Magnetic elastic electron scattering from 3Be and 13C

Elastic scattering through 180° from ⁹Be, ¹²C and ¹³C targets has been observed for electrons of 35 to 90 MeV. Magnetic scattering cross sections for ⁹Be and ¹³C have been obtained by subtracting charge scattering as deduced from the scattering from the spin-zero nucleus ¹²C. Theoretical shell model predictions for the magnetic cross sections are derived for (1s)⁴(1p)^A?4 configurations and various coupling schemes. Both harmonic oscillator and Woods-Saxon radial wave functions are used. A comparison of our results with magnetic cross sections calculated in DWBA yields magnetic rms radii $\text{〈r}{}^2\text{〉}{}_{\mathrm{<mtext>M</mtext>}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 3.2 ± 0.3}\text{fm}$ and $\text{〈r}{}^2\text{〉}{}_{\mathrm{<mtext>M</mtext>}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 3.3 ± 0.3}\text{fm}$ for ⁹Be and ¹³C. For ¹³C a combined flt to our low-q data and to earlier high-q data, yields $\text{〈r}{}^2\text{〉}{}_{\mathrm{<mtext>M</mtext>}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 3.4 ± 0.1}\text{fm}$ and a strong preference for intermediate coupling (IC) wave functions. Magnetic dipole scattering from ⁹Be is also close to the IC prediction, as deduced from a fit to our data and earlier high-q data. The fitted value of the octupole moment $\text{Ω = 5±1 μ}{}_{\mathrm{<mtext>N</mtext><mtext>fm</mtext>}}{}^1$ can only be explained by a deformation of the average nuclear potential. The radial size $\text{〈r}{}^2\text{〉}{}_{\mathrm{<mtext>1</mtext><mtext>p</mtext>}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 2.85 ± 0.05}\text{fm}$ for the 1p radial wave function is in agreement with both the ⁹Be and ¹³C data.     

Polarized deuteron elastic scattering from a polarized proton target

Measurements are reported of the spin correlation parameter C_y,y for the elastic scattering of 10.0 MeV vector polarized deuterons from a polarized proton target at five CM angles (76°, 85°, 98°, 115°, 132°). The experimental results are compared with different predictions. A Faddeev type calculation on the basis of local potentials also including approximate Coulomb distortion is favoured by our experimental results.     

Microscopic potentials for polarized triton elastic scattering

The double folding model is used to calculate real central and spin-orbit potentials for triton elastic scattering. These potentials are used to fit cross sections and analysing powers at 17 MeV for targets ranging from ²⁶Mg to ²⁰⁸Pb. For most targets the data are described as well as with phenomenological potentials. The real central potential can be used without any substantial renormalisation, but the spin-orbit potential needs to be increased in strength by a factor between 2 and 6. Comparisons are made with phenomenological studies of triton and ³He elastic scattering and with similar microscopic studies of ³He scattering.     

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.     

Nearside-farside analysis of elastic scattering of polarized 3He

An exact decomposition of the scattering amplitudes into the nearside and farside components has been performed for the elastic scattering of 33 MeV ³He particles by nuclei. Calculations have been carried out for ⁴⁰Ca, ⁵⁴Fe, ⁸⁹Y, ^90,91Zr, ^207,208Pb and ²⁰⁹Bi and compared with the available cross section and polarization data. In particular the behaviour of the vector analysing powers is examined. Calculations of the interference between the nearside and farside components demonstrate that the interference plays a significant role in certain mass/energy regions. Regions where the scattering is dominated by the nearside component are discussed.     

Microscopic spin-orbit potentials for polarized 3He elastic scattering

The M3Y double folding model is used to calculate real central and spin-orbit potentials for ³He elastic scattering. These potentials are used to fit cross sections and analysing powers at 33 MeV for targets ranging from ¹⁶O to ⁵⁸Ni. The real central potential needs a normalization factor of about 0.85, but no change in the strength of the spin-orbit potential is necessary. Comparison is made with phenomenological and other microscopic studies of ³He elastic scattering.     

Virtual breakup effects in elastic scattering of polarized deuterons

Elastic scattering of polarized deuterons at E_d = 56 MeV is investigated for ¹⁶O, ⁴⁰Ca, ⁵⁸Ni, ¹¹⁸Sn and ²⁰⁸Pb target nuclei by the use of folding interactions. Effects of virtual breakup of the deuteron to S- and D-states in the continuum region are taken into account by the CDCC method and are found to make indispensable contributions to cross sections and analyzing powers, where continuum-continuum couplings are substantial. The contribution of the D-state admixture in the ground state is important for the tensor analyzing powers. The calculated results agree well with experimental data. The invariant-amplitude method and the second-order sum rule study clarify the characteristic feature of the spin dependence of the effective interactions due to the virtual breakup. The near-side/far-side decomposition of scattering amplitudes illuminates the difference of the reaction mechanism between light and heavy target nuclei. The investigation for the ²⁰⁸Pb target at E_d = 21.5 MeV gives important information on the energy dependence of the effective interactions. The use of different parameter sets for the input nucleon-target optical potentials shows that the detailed results depend significantly on the choice of the parameter sets.     

Vector analyzing power of polarized deuterons in elastic scattering

Isotope dependence of vector analyzing powers of polarized deuterons in elastic scattering off Se targets is discussed by optical-model and coupled-channel calculations. Attention is particularly directed to relations between analyzing power and imaginary potential.     

