Elastic scattering of electrons by nuclei of half-integer spin and discrete symmetries

Analytical expression is obtained for the right-left asymmetry A _RL ^(3/2) for the process of elastic scattering of the longitudinally polarized electrons by nuclei with spin 3/2, described in the framework of Rarita-Schwinger formalism by invariant form factors of electromagnetic and weak vertex functions. It is shown, that this asymmetry directly depends on the nuclear anapole form factors G ₁ ⁽ⁿ⁾, and structurally is equivalent to asymmetry A _RL ^(1/2), which arises in electron scattering by proton.     

Recent STAR Spin Results and Spin Measurements at RHIC

The STAR experiment provides measurements of single and double-spin asymmetries in longitudinally and transversely polarized p + p collisions at \(\sqrt s \) = 200 and 510 GeV to deepen our understanding on the proton spin structure and dynamics of parton interactions over a wide range of collision energy, momentum and rapidity of the various produced probes. Polarized processes with W^± production allow us to study the spin-flavor structure of the proton. Recent results obtained by STAR on the double longitudinal asymmetry, A_LL, of pion and jet production at \(\sqrt s \) = 200 and 510 GeV, the single longitudinal, A_L, and transverse, A_N, asymmetry of W^± production at \(\sqrt s \) = 510 GeV are overviewed. STAR results on azimuthal single transverse asymmetry of pion in p^↑ + (p, Au) and jet + π^± in p^↑ + p collisions are discussed. The proposed Forward Calorimeter System (FCS) and Forward Tracking System (FTS) upgrades at STAR would significantly improve the capabilities of existing detectors for measurements of observables such as asymmetries of pion, jet, Drell-Yan pairs produced at forward rapidities.     

Spin physics at HERMES

The primary goal of the HERMES experiment is the study of the spin structure of the nucleon. Results on the measured inclusive and semi-inclusive hadron asymmetries using a polarized positron beam on polarized ³He, hydrogen and deuterium targets are here presented. In the covered kinematic range, 0.023<x _Bj <0.6 and 1 GeV²<Q ²<10GeV² the polarized quark distribution were determined for all up (u+?u) and down (d+?) quarks, and separately for valence and sea quarks. The up quark polarization is positive, and the down quark polarization is negative. The polarization of the sea is consistent with zero in the measured range. A first indication of a positive gluon polarization is presented, based on the measured spin asymmetry in the photo-production of hadron pairs with high transverse momentum p _T . This asymmetry is negative, which is in contrast to the measured positive asymmetry for inclusive experiments.     

Regge description of spin-spin asymmetry in photon diffractive dissociation

We explore the possibility to extract Δ(G(x) from a comparison of experimental data on the longitudinal spin-spin asymmetry A _LL in diffractive scattering of the heavy photon on the proton with calculations performed in perturbative QCD (pQCD). The data could be obtained at the HERA collider in scattering of polarized leptons off polarized protons. We have found a kinematic region where contributions to A _LL from soft processes are suppressed to guarantee an applicability of pQCD, hence the pQCD prediction can be reliably compared with data in this kinematic region.     

Formfaktor des π-Mesons und Struktur der Nukleonen

Recent measurements of electron-proton scattering at Stanford have shown that the electric and magnetic form factors are not equal. Therefore, the isotopic vector parts of the form factorsG _e ^v andG _m ^v are recalculated with unsubtracted dispersion relations in the 2π-approximation. For the isotopic scalar parts we useG _e ^s (s)≈G _e ^v (s) andG _m ^s (s)≈ 0 which is known to be valid for moderate energy-momentum transfers. We obtain a simple closed expression for the electromagnetic form factor of the pionF _π in terms of the scattering lengtha ₁ and the effective ranger ₁ of the π-π-scattering in the stateL=T=1.a ₁ is roughly known from pion production by pions. With this value and a suitabler ₁,F _π has a resonance in the region of time-like energy-momentum transfer; and the pion rms-radius becomes\(\overline {v_\pi ^2 } = (0.82 \times 10^{ - 13} cm)^2 \). The calculated anomalous magnetic moment, the electric and the magnetic rms-radii of the proton are then within 10% of the experimental values, the electric charge within 30%. Moreover, the proton form factors are different from each other and up to an energy-momentum transfer of\(s = \frac{{ - q^2 }}{{m_\pi ^2 }} = 23\) within the experimental error of the new measurements. The deviations for higher values of the energy-momentum transfer may be explained in terms of the isotopic scalar parts of the form factors. In this case the electric form factor of the neutron will be different from zero in that region and the magnetic form factor of proton and neutron will no longer be equal. For comparison with other experiments we also calculate the π⁺?π^? cross section with neglect of other states thanL=T=1. Under this assumption the π?π cross section has a resonance for low energy-momentum transfer.     

