Extreme Backward Angles Research Articles

Tensor analyzing power component [formula omitted] of the [formula omitted] process in the photon energy range from 200 to 400 MeV

The tensor analyzing power component, T20, of the γd→→π0d process in the photon energy range from 200 to 400 MeV is investigated. This work is motivated by the most recent and unique measurements from the VEPP-3 electron storage ring at the Budker Institute of Nuclear Physics in Novosibirsk, Russia. We point out a special sensitivity of T20 to the elementary γN→πN amplitude and to the realistic NN potential model adopted for the deuteron wave function at backward pion angles, especially in the region 90°<θ<150°. The estimated results for T20 are compared with the experimental data from VEPP-3 and a satisfactory agreement is obtained at incident photon energies below 375 MeV. At higher photon energies and extreme backward pion angles, the estimated results of T20 considerably underestimate the data.

Excitation of the electric pygmy dipole resonance by inelastic electron scattering⋆

To complete earlier studies of the properties of the electric pygmy dipole resonance (PDR) obtained in various nuclear reactions, the excitation of the 1$^-$ states in $^{140}$Ce by $(e,e')$ scattering for momentum transfers $q=0.1-1.2$~fm$^{-1}$ is calculated within the plane-wave and distorted-wave Born approximations. The excited states of the nucleus are described within the Quasiparticle Random Phase Approximation (QRPA), but also within the Quasiparticle-Phonon Model (QPM) by accounting for the coupling to complex configurations. It is demonstrated that the excitation mechanism of the PDR states in $(e,e')$ reactions is predominantly of transversal nature for scattering angles $\theta_e \approx 90^o-180^o$. Being thus mediated by the convection and spin nuclear currents, the $(e,e')$ like the $(\gamma,\gamma')$ reaction, may provide additional information to the one obtained from Coulomb- and hadronic excitations of the PDR in $(p,p')$, $(\alpha,\alpha')$, and heavy-ion scattering reactions. The calculations predict that the $(e,e')$ cross sections for the strongest individual PDR states are in general about three orders of magnitude smaller as compared to the one of the lowest $2^+_1$ state for the studied kinematics, but that they may become dominant at extreme backward angles.

Tensor Target Spin Asymmetries in Coherent π0-Photoproduction on the Deuteron Including Intermediate ηNN Interaction Within a Three-Body Approach

Motivated by the recent measurements from the VEPP-3 electron storage ring, we investigate the tensor target polarization asymmetries T2M (M = 0, 1, 2) in the reaction γd → π0d with a particular interest in the effect of the intermediate ηNN three-body approach. This approach is based on realistic separable representations of the driving two-body interaction in the πN, ηN, and NN subsystems. It is shown that the influence of rescattering effects in the intermediate state on the tensor target spin asymmetries is sizable at extreme backward pion angles. At forward angles, the contribution from the pure impulse approximation is dominated and the spin asymmetries show very little influence of rescattering effects. The sensitivity of results to the elementary pion photoproduction operator and to the NN potential model adopted for the deuteron wave function is investigated, and considerable dependences are found. The predicted spin asymmetries are also compared with available experimental data, and a satisfactory agreement with the recent data from VEPP-3 is obtained at photon energies below 400 MeV. At higher energies, the calculated spin asymmetries slightly underestimate the data.

Influence of the Choice of NN Potential Model on γd → π0d Observables near η-Threshold

Influence of the choice of the NN potential model governing the deuteron wave function on the observables for coherent π0-photoproduction on the deuteron near η-threshold is investigated by using a three-body model for the intermediate ηNN system with separable two-body interactions. Results for unpolarized differential cross section and polarization observables are predicted. It is revealed that the choice of the NN potential model has a visible effect on the differential cross section and most of the polarization observables, especially in the photon energy range of 600–800 MeV and extreme backward pion angles. We find that the deviation among results obtained by using different deuteron wave functions is quite large. The use of the CD-Bonn NN potential for deuteron wave function doubles the differential cross section in this kinematic region. Compared with the experimental data from CLAS collaboration for differential cross section, sizeable discrepancies are found.

