Spin-dependent effects in inelastic scattering

The differential cross sections for the inelastic scattering of 10 MeV, 19.6 MeV, 30.4 MeV, 40 MeV and 49.35 MeV protons to the 2⁺ state (1.409 MeV) in ⁵⁴Fe and of 19.6 MeV protons to the 2⁺ state (0.846 MeV) in ⁵⁶Fe are analyzed in conjunction with the available data on the asymmetries and spin-flip probability amplitudes. The scattering amplitudes for both one step (valence plus core polarization) and two step (intermediate resonance) processes are evaluated using an antisymmetrized distorted wave approximation. Collective model representations for both the one step (core polarization) and two step (intermediate resonance) processes are used, and included are the effects of deforming the full Thomas spin-orbit potentials. The one step processes are fixed by the analyses of the scattering of 30.4, 40 and 49.35 MeV protons, with the core polarization contributions being constrained by the B(E2) values for the γ-ray deexcitation of the 2⁺ states. The analyses of the 19.6 MeV data demonstrates the need for an extra (two step) contribution to the reaction process and are consistent with the virtual formation of an L = 3 giant resonance. The 10 MeV data most certainly demonstrate compound nucleus effects but could also have some strength due to the virtual formation of an intermediate L = 2 giant resonance. The resonance parameters are consistent with recent information concerning the mass variation of giant resonances.     

Current and constituent quarks: Their implications for resonance excitations polarized and unpolarized inelastic structure functions

The transformation between constituent and current quarks is discussed and applied to the calculation of matrix elements for nucleon to resonance transitions induced by arbitrary currents belonging to an octet. In particular, previous results on πN and γN transitions are subsumed while weak interactions (ΔQ = 0 or 1) and longitudinal photon induced transitions are discussed for the first time. The implications of a non-trivial Melosh transformation upon previous calculations in quark parton models of the non-diffractive component of the deep inelastic structure functions are discussed. The magnitudes of the unpolarized structure functions are found to be unchanged but for the polarized structure functions significant corrections to previous calculations are discovered. In particular it is found that it is not necessary that the polarization asymmetry A^γP be positive in the deep inelastic region. Our approach is valid for all Q², even for photoproduction, and is not restricted to deep inelastic scattering in contrast to earlier parton model calculations. The saturation of various current algebra sum rules is discussed.     

Possible mesonic effects on inelastic proton scattering to the 10.24 MeV 1+ state in 48Ca

Differential cross sections and analyzing powers were measured for inelastic scattering of 160 MeV protons to the ⁴⁸Ca 10.24 MeV, 1⁺ state. DWIA calculations with shell-model wave functions which fit inelastic electron scattering form factors predict too much cross section at small q and too little at large q for inelastic proton scattering. These results are consistent with the q-dependent modification of magnetic transitions anticipated from mesonic effects such as virtual Δ(1232)-hole excitations.     

Longitudinal and transverse contributions to the threshold cross-section slope of single-pion electroproduction by a proton

The cross sections of inelastic electron scattering are measured near the threshold of single-pion production by a proton at k²=2.5, 3.5, 5.0 and 8.0 fm^? in the polarization range of the virtual photon ?=0.3–0.9. The separation of the |E₀₊|² and k²|S₀₊|² contributions to the cross-section slope at threshold is carried out and thus a new method of determining the F_A and F_π form factors is realized. The values for the axial mass and mean-square radius of the pion are obtained.     

Determination of nuclear parameters by inelastic electron scattering at low-momentum transfer

The second-order Born-approximation treatment of Cutler and Schucan was applied to inelastic electron scattering data on ⁶Li, ⁶⁰Ni, and ¹¹⁴Cd acquired at low momentum transfers. The form factors as a function of momentum transfer q in the range of 0.25–0.57 fm^?1 were obtained by angular distribution measurements performed at incident energies of 30 to 60 MeV. The correlation between two parameters deduced from the measurements, the reduced transition probability B(E2↑) and the transition radius R⁽²⁾_tr, is discussed. It is suggested that inelastic electron scattering data at low-q is best used either in conjunction with an accurate value of B(EL↑) (available from the model-independent analysis of “photon” experiments at zero momentum transfer) to allow accurate determination of R⁽²⁾_tr, or in conjunction with high-q inelastic electron scattering data to allow accurate determination of B(EL↑) as well as R⁽²⁾_tr.     

