Coulomb-nuclear Interference Effects Research Articles

Some applications of the eikonal model with Coulomb and curvature corrections in pp and p¯p scattering

Using a simple eikonal approach to the treatment of Coulomb-nuclear interference and form-factors effects and taking into account the curvature effects in high-energy $pp$ and $\overline{p}p$ scattering, we determine the basic parameters $B$, $\ensuremath{\rho}$, and ${\ensuremath{\sigma}}_{\mathrm{tot}}$ from fits to experiment at $W=\sqrt{s}=53\text{ }\text{ }\mathrm{GeV}$, 62.3 GeV, 8 TeV, and 13 TeV. We then investigate the differential cross sections in the dip region for $pp$ and $\overline{p}p$ elastic scattering at $W=53\text{ }\text{ }\mathrm{GeV}$ and 1.96 TeV. We find that the results of the basic parameters calculated using the simple eikonal approach agree well with the values determined in other analyses. We also find that Coulomb effects are significant in the dip region at 53 GeV and 1.96 TeV, and must be taken into account in searches for odderon effects through cross section differences in that energy region.

Reply to “Comment on ‘Coulomb-nuclear interference effects in proton-proton scattering: A simple new eikonal approach’”

We clarify the connection between the results of Petrov in the preceding Comment and those in our previous paper on Coulomb-nuclear interference in proton-proton scattering in the region of very small momentum transfers. We calculate the correction to the approximation we used in that region, but not elsewhere, and show that it agrees with corresponding terms in Petrov's expression. The corrections are negligible in either form, and do not affect our previous results.

Comment on “Coulomb-nuclear interference effects in proton-proton scattering: A simple new eikonal approach”

This is a brief analysis of the basic formula from arXiv:2007.07827. Some inconsistency has been identified.

Coulomb-nuclear interference effects in proton-proton scattering: A simple new eikonal approach

We present a simple new approach to the treatment of Coulomb-nuclear interference and form-factor effects in high-energy proton-proton scattering in the context of an eikonal model for the spin-averaged scattering amplitude. We show that the corrections to the nuclear and Coulomb amplitudes do not depend sensitively on the details of the eikonal amplitude and can be taken as universal, and present parametrizations for the necessary corrections. We also present a simple model for the nuclear scattering amplitude useful for data analysis at small momentum transfer which builds in the proper nuclear phase and the diffraction zeros in the real and imaginary parts of the amplitude.

Antiproton scattering off3He and4He nuclei at low and intermediate energies

Antiproton scattering off ${}^{3}\mathrm{He}$ and ${}^{4}\mathrm{He}$ targets is considered at beam energies below 300 MeV within the Glauber-Sitenko approach, utilizing the $\overline{N}N$ amplitudes of the J\"ulich model as input. A good agreement with available data on differential $\overline{p}{\phantom{\rule{0.16em}{0ex}}}^{4}\mathrm{He}$ cross sections and on $\overline{p}{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{He}$ and $\overline{p}{\phantom{\rule{0.16em}{0ex}}}^{4}\mathrm{He}$ reaction cross sections is obtained. Predictions for polarized total $\overline{p}{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{He}$ cross sections are presented, calculated within the single-scattering approximation and including Coulomb-nuclear interference effects. The kinetics of the polarization buildup is discussed.

Spin-dependent p̄d cross sections at low and intermediate energies

Antiproton-deuteron (p̄d) scattering is calculated at beam energies below 300 MeV within the Glauber approach, utilizing the amplitudes of the Jülich N̄N models. A good agreement is obtained with available experimental data on upolarized differential and integrated p̄d cross sections. Predictions for polarized total p̄d cross sections are presented, obtained within the single scattering approximation including Coulomb-nuclear interference effects. It is found that the total longitudinal and transversal p̄d cross sections are comparable in absolute value to those for p̄p scattering. The kinetics of polarization buildup is considered.

Total spin-dependent p̄d cross sections at low and intermediate energies

The pd scattering reaction is investigated at beam energies 20–300 MeV within the Glauber approach, utilizing the amplitudes of the Julich pd models. The obtained results are in good agreement with available experimental data on differential and integrated pd cross sections. Double-scattering effects are evaluated explicitly and found to be in the order of 10–20%. Calculations of the polarized total pd cross sections are performed within the single scattering approximation. Coulomb-nuclear interference effects are taken into account. It is found that the total longitudinal and transversal pd cross sections are comparable in absolute value to those for pd p scattering.