Helicity-dependent reaction γd → π0d near the η-threshold and its contribution to the E-asymmetry and the GDH sum rule for the deuteron

The helicity-dependent coherent π0-photoproduction in the reaction γd → π0d near the η-threshold is investigated. The calculations are performed within an approach which includes the reaction amplitudes of the impulse approximation (IA), two-step process with intermediate πN- and ηN-rescattering, and the higher order terms in the multiple scattering series for the intermediate ηNN interaction. The contribution of γd → π0d to the deuteron spin asymmetry is calculated and its contribution to the Gerasimov–Drell–Hearn (GDH) integral is explicitly evaluated by integration up to a photon energy of 900 MeV. In addition, the helicity E-asymmetry is calculated. The results revealed that the doubly polarized differential cross-sections and the helicity E-asymmetry are sensitive to the interference of rescattering effects, specially at photon energies 600–800 MeV and extreme backward pion angles. The sensitivity of the obtained results for the GDH integral to the choice of NN potential model governing the deuteron wave function is discussed. We find that the deviation among results obtained for the deuteron GDH integral using different deuteron wave functions is quite large.

Influence of intermediate [formula omitted] interaction on spin asymmetries for [formula omitted] reaction near the [formula omitted]-threshold within a three-body approach

The influence of intermediate ηNN interaction on spin asymmetries for coherent π0-photoproduction on the deuteron in the energy region around the η-threshold is studied using a three-body model with separable two-body interactions. We calculate all possible spin asymmetries with polarized photons and/or oriented deuterons and compare our results with available data. The calculations are based on a theoretical approach which includes the amplitudes of the impulse approximation, two-body process with πN- and ηN-rescattering, and the higher order terms in the multiple scattering series for the intermediate ηNN interaction. We found that the results for spin asymmetries of the differential cross section differ significantly from those calculated by a simple model in which only the impulse approximation and first-order rescattering contributions are considered. The effect of intermediate ηNN interaction is significant in certain spin asymmetries, specially at extreme backward pion angles. It turns out that the inclusion of a full ηNN three-body contribution is quite essential. The spin asymmetries of the total cross section are much less affected by rescattering contributions. Compared to the experimental data from YerPhi Collaboration for the linear photon asymmetry, sizeable discrepancies are found.

Energy and angular distribution of electrons in ionization of He and Ne by 6-MeV/u bare carbon ions: Comparison with continuum-distorted-wave eikonal-initial-state calculations in prior and post forms

We have measured the absolute double-differential cross sections (DDCS) for electron emission in ionization of He and Ne atoms under the impact of 6-MeV/u ${\mathrm{C}}^{6+}$ ions. Data were collected between 1 and 500 eV for He, while for Ne this range was extended up to 1000 eV. The angular ranges covered in the experiment are ${30}^{\ensuremath{\circ}}$ to ${150}^{\ensuremath{\circ}}$ and ${20}^{\ensuremath{\circ}}$ to ${160}^{\ensuremath{\circ}}$ for He and Ne, respectively. The DDCS spectra are compared with the prior and the post forms of the state-of-the-art continuum-distorted-wave eikonal-initial-state model. Both the theoretical models show very good agreement with the energy and angular distributions of the DDCS in the case of He. For Ne, at low energies both are going together and matching very well with the data. In the high-energy region, at extreme forward and backward angles, although both the forms are underestimating the experimental data to some extent, the prior form shows much better agreement compared to the post form. This post-prior discrepancy is attributed to the influence of dynamic screening, on the ionized one, produced by the electrons remaining in the target. The single differential cross sections (SDCS) in emission angle $(\frac{d\ensuremath{\sigma}}{d{\ensuremath{\Omega}}_{e}})$ and electron energy $(\frac{d\ensuremath{\sigma}}{d{\ensuremath{\epsilon}}_{e}})$ are deduced by integrating the electron DDCS spectra. While excellent agreement is obtained for the $\frac{d\ensuremath{\sigma}}{d{\ensuremath{\epsilon}}_{e}}$ spectrum, the $\frac{d\ensuremath{\sigma}}{d{\ensuremath{\Omega}}_{e}}$ provides a further sensitive test to the adequacy of the theoretical model employed. The total cross section obtained from the SDCS spectra is about 11% higher than the prior model for He and about 6% lower for Ne. To get the quantitative picture of the two-center effect, the forward-backward angular asymmetry parameter has been deduced as a function of velocity of the ejected electrons. For both the targets, it is very well reproduced by both the forms of the theory. For the Ne target, $K$-LL Auger angular distribution has also been studied, which shows small asymmetry caused by multiple vacancies in the $L$ shell along with the $K$-shell vacancy.

