Farside Components Research Articles

Study of the rainbow-like pattern in the elastic scattering of 16O on 27Al at Elab. = 100 MeV

Recently, a rainbow pattern in the elastic scattering of 16O + 27Al at Elab. = 100 MeV was reported. In the present paper, we show that the predicted change of slope of the cross section, as a function of angle, is mostly due to the far-side component of the scattering, which is affected by the inelastic couplings. The experimental data is consistent with the calculations up to the inflection point, where the effect of the couplings is significant. New experimental data, in very good agreement with the theoretical expectations around the Coulomb rainbow angle, are also presented.

Elastic scattering of heavy ions and nucleus-nucleus potential with a repulsive core

Elastic scattering of 12C + 12C at 139.5, 158.8 MeV and 16O + 12C at 132, 169 MeV was analyzed in the framework of an optical model using the repulsive-core nucleus-nucleus potential. Calculations with and without consideration of the core were performed and the influence of the core on the elastic scattering cross section was analyzed. It was shown that taking account of the core leads to an increase in the elastic scattering cross section for backward angles. The decomposition of the scattering amplitude into nearside and far-side components was studied.

Deuteron elastic scattering and stripping processes offC12as a three-body problem

Deuteron elastic scattering and stripping processes off a target nucleus consisting of A nucleons are treated within the framework of the few-body integral equations theory. By projecting the ($A+2$)-body operators onto target states, matrix three-body integral equations are derived that allow for the incorporation of the excited states of the target nucleons. This approach is applied to deuteron scattering off $^{12}\mathrm{C}$ when the latter is in its ground state before and after the reaction. For the nucleon-$^{12}\mathrm{C}$ subsystem three sets of (quasi-separable) potentials are employed. The first such potential is based on the one derived by Cattapan et al. [Nucl. Phys. A241, 204 (1975)] for orbital angular momentum states with $L\ensuremath{\leqslant}2$, which is valid for low energies. As second set we use the potential of Miyagawa and Koike [Prog. Theor. Phys. 82, 329 (1989)] fitted to semiphenomenological higher-energy phase shifts for states up to $L=6$. The third one finally consists for $3\ensuremath{\leqslant}L\ensuremath{\leqslant}5$ of the potential set of Miyagawa and Koike, whereas the potential parameters for $L\ensuremath{\leqslant}2$ are determined by simultaneously fitting the elastic-channel T matrix obtained as solution of multichannel two-body Lippmann-Schwinger equations, to the experimental low-energy and the semiphenomenological higher-energy phase shifts. For the nucleon-nucleon interaction we take one of the separable ${}^{3}{S}_{1}\ensuremath{-}{}^{3}{D}_{1}$ potentials of Phillips [Nucl. Phys. A107, 207 (1968)]. Differential cross sections for the elastic-scattering reaction $d+$$^{12}\mathrm{C}$ $\ensuremath{\rightarrow}d+$$^{12}\mathrm{C}$ and the transfer reaction $d+$$^{12}\mathrm{C}$ $\ensuremath{\rightarrow}p+$$^{13}\mathrm{C}$($^{13}\mathrm{C}$${}^{*}$) are calculated at deuteron bombarding energies of 4.66 and 15 MeV (up to 36-channel calculation), and at 56 MeV (up to 76-channel calculation) together with some selected analyzing powers, and are compared with experimental data. At the highest energy considered, the decomposition of the differential cross section into the near-side and the far-side components shows the appearance of nuclear rainbow scattering.

Rotation Measure and Opacity Asymmetry in 2134+004

AbstractBased on the free–free absorption (FFA) model of gigahertz peaked spectrum (GPS) sources, we explain both Faraday rotation asymmetry and opacity asymmetry consistently between two components of a GPS quasar 2134+004. The FFA model assumes dense plasma around the central core to produce FFA, and the difference of path lengths in the plasma toward each component could cause these asymmetries. The component that is closer to the observer has a shorter path length, and consequently, smaller opacity of FFA and lower Faraday rotation. In a simple case, the ratio of Faraday rotation between two components is a function of the ratio of path length, and is the same as the ratio of opacity. Then these two ratios are shown to be essentially the same by our observations. We could thus distinguish between near-side and far-side components by the asymmetries.