Forwardp¯delastic scattering and total spin-dependentp¯dcross sections at intermediate energies

Spin-dependent total $\overline{p}d$ cross sections are considered using the optical theorem. For this aim the full spin dependence of the forward $\overline{p}d$ elastic scattering amplitude is considered in a model independent way. The single-scattering approximation is used to relate this amplitude to the elementary amplitudes of $\overline{p}p$ and $\overline{p}n$ scattering and the deuteron form factor. A formalism allowing to take into account Coulomb-nuclear interference effects in polarized $\overline{p}d$ cross sections is developed. Numerical calculations for the polarized total $\overline{p}d$ cross sections are performed at beam energies 20--300 MeV using the $\overline{N}N$ interaction models developed by the J\ulich group. Double-scattering effects are estimated within the Glauber approach and found to be in the order of 10--20%. Existing experimental data on differential $\overline{p}d$ cross sections are in good agreement with the performed Glauber calculations. It is found that for the used $\overline{N}N$ models the total longitudinal and transversal $\overline{p}d$ cross sections are comparable in absolute value to those for $\overline{p}p$ scattering.

Scaling and interference in the dissociation of halo nuclei

The dissociation of halo nuclei through their collision with light and heavy targets is considered within the Continuum Discretized Coupled Channels theory. We study the one-proton halo nucleus $^8$B and the one-neutron halo nucleus $^{11}$Be, as well as the more normal $^7$Be. The procedure previously employed to extract the Coulomb dissociation cross section by subtracting the nuclear one is critically assessed, and the scaling law usually assumed for the target mass dependence of the nuclear breakup cross section is also tested. It is found that the nuclear breakup cross section for these very loosely bound nuclei does indeed behave as $a+bA^{1/3}$. However, it does not have the geometrically inspired form of a circular ring which seems to be the case for normal nuclei such as $^{7}$Be. We find further that we cannot ignore Coulomb-nuclear interference effects, which may be constructive or destructive in nature, and so the errors in previously extracted B(E1) using the subtraction procedure are almost certainly underestimated.

Coulomb-nuclear coupling and interference effects in the breakup of halo nuclei

Nuclear and Coulomb breakup of halo nuclei have been treated often as incoherent processes and structure information have been extracted from their study. The aim of this paper is to clarify whether interference effects and Coulomb-nuclear couplings are important and how they could modify the simple picture previously used. We calculate the neutron angular and energy distributions by using first order perturbation theory for the Coulomb amplitude and an eikonal approach for the nuclear breakup. This allows for a simple physical interpretation of the results which are mostly analytical. Our formalism includes the effect of the nuclear distortion of the neutron wave function on the Coulomb amplitude. This leads to a Coulomb-nuclear coupling term derived here for the first time which gives a small contribution for light targets but is of the same order of magnitude as nuclear breakup for heavy targets. The overall interference is constructive for light to medium targets and destructive for heavy targets. Thus it appears that Coulomb breakup experiments need to be analyzed with more accurate models than those used so far.

Can one see Coulomb-nuclear interference effects in nucleon-nucleus scattering?

In Dirac phenomenology, a large Coulomb-nuclear interference term appears in the effective potential of the Schroedinger-like equation equivalent to the Dirac equation. This is apparently in strong contrast with the nonrelativistic approach and could be checked by a comparative study of neutron- and proton-nucleus scattering. A detailed calculation in a realistic case shows, however, that the interference effect is elusive.

Elastic and inelastic scattering of 16O and 18O ions from 64Zn at energies near the Coulomb barrier.

