Analyzing Power Data Research Articles

Cross section and analyzing power Ay in the breakup reaction 2H(p

Kinematically complete breakup cross section and proton analyzing power data for four different collinearity configurations (neutron at rest in the c.m. system) have been measured in the reaction [sup 2]H([ital [rvec p]],[ital pp])[ital n] at [ital E][sub [ital p]][sup lab]=65 MeV. The experimental data are compared with rigorous solutions of the Faddeev equations using the Argonne AV14, Bonn B, Nijmegen, and Paris potentials. While the overall agreement is quite good there exist distinct discrepancies between theoretical and experimental cross section and analyzing power data in some regions of phase space.

Measurement of polarization transfer in p-p scattering for a test of nucleon-nucleon potentials

Abstract We have measured polarization transfer observables Ky′y (θ), Kx′x (θ) and Kx′z(θ) for proton-proton scattering at 25.68 MeV with an accuracy of 0.007–0.012. Phase shift analyses of these data together with differential cross section and analyzing power data at the same energy yield an essentially model independent determination of the 1S0, 3PJ and e2 parameters at this energy. These parameters provide a test of nucleon-nucleon potential models and favour Paris and Nijmegen potentials.

Configuration mixing in 56Co and 46Sc using (d

Two-nucleon spectroscopic amplitudes are investigated using cross-section measurements and tensor analyzing powers for the $^{58}\mathrm{Ni}$(d\ensuremath{\rightarrow},\ensuremath{\alpha}${)}^{56}$Co and $^{48}\mathrm{Ti}$(d\ensuremath{\rightarrow},\ensuremath{\alpha}${)}^{46}$Sc reactions. Angular distributions of cross sections, and analyzing powers ${\mathit{A}}_{\mathit{y}}$, ${\mathit{A}}_{\mathit{x}\mathit{x}}$, and ${\mathit{A}}_{\mathit{y}\mathit{y}}$, were measured in steps of 5\ifmmode^\circ\else\textdegree\fi{} from 10\ifmmode^\circ\else\textdegree\fi{} to 65\ifmmode^\circ\else\textdegree\fi{} at a bombarding energy of 22 MeV. Data were analyzed using full finite-range DWBA calculations including a realistic \ensuremath{\alpha}-particle wave function. The L-mixing ratios for several strong unnatural-parity transitions have been determined from comparison of calculations with analyzing power data. These ratios are compared to predictions of shell-model calculations to deduce predominant two-nucleon configurations.

Angular dependence of analyzing power in np elastic scattering between 0.312 and 1.10 GeV

We present a total of 427 np analyzing power data points in a large angular interval at 12 energies between 0.312 and 1.10 GeV. The SATURNE II polarized beam of free monochromatic neutrons was scattered either on the Saclay frozen-spin polarized proton target or on CH 2 and C targets. Present results are compared with existing elastic and quasieleastic data.

Proton-90Zr mean field between -60 and +185 MeV from a dispersive optical model analysis.

Elastic scattering of protons from $^{90}\mathrm{Zr}$ in the energy range ${\mathit{E}}_{\mathit{p}}$=9.8 to 135 MeV is analyzed using a dispersive optical model potential (OMP). In this analysis, a dispersion relation connects the volume integrals of the imaginary and the real parts of the OMP. Best-fit dispersive OMP parameters are obtained from fits to experimental cross section and analyzing power data at each energy, while the volume integrals of the imaginary potential and dispersive correction terms are fixed at the empirical values obtained in the individual proton elastic scattering analyses from 9.8 to 135 MeV. Predictions of the cross section and analyzing power angular distributions from the best-fit dispersive OMP and conventional OMP are obtained, and give similar quality fits to data. A dispersive OMP with parameters that show a smooth energy dependence are determined from fits to the entire data set. Comparison of cross sections and analyzing powers calculated by the dispersive OMP with experimental data at 160 and 185 MeV is also presented. The dispersive OMP with a smooth energy dependence is extended to the negative energy region with the guidance of the known first single-particle and single-hole state energies near the Fermi energy, ${\mathit{E}}_{\mathit{F}}$=-6.8 MeV, to provide parameters for the shell model potential. This analysis also provides estimates for single-particle and hole energies ${\mathit{E}}_{\mathit{n}\mathit{l}\mathit{j}}$, root-mean-square radii ${\mathit{R}}_{\mathit{n}\mathit{l}\mathit{j}}$, expectat ion values of the effective mass 〈${\mathit{m}}^{\mathrm{*}}$/m${\mathrm{〉}}_{\mathit{n}\mathit{l}\mathit{j}}$, occupation probabilities ${\mathit{N}}_{\mathit{n}\mathit{l}\mathit{j}}$, absolute spectroscopic factors ${\mathit{S}}_{\mathit{n}\mathit{l}\mathit{j}}$, and spectral functions ${\mathrm{\ensuremath{\zeta}}}_{\mathit{n}\mathit{l}\mathit{j}}$(${\mathit{E}}_{\mathit{x}}$) for proton single-particle and single-hole orbits in $^{90}\mathrm{Zr}$. These estimates are compared with available experimental information.

