascades (i)β-rays ofE _max=0.12 MeV,γ-rays of 557 keV andγ-rays of 53 keV and (ii)β-rays ofE _max=0.21 MeV,γ-rays of 444 keV andγ-rays of 53 keV have been made. The triple correlation functionsW(θ) were obtained to beW(θ)=1+(−0.153±0.031)P ₂(cosθ)+(0.004±0.035)P ₄(cosθ) forβ-rays ofE _max 0.12 MeV→557→53 keV cascade andW(θ)=1+(0.163±0.042)P ₂(cosθ)+(−0.035±0.058)P ₄(cosθ) forβ rays ofE _max=0.21 MeV→444 keV→53 keV cascade. Spins and parities of the 650, 537 and 93 keV levels of¹⁰³Rh are deduced by triple angular correlation and the internal conversion coefficient studies. Multipolarities of the transitions are also determined.     

Stability of QED Vacuum and 3+1 Dimensional Scattering Problem in the Presence of a Coulomb Scalar Potential and Vector Field

We show that, in the presence of a scalar field the range of the value of external field parameters a and b, at which corresponding Hamiltonian operator is hermitian, essentially wider than in its absence. It allows us to study precisely the question on stability of QED vacuum in the presence of a strong electric field of a point charge Z|e| and external scalar Coulomb field with respect to electron-positron pair production. Also, we consider the scattering of Dirac particle by the specified fields in 3+1 dimensions. The phase shift and wave functions are obtained exactly. We calculate the scattering amplitude in a quasi-classical approximation as a partial wave series. By means of figures obtained for the cross section σ(θ) in general and special cases, such as a≠b and a=b, we find that σ(θ) is not exactly symmetric about θ=π.     

(EC+β +) decay of 130Nd and 140Tb

The available astrophysical S(E) factor data for the reaction ⁷Li (p,α)α at 10 < E < 1000keV exhibit an exponential increase at low energies due to the effects of electron screening. A parametrisation of the data using a non-resonant, direct process and two subthreshold resonances reproduces the data at energies E≥ 100keV, while at lower energies this calculated S _b(E) factor curve for bare nuclides drops below the data, which in turn represent the case of electron-shielded nuclides, i.e. the electron-shielded S _s(E) factor. The comparison between S _b(E) and S _s(E) leads to an electron-screening potential energy U _e = 350eV, which is much higher than the adiabatic limit of 175eV and not understood at present. The deduced value of S _b(0) is considerably smaller than the previously adopted value of 59keV b, significantly increasing the calculated abundance of ⁷Li in big-bang nucleosynthesis. The Trojan-horse method was applied to the reaction ⁷Li (p,α)α to determine the energy dependence of the S _b(E) factor for 10 < E < 370keV, free from the effects of the Coulomb barrier and electron screening. The THM results are close to the calculated S _b(E) curve and suggest that the THM may become a powerful way to obtain improved information on low-energy cross-sections and associated electron-screening effects in a model-independent way. Received: 9 September 2000 / Accepted: 5 December 2000     

Measurements of elastic scattering for 7Be, 7Li + 9Be systems and fusion cross sections for 7Li + 9Be system

Elastic scattering angular distributions have been measured for ⁷Be + ⁹Be system at E_lab = 17, 19 and 21 MeV in the angular range θ_cm=26^○–58°, and for ⁷Li + ⁹Be system at E_lab= 15.75, 24 and 30 MeV. An optical model (OM) analysis of these data have been carried out. For the ⁷Li + ⁹Be system fusion cross sections were obtained at E_lab = 15.75, 24 and 30 MeV by measuring the α-evaporation spectra from the compound nucleus at backward angles. The measured α-evaporation spectra were reproduced by the statistical model calculations and fusion cross sections were extracted therefrom. The ratios of the experimental fusion cross sections to the total reaction cross sections (obtained form OM analysis) were found to be rather small. This result suggests that break-up process has a strong influence on fusion process leading to a reduction in fusion cross section.     

Spin observables of the NN interaction in a relativistic harmonic model with confined gluons and mesons

Polarization observables for the nucleon-nucleon (NN) scattering are investigated in the frame work of relativistic harmonic model belowE _lab=250 MeV, with the inclusion of theσ andπ meson exchange. The results can be interpreted as the ‘Cheshire cat principle’ of NN interaction.     