Polarimetry of the polarized proton and deuteron beams at intermediate energies

Method and results of the beam polarization measurements are presented. The measurements were carried out at the proton polarized beam of Saturne-II accelerator as well as at the JINR (Dubna) synchrophasotron vector polarized deuteron beam. The analysis of the elastic (quasi-elastic) pp-scattering polarization is used as a method of the polarization measurements. The energy range of the measurement is 1.0≤T _p ≤2.8 GeV for polarized proton and 1.66≤T _d ≤7.3 GeV for polarized deuteron beams.     

Physics results from HERMES

The Hermes experiment at the Desy laboratory in Hamburg, Germany, studies the spin structure of the nucleon. Its unique feature is the combination of a polarized internal gas target with the longitudinally polarized 27.5 GeV electron/positron beam of the Hera accelerator. Recent Hermes measurements include the proton spin structure function g ₁ ^p , the flavor decomposition of the polarized quark distributions in the nucleon, the DIS contribution to the generalized GDH sum rule, the first observation of a spin asymmetry in exclusive vector meson production and the first observation of a single-spin azimuthal asymmetry in semi-inclusive pion production. Additionally, the possibility of using various unpolarized gases as target material broadens the spectrum of physics measurements with Hermes.     

Theory of the muonic hydrogen-muonic deuterium isotope shift

Corrections of the α³, α⁴, and α⁵ orders are calculated for the Lamb shift of the 1S and 2S energy levels of muonic hydrogen μp and muonic deuterium μd. The nuclear structure effects are taken into account in terms of the charge radii of the proton r _p and deuteron r _d for one-photon interaction, as well as in terms of the electromagnetic form factors of the proton and deuteron for the case of one-loop amplitudes. The μd-μp isotope shift for the 1S-2S splitting is found to be equal to 101003.3495 meV, which can be treated as a reliable estimate when conducting the corresponding experiment with an accuracy of 10^?6. The fine-structure intervals E(1S)-8E(2S) in muonic hydrogen and muonic deuteron are calculated.     

Comparison of theK ± p scattering data with the forward dispersion relations

The dispersion relations forK ^± p forward scattering were evaluated in order to test the compatibility with the experimental data and to obtain an estimation of the effective coupling constantG ^2/4π=(G _Λ ² +G _Σ ² )/4π.     

Probable Decay Modes at Limits of Nuclear Stability of the Superheavy Nuclei

The modes of decay for the even–even isotopes of superheavy nuclei of Z = 118 and 120 with neutron number 160 ≤ N ≤ 204 are investigated in the framework of the axially deformed relativistic mean field model. The asymmetry parameter η and the relative neutron–proton asymmetry of the surface to the center (R _η ) are estimated from the ground state density distributions of the nucleus. We analyze the resulting asymmetry parameter η and the relative neutron–proton asymmetry R _η of the density play a crucial role in the mode(s) of decay and its half-life. Moreover, the excess neutron richness on the surface, facets a superheavy nucleus for β^? decays.     

Experimental Research to Confirm the Excitation of Gamov–Teller Resonance in Compound Nucleus <Superscript>118</Superscript>Sb

At proton energies of 4–9 MeV, trial experimental investigations were performed to confirm the excitation of Gamov–Teller resonance (GTR) 1⁺ in the compound nucleus ¹¹⁸Sb discovered by B.Ya. Guzhovskiy’s research group in the ¹¹⁷Sn(p,xn) reaction at proton energies of 7.2 MeV (the first component is GTR1) and 9.9MeV (the second component is GTR2). The ¹¹⁷Sn(p,xn) reaction was used, whose neutrons and background neutrons were registered by an all-wave long counter arranged at an angle of 140° to the direction of the proton beam propagation. Simultaneously, along with the registration of neutrons, elastically and inelastically scattered protons at angles of 20° and 160° were registered. At the proton energy equal to ~7.2 MeV, in the excitation functions for ¹¹⁷Sn(p,xn), ¹¹⁷Sn(p,p₀), and ¹¹⁷Sn(p,p₄)¹¹⁷Sn* (1004.5 keV, 3/2⁺), a resonance with a width of ≈1.2 MeV having an energy structure was discovered. Its possible quantum numbers are 1⁺.     

Constraints on nonsinglet polarized parton densities from the infrared-renormalon model

Using the infrared-renormalon approach, we obtain the constraints on the next-to-leading order nonsinglet polarized parton densities. The advocated feature follows from the consideration of the effect revealed in the rocess of the next-to-leading order fits to the data for the asymmetry of polarized lepton-nucleon scattering, which result in the approximate nullification of the 1/Q²-correction to A ₁ ^N (x, Q²).     

