The analysing powers iT11, T20, T21 and T22 in deuteron-deuteron elastic scattering between 6 and 11.5 MeV

The angular distributions of the analysing powers iT₁₁(θ), T₂₀(θ), T₂₁(θ) and T₂₂(θ) of the elastic scattering of polarized deuterons on deuterons have been measured at deuteron energies of 6.0, 8.0, 10.0 and 11.5 MeV. The vector component has small but non-zero values which change sign between 6.0 and 10.0 MeV. The tensor components have increasing values with increasing energy. The results are discussed in respect of resonances in ⁴He and a term scheme is proposed for a complete phase-shift analysis.     

Investigation of the 6Li(d, α)4He reaction between 1.5 and 11.5 MeV

The differential cross section σ₀(θ) and the analysing powers T₁₁(θ), T₂₀(θ), T₂₁(θ) and T₂₂(θ) of the reaction ⁶Li(d, α)⁴He have been measured for twelve energies between 1.5 and 11.5 MeV at c.m. angles between 3.5° and 90°. The results were fitted with Legendre polynomials. The energy dependence of the resulting coefficients indicates resonance-like behaviour at several energies corresponding to excitation between 22 and 32 MeV in ⁸Be. The reaction ⁶Li(d, α)⁴He shows excellent features as an analyser for deuteron vector and tensor polarization over the whole energy range investigated.     

Electromagnetic form factors for nucleons and pions at positive and negative q 2 in the model of quark-gluon strings

The electromagnetic form factors for pions and nucleons are considered within the model of quark-gluon strings, where the momentum-transfer dependence of hadronic form factors is determined by the intercepts of the corresponding Regge trajectories and by the Sudakov form factor. Analytic expressions found for form factors in the timelike region admit an analytic continuation to the spacelike region. The resulting form factors for pions and nucleons comply well with experimental data both for positive and for negative values of the squared momentum transfer q ². It is shown that the distinctions between the absolute values of the pion and nucleon form factors F _π(q ²), G _m (q ²), and F ₂(q ²) at positive values of q ² and those at negative values of this variable are associated with the analytic properties of the double-logarithmic term in the exponent of the Sudakov form factor. The spin structure of the amplitudes for quark transitions into hadrons that is proposed in the present study makes it possible to describe fairly well available experimental data on the Pauli form factor F ₂ and on the ratio G _e /G _m .     

ωNN vertex function and the γπππ anomaly

We show that the empirical ωNN form factor (cut-off 1400–C1500 MeV) can be understood as arising from a combination of a quark model form factor (typical cut-off 700–C800 MeV) and an anomalous form factor ～ q ² arising from the 3π-intermediate state. The anomaly contributes to the Dirac form factor F ₁(q ²) with F ₁(0) = 0, (and sizable), and to the Pauli form factor F ₂(q ²) with F ₂(0) ≠ 0. The resulting tensor coupling F2(0) is sensitive to the cut-off of the pion momenta in the two-loop integrals and turns out to be small for values around 1 GeV. The quark model ωNN tensor coupling F ²(0) vanishes for point-like quarks. The anomaly, however, contributes a non-vanishing tensor coupling which can be seen to effectively enhance the vector coupling in NN models which do not include a tensor coupling.     

Form factors,threshold relations,and large angle elastic scattering of pions

The form factor F(q²) of the pion in a simple core model is investigated, together with the deep inelastic electroproduction structure function, F₂(ω). A relation between these two, analagous to the Drell-Yan-West relation for nucleons, is derived and it is found that F₂ is related to either the form factor or the square of the form factor depending on how rapidly F(q²) ultimately falls with momentum transfer. The unitarity equation and its implications for this kind of threshold relation are discussed. The simple core model is also applied to elastic large angle ππ scattering.     