Cross section and resonance strength measurements of 19F(p, αγ)16O at Ep= 200–800 keV

An excitation function of the ¹⁹F(p, αγ)¹⁶O reaction has been measured over the proton beam energy range E_p= 200–800 keV using a 4 π NaI summing spectrometer. A new resonance was found at E_R= 237 keV and its properties Γ_R, σ_R and ωγ have been extracted. The strengths of all resonances at E_p= 200–800 keV have been also extracted. The importance of the 1⁺ resonance at E_R= 11 keV is discussed and its width has been estimated taking into account interference effects with the strong 1⁺ resonance at E_R= 340 keV. The reaction rates have been calculated over a wide range of temperatures and compared with the rates of the (p, α₀) and (p, α_π) branches of the ¹⁹F(p, α)¹⁶O reaction. Received: 21 June 1999 / Revised version: 30 September 1999     

Calculation of the photoionization with deexcitation cross sections of He and helium-like ions

We discuss the results of the calculation of the photoionization with deexcitation of excited He and helium-like ions Li⁺ and B³⁺ at high but nonrelativistic photon energies θ. Several lower ¹ S and ³ S states are considered. We present and analyze the ratios R _d ⁺ * of the cross sections of photoionization with deexcitation, σ _(d) ⁺ *(θ), and of the photoionization with excitation, σ⁺*(θ). The dependence of R _d ⁺ * on the excitation of the target object and the charge of its nucleus is presented. In addition to theoretical interest, the results obtained can be verified using long-lived excited states such as 2³ S of He. The text was submitted by authors in English.     

Phase shift analysis of the <Superscript>6</Superscript>He+<Superscript>208</Superscript>Pb and the <Superscript>6</Superscript>He+<Superscript>197</Superscript>Au systems

We present the elastic scattering of the ⁶He+²⁰⁸Pb and the ⁶He+¹⁹⁷Au systems at the laboratory energy of E _lab=27 MeV within the framework of the McIntyre parametrization, and systematically investigate χ ²/N analysis of both systems to obtain an excellent agreement between the theoretical results and the experimental data. We find large diffusivity parameters indicating long range absorption mechanisms. We also show that both systems lack both the nuclear and the Coulomb rainbow scattering for obtained S-matrix parameters.     

Transverse beam asymmetries measured from <Superscript>4</Superscript>He and hydrogen targets

The HAPPEX Collaboration at Jefferson Lab has measured the transverse beam spin asymmetries (A_T) for elastic electron scattering from proton and ⁴He targets. The experiment was conducted using a vertically polarized electron beam of energy ∼ 3 GeV, at a Q ² ∼ 0.1 GeV^2 and a scattering angle θ_lab ∼ 6^° . The preliminary results are reported here. The ⁴He measurement is the first measurement of A_T from a nucleus. A_T for ⁴He is non-negligible; therefore, it will be necessary to make measurements of A_T for future parity-violating experiments using nuclear targets.     

Rotational excitations in muonic atom scattering by molecular hydrogen

A computational scheme based on the infinite order sudden approximation (IOS) is proposed for treating molecular and screening effects in muonic atom scattering at low energies. With this scheme the differential (dσ/dΩ(ɛj← 0|θ) and the total σ_tot(ɛ) cross-sections of muonic atom scattering on molecules of hydrogen isotopes are calculated at energies ɛ_rot=ℏω_I⩽ɛ⩽ɛ_vib= ℏω_03BD;. The IOS permits a quantitative analysis of the dependence of the differential cross-sections on the scattering angle and on the rotational excitations, particularly the rotational rainbow effects. An attractive feature of this approach is also to include the energy and the angular dependencies in the “input” cross-sections describing the muonic atom scattering on each bare nucleus of the molecule. The calculated total cross-sections ω_tot(ɛ) are in agreement with the data obtained earlier with the pseudopotential approach. This revised version was published online in August 2006 with corrections to the Cover Date.     