Refractive scattering and the nuclear rainbow in the interaction of12, 13C with12C at 20MeV/N

The elastic and inelastic scattering and the neutron transfer have been measured for the systems¹²C +¹²C and¹³C +¹²C at 20MeV/N up to θ_cm= 60° with theQ3D -spectrometer. The angular distributions of the elastic scattering show an enhanced cross section at angles larger than 40°. It can be identified as refractive scattering with the clear signature of a nuclear rainbow.L-cut-off calculations show that these contributions come fromL-values which are significantly lower than the grazingL-value. The deflection function has a broad minimum in thisL-range which is typical for rainbow scattering. TheS-matrix is decomposed by a phenomenological parametrization into a refractive and a diffractive part. The interference of these amplitudes plays an important role in the rainbow enhancement. The spatial localization of the refractive scattering is deduced from the turning points of the corresponding trajectories; a localization between 2.5 fm and 4 fm is found. Semi-classical calculations with complex trajectories in the single-turning-point approximation show good agreement with the quantummechanical calculations. Refractive contributions are not observed in the inelastic scattering. This can be explained by reducing the strength of the conventional collective form factor in the internal region. In contrast to this the enhancement at large angles is seen in the one-neutron transfer channels where the refractive scattering is dominant. This is the first observation of such contributions to heavy-ion transfer reactions.     

Selective Reflection of Potassium Vapor Nanolayers in a Magnetic Field

The selective reflection of laser radiation from the interface between a dielectric window and the atomic vapors confined in a nanocell of thickness L ≈ 350 nm is used to develop effective Doppler-broadening- free spectroscopy of potassium atoms. A small atomic line width and a relation between the signal intensity and the transition probability allowed us to resolve four lines of atomic transitions responsible for the D1 lines of the ³⁹K and ⁴¹K isotopes. Two groups containing four atomic transitions form in an applied magnetic field upon pumping by radiation with circular polarization σ⁺ or σ^–. Different intensities (probabilities) of transitions for the σ⁺ and σ^– excitations are detected in magnetic field B₀ ≈ A _hfs /μ_B ≈ 165 G (A _hfs is the magnetic dipole constant for the ground state and μ_B is the Bohr magneton). A substantially different situation is observed at B ? B₀, since high symmetry appears for the two groups formed by radiation with circular polarization σ⁺ or σ^–. Each group is the mirror image of the other group with respect to the frequency of the 4²S_1/2–4²P_1/2 transition, which additionally proves the occurrence of the complete Paschen–Back regime of the hyperfine structure at B ≈ 2.5 kG. A developed theoretical model well reproduces the experimental results. Possible practical applications are described. The results obtained can also be applied to the D₁ lines of ⁸⁷Rb and ²³Na.     

Electron scattering from trans 1,3-butadiene molecule: cross-sections, oscillator strength and VUV photoabsorption cross-sections

Electron energy-loss spectra for the butadiene molecule were measured in the scattering angular range of 2.0° to 8.0°, in an energy-loss range from 2 to 50 eV, using 1000 eV incident electrons. The absolute generalized oscillator strength (GOS) and inelastic cross section have been determined for the \hbox{$\tilde{\rm X}^{1}$}?X1A _g  → 1¹B _u transition. The absolute elastic differential cross section was also determined spanning an angular range from 2.0° to 40.0°. From a small angle electron energy-loss spectrum, the optical oscillator distribution (photoabsorption spectrum) for the butadiene molecule was obtained in the 2 to 100 eV photon energy range. Accurate ab initio calculations have been performed, within the First Born Approximation, for generalized oscillator strength (GOS) and excitation energies for the \hbox{$\tilde{\rm X}^{1}$}?X1A _g  → 1¹B _u and \hbox{$\tilde{\rm X}^{1}$}?X1A _g  → 2¹A _g transitions. Our results emphasize the importance of using highly correlated wavefunctions and accurate methodologies in the calculation of the GOS for electron impact-induced electronic transitions in molecules.     

Dynamic deformation of light nuclei in excited states

An important property—the dynamic deformation of B* light aligned nuclei—is investigated for the nuclear reactions A(x, y)B* → γ + B ₀ by measuring the y-γ correlations. Dynamic deformation is determined from the orientation tensors of multipolar moments. Normalization constants of the contributions from even-rank orientation tensors are determined from the condition of coincidence between dynamic and static deformations of the B* nucleus for θ _y = 0°. Experimental dynamic deformations of ¹²C(2⁺) nuclei caused by the inelastic scattering of α particles and deuterons are determined, along with the ¹⁰Be(2⁺) nuclei formed in reaction ⁹Be(d, p)¹⁰Be(2⁺). It is shown that the dynamic deformation of the aligned nuclei depends on how they are formed and their structure, and evolves substantially when the angle θ _y is varied.     