Non-equilibrium structure factor for the disordering of adsorbed monolayers

We consider the non-equilibrium, time-dependent elastic-scattering structure factor S(q,t), for the disordering of an ordered overlayer, initially in equilibrium at temperature T_I and characterized by the structure factor S(q,0)=x(q,T_I, upon a sudden increase in temperature T_I→T_F at constant coverage, such that the adsorbates equilibrate at T_F in a disordered phase. The initial decay of a peak in x(q,T_I) proceeds exponentially in time, $\text{exp}\text{(−}\text{t}\text{τ}{}_{\mathrm{q}}\text{)}$, where τ_q is a wavevector-dependent lifetime, before it crosses over to a power-law, t⁻¹ decay. When x(q,T_I) is peaked at the boundaries of the Brillouin zone (BZ), the peak approximately maintains its shape in q-space as it decays exponentially. Except near the center of the BZ, after the peak has decayed sufficiently, the dependence of S(q,t) on q is as though the spins quasi-equilibrate to the equilibrium structure factor associated with T_F, x(q,T_F), in that the ratio $\text{S(q,t)}\text{x(q,T}{}_{\mathrm{<mtext>F</mtext>}}\text{)}$ is independent of q, is dependent on time, approaching unity as t⁻¹ for large t. For systems exhibiting an initial peak for q ≈ 0, the peak decays exponentially but does not preserve its shape, since τ_q strongly depends on q, diverging as q⁻² for q→0. For these systems too, away from the center of the BZ, $\text{S}\text{(q,t)}\text{x(q,T}{}_{\mathrm{<mtext>F</mtext>}}\text{)}$ rapidly evolves to a slowly decaying function of $\text{t}\text{t}{}_{\mathrm{w}}$, independent of q. In this case, however, the characteristic time scale, t_w, is anomalously long, proportional to ξ², where ξ is the correlation length associated with the initial state. This behavior of t_w can be related to the random walk of domain boundaries.     

The deuteron wave function at short range and the triton

It is shown that if one assumes something between zero and the prediction of the scaling model with dipole fit for the neutron electric form factor, then a variety of short-range behaviour for the deuteron wave function is consistent with existing experimental data on the deuteron electric form factor. This still relatively wide latitude for the inner deuteron wave function, consistent with existing experimental electromagnetic data, gives rise to an off-shell variation of approximately 1.2 MeV in the triton binding energy with a fixed ¹S₀ interaction and a P_D varying from 4.5 to 6.5 %. Interactions with greater densities of matter at short range bind the triton more strongly and closer to the experimental value. An off-shell variation of 0.7 MeV is obtained with a fixed p_d and singlet interaction. However, a single measurement of the deuteron tensor polarization at about q² = 20 fm^?2 would severely restrict this variation.     

The differential cross section and polarization quantities in the 4He(d,p)n4He and 2H(α, n)p4He reactions

The differential cross section and the polarization quantities (T₁₁, T₂₀, T₂₁, T₂₂, P_γ') in the deuteron breakup reaction by an α-particle are calculated in the framework of the recently developed three-body model. All values are discussed under the incomplete kinematical condition. All polarization quantities are caused by the difference of the potential between $\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ waves of the N-α interaction. Results of the calculation are compared with the available measurement of (i) the differential cross section and the deuteron vector analysing power in the ⁴He($\text{d}$, p)n⁴He reaction and (ii) the differential cross section and neutron polarization in the ²H(α, $\text{n}$)p⁴He reaction. The agreement with experiment is very satisfactory in each case. Among the tensor analysing powers of the deuteron the absolute value of T₂₀ is very large. Observables at the FSI peak corresponding to ⁵He_g.s. are discussed systematically in the energy region of 5.4–20 MeV of the incident deuteron in the ⁴He(d, p)n⁴He reaction. Although the differential cross section is not sensitive to the energy of the three-body resonance, the polarization quantities T₁₁, T₂₀, P_γ' are quite sensitive to it.     