Experimental determination of the electron screening potential energy for the d(d, n)3He Reaction in ZrD2 and D2O in the ultralow energy region

This work is devoted to measuring of the values of the astrophysical S-factors and electron screening potential energy for a d(d,n)³He reaction occurring at ultralow energies in zirconium deuteride ZrD₂ (3.5–7.0 keV) and heavy water D₂O (2.2–6.0 keV). The experiment was performed on the Hall pulsed plasma accelerator at the TPU Nuclear Physics Institute (Tomsk) with ZrD₂ and D₂O targets produced by the magnetron sputtering of zirconium in a deuterium environment and heavy water freezing-out on a copper support, respectively. A χ ² analysis of the dependence of the neutron yields and astrophysical S-factors for the dd reaction on the deuteron collision energy E revealed that the upper bounds of the electron screening potential energy for interacting deuterons in ZrD₂ and D₂O and of the astrophysical S-factors at the deuteron collision energy E = 0 were U _e (ZrD₂) < 30 eV, U _e (D₂O) < 25 eV, S(0) = (57.2 ± 3.9) keV · b (ZrD₂), S(0) = (58.6 ± 3.6) keV · b (D₂O) at the 90% confidence level.     

New data for the 197Au(γ, nX) and 197Au(γ, 2nX) reaction cross sections

The results from experimental and theoretical studies of the total and partial cross sections of photoneutron reactions on the ¹⁹⁷Au isotope were analyzed. The cross sections for reactions σ(γ, nX) = σ(γ, n) + σ(γ, np) + … + σ(γ, 2nX) = σ(γ, 2n) + σ(γ, 2np) + … were evaluated in the energy range 7 ≤ E _γ ≤ 30 MeV using an approach free of the shortcomings of experimental photoneutron multiplicity sorting methods. The total photoneutron reaction cross sections σ^exp(γ, xn) = σ^exp(γ, nX) + 2σ^exp(γ, 2nX) + … = σ^exp(γ, n) + σ^exp(γ, np) + 2σ^exp(γ, 2n) + 2σ^exp(γ, 2np) + … were used as the initial experimental data. The contributions from the cross sections σ(γ, nX) and σ(γ, 2nX) to the cross sections σ^exp(γ, xn) were separated using the multiplicity transition functions F ₁ ^theor = σ^theor(γ, 1nX)/σ^theor(γ, xn) and F ₂ ^theor = σ^theor(γ, 2nX)/σ^theor(γ, xn), calculated within an updated version of the pre-equilibrium model of photonuclear reactions. New evaluated data for both partial reaction cross sections, i.e., σ^eval (γ, 1nX) = F ₁ ^theorσ^exp(γ, xn) and σ^eval(γ, 2nX) = F ₂ ^theorσ^exp(γ, xn), were obtained. The cross sections σeval(γ, nX) and σ^eval.(γ, 2nX) evaluated using the theoretically calculated functions F _1,2^theor are consistent with the Livermore data, but substantially contradict the Saclay data.     

Reciprocity relations for the effective electrical conductivity of randomly inhomogeneous media in the fractal regime

An exact relation for the realization-averaged effective conductivities in the fractal region is found for two-dimensional randomly inhomogeneous media. It has the form {σ _e (τ,L)~× {1/σ _e (−τ,L)~⁻¹=σ _e ² (τ=0, L≫ξ), where ξ is the correlation length (the self-averaging scale), L is the size of the system, τ=(p-p _c )/p _c , and p _c is the percolation threshold. For L≫ ξ, the system is self-averaged, and the relation transforms into the Dykhne reciprocity relation, A. M. Dykhne, Zh. éksp. Teor. Fiz. 59, 110 (1970) [Sov. Phys. JETP 32, 63 (1971)] σ _e (τ)σ _e (−τ])=σ _e ² (τ=0)= σ ₁ σ ₂. A similar relation is obtained for media with an exponentially broad distribution of local conductivities, as well as for individual realizations of some deterministic structures. Zh. éksp. Teor. Fiz. 113, 1484–1490 (April 1998)     

Electronic structure of TiO<Subscript>2</Subscript> rutile with oxygen vacancies: Ab initio simulations and comparison with the experiment