Neutron transition densities from 88Sr(p,p') at Ep=200 MeV.

New cross section and analyzing power data for $^{88}\mathrm{Sr}$(p,p') at ${\mathit{E}}_{\mathit{p}}$=200 MeV are reported and analyzed together with earlier cross section data. Neutron transition densities for low-lying normal-parity excitations were extracted using an empirical density-dependent effective interaction and an expansion of the radial density which permits analysis of uncertainties due to penetrability, distortion, incompleteness, statistics, and normalization. The densities were compared with shell-model calculations using effective operators based upon a density-dependent Hartree-Fock approximation. Good agreement between theory and experiment is obtained for the ${2}_{1}^{+}$, ${3}_{1}^{\mathrm{\ensuremath{-}}}$, and ${5}_{1}^{\mathrm{\ensuremath{-}}}$ states, but the experimental neutron densities for the ${2}_{2}^{+}$ and ${7}_{1}^{\mathrm{\ensuremath{-}}}$ states are considerably stronger than expected. Both proton and neutron transition densities for the ${2}_{2}^{+}$ state have strong interior lobes, but the theory fails to reproduce the accompanying surface lobes.

Analyzing powers for 9Be(6Li

Vector and tensor analyzing powers ([ital iT][sub 11], [sup [ital T]T][sub 20], [ital T][sub 20], and [ital T][sub 22]) for the [sup 9]Be([sup 6]L[rvec i],[sup 6]He)[sup 9]B reaction are presented for a [sup 6]L[rvec i] bombarding energy of 32 MeV over the angular range from 14[degree] to 80[degree] c.m. A one-step reaction calculation is consistent with the angular distribution and vector analyzing power [ital iT][sub 11] for the ground-state transition but does not describe the tensor analyzing power [sup [ital T]T][sub 20]. Coupled channels calculations that include inelastic coupling in the entrance and exit channels do not reproduce either the vector or tensor analyzing powers. Sequential transfer calculations via ([sup 6]Li,[sup 7]Li)([sup 7]Li,[sup 6]He) do not reproduce the ground-state angular distribution but do reproduce the analyzing powers. The analyzing power data to the [sup 9]B(5/2[sup [minus]], 2.36 MeV state) are well reproduced by the coupled channels calculation although the cross section is under predicted by a factor of 3.

Investigation of the NN interaction from polarization transfer experiments in low energy pp scattering

The polarization-Transfer observables Kyy1(θ), Kxx1(θ) and Kzx1(θ) for proton-proton scattering have been measured at Ep = 25.68MeV. A simultaneous phase-shift analysis of these new data with differential cross section and analyzing power data at the same energy resulted in a very accurate determination of the p-wave phase-shift combinations ΔC, ΔLS and ΔT and of the 3F2−3P2 mixing parameter ϵ2. With this complete set of high precision data a critical test of microscopic NN-potential models has been performed.

Neutron-proton analyzing power data between 7.6 and 18.5 MeV.

Measurements of the analyzing power ${\mathit{A}}_{\mathit{y}}$(\ensuremath{\theta}) for neutron-proton scattering have been performed at 7.6, 12.0, 14.1, 16.0, and 18.5 MeV. The experimental setup is described as are the finite-geometry corrections applied to the data. One of these corrections, due to the presence of carbon in the scintillators used for neutron detection, is discussed in detail. The ${\mathit{A}}_{\mathit{y}}$(\ensuremath{\theta}) data are compared to the predictions of the Paris and Bonn nucleon-nucleon potentials and the predictions of two phase-shift analyses, one of which incorporates charge-independence breaking effects in the $^{3}$P waves.

Role of the Δ-isobar in the A(p, π) A+1 reaction

We have applied a microscopic model of the A(p, π) A+1 reaction that includes both the one-nucleon mechanism and the resonance p-wave rescattering part of the two-nucleon mechanism to the 16 O( p, π +) 17 O and 12,13,14 C( p, π −) 13,14,15 O reactions leading to two-particle one-hole final states to test separately the two-nucleon mechanism part of the model. The calculations reproduce fairly well the differential cross section and analyzing power data for 16 O( p ̄ , π +) transitions leading to high-spin, two-particle one-hole states in 17O at 7.76 MeV( 11 2 −) and 15.8 MeV( 13 2 −) at bombarding energies of 200, 250 and 354 MeV, but underestimate appreciably the differential cross sections for 12,13,14 C( p ̄ , π −) transitions leading to the ground states 13,14,15O and the 7.28 MeV( 7 2 +) excited state of 15O and fail to reproduce the analyzing-power angular distributions for these (p, π −) transitions. These results verify that NN → NN Δ → NN π is the underlying two-nucleon process in the 16O(p, π +) reactions, but that non-Δ channels dominate the 12,13,14C(p, π −) reactions. The latter conclusions is consistent with results of recent studies of the pn ↔ π −pp reaction.