Coulomb-nuclear interference effects were investigated in the inelastic scattering of [sup 16]O and [sup 18]O by [sup 64]Zn. Measurements of elastic and inelastic angular distributions of [sup 18]O were performed at a laboratory energy of 49 MeV, over the angular range from [theta][sub lab][similar to]30[degree] to 85[degree]. The excitation functions of [sup 16]O and [sup 18]O ions were measured at incident energies between 29 and 46 MeV at [theta][sub lab]=174[degree]. The experimental angular distributions show structures which are more pronounced for projectile excitation than for target excitation. The interference minimum for the excitation of the [sup 18]O first 2[sup +] state was found to be shifted towards forward angles by approximately 5[degree] (c.m.) with respect to the distorted-wave Born approximation calculations and by approximately 3.5[degree] (c.m.) with respect to the coupled-channels calculations. A pronounced Coulomb-nuclear interference minimum was seen in the excitation of [sup 64]Zn(2[sup +]) state by inelastic scattering of [sup 16]O projectiles, whereas no pronounced minimum was observed in target excitation by [sup 18]O projectiles. The elastic scattering data were analyzed with the optical model. The inelastic differential cross sections for the excitation of the first 2[sup +] states in the target and in the [sup 18]O projectilemore » were analyzed using the distorted-wave Born approximation and also the coupled-channels approach with collective form factors.« less

Coulomb nuclear interference effects in the elastic and inelastic scattering of16O and18O ions on70Ge

Excitation functions of the elastic and inelastic scattering cross sections of16O and18O nuclei on70Ge have been measured at angles between 45° and 175° and at beam energies from 31.5 to 57 MeV. A DWBA analysis has been performed in which the composite structure of18O has been taken into account according to the approach developed by Landowne and Wolter. Starting from an optical model potential determined from the elastic scattering data in the16O+70Ge channel, a consistent description of the16O+70Ge (2+, 3−) target excitation, the18O+70Ge elastic scattering and18O(2+)+70Ge projectile excitation cross sections near the Coulomb barrier has been obtained.

Exclusion of nuclear forces in heavy-ion Coulomb excitation and Coulomb fission experiments

A simple prescription for estimating the energy at which nuclear forces begin to play a role in heavy-ion Coulomb excitation and Coulomb fission experiments is presented. The method differs from most commonly used recipes in accounting for projectile and target nucleus deformation effects. Using a single adjustable parameter the formula reproduces the energy for the onset of Coulomb-nuclear interference effects for a broad range of heavy-ion systems. It is suggested that most Coulomb fission experiments which have been done involve both Coulomb and nuclear excitation processes and should more properly be termed Coulomb-nuclear fission experiments.

Coulomb-nuclear interference in the inelastic projectile excitation ofNe20byCa40

Coulomb-nuclear interference effects were investigated in the inelastic scattering of /sup 20/Ne by /sup 40/Ca with excitation of the first 2/sup +/ state in /sup 20/Ne. Measurements were performed at 54 and 60.5 MeV for the elastic and inelastic angular distributions and from 36 to 95 MeV for the excitation functions. The elastic data were analyzed in terms of the optical model. The inelastic results were compared with distorted-wave Born-approximation and coupled channel calculations. The reorientation effect was investigated.

Integrated pion-nucleus cross sections

We propose an improved analysis for transmission experiments which determines uniquely, up to statistical error, the imaginary part of the forward nuclear amplitude. The analysis we propose takes the Coulomb interaction into account and is especially useful when the Coulomb-nuclear interference effects are large. In some cases the real part of the forward nuclear amplitude may also be extracted.

Derivation of a coupling potential for Coulomb-nuclear interference effects

A collective coupling potential for surface vibrations is calculated from an extended liquid drop model. It describes Coulomb and nuclear excitations. Applying the potential to the reaction $^{58}\mathrm{Ni}$($^{16}\mathrm{O}$, $^{16}\mathrm{O}\ensuremath{'}$)$^{58}\mathrm{N}\mathrm{i}*$, we obtain a good agreement with recent experimental data.NUCLEAR REACTIONS $^{58}\mathrm{Ni}$($^{16}\mathrm{O}$, $^{16}\mathrm{O}$)$^{58}\mathrm{N}\mathrm{i}*$, $E=34\ensuremath{-}58$ MeV; derivation of coupling potentials; calculated $\ensuremath{\sigma}(E)$.