The electronic structure of TiO₂ rutile with oxygen vacancies, which is a promising insulator, has been analyzed. The ab initio density functional calculations, as well as the comparative analysis of the results obtained in the σ-GGA spin-polarized generalized approximation and those obtained by the σ-GGA + U method with allowance for Coulomb correlations of d electrons titanium atoms in the Hartree-Fock approximation for the Hubbard model, have been performed. It has been found that the effective electron mass in rutile is anisotropic and there are both light (m _e ^* = (0.6–0.8)m ₀, where m ₀ is the free-electron mass) and heavy (m _e ^* > 1m ₀) electrons, whereas holes in rutile are only heavy (m _e ^* ⩾ 2m ₀). It has been shown that the σ-GGA + U method gives a deep occupied level in the band gap and that an oxygen vacancy in rutile is an electron and hole trap.     

Determination of the neutron electric form factor from the reaction 3 He(e,e'n) at medium momentum transfer

The electric form factor of the neutron G_En has been determined in double polarized exclusive ³ He(e,e'n) scattering in quasi–elastic kinematics by measuring asymmetries A _⊥, A _∥ of the cross section with respect to helicity reversal of the electron, with the nuclear spin being oriented perpendicular to the momentum transfer q in case of A_⊥ and parallel in case of A_∥. The experiment was performed at the 855 MeV c. w. microtron MAMI at Mainz. The degree of polarization of the electron beam and of the gaseous ³ He target were each about 50%. Scattered electrons and neutrons were detected in coincidence by detector arrays covering large solid angles. Quasi–elastic scattering events were reconstructed from the measured electron scattering angles ϑ_e, φ_e and the neutron momentum vector p _n ^′ in the plane wave impulse approximation. We obtain the result <G _En>_{(0.27 < Q2c2/GeV2 < 0.5)}= 0.0334 ± 0.0033_stat± 0.0028_syst which is averaged over the indicated range of Q ², the squared momentum transfer. This G _En value is significantly smaller than measured from the D(e,e'n) reaction under similar kinematical conditions. To what extent final state interactions in ³He quench the G _En result is subject of calculations currently in progress elsewhere. Received: 29 April 1999     

Identification of lagrangian coherent structures in the turbulent boundary layer

Using Finite-Time Lyapunov Exponents (FTLE) method, Lagrangian coherent structures (LCSs) in a fully developed flat-plate turbulent boundary layer are successfully identified from a two-dimensional (2D) velocity field obtained by time-resolved 2D PIV measurement. The typical LCSs in the turbulent boundary layer are hairpin-like structures, which are characterized as legs of quasi-streamwise vortices extending deep into the near wall region with an inclination angle θ to the wall, and heads of the transverse vortex tube located in the outer region. Statistical analysis on the characteristic shape of typical LCS reveals that the probability density distribution of θ accords well with t-distribution in the near wall region, but presents a bimodal distribution with two peaks in the outer region, corresponding to the hairpin head and the hairpin neck, respectively. Spatial correlation analysis of FTLE field is implemented to get the ensemble-averaged inclination angle θ _R of typical LCS. θ _R first increases and then decreases along the wall-normal direction, similar to that of the mean value of θ. Moreover, the most probable value of θ saturates at y ⁺=100 with the maximum value of about 24°, suggesting that the most likely position where hairpins transit from the neck to the head is located around y ⁺=100. The ensemble- averaged convection velocity U _c of typical LCS is finally calculated from temporal-spatial correlation analysis of FTLE field. It is found that the wall-normal profile of the convection velocity U _c(y) accords well with the local mean velocity profile U(y) beyond the buffer layer, evidencing that the downstream convection of hairpins determines the transportation properties of the turbulent boundary layer in the log-region and beyond. Supported by the National Natural Science Foundation of China (Grant Nos. 10425207 and 10832001)     

| m | Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

The symmetry and |m| partial-wave analysis for two-dimensional (2D) Coulomb-scattering is investigated. As a function of energyE, the |m| partial-wave scattering amplitudef _|m|(θ) is analytically continuated to the, negativeE (complexk) plane, and it is found that the bound state energy eigenvalues (E<0) are just located at the poles off _|m|(θ) on the positive imaginaryk axis as is expected. In addition, as a function of |m|,f _|m|(θ) is analytically continuated to the complex |m| plane, the bound state energy eigenvalues are just located at the poles off _|m|(θ) on the positive real |m| axis.