Dispersion relation analysis of d+208Pb elastic scattering.

Elastic scattering of deuterons from $^{208}\mathrm{Pb}$ in the energy range ${\mathit{E}}_{\mathit{d}}$=9 to 79.2 MeV is analyzed using a dispersive optical model potential (OMP). In this analysis, a dispersion relation connects the volume integrals of the imaginary and the real parts of the OMP. Best-fit dispersive OMP parameters are obtained from fits to experimental cross-section and analyzing power data at one energy, and dispersive OMP parameters with a smooth energy dependence are determined from fits to the entire data set. Comparisons, showing fits of similar quality, of the predictions of the cross sections and analyzing powers given by the best-fit dispersive OMP and standard OMP are presented. Dispersive OMP parameters with a smooth energy dependence also give a good description of the experimental data.

Deviations from tidal symmetry in polarized 7Li excitation

A simple model that describes the excitation of polarized projectiles is proposed. The disagreement between the experimental analysing power data for 7Li on 120Sn at 44 MeV and the shape effect relations, and the value of the vector analysing power are explained as a consequence of deviations from the tidal symmetry.

Empirical density-dependent effective interaction for nucleon-nucleus scattering at 500 MeV.

We report new cross-section and analyzing-power data for the excitation by 498-MeV protons of all narrow normal-parity states of {sup 16}O below 12.1-MeV excitation. In addition, spin-rotation measurements for elastic scattering and depolarization measurements for the 1{sub 1}{sup {minus}}, 2{sub 1}{sup +}, and 3{sub 1}{sup {minus}} states of {sup 16}O have been performed. These data are used in conjunction with existing data for {sup 40}Ca to study medium corrections to the effective interaction for nucleon-nucleus scattering at 500 MeV. Systematic differences between the data and nonrelativistic impulse approximation calculations based upon either the free {ital t} matrix or a recent density-dependent effective interaction are interpreted within the framework of the local-density approximation. An empirical effective interaction has been constructed which parametrizes the density dependence of the medium modifications in a simple form amenable to phenomenological analysis of data.

Scattering of polarized protons from 7Li at 200 MeV.

New cross-section and analyzing-power data are presented for elastic and inelastic scattering of 200-MeV protons from $^{7}\mathrm{Li}$, which has a ${\frac{3}{2}}^{\ensuremath{-}}$, $T=\frac{1}{2}$ ground state. A microscopic foldingmodel optical potential, obtained by convoluting a Pauli-corrected effective nucleon-nucleon ($\mathrm{NN}$) interaction with $^{7}\mathrm{Li}$ ground-state densities constrained by weak and electromagnetic data, produces a satisfactory description of the elastic data. The effects of the nonspherical terms in the optical potential, estimated via the distorted-wave approximation (DWA), are appreciable. The inelastic transitions leading to the ${\mathrm{\textonehalf{}}}^{\ensuremath{-}}$, $T=\frac{1}{2} \mathrm{and} {\frac{7}{2}}^{\ensuremath{-}}$, $T=\frac{1}{2}$ states at 0.48 and 4.63 MeV, respectively, are also examined within the framework of the microscopic folding model and the DWA. Transition potentials are generated by convoluting the effective $\mathrm{NN}$ interaction considered with target transition densities constrained by weak, electromagnetic, and low-energy proton and neutron scattering data. These potentials are employed in DWA calculations along with the folded optical potential that is consistent with the transition potentials. These self-consistent calculations also provide a good description of the inelastic data. The results provide a clear indication that there are important shape differences between the $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$ radial densities and that the two inelastic transitions in $^{7}\mathrm{Li}$, which are primarily quadrupole in character, have $\frac{{\ensuremath{\rho}}_{2n}^{m}}{{\ensuremath{\rho}}_{2p}^{m}}\ensuremath{\approx}0.9 \mathrm{and} 0.9\ensuremath{-}1.2$, respectively.

Effective interaction for 16O(p,p') at Ep=318 MeV.