Electric moments and charge deformation in even rare-earth nuclei

We present measurements of $E2$ and $E4$ transition matrix elements, and related ${\ensuremath{\beta}}_{2}$ and ${\ensuremath{\beta}}_{4}$ deformations, for eight even rare earth nuclei, by exploiting the effect of electric quadrupole and electric hexadecapole excitation on the multiple Coulomb excitation of states in their ground state bands. The Coulomb excitation probabilities for the ${0}^{+}$, ${2}^{+}$, and ${4}^{+}$ states in the ground state bands of the even rare earth nuclei $^{152,154}\mathrm{Sm}$, $^{158,160}\mathrm{Gd}$, $^{164}\mathrm{Dy}$, $^{166,168}\mathrm{Er}$, and $^{174}\mathrm{Yb}$ have been measured with $^{4}\mathrm{He}$ projectiles at several incident energies below the respective Coulomb barriers by direct detection, at backward angles, of elastically and inelastically scattered particles. The direct detection of scattered $^{4}\mathrm{He}$ particles was employed in order to eliminate the uncertainties involved in the detection of the deexcitation $\ensuremath{\gamma}$ rays, and to facilitate the determination of $M(E2;{0}^{+}\ensuremath{\rightarrow}{2}^{+})$ to about the $\frac{1}{2}$% accuracy required to obtain a meaningful measurement of $M(E4;{0}^{+}\ensuremath{\rightarrow}{4}^{+})$. Coulomb-nuclear interference effects in elastic and inelastic scattering were investigated, and it was demonstrated that Coulomb nuclear interference occurs at a much lower projectile energy than predicted by the simple classical formula for the Coulomb barrier, and manifests itself at different incident energies for elastic and inelastic scattering. The data on excitation probabilities were analyzed both with a semiclassical Coulomb excitation calculation, corrected for quantal effects in second order perturbation theory, and with a full quantal calculation, to determine the reduced electric transition matrix elements $M(E2;{0}^{+}\ensuremath{\rightarrow}{2}^{+})$ and $M(E4;{0}^{+}\ensuremath{\rightarrow}{4}^{+})$. Significant differences were found between the perturbation theory quantal treatment and the full quantal calculations. Static quadrupole and hexadecapole moments of the charge distribution were extracted from the measured transition matrix elements within the context of the rotational model. Using an axially symmetric deformed Fermi shape to parametrize the charge distribution, charge deformation parameters ${\ensuremath{\beta}}_{2}^{C}$ and ${\ensuremath{\beta}}_{4}^{C}$ deduced from the static moments, were found to follow the same general trends as the potential deformation parameters measured in nuclear scattering experiments well above the Coulomb barrier. For some nuclei the Coulomb excitation ${\ensuremath{\beta}}_{\ensuremath{\lambda}}^{C}$ values show what may be significant deviations from the nuclear potential deformations parameters. However, it is emphasized that, presently, the significance of such a comparison as well as the significance of a comparison with deformation parameters determined with other electromagnetic probes, is subject to the considerations introduced by the model dependence of each measurement, and diluted by the ambiguous correspondence between the quantities being measured in the different experiments.NUCLEAR REACTIONS $^{152,154}\mathrm{Sm}(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}})$, $^{158,160}\mathrm{Gd}(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}})$, $^{164}\mathrm{Dy}(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}})$, $^{166,168}\mathrm{Er}(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}})$, $^{174}\mathrm{Yb}(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}})$, ${E}_{\ensuremath{\alpha}}=8\ensuremath{-}17$ MeV; measured Coulomb excitation probabilities. Deduced $B(E2)$, $B(E4)$; extracted ${\ensuremath{\beta}}_{2}$, ${\ensuremath{\beta}}_{4}$ from rotational model and Fermi charge distribution. Enriched targets.

Elastic Scattering of 96-Mev Protons

The elastic scattering of 96-Mev protons from C, Al, Cu, Ag, Ta, Pb, and Th has been investigated at laboratory angles between 3\ifmmode^\circ\else\textdegree\fi{} and 60\ifmmode^\circ\else\textdegree\fi{}. A range telescope with an over-all energy resolution of 2.8 Mev was used to obtain the energy distribution of scattered protons at each angle of observation. The energy distributions are analyzed to obtain values for (1) an "upper limit" to the elastic cross section which includes slightly inelastic events, and (2) an "extrapolated" elastic cross section in which inelastic events are subtracted by an extrapolation procedure. All targets show diffraction minima and Coulomb-nuclear interference effects. The depth of the diffraction minima in general increases with atomic number, except that Ta and Th have less pronounced minima than either Ag or Pb.