Coulomb-nuclear Interference Region Research Articles

ALL at small momentum transfers for the first complete determination of the forward pp scattering amplitudes

The asymmetryALL for pp elastic scattering has been measured at 650 and 800 MeV in the region of Coulomb-nuclear interference. The real part of the double-spin-flip amplitude extracted from these data completes our determination of the forward pp scattering amplitudes at these energies. Comparison with the predictions of forward dispersion relations reveals a discrepancy in the spin-dependent channels at 650 MeV.

Relativistic effects in forward angle proton-nucleus elastic scattering.

Scattering models with either relativistic or nonrelativistic dynamics are used to predict elastic scattering observables in the forward angle, Coulomb-nuclear interference region for 500 and 800 MeV ${\mathrm{p}+}^{16}$O, $^{40}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$. At 500 MeV the differential cross sections for the relativistic model are 15--25 % larger than those of the nonrelativistic model. Ambiguities in the theoretical predictions which arise from empirical input used by the models and from approximations made in numerically evaluating higher order corrections are estimated and found to contribute \ifmmode\pm\else\textpm\fi{}2%--\ifmmode\pm\else\textpm\fi{}6% to the uncertainty of the differential cross sections in the forward angle region at 500 MeV for ${\mathrm{p}+}^{40}$Ca and $^{208}\mathrm{Pb}$. The sensitivity of the relativistic model cross sections to the use of a variety of relativistic nuclear structure models and different prescriptions for the virtual NN\ifmmode\bar\else\textasciimacron\fi{} pair process for the projectile is investigated and found to be largest at 500 MeV.

Microscopic analysis of projectile excitation for 18O+64Ni.

A microscopic analysis of the inelastic scattering of $^{18}\mathrm{O}$ from $^{64}\mathrm{Ni}$ is presented. The real transition potential for the excitation of the first ${2}^{+}$ state in $^{18}\mathrm{O}$ for $^{18}\mathrm{O}$ is calculated from the double folding model using proton and neutron transition densities determined from new medium energy electron and proton scattering data. The longer radial tail of the real transition potential obtained using this neutron transition density describes correctly the amplitude of oscillations in the Coulomb-nuclear interference region of the ${2}^{+}$ cross section. Unfortunately, coupled channels calculations, employing real double folded and imaginary Woods-Saxon interaction potentials and including reorientation of the $^{18}\mathrm{O}$ ${2}^{+}$ state, still fail to reproduce the phase of the Coulomb-nuclear interference pattern observed in the data. The imaginary part of the interaction potential, as the only phenomenological term remaining in the analysis, is suggested to be responsible for this defect.

First measurement of the real part of a pp double-spin-flip amplitude.

The asymmetry ${A}_{\mathrm{NN}}$ for pp elastic scattering has been measured at 800 and 650 MeV in the region of Coulomb-nuclear interference. The data have been analyzed to extract the real part of a spin-spin scattering amplitude. Results are compared with the predictions of forward dispersion relations. They disagree significantly at 650 MeV.

On the optical-potential deformation in heavy-ion inelastic scattering

The descriptions of heavy-ion inelastic scattering given by the folding model and phenomenological potentials require different degrees of deformation of the optical potential. This is because the rule of equal normalised multipole moments of the optical potential and the nucleon density distribution, imposed by the folding model, conflicts with the rule of equal deformation lengths borne out by analyses with Woods-Saxon potentials. It is shown, in an example of inelastic scattering of heavy ions from deformed nuclei in the region of strong Coulomb-nuclear interference, that the double-folding model description of the experimental data is as good as any description with deformed Woods-Saxon potentials. Thus neither of the two different rules for deforming the optical potential is a universal prescription since they only apply to specific classes of potentials.

Heavy-ion inelastic scattering from deformed nuclei

Theoretical and experimental methods for studying heavy-ion inelastic scattering from deformed nuclei are described. The theoretical methods involve classical-limit approximations, while particle- γ-spectroseopy techniques are employed experimentally. With these approaches, heavy-ion excitation in the Coulomb-nuclear interference region acquires a transparent interpretation, despite the apparent complexity of the multistep excitation processes involved. The examples discussed provide a good illustration of the relationship between classical and quantum physics. The sensitivity of the inelastic scattering to details of the surface ion-ion potential due to radial and angular localization is exploited to provide a method of determining the equipotential contours in a direct manner which bypasses particular model-dependent parametrizations. The method is used to construct ion-ion potentials from inelastic scattering data for the systems 40Ar + 160Gd, 156Gd, 162Dy, 164Dy, and 180Hf. The contribution of adiabatic giant resonance polarization to this potential is discussed. The relation between the deformed ion-ion potential and nuclear shapes is illustrated by comparing the experimental potentials to deformed double-folding and deformed proximity-potential calculations.