Shrinking  as a recipe for revealing classical-like properties of optical-potential cross-sections

A simple recipe for revealing classical-like properties of optical-potential cross-sections is proposed. The recipe is based on the fact that the classical properties are not expected to depend on the actual value of . This allows us to identify the classical-like characteristics of an optical-potential cross-section by simply repeating the calculation with different values of , and observing which properties of the cross-section are invariant. The method is applied to the cross-sections of a few optical potentials used to describe the recent data of light heavy-ion elastic scattering. An improved near-side/far-side decomposition is used to separate the near-side and far-side components of the optical-potential cross-sections.

COULOMB-MODIFIED EIKONAL MODEL ANALYSIS OF REFRACTIVE12C+12CELASTIC SCATTERING AT Elab= 240 AND 360MeV

We present the Coulomb-modified eikonal model by using a tangential velocity at the distance of closest approach. The Fraunhöfer oscillations observed in the elastic angular distributions of the12C +12C system at Elab= 240 and 360 MeV can be explained due to the strong interference between the near- and far-side scattering amplitudes. We have found that the strongly real and weakly imaginary potentials are required to describe the refractive12C +12C elastic scatterings at Elab= 240 and 360 MeV. The refractive pattern, dominated by the far-side component of the scattering amplitude, can be shown to be sensitive to the real part of optical potential at small radius. Introducing the tangential velocity, it is shown that the Coulomb-modified eikonal model satisfactorily reproduces experimental data concerning the refractive pattern in the angular distributions of the12C +12C system at Elab= 240 and 360 MeV.

Airy structure in16O+16Oelastic scattering between 5 and 10 MeV/nucleon

We have applied the barrier-wave/internal-wave decomposition technique to ${}^{16}\mathrm{O}{+}^{16}\mathrm{O}$ elastic scattering optical model angular distributions between 75 and 145 MeV, an energy region where strong refractive effects---in particular Airy maxima and minima---are clearly observed; this technique, introduced in a semiclassical framework more than 20 years ago by Brink and Takigawa, and which was successful in clarifying the light-ion elastic scattering mechanism, has practically never been used in the context of light heavy-ion scattering. The decomposition is accomplished by using a fully quantum-mechanical method, which bypasses the intricacies of the semiclassical approach. The Airy minima are found to be due to the interference of the barrier-wave and internal-wave subamplitudes; the presence of a substantial internal-wave contribution demonstrates in a very clear way the exceptional transparency displayed by the ${}^{16}\mathrm{O}{+}^{16}\mathrm{O}$ system. The results obtained contrast with those of the nearside/farside decomposition technique, where the Airy minima are fully carried by the farside contribution. By combining the two approaches it is possible to calculate in a straightforward way the two components underlying the structure of the farside component, which up to now have been obtained through delicate semiclassical calculations or the use of an approximate empirical method. The complicated evolution of the full elastic cross section can eventually be explained in terms of the interference of several subamplitudes with a much smoother, and thus much simpler to understand, behavior. A barrier-wave/internal-wave decomposition of the 132 MeV ${}^{16}\mathrm{O}{+}^{12}\mathrm{C}$ and 100 MeV ${}^{18}\mathrm{O}{+}^{12}\mathrm{C}$ elastic scattering amplitudes is also presented.

Nuclear-rainbow effect by transfer reactions

Nuclear-rainbow effects in elastic and inelastic scattering and transfer reactions by the 3He + 12C and 4He + 12C interactions at E( 3He) = 98 MeV and E( 4He) = 90 MeV respectively are observed analyzing the angular distributions of the 2,3H, 3,4He and 6Li particles. The data have been analyzed by a near/far-side formalism using Fuller's model. It has been shown that the far-side component plays the main role in all studied processes. The present investigation proposes a method for the optical model parameter choice for entrance and exit channels. We also observe the different characteristics of the rainbow effects and of the shape of the angular distributions for very deep inelastic processes (high excitation energies) and transfer reactions.

Nuclear-rainbow effects by transfer reactions in the α_12C interaction

Angular distributions of the12C (α, α′)12C elastic and inelastic 0 scattering at 72, 81 and 90MeV incident energy and of the12C(α,3He)13C,12C(α,3H)13N and12C(α, d)14N reactions atE α=90 MeV with one-and two-nucleon transfer have been measured. The data have been analysed by a near/far-side formalism. It has been shown that the far-side component plays the main role in all studied processes. The present investigation proposes a method for the optical-model parameter choice for entrance and exit channels. Nuclear rainbow in very deep inelastic processes (high excitation energies) and transfer reactions was observed.