We report new cross-section and analyzing power data for the excitation by 318 MeV protons of 20 states of $^{16}\mathrm{O}$ below 14 MeV. The data for normal-parity isoscalar excitations are compared with calculations based upon the nonrelativistic impulse approximation using both density-independent and density-dependent interactions in the local-density approximation. These comparisons clearly indicate that density-dependent modifications of the effective interaction are required. Although the Paris-Hamburg, Nakayama-Love, and Ray interactions all predict significant medium modifications, none describes the data particularly well. Therefore, we fitted an empirical effective interaction to the data for five inelastic transitions simultaneously using a self-consistency cycle that maintains consistency between transition potentials and microscopic distorting potentials. This interaction describes the inelastic data as well as elastic data and data for $^{40}\mathrm{Ca}$ which were not included in the fitting procedure. Therefore, the local-density approximation is supported by the phenomenology. However, medium modifications of the effective interaction are substantially stronger than predicted and persist to low density. The optical potentials are similar to the Schr\"odinger-equivalent potentials from the relativistic IA2 model, showing that the equivalent density dependence due to virtual NN\ifmmode\bar\else\textasciimacron\fi{} pairs is comparable to the short-range repulsion fitted to inelastic-scattering data.

Resolution of the twofold ambiguity in theE1 capture amplitudes for theC13(p→,γ)14N reaction

The analysis of the cross section and analyzing power data of the {sup 13}{ital C}({ital {rvec p}},{gamma}{sub 0}){sup 14}N reaction leads to two solutions for the {ital E}1 amplitudes and phases which contribute in the region of the giant dipole resonance. One of these solutions indicates that the reaction proceeds predominantly via {ital d}-wave capture while the other corresponds to predominant {ital s}-wave capture. In the present work, we have used the interference between the {ital E}{sub {ital p}}=3.11 MeV {ital M}1 resonance and the {ital E}1-dominated background to determine which of the two off-resonance {ital E}1 solutions is the correct (physical) one. The results show that the dominant {ital d}-wave capture solution is the correct one in the region of this resonance, demonstrating that the low-energy off-resonance {ital E}1 strength has the same (dominant {ital d}-wave) structure as that expected from the giant dipole resonance.

Semiclassical Coupled Channels Theory

AbstractA semiclassical theory for heavy ion scattering in the Fresnel diffraction regime covering coupled elastic and inelastic channels is developed. The scattering is described as diffraction off the rainbow trajectory along which the development of the internal degrees of freedom is calculated. Simple formulae for the transition amplitudes are derived and interpreted in terms of matching conditions, time scales and potential strengths at closest approach. Polarization potentials comprising of real and absorptive terms and of tensors of various ranks are constructed. Analyzing power data for elastic and inelastic scattering of polarized 7Li on 120Sn are analyzed.

MEDIUM EFFECTS ON KNOCKOUT OF DEEPLY BOUND NUCLEONS

MEDIUM EFFECTS ON KNOCKOUT OF DEEPLY BOUND NUCLEONS

Analyzing power measurements in pn--> pi -pp(1S0).

A recent experiment has measured analyzing powers in d(p\ensuremath{\rightarrow},${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$pp)p in a geometry which selected the quasifree two-body reaction p\ensuremath{\rightarrow}n\ensuremath{\rightarrow}${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$pp${(}^{1}$${\mathit{S}}_{0}$). Analysis of the results indicated a significant contribution from a very-short-range part of the nucleon-nucleon interaction. We show that the analyzing power data measured in the above experiment is reasonably well described by a unitary NN \ensuremath{\rightarrow} NN\ensuremath{\pi} model containing only the one-pion-exchange driving force.

Scattering of polarized protons from 6Li at 200 MeV.

New cross section and analyzing power data are presented for elastic and inelastic scattering of 200 MeV protons from $^{6}\mathrm{Li}$. The elastic data are well described by a standard, spherical, 12-parameter phenomenological Woods-Saxon (WS) optical potential. Microscopic folding-model optical potentials, obtained by convoluting free and Pauli-corrected effective nucleon-nucleon (NN) interactions with $^{6}\mathrm{Li}$ ground-state densities constrained by electromagnetic data, produce satisfactory descriptions of the elastic data. The effects of the spin-spin optical potential, estimated via the distorted wave approximation (DWA), are small but not negligible. The inelastic transitions leading to the ${3}^{+}$,T=0 state at 2.18 MeV and the ${0}^{+}$,T=1 state at 3.56 MeV are also examined within the framework of the microscopic folding model using the DWA. Transition potentials are generated by convoluting the two effective NN interactions considered with target transition densities constrained by weak and electromagnetic data. These are employed in DWA calculations using both folded optical potentials consistent with the transition potentials and the WS optical potential. The self-consistent calculation with the Pauli-corrected interaction provides a good description of the data for the ${3}^{+}$ excitation. The results for the ${0}^{+}$ excitation provide a clear indication that shell model configurations outside the p shell are important for a complete description of this transition.