Two-photon exchange corrections to the pion form factor

We compute two-photon exchange corrections to the electromagnetic form factor of the pion, taking into account the finite size of the pion. Compared to the soft-photon approximation for the infrared-divergent contribution, which neglects hadron structure effects, the corrections are found to be $\ensuremath{\lesssim}1%$ for low ${Q}^{2}$ values (${Q}^{2}&lt;0.1$ GeV${}^{2}$) but increase to several percent for ${Q}^{2}\ensuremath{\gtrsim}1$ GeV${}^{2}$ at extreme backward angles.

Low-energy neutron-proton analyzing power and the new Bonn potential and Paris potential predictions.

Instrumental asymmetries recently observed by Haeberli and co-workers, limit the accuracy of neutron-proton analyzing power ${A}_{y}$(\ensuremath{\theta}) data. These instrumental effects are discussed and calculated for previously published n-p ${A}_{y}$(\ensuremath{\theta}) data at 16.9 MeV. To enable these calculations, the analyzing power for the $^{2}\mathrm{H}$(d\ensuremath{\rightarrow},n${)}^{3}$He reaction was measured at small angles. Additional n-p ${A}_{y}$(\ensuremath{\theta}) data at extreme backward angles, obtained via proton recoil detection, are also reported for this energy in this paper. The composite data set is compared to calculations based on the new Bonn NN potential, the Paris NN potential, and to the recent NN phase-shift solution of Arndt. In addition, a detailed comparison between ${A}_{y}$(\ensuremath{\theta}) calculated from the new Bonn and the Paris potentials between 10 and 50 MeV is shown to reveal unexpectedly large relative differences. The experimental data in this energy range are better described by the Paris potential than by the new Bonn potential.

Measurement of $$D(\vec p,p)D$$ elastic scattering at 10.0, 12.0, 14.1 and 16.5 MeV especially for small forward and extreme backward scattering angles

The $$D(\vec p,p)D$$ elastic scattering was investigated especially in the Coulomb sensitive scattering regions. Angular distributions of the differential cross section and of the analyzing powerA y, with emphasis on small scattering angles, were measured at 10.0 and 14.1 MeV. For extreme backward angles up toJ c.m.=179° the differential cross section was measured at 12.0, 14.1 and 16.5 MeV. The data have been compared with recent Faddeev calculations based on the realistic meson-exchange Paris potential and including an approximate Coulomb correction. There are discrepancies between the data and the calculations especially for the analyzing power. This indicates that the approximate treatment of Coulomb effects and possibly also the purely nuclear part of the calculations need to be improved.