Target asymmetry and effective neutron polarization with polarized deuteron targets

A careful discussion is given of the definitions of “target asymmetry” and “effective neutron polarization” in the reaction $\text{d}\text{(γ,π}{}^{\mathrm{?}}\text{)2}\text{p}$ with polarized deuterons. The connection between the analyzing powers, T_q^k of the reaction and the target asymmetry, T is established taking into account the method of preparation of the polarized target. It is further shown that the concept of effective neutron polarization P_eff is valid only in a very approximate way, even when the target deuteron is purely vector polarized.     

Deuteron structure and diffractive deuteron-nucleus interaction

A nonrelativistic deuteron wave function involving the D-wave state and having a correct asymptotic behavior is constructed on the basis of the experimentally measured deuteron charge form factor G _C(q) and deuteron structure function A(q). The differential cross section for elastic deuteron-nucleus scattering is calculated by using this wave function and is found to agree with experimental data at an energy of 110 MeV. Integrated cross sections for various processes involving deuteron-nucleus interactions are also calculated. The distribution in the emission angle of the center of mass of the neutron-proton system produced in the diffractive dissociation of 110-MeV deuterons in the field of ²⁰⁸Pb nuclei is obtained.     

Constraints on the behaviour of the e+e− hadron annihilation cross section in asymptotically free theories and in theories with anomalous dimensions

A new approach is proposed to the problem of the relationship between the e⁺e^? hadron annihilation cross section and the behaviour of the hadronic vacuum polarization tensor Π_μν(q) in the space-like region. By using this approach based on the principles of functional analysis, one can uniquely transform the information about the behaviour of Π_μν(q) at q² → ?∞, which is available in asymptotically free theories and in theories with anomalous dimensions, into constraints on the e⁺e^? total cross section.     

Elastic electron deuteron scattering on a tensor polarized solid ND3 target

Elastic electron deuteron scattering has been measured at the Bonn 2.5 GeV electron-synchrotron using a tensor polarized ND₃ target. The scattered electrons and deuterons were detected in coincidence by two magnetic spectrometers. Data were taken at an average value of four momentum transfer ofQ ²=0.495 (GeV/c)² in order to separate the electric monopole and quadrupole form factors of the deuteron. To have a sufficient control of systematic effects, both polarized and unpolarized cross sections were measured with an identical experimental set up. In the ratioR _EXP=dσ_pol/dσ_unp systematic effects are expected to cancel. This ratioR _EXP is related to the theoretical polarized cross section d dσ _T where the spin quantization axis for the deuterons is orientated in the ed-scattering plane, perpendicular to the virtual photon direction. Our final result for the corresponding recoil tensor polarization ist ₂₀=?2.01±1.13.     

Bounds for Kℓ3 decay parameters

The extremum of the integral ∫^∞f(x) ‖F (x)‖² dx is determined for the case when the values taken by the function F (x)¹ at three points are known. The result is applied to the K_?3 problem, the function F (x) being replaced by the form factor f₊(q²)+f₋(q²)q²(m_K²−m_π²) of the divergence of the strangeness changing vector current.     

Experiments with internal targets at the VEPP-3 electron storage ring

An overview of the recently completed, current, and planned experiments with internal targets at the VEPP-3 electron-positron storage ring in Novosibirsk is given. The results of the experiment to separately measure the deuteron form factors in elastic ed scattering in the range of momentum transfer Q ² = 8?15 fm^?2 are provided. The results of measuring the tensor analyzing power components of the tensor-polarized deuteron photodisintegration reaction in the range of γ-quantum energies E _γ = 25?600 MeV are presented. The tensor analyzing powers of the coherent photoproduction of a neutral pion on a tensor-polarized deuteron have been measured for the first time. The almost-real photon tagging system being created is discussed. The status of the experiment under way to determine the contribution of two-photon exchange to the elastic ep scattering cross section is described.     