Coulomb-nuclear interference in the scattering of pions on 12C at 76 MeV

Abstract The differential cross sections for elastic scattering of positive and negative pions on 12C at 76 MeV have been measured in the Coulomb-nuclear interference region. The results have been compared with calculations, which represent a new more rigorous treatment of the Coulomb corrections.

Excitation of 17O and 18O scattered by 208Pb in the Coulomb-Nuclear interference region

Inelastic scattering of 17O and 18O by 208Pb has been measured at 78 MeV, and compared with theoretical predictions. In both cases the nuclear amplitude is dominated by the valence nucleon contribution. Direct excitation is the principal mechanism in 18O scattering, while for 17O excitation, two-step transfer is more important. Recoil and non-orthogonality effects must be taken into account.

Experiments on Coulomb-nuclear interference in [formula omitted] scattering at superhigh energy colliding beams

The possibility of setting up experiments on photon-antiproton scattering at small angles in the region of Coulomb-nuclear interference on superhigh energy colliding p p beams is discussed. It is shown that the implication of high energy electron cooling allows one to obtain the required resolution. The latter condition becomes very severe at superhigh energies.

Differential cross sections and analyzing powers forppelastic scattering at 1.46 GeV/cin the Coulomb-nuclear interference region

Differential cross sections sigma(theta) and analyzing powers A(theta) for pp elastic scattering have been measured in the Coulomb-nuclear interference region at 800 MeV. The measurements, which extend down to 0.5 deg in the laboratory, have been analyzed to deduce the zero-degree pp scattering amplitudes. The ratio rho of the real to imaginary parts of the spin-independent amplitude was found to be -0.04 +- 0.04; the contribution of the double-spin-flip amplitudes to sigma(0) was found to be 0.16 +- 0.03 times that of the spin-independent amplitude; while the ratios of the imaginary and real parts of the single spin-flip amplitude to sintheta were found to be 0.74 +- 0.04 and -0.03 +- 0.08 fm, respectively. Except for the last, these experimental values agree with the predictions of forward dispersion relations and phase shift analyses.

Reply to "Slope parameter and zero trajectories inπ−pscattering"

Shortcomings of the new zero trajectories of H\"ohler and Sabba Stefanescu are pointed out. The errors in the imaginary part could be large enough to make their results consistent with at least one real zero for every energy. Whether or not a real zero exists, it is possible to have convergent polynomial expansion (CPE) without any spurious cut with (very nearly) the same ansatz for the forward slope. We disagree with most of the criticisms on the applications of CPE to scaling without any spurious cuts. Even if one uses slope values obtained from parametrizations in the Coulomb-nuclear interference region, scaling is described in an excellent fashion.

Coulomb-nuclear interference and reaction cross-section in charged particle scattering

The importance of charged particle elastic scattering data in the Coulomb-nuclear interference region is discussed, with a view to evaluating the contribution to the reaction cross-section from single partial waves.

Alpha-particle inelastic scattering form factors in the Coulomb-nuclear interference region

Alpha-particle scattering cross sections have been measured at 15, 18 and 19 MeV from the ground state and first excited state of 52Cr, 56Fe, 60Ni and 64Zn. Excitation functions have also been measured for inelastic α-scattering from 52Cr and 60Ni. The data extends into the forwardangle Coulomb-nuclear interference region. The results are analysed with the optical model and DWBA, using the deformed potential model. The relative and absolute magnitudes of the nuclear and Coulomb deformation parameters and the shapes of the form factors have been deduced from the data. The importance of data in the Coulomb-nuclear interference region in determining these quantities is demonstrated.

Heavy-ion excitation of 3 − states in deformed nuclei

Previously measured data for 70.4 MeV 12C excitation of 3 − states in 148, 150Nd are reanalyzed using a third-order rotational-vibrational model. Calculations using 3 − quadrupole moments which are expected if they are K = 0 states are in reasonable agreement with the magnitude of the large-angle data, but the quality of the fit in the Coulomb-nuclear interference region is only fair. It is found that the matrix element 〈2 +∥ M(E3)∥3 −〉 plays an important role in the calculations making the “measurement” of the 3 − quadrupole moments very difficult, if not impossible.