Fast neutron scattering from hydrogen and carbon

A method is described to measure the n-p differential cross section between 14 and 20 MeV precisely in order to determine the 1p 1 nueleon-nucleon phase shift. To clarify the influence of F-wave phase shifts on n-p scattering at 16.9 MeV new n-p analyzing power measurements have been made at extreme backward angles by detecting recoil protons from a scintillating radiator foil. Discrepancies with global phase shift predictions are found. The n-d system is being studied by analyzing power measurements with 6.5 MeV neutrons. The data will extend the basis of new precision analyzing power data to lower energies in order to compare with p-d data and Faddeev calculations available. A method to measure differential n- 12C cross sections between 15 and 20 MeV by the carbon recoil method using an organic scintillator is described. The normalization is done relative to n-p scattering in the same scintillator simultaneously to the n- 12C scattering.

A measurement of the neutron-proton differential cross section at extreme forward and backward angles between 45 and 75 MeV

To determine theδ(1P1) phase parameter, thenp cross section has been measured from 45 to 75 MeV, by 5 MeV steps, from 6° to 20° at forward angle, and from 168° to 180° at backward angle.

Forward- and Backward-Angle Differential Cross Section for Neutron-Proton Capture at 72 MeV

The neutron-proton capture differential cross section has been measured at extreme forward and backward angles for 72-MeV neutron energy corresponding to a gamma -ray energy of 38.2 MeV in the inverse reaction. The results agree well with recent photodisintegration data at forward angles, but only partially with potential model calculations.

Neutron elastic scattering cross section measurements at back angles

The optical model has frequently been used to give a theoretical description of experimental neutron elastic scattering angular distributions. In such experiments the differential cross sections should be studied in as large an angular interval as possible. However, hitherto the published results have mostly been confined to the angular region 20° to 160°. The extension of the studied angular range to extreme backward angles is of theoretical interest since this would provide an opportunity for studying the influence of the depth of the spin-orbit term of the optical-model potential on the shape of the angular distribution in greater detail. This is possible because of the high sensitivity of the calculated differential elastic scattering cross sections at backward angles to the depth of the spin-orbit term. Thus in this paper an experimental arrangement is described which allows measurements at extreme backward angles. With this arrangement measurements have been performed at angles up to 174° for Fe, Co, In and Bi at a primary neutron energy of 7.05 MeV. It has been found that the observed differential cross sections for Fe and Co are best described by those calculated with the depth of the spinorbit term equal to 6 MeV while a value of 4 MeV may be a better choice for In and Bi.

The [formula omitted] resonances at Ep = 11.26,12.71 and 14.57 MeV

Excitation functions for 16O+p reactions have been measured with high energy resolution in the region of the first, second and seventh T = 3 2 resonances in 17F at extreme backward angles. The observed resonance shapes have been analyzed with a single-level resonance formula taking the off-resonance spin-flip amplitude into account. The resonance parameters of the 17F first T = 3 2 state studied with special emphasis are E x = 11193.3 ± 2.3 keV, Γ = 200 ± 40 eV and Γ p 0 = 19 ± 3 eV. This result and other results are compared with previous studies and theoretical predictions. The comparison with data of the mirror nucleus 17O is discussed with respect to the observed charge asymmetry of the isospin-forbidden particle decay widths.

Precision Measurement ofn−pCharge-Exchange Cross Section at 647 MeV

The differential cross section for n--p elastic scattering in the angular region 145$sup 0$ < theta/sub c.m/ < 180$sup 0$ has been measured with high statistical accuracy using the monoenergetic neutron beam at Clinton P. Anderson Meson Physics Facility. The results differ significantly from previous Dubna and Princeton-Pennsylvania Accelerator results but agree reasonably well with recent Saclay data except at extreme backward angles. (AIP)

Optical model analysis of proton elastic scattering excitation functions around A = 90

Excitation functions of protons elastically scattered from 88Sr, 89Y, 90Zr and 92Mo over an energy range from 8 to 15 MeV were analysed with the optical model. The deep minima exhibited by these excitation functions especially at extreme backward angles can be described by an imaginary potential which is smaller than that of Becchetti and Greenlees. Compound nucleus contributions were taken into account by appropriate weighting of the data. The magnitude of these contributions in the minima could thus be estimated.