Resonant two-photon absorption in the Cr2O3 antiferromagnet

Two-photon absorption (TPA) spectra of the Cr₂O₃ model antiferromagnet have been studied for two polarization configurations at energies ranging from 2.5 to 3.55 eV. Several strong TPA peaks with the maximum coefficient β ～ 0.08 cm/MW are observed in the 2.7–3.1-eV range characterized by the ⁴ A ₂(F) → ⁴ T ₁(F) d-d one-photon transition of the Cr³⁺ ion. An analysis of the results obtained suggests that the general form of the TPA spectrum in this range is primarily determined by the resonance at the ² E(G) and ² T ₁(G) intermediate levels. At energies above 3.44 eV, the TPA coefficient sharply increases up to β ～ 0.1 cm/MW due to transitions between the valence and conduction bands.     

Optical absorption spectrum of Cr3+ ion doped in zinc cesium sulphate hexahydrate

Optical absorption spectrum of Cr³⁺ ion doped in zinc cesium sulphate hexahydrate single crystal has been studied both at room and liquid nitrogen temperatures. From the nature and position of the bands a successful interpretation of all the bands could be made assuming octahedral symmetry for the Cr³⁺ ion in the crystal. The observed bands are assigned to the transitions from the ground ⁴A_2g(F) state to the excited ²E_g(G), ²T_1g(G), ⁴T_2g(F) and ⁴T_1g(F) states.The crystal field parameters Dq = 1735 cm^?1, B = 635 cm^?1 and C = 4.75 B are found to give a good fit to the observed band positions.     

Observation of deuteron D-state and compound nucleus effects in (d,p) reactions on 46Ti and 52Cr with a polarized deuteron beam

The cross section and the vector and tensor analyzing powers have been measured for ⁴⁶Ti(d, p)⁴⁷Ti at deuteron energies of 6 and 10 MeV and ⁵²Cr(d, p)⁵³Cr at 6 MeV. Transitions were observed to the states at E_x=0.159, 1.549 and 1.793 MeV in ⁴⁷Ti and the states at E_x=0.0, 0.564, 1.006 and 2.321 MeV in ⁵³Cr. In addition, the cross sections and vector analyzing powers for deuteron elastic scattering were measured for the same targets and deuteron energies and compared to optical model calculations. The choice of optical parameters for the DWBA analysis of the (d, p) reactions is discussed. Calculations made with the DWBA method show that the deuteron D-state must be included to reproduce even qualitatively the (d, p) tensor analyzing power measurements. The j-dependence of the tensor analyzing power T₂₂ is discussed. The validity of the local energy approximation (which was used to incorporate the deuteron D-state into the DWBA calculations) is evaluated by comparison to finite range calculations. The contribution of compound nucleus reactions to the measured cross sections and analyzing powers was investigated. In order to determine the compound cross section, the Ericson fluctuations in excitation functions of cross section and vector analyzing power were measured from 5 to 7 MeV on each target. The formulas used to calculate the polarization observables from the Hauser-Feshbach theory are presented.     