Elastic scattering of π− mesons on protons in the Coulomb-nuclear interference region at 33–60 GeV/c

Elastic scattering of π− mesons on protons in the Coulomb-nuclear interference region at 33–60 GeV/c

Measurement of the real part of the K −n forward scattering amplitude between 1.2 and 2.6 GeV/ c

The differential cross sections of the combined elastic and break-up K −d reaction have been measured at 1.21, 1.42 and 2.61 GeV/ c incident K − momentum. The measurements have been performed at the CERN PS using multiwire proportional chambers. The values of the invariant momentum transfer t explored (0.0005<| t|<0.1 GeV 2) include the Coulomb-nuclear interference region. The differential cross sections have been analysed in the framework of the Glauber impact-parameter formalism. The observed interference effects have been used to derive the ratio of the real to imaginary part of the forward K −n nuclear amplitude.

Elastic scattering of π− mesons on protons in the coulomb-nuclear interference region at 33–60 GeV/ c

Differential cross sections for the elastic scattering of negative pions on protons, as well as total cross sections have been measured for the incident momentum range from 33 up to 60 GeV/ c. The values for four-momentum transfer were within the limits of −(10 −3−8·10 −2) (GeV/ c) 2. The energy dependence of the ratio ϱ(0) of the real part of the forward elastic scattering amplitude to the imaginary part has been determined from the experimental data. The magnitude ϱ(0) smoothly increases from (−10.9 ± 1.2)% at momenta 33.52 GeV/ c up to (−1.8 ± 1.8)% at 59.4 GeV/ c. The results obtained are compared with the predictions of theoretical models.

Coulomb effects in hadron-nucleus and nucleus-nucleus collisions and the hadron-neutron amplitude

Coulomb effects in high energy charged hadron-nucleus collisions are studied in a formalism which is exact within the framework of multiple diffraction theory and takes into account the extended charge effects of the incident hadron and the bound protons. Several more approximate but simpler formulas are also considered and their accuracy discussed. Results are extended to include heavy-ion collisions in the optical limit of the Glauber theory and in the Chou-Yang model. Applications are made to the proton-deuteron elastic and elastic plus quasielastic scattering measurements below 70 GeV to extract the ratio of real to imaginary part and the slope parameter of the proton-neutron elastic scattering amplitude. The results are compared with those from dispersion relation calculations and from earlier analyses. Approximate analytic formulas derived for $p\ensuremath{-}d$ scattering give results almost identical to the more exact expressions. For nucleus-nucleus collisions the Coulomb effects are found to be important over a rather wide range of momentum transfers.NUCLEAR REACTIONS $d(p, p)$, $E=10\ensuremath{-}70$ GeV; calculated $\ensuremath{\sigma}(E, \ensuremath{\theta})$ in Coulomb-nuclear interference region; deduced $p\ensuremath{-}n$ scattering amplitude parameters. $^{12}\mathrm{C}$, $^{58}\mathrm{Ni}$, $^{208}\mathrm{Pb}(p, p)$, $E=1.04$ GeV, $^{12}\mathrm{C}$($^{12}\mathrm{C}$, $^{12}\mathrm{C}$), $E=2.1$ GeV/nucleon; Coulomb effects, calculated $\ensuremath{\sigma}(\ensuremath{\theta})$.

Measurement of small-angle elastic scattering of pions and protons by nuclei

Targets made of C, Al, Cu, Pb, and U were exposed to ${\ensuremath{\pi}}^{+}$, ${\ensuremath{\pi}}^{\ensuremath{-}}$, and proton beams of 9.92 and 19.85 GeV/c (for $p$-Pb only) at the Brookhaven AGS. A magnetic spectrometer with spark chambers was used to detect elastically scattered particles in the Coulomb-nuclear interference region (5-35 mrad). Differential cross sections are presented and compared with an optical model, taking full account of multiple scattering in the target.

Polarization in Heavy-Ion Inelastic Scattering in the Coulomb-Nuclear Interference Region.

The polarization in the region of Coulomb-nuclear interference has been determined from the $\ensuremath{\gamma}$-ray correlation following excitation of the 856-keV ${2}^{+}$ state in $^{56}\mathrm{Fe}$ by 43-MeV $^{16}\mathrm{O}$ ions. Elastic and inelastic scattering cross sections were also measured. Dramatic interference effects are observed in the transition amplitudes which can be reproduced by coupled-channel distorted-wave calculations.