CO elastic scattering

Elastic scattering data of ¹⁶O¹²C are analysed by the Feynman graphs techniques. Comparisons with the experimental results are satisfactory.     

Violation of P- and T-symmetries in polarized neutrino-proton elastic scattering

Analytical expressions are obtained and studied for the angular distributions of the recoil protons and spin asymmetries of elastic electroweak scattering of neutrinos on polarized/unpolarized proton targets with account of the C-, P- and T/CP-symmetries violating anapole and electric dipole moments, along with the neutral weak form factors of a proton and the neutrino charge radius and magnetic moment.     

Violation of P- and T-symmetries in double polarized elastic electron-proton scattering

Analytical expressions are obtained for the differential cross section and right-left asymmetry A _RL ^γ,γZ of the process of elastic scattering of longitudinally polarized electrons from a polarized proton target with account of anapole and electric dipole moments, and the neutral weak electric, magnetic and axial form factors of a proton violating the C, P- and T/CP invariance. Contributions from the P and T odd spin correlations to asymmetry A _RL ^γ,γZ are studied as a function of the electron energy, scattering angles, and the proton form factors.     

T-odd correlation in muon neutrino elastic scattering on polarized proton target

In this paper, we analyze the elastic scattering of the muon neutrino (_νμ${\nu }_{\mu }$) beam on the polarized proton target (PPT) in a presence of induced couplings, and predict how the existence of relative phases between the complex vector (weak magnetism) and axial (induced pseudoscalar) form factors of the proton with left-chirality _νμ${\nu }_{\mu }$ affects the azimuthal dependence of the differential cross section. The neutrinos are assumed to be Dirac fermions with non-zero mass and CPT symmetry is conserved. We show that the azimuthal asymmetry of recoil protons depends on the neutrino mass, but contributions are very tiny (∼10⁻⁵$\sim {10}^{-5}$). Analysis of the differential cross section in the case of pure vector and axial couplings at zero _νμ${\nu }_{\mu }$ mass limit and zero momentum transfer shows that the T-violating phase _βVA${\beta }_{\mathit{VA}}$ generates the T-odd, P-even triple correlation and it could be detected by measuring the asymmetry between the (0,π)$(0,\pi )$ and (π,2π)$(\pi ,2\pi )$ angles. It should be clearly stressed that the considered T-odd observable is not a genuine CP-violating quantity as it can also be produced by the T-invariant contributions due to the final state interactions (FSI). Their magnitude must be precisely estimated and subtracted from the measured observable to extract information on the possible time reversal violation (TRV). We also indicate the possibility of using the PPT in the neutrino telescope.     

Levels in 13N examined by 12C p elastic resonance scattering with thick target

The elastic resonance scattering of 12C p has been studied in inverse kinematics via a novel thick target method at GIRAFFE facility of HI-13 tandem accelerator laboratory, Beijing. The recoil protons were measured by a △E-E counter telescope based on a large area double-sided silicon strip detector at laboratory angles around θ0 = 15°. The excitation function for 12C(p,p) elastic scattering has been obtained over a wide energy range of Ec.m.=0.31—3.45 MeV, which was explained quite well by the R-matrix calculation with known resonance parameters of the first three levels in 13N nucleus. Thus it is demonstrated that the present setup can be directly applied to the study of elastic resonance scattering with secondary radioactive beams.     

Polarized electron scattering on spin zero and polarized spin-1/2 targets: Deep inelastic scattering,elastic electron-muon scattering,and elastic electron-nucleon scattering

A covariant formulation is developed and used to derive cross sections for the analysis of experiments in which polarized electrons (muons) are scattered from spin-zero and from polarized spin-1/2 targets. The analysis is based upon the single virtual photon representation of the electromagnetic interaction, initially, neither high-energy nor low-energy approximations are made so that one may derive results in which the orientation of the polarization vectors of the interacting particles changes as a result of the scattering. The general formulation is valid for all polarization configurations for the electron and nucleon in deep inelastic scattering, and for all polarization configurations for the initial and final state particles in elastic scattering. From the general covariant results, specific cross sections are derived for deep inelastic scattering as well as elastic scattering of electrons on muons, nucleons, and spin zero targets. In the latter case, the actual polarization vector for the scattered electron is determined. In the other cases discussed, this vector may be obtained from the cross sections. In addition, a method is presented for defining covariant cross sections, and this method is used to obtain results in the center-of-mass system as well as the laboratory system. Furthermore, explicit cross sections for virtual photon absorption are derived. Finally, in the appendices, an alternative method for the evaluation of traces is given as well as a discussion of the relativistic limit.     

65 MeV polarized proton elastic scattering and the effective two-body interaction range

Elastic scattering of polarized protons from sd and fp shell nuclei has been studied with high-purity germanium detectors. The mean square radius of the central real part of the fitted optical potential was found to be of the form $\text{a}\text{+}\text{bA}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$. Comparison with the radius from electron scattering gives the range of the effective two-body interaction and its A dependence as $\text{〈}\text{r}{}^2\text{〉}{}_{\mathrm{d}}\text{=(4.5±0.4)+(0.16±0.03)}\text{A}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{fm}{}^2$.