Enormous spin polarization in heavy-ion-induced one-nucleon transfer reactions.

We show a possible large spin polarization of nuclei produced by one-nucleon transfer reactions predicted by the direct reaction theory. We investigate its origins in terms of the magnetic-sub-state cross sections by decomposing those into near-side and far-side components. The asymmetry of the particle-\ensuremath{\gamma} angular correlation followed by decay of the spin-polarized nucleus is also calculated.

Evidence for a nuclear halo from 11Li elastic scattering measured at 637 MeV incident energy on a 12C target.

An optical model analysis of the elastic scattering of $^{11}\mathrm{C}$ and $^{11}\mathrm{Li}$ on $^{12}\mathrm{C}$ target nuclei has been performed, for measurements at 620 and 637 MeV laboratory incident energy, respectively. The data are from the group of the University of Notre Dame. It has turned out, in the case of the $^{11}\mathrm{Li}$ projectile, that it was necessary to use a real and imaginary surface potential peaked very far outside of the nucleus core, in order to reproduce the elastic scattering angular distribution at very forward angles. The extracted optical model reaction cross section leads to a radius of 3.7 fm for $^{11}\mathrm{Li}$ in agreement with what is already known in the literature from interaction cross section measurements. On the contrary, the extracted radius for the $^{11}\mathrm{C}$ nucleus is 2.5 fm in this experiment. Furthermore, at this high incident energy, a strong far-side component on $^{11}\mathrm{Li}$ is evidenced by a Fuller analysis. This large radius for the $^{11}\mathrm{Li}$ nucleus, added to the fact that strong refractive effects are observed in the elastic scattering, is a clear signature of a nuclear halo for the $^{11}\mathrm{Li}$ nucleus.

Symmetry properties of nearside and farside amplitudes in polarised heavy-ion scattering

The elastic and inelastic scattering amplitudes in the collision of 44 MeV polarised 7Li by 26Mg are analysed in terms of their nearside and farside components. It is shown that in the case of kinematic matching (elastic scattering and inelastic scattering to the first excited 1/2- state of 7Li), the nearside amplitude has a symmetry around the recoil direction and the tidal spin is conserved, and thus the corresponding analysing powers satisfy shape-effect relations. The symmetry is violated in the nearside amplitude in the case of kinematic mismatch and the farside amplitude is not symmetric around the recoil direction irrespective of kinematic matching conditions.

The effects of far-side dominance on the j-dependence of the medium energy 116Sn(d, p) 117Sn reaction

We report measurements of the 116Sn(d, p) 117Sn reaction to the d 3 2 , g 7 2 , and h 11 2 low-lying states at 79.0 MeV. Transfer reaction calculations which include an adiabatic deuteron channel wavefunction, finite range including the deuteron S- and D-state, and non-locality corrections are performed for these transitions. A separation of the reaction amplitude into the near- and far-side components shows that the g 7 2 and h 11 2 reaction calculations are far-side dominated. In this context, the proton channel spin-orbit distortions modify the j-dependence of the A y vector analyzing power and introduce a strong j-dependence in the A yy tensor analyzing power.

Nearside-farside analysis of elastic scattering of polarized 3He

An exact decomposition of the scattering amplitudes into the nearside and farside components has been performed for the elastic scattering of 33 MeV 3He particles by nuclei. Calculations have been carried out for 40Ca, 54Fe, 89Y, 90,91Zr, 207,208Pb and 209Bi and compared with the available cross section and polarization data. In particular the behaviour of the vector analysing powers is examined. Calculations of the interference between the nearside and farside components demonstrate that the interference plays a significant role in certain mass/energy regions. Regions where the scattering is dominated by the nearside component are discussed.