An experimental technique for studying 180° scattering

Using the associated particle method and a thin reaction target an experimental technique was developed for studying 180° scattering. This technique can be used to obtain the scattering cross section for neutrons and charged particles at extreme backward angles (165° to 180° to −165°). This technique was tested by measuring the elastic scattering cross section of 3.65 MeV neutrons from Pb at 180°.

Nucleon-Nucleon Scattering Near 50 MeV. I. Phase-Shift Analysis of the Data

We carry out a phase-shift analysis of $p\ensuremath{-}p$ and $n\ensuremath{-}p$ elastic scattering data in the laboratory kinetic energy range of 47.5 to 60.9 MeV. Despite the inclusion of new $n\ensuremath{-}p$ total and differential cross-section data since the phase-shift analyses of MacGregor, Arndt, and Wright (papers VI and X in particular), the ${\ensuremath{\chi}}^{2}$ vs ${\ensuremath{\epsilon}}_{1}$ curve retains its double minimum, and the anomalous value for the phase parameter $\ensuremath{\delta}(^{1}P_{1})$ persists. The data yield a range of solutions rather than a unique $I=0$ phase-shift solution, and, in fact, the ${\ensuremath{\chi}}^{2}$ vs ${\ensuremath{\epsilon}}_{1}$ curve is even flatter than it was in paper VI. The allowed range of ${\ensuremath{\epsilon}}_{1}$ is found to be from -10\ifmmode^\circ\else\textdegree\fi{} to +3\ifmmode^\circ\else\textdegree\fi{}, approximately. To find a unique solution, we constrain ${\ensuremath{\epsilon}}_{1}$ to have a reasonable theoretical value of +2.78\ifmmode^\circ\else\textdegree\fi{}, and present the corresponding constrained phase-shift solution. This yields $\ensuremath{\delta}(^{1}P_{1})=\ensuremath{-}3.52\ifmmode^\circ\else\textdegree\fi{}\ifmmode\pm\else\textpm\fi{}1.04\ifmmode^\circ\else\textdegree\fi{}$, which is 4.5 standard deviations or more above predictions by meson-theoretical models. In fact, throughout the allowed range of ${\ensuremath{\epsilon}}_{1}$, the searched value of $\ensuremath{\delta}(^{1}P_{1})$ remains at least this far above theoretical predictions. We determine that the Harwell $n\ensuremath{-}p$ $\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}$ data at extreme forward and extreme backward angles are responsible for the high value of $\ensuremath{\delta}(^{1}P_{1})$, and recommend that these measurements be retaken. We emphasize that contrary to popular belief, it is not sufficient just to fix the relative backward $n\ensuremath{-}p$ $\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}$, because incorrect forward values will result in a wrong value for $\ensuremath{\delta}(^{1}P_{1})$. With regard to forward data, good extreme forward absolute $\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}$ data will be more effective than relative forward data spanning the 0\ifmmode^\circ\else\textdegree\fi{}-90\ifmmode^\circ\else\textdegree\fi{} range. Finally, with respect to ${\ensuremath{\epsilon}}_{1}$, we emphasize that the existing types of $n\ensuremath{-}p$ data ($\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}$, ${\ensuremath{\sigma}}_{\mathrm{tot}}$, and $P$) will not remove the ambiguity in this phase parameter. Some other type of experiment must be done, as we intend to discuss in a succeeding paper.

Fast Neutron Scattering at 180° from Pb and Sn

A measurement of the differential scattering of 3.65 MeV neutrons from the D(d,n)3He reaction at the angles 10° and 180° by Pb and Sn was made. The results at 180° were anomalously high compared with optical model predictions. An experimental arrangement using the associated particle technique and large thin film (CD2)x targets is described which has made measurements of the differential scattering of neutrons at the extreme backward angles (~180°) possible.