Electron-electron interaction and instabilities in one-dimensional metals

The possible instabilities of a 1-dimensional itinerant electron gas are discussed, assuming electron-electron interaction to play the dominant role. As is well known, in the RPA, a 1-dimensional metal is prone to spin density wave (SDW), charge density wave (CDW) and Cooper pair (CP) instabilities. The spin channel decomposition of the irreducible scattering amplitude I is made and the spin channel projections are evaluated in terms of the matrix elements of bare electron-electron interactionV(x) for momenta of interest. It is found that if the bare electron interactionV(x) is repulsive and decreases monotonically with separation, only the SDW instability will occur. If the small separation (x?(2k _F )^?1) part of the interaction is greatly reduced or is made attractive,V(x) is non-monotonic,V _q (q?2k _F ) is negative, and a CDW instability is preferred. A CP instability is possible if the electron interaction is attractive,i.e., if [V _q (0<q<k _F )+V _q (q?2k _F )]<0. The above RPA results serve only as rough indicators, since in general there are important two-electron configurations with two-electron momentum close to zero and with electron hole momentum close to 2k _F , an example being the near Fermi energy configurationk ₁?k _F ,k ₂??k _F ,k ₃??k _F k ₄?k _F . Therefore as pointed out first by Bychkov, Gorkov and Dzhyaloshinskii (BGD), cross channel coupling is especially significant. It is shown that the cross channel coupling is constructive is some cases,eg., exchange of CD fluctuations leads to an effective electron-electron spin singlet attraction and vice-versa. A formalism for studying such effects is set up, and the particular example mentioned above is discussed. An RPA-like approximation is made for the form of the reducible singlet electron hole scattering amplitudeγ _s ^d and the resulting induced Cooper pair attraction is calculated to be $$\begin{gathered} [I_s ^e ]_{ind.} \rho _{{}^\varepsilon F} = [ln(\lambda \beta \omega _c )]^{ - 1} ln\{ [1 + 2\pi ^{ - 1} ln(\lambda \beta \omega _c )^2 ]/ \hfill \\ 1 + [8\pi ^{ - 1} \gamma _s ^d (q = 2k_F )^{ - 1} )^2 ]\} \hfill \\ \end{gathered} $$ where λ=1.14,β=(k _B T)^?1 andω ₀ is an electronic energy cut-off ～ε _F . The induced electron hole attraction due to the exchange of virtual Cooper pairs has a similar expression, but with a factor of (1/4) and withγ _s ^e (q=0) replacingγ _s ^d (q=2k _F ). The induced Cooper pair attraction is seen to be quite large over a broad range of temperatures close to but aboveT _CDW [i.e., aboveT such thatγ _s ^d (q=2k _F )^?1=0]. There is no requirement thatγ _s ^d (q=2k _F ) andγ _s ^e (q=0) become singular at the same temperature, as found by BGD. The BGD prediction is seen to arise from the neglect of real particle hole and particle-particle excitations while calculatingγ _s ^d andγ _s ^e . The effect of impurities, of electron-phonon coupling, of interchain coupling and of interaction between thermal order parameter fluctuations is discussed. The results are then applied to a discussion of the properties of TTF-TCNQ, where it is suggested that a CDW instability occurs becauseV _q (q=2k _F )<0,i.e., because the small separation electron repulsion is strongly reduced by the highly polarizable TTF. Because of substantial interchain coupling, the bulk CDW instability occurs close to the RPA instability temperature. The giant conductivity observed by Colemanet al is attributed to superconductive fluctuations in a 1-dimensional system with large mean field superconductive transition temperatureT _CP ^MF of order 300°K. Such a largeT _CP ^MF is shown to result from the induced Cooper pair attraction due to CD fluctuation exchange.     

Search for possible anapole and electric dipole moments of the proton on the basis of the pp ⇌ e+ e− annihilation reaction

Differential and total cross sections are found for the formation of an electron-positron pair during the annihilation of longitudinally polarized protons and antiprotons (pp e⁺ e^–) and for the inverse reaction (e⁺ e^- pp) in the single-photon approximation, account is taken of the anapole and electric dipole moments of the proton, which violate C, P, and T parity. Possible ways to determine the square moduli of the form factors for the anapole [G₁(q²)] and electric dipole [G₂(q²)] moments and to determine the relative phase of the form factors F_e(q²) and G₂(q²) [F_m(q²) and G₁(q²)] are pointed out. Estimates are found for ¦(G₁q²)¦² and ¦G₂(q²) ¦² with q² = –6.8 (GeV/c)².Translated from Izvestiya VUZ. Fizika, No. 8, pp. 59–65, August, 1970.The authors thank Professor A. A. Sokolov, Professor I. M. Ternov, and Yu. M. Loskutov for discussions of these results.