On the test ofT-invariance in elastic scattering of electrons from polarized deuterons

An additional (magnetic) form factor G₂ which violatesT-invariance is introduced in the electromagnetic vertex of the deuteron. This additional interaction yields a right-left asymmetry in the scattering of electrons from polarized deuterons. For our numerical evaluations we used values of G₂ which are consistent with the deviations from the impulse approximation found in measurements of the unpolarized cross section. A maximum asymmetry of approximately 40 percent was obtained at q=3.5 f^?1. However, care must be taken in the preparation of the polarized target, as a suitable tensor polarization may also produce asymmetry.     

PHENIX spin program,recent results

Acceleration of polarized protons in Relativistic Heavy Ion Collider (RHIC) provides unique tool to study the spin structure of the nucleon. We give a brief overview of the PHENIX program to investigate poorly known gluon and flavor decomposed see quark polarization in the proton, utilizing polarized proton collisions at RHIC. We report PHENIX first results on transverse single-spin asymmetry inπ ⁰ and charged hadron production and longitudinal double-spin asymmetry inπ ⁰ production at mid-rapidity.     

Raman scattering spectroscopy of inclusions of carbon in Al<Subscript>2</Subscript>O<Subscript>3</Subscript> films and its solid solutions with HfO<Subscript>2</Subscript>

We apply Raman scattering spectroscopy to study the nature of carbon inclusions in Al₂O₃ and (HfO₂) _x (Al₂O₃)_{1 ? x} films deposited using volatile complex compounds. Raman spectra of the films under investigation contain D and G vibrational modes, which indicate that carbon clusters of the sp ² configuration tend to form in the films. We estimate the size of clusters from the integrated intensity ratio I _D /I _G and find it to be in the range of 14–20 Å. The content of hydrogen in carbon clusters is calculated from the height of the photoluminescence pedestal and is found to vary from 14 to 30 at % depending on the regime of the film’s synthesis.     

Untersuchungen über den nichtresonanten Anteil der Li7 (p,γ)-Strahlung

The angular distributions of the 17,6 MeVγ-rays from the reaction Li⁷(p,γ) Be⁸ have been measured betweenE _p=0,4 MeV andE _p=0,65 MeV. The known strong asymmetry resulting from interference of the 441 keV-resonance radiation and the nonresonant radiation, and a cos² Θ-term, slowly increasing with energy have been observed. According to our results the nonresonant radiation is predominantly due tos-wave capture, but in addition to this a small contribution ofp-waves must be considered.     

Tensor asymmetry of π<Superscript>−</Superscript>-meson photoproduction on polarized deuterons

The tensor asymmetry of exclusive π^?-meson photoproduction on polarized deuterons was investigated. The T ₂₀ and T ₂₂ components of the reaction analyzing power contribute to the measured asymmetry. The detector made it possible to record two outgoing protons in coincidence in the range of polar angles θ_1,2 = 44° ? 88° and in the momentum range p _1,2 = 350 ? 700 MeV c ^?1. The measurements were performed at the VEPP-3 storage ring (Novosibirsk) using an internal target. The experimental results are compared with theoretical calculations.     

Angular correlation measurements in the Be9(d,p, γ)Be10 reaction

Thep-γ angular correlations in the Be⁹(d, p, γ)Be¹⁰ reaction have been measured in the reaction plane atE _d =1.3, 1.5, 1.9, 2.3 and 2.45 MeV for proton anglesθ _p =35°, 80° and 120°. The anisotropy of the angular correlations measured forθ _p =35° is independent of deuteron energy. A systematic shift of the symmetry axis from the recoil direction has been observed. The shift is 20.5° at E_d=2.45 MeV. The anisotropy decreases with increasing proton angle and vanishes atθ _p =120°.     

Relativistic Slater's integrals for theK andL shells

TheZ-dependent form of theSlater's integrals for electrons in theK andL shells is studied by expanding the relativistic hydrogenic radial wave functions in the manner explained byLayzer andBahcall. When screening is not taken into consideration, theseSlater's integrals can be put in the form AZ(1+a Z²) wherea is positive for all integrals considered except G¹(1s, 2p) and G²(2¯p, 2p). Values ofA anda are given.     

Single and double spin asymmetries in the elastic <Emphasis Type="Italic">e</Emphasis>-<Emphasis Type="Italic">d</Emphasis> scattering and their dependence on the deuteron wave function

Single and double spin asymmetries in the elastic electron-deuteron (e-d ) scattering were investigated. The tensor-deuteron asymmetries T_2i(i = 0, 1, 2) and the beam-vector-deuteron asymmetries T ^e _1i(i = 0, 1) were calculated and compared with the available experimental data. The sensitivity of the results for these spin asymmetries to the deuteron wave function has been investigated. The predicted asymmetries were found to be agree with one another and with experiment. It was found that, the double spin asymmetry T ^e ₁₀ is much smaller than the T ^e ₁₁-asymmetry. Therefore, in addition to the single tensor-deuteron asymmetry T₂₀, the doubly beam-vector-deuteron asymmetry T ^e ₁₁ can be used as an another tool for extracting the deuteron electromagnetic form factors.