Folding-model analysis of elastic and inelastic α-particle scattering using a density-dependent force

A folding model with a density-dependent form of the semi-realistic M3Y effective interaction is applied to α-particle scattering. A previous analysis of elastic scattering at 140 and 172 MeV is now applied to data at other energies from 25 to 120 MeV. The model is also extended to inelastic scattering, using both the collective model and a valence-plus-core-polarization model for the transition densities. The proton transition densities were normalized to measured B(EL) values. When necessary, the neutron transition densities were rescaled to fit the (α, α′) data, providing a source of information on the neutron contributions. The neutron transition multipole moments thus obtained are compared to those derived from (p, p′) data at 800 MeV, as well as from other sources.     

Transverse single spin asymmetry measurements at STAR

Transverse single spin asymmetries A _N are expected to be sensitive to par-ton polarization and orbital angular momentum contributions to the nucleon spin. Significantly large A _N has been observed in different collision systems such as semi-inclusive deep inelastic scattering (SIDIS) and polarized proton-proton (pp) collisions, indicating a dominant contribution of partonic interactions in the non-perturbative regime. Therefore it’s critical to measure A _N in various channels of polarized pp collisions in order to complement SIDIS data and to constrain theoretical models. We report STAR asymmetry measurements on mid-rapidity hadron-jet and di-hadron correlations at √s = 200 GeV and forward rapidity inclusive hadron production at √s = 500 GeV polarized pp collisions.     

Systematics of vector meson-proton scattering

The systematics of Vp scattering (V = ?, ω, φ, ψ) is studied using unitarity to relate the elastic and inelastic amplitudes. Assuming that φ and ψ are pure strange and charmed quark states, respectively, φp and ψp elastic amplitudes are shown, in the first approximation, to be generated by diffractive inelastic states. This leads to the relations B_ψ ≈ B_φ ≈ B_ω/2 ≈ B_?/2 for the elastic differential cross section slopes. The approximate m_V² is related to a similar suppression in inelastic Vp cross sections and, more speculatively, to the m_A² suppression of the hadronic production cross sections σ(pp → A).     

Effects of new neutral currents at linear electron-positron colliders

Effects that are induced by contact four-fermion interactions in the processes e ⁺ e ^? → μ ⁺ μ ^?, $\bar bb$ , and $\bar cc$ at $\sqrt s = 0.5$ TeV linear electron-positron colliders are investigated for the case of longitudinally polarized initial beams. This analysis employs new integrated observables constructed from the polarized cross sections for the scattering of final fermions into the forward (σ _F) and the backward (σ _B) hemisphere in such a way that they single out the helicity cross sections for the processes in question. This property of the observables makes it possible to perform, in the most general form, a model-independent analysis of contact four-fermion interactions and to set constraints on their parameters. It is also shown that the sensitivity of new polarization observables to contact interactions is noticeably higher than the corresponding sensitivity of canonical observables like σ, A _FB, A _LR, and A _LR,FB.     

Tensor interactions and polarization phenomena in heavy-ion scattering

Elastic and inelastic scattering of ⁷Li by ⁵⁸Ni at E_lab = 14.2 and 20.3 MeV is investigated theoretically, special emphasis being laid on polarization phenomena. A parameter-independent study shows second-rank tensor interactions to be the main origin of tensor analyzing powers for both elastic and inelastic scattering. Coupled-channel (CC) calculations using cluster-folding interactions which include the tensor terms are found to be successful in reproducing the data for cross sections and vector and tensor analyzing powers, when projectile excitation effects are sufficiently taken into account. Scattering of ⁶Li by ⁵⁸Ni at E_lab = 20.0 MeV is also investigated by the CC calculation, where successes similar to the ⁷Li case are obtained in understanding experimental data.     

Nucleon scattering analysis from90,92,594Zr and isospin decomposition of transition matrix elements for low-lying collective transitions

Simultaneous analysis of neutron and proton inelastic scattering to low-lying collective states in^{90, 92, 94}Zr are used to derive an isospin decomposition of the corresponding transition matrix elements. The deduced (M _n/M_p) ratios for the strongest transitions are in sharp disagreement with values derived from Coulomb-nuclear interference observed in 35.4 MeV inelastic α-scattering from even Zr isotopes.     