Asymmetric deflection functions and the extinction of rainbows: A comparison of α-particle scattering from 40Ca and 44Ca

A decomposition of elastic scattering amplitudes into their nearside and farside components is employed to exhibit the presence of a striking farside (“nuclear”) rainbow in the angular distributions for α + 40Ca scattering at energies from 36 to 61 MeV. The rainbow is identified by a deep “Airy minimum” which is present in the farside components of the angular distributions throughout this energy region. Over the same energy range, the angular distributions for the more absorptive α + 44Ca scattering exhibit no Airy minima, and, in this sense, show no nuclear rainbow. However, a steepening of the slope of their smooth farside component, which appears at energies above that (∼60 MeV) for which the rainbow angle for α + 40Ca becomes less than 180°, may serve to identify a residual rainbow effect, even in α + 44Ca, at energies above 60 MeV. The manner in which the Airy minima of this and other nuclear rainbows are extinguished by absorption is examined in detail and is found to depend critically on the asymmetry in the shape of their deflection functions at low energies.

Microscopic optical-model analysis of α- 40Ca elastic scattering at 104 MeV through the near/far decomposition

The microscopic α- 40Ca optical potential constructed in previous papers is examined with respect to the near/far components of the α elastic scattering cross section at 104 MeV recently extracted from the experimental data. A renormalization of the real part of the potential by a multiplicative constant allows one to reproduce the position of the oscillations of the farside component. However, their amplitude is too weak and the absolute value of the farside component is overestimated. Adding a very weak surface term to the imaginary potential, which was shown to be sufficient to describe the (α, α) elastic scattering and the ( 3He, α) transfer reaction beyond 100 MeV, improves the absolute value of the farside component but is insufficient to reproduce the amplitude of the oscillations which is shown to be determined by the strength of the imaginary potential. Once the microscopic imaginary potential is modified at small distances the agreement with “experimental” near/far components is quite satisfactory.

Microscopic optical-model analysis of α-Ca elastic scattering at 104 MeV through the near/far decomposition

The microscopic α- 40 Ca optical potential constructed in previous papers is examined with respect to the near/far components of the α elastic scattering cross section at 104 MeV recently extracted from the experimental data. A renormalization of the real part of the potential by a multiplicative constant allows one to reproduce the position of the oscillations of the farside component. However, their amplitude is too weak and the absolute value of the farside component is overestimated. Adding a very weak surface term to the imaginary potential, which was shown to be sufficient to describe the (α, α) elastic scattering and the ( 3 He, α) transfer reaction beyond 100 MeV, improves the absolute value of the farside component but is insufficient to reproduce the amplitude of the oscillations which is shown to be determined by the strength of the imaginary potential. Once the microscopic imaginary potential is modified at small distances the agreement with “experimental” near/far components is quite satisfactory.

Nearside-farside analyses of heavy-ion direct reactions to the continuum

Decompositions into nearside and farside (NF) components are made of heavy-ion continuum cross sections calculated within the multi-step direct reaction (MSDR) method including one- and two-step processes. The approach is applied to the 16O + 48Ti system at E lab around 100 MeV and to the 16O + 208Pb system at E lab = 192 MeV, and both cross sections and polarizations of the residual nucleus are considered. It is seen that at higher energy losses the two-step contributions become dominant, and that for scattering angles beyond the grazing angle these two-step contributions are mainly farsided. The relative importance of the NF components depends sensitively on the balance between Coulomb repulsion and nuclear attraction. The magnitude of the farside contribution also depends critically on the use of a polarization potential in the excited states. This potential is treated empirically. The decompositions are usefully interpreted in terms of a simple model for multi-step deflection functions. The results of the present quantum-mechanical approach to continuum heavy-ion reactions exhibit many of the features of classical calculations of deepinelastic processes.

Nearside-farside analysis of inelastic heavy-ion scattering

Using a 'turning-wave' decomposition of the inelastic scattering amplitude, analogous to that employed in the elastic scattering of spin-zero nuclei, the authors give a qualitative interpretation of various properties of inelastic reactions. As in the elastic case, amplitudes of various dynamical origins exist, though they do not discuss here the effect of internal waves or of Coulomb excitation. Many of the arguments are based on the form of the DWBA radial integral and show how the concept of an angular momentum mismatch, due to the nonadiabaticity of the reaction, may be applied directly at the level of the entrance- and exit-channel wavefunctions. The authors discuss particularly a 'quasiclassical' limit in which the populations of the various magnetic substates are related in a simple way to one basic amplitude. At a given scattering angle these populations are essentially proportional to the angular part of the excited state's wavefunction evaluated at the points of closest approach for the corresponding nearside and farside 'trajectories'. It is shown that it is the relative sign of these wavefunctions for points on opposite sides of the nucleus which gives rise