The 90,92Zrd(p,p′) reactions at Ep = 800 MeV+

Angular distributions of analyzing powers and differential cross sections have been measured for elastic and inelastic scattering of 800 MeV protons from ⁹⁰Zr and ⁹²Zr. The data have been interpreted using both the collective-model distorted-wave Born approximation and the semimicroscopic distorted-wave impulse approximation with the Love and Franey t-matrix. Clear differences in the data for transitions to both the 2⁺₁ and the 4⁺ states in the two nuclei, attributable to differences in the microscopic structures of the states, have been observed. These differences are only partially explained by the semimicroscopic analyses. Interpreting the A_y data with the help of recent data-to-data relations suggests that the free L · S interaction used at 800 MeV is incorrect.     

A study of coupled-reaction channel effects in the36S +37Cl system,hybridization between single particle orbits

Elastic and inelastic scattering as well as transfer transitions involving a valence proton in thesd- andfp- shell orbits are studied in the interaction of³⁷Cl +³⁶S at E_CM=50 MeV. Experimental angular distributions of single particle states of³⁷Cl (elastic and inelastic transfer) are presented with a CRC analysis. In the CRC calculations the effects of inelastic and transfer couplings are studied using known spectroscopic information. In the CRC analysis six single particle bound states and the collective 2⁺ excitation of³⁶S are included in the coupling scheme. Higher order coupling effects are found to be important. A distinct effect, the mixing of single particle states (of different parity) due to direct and transfer interactions is observed to produce an enhancement of the transfer cross section to the low lying states. This feature is due to a change of the asymptotically defined single nucleon orbits via polarization in the field of the other nucleus, an effect which is analogous to hybridization, known from atomic physics.     

Distinguishability ofSU(2)×U(1)×U′(1) andSO(10) gauge models from the Weinberg-Salam model

The predictions ofSU(2)×U(1)×U′(1) andSO(10) gauge models for the asymmetry parametersA-,B-,C _L andC _R in the deep inelastic scattering of polarized electrons and positrons by unpolarized protons and deuterons are compared with those calculated in the Weinberg Salam model for different values ofy. The model based on,SU(2)×U(1)×U′(1) group has been found almost indistinguishable from the Weinberg Salam model with regard to the parametersA-,B- andC _L (except forB- in the region 0≦y≦0.2) althoughC _R exhibits marked distinguishability. TheSO(10) model, for certain choice of its model parameters, can be distinguished from the Weinberg Salam model through measurement of the asymmetry parameters for different values ofy.     

F L structure function and heavy quark contributions

In this paper we obtain the heavy-quark contribution to the longitudinal structure functions F _L (x, Q ²). Since F _L structure functions contains rather large heavy flavor contributions in the small x region, we need to use the massive operator matrix elements, which contribute to the heavy flavor Wilson coefficients in unpolarized deeply inelastic scattering in the region Q ²?>?>?m ². The method of QCD analysis, based on the Jacobi polynomials method, is also described. Our results for longitudinal structure function are in good agreement with the available experimental data.     

Polarized Fluorescence of Jet-Cooled indole and Carbazole and Their Complexes with Water

The spectra of the fluorescence excitation within the rotational contours of the bands of the pure electronic long-wavelength S ₀-S ₁ transitions of jet-cooled indole and carbazole molecules and their complexes with water are measured. For the carbazole-water complex, a contour with three maxima is registered, which is possibly related to the occurrence of two isomers, differing in a slight displacement of hydrogen between the nitrogen atom of the imine group of carbazole and the oxygen atom of the water molecule. The degrees of polarization of integral fluorescence upon excitation within the rotational contours of the S ₀-S ₁ electronic transition bands of the above molecules and their complexes with water are determined for the first time. The coincidence of the calculated (7.7%) and measured (7.3%) values of the degree of polarization upon excitation in the rotational Q branch of the ^b L ₁-A electronic transition of indole confirms the accepted intramolecular orientation of the transition dipole moment at an angle of 38.3° with respect to the principal axis of inertia A. Upon excitation of indole, its complex with water, and carbazole into the P and R branches, the measured and calculated degrees of polarization are also close to each other and amount to 2–3%. This confirms the occurrence of contributions to the fluorescence polarization due to the rotations of the indole molecules around the principal axes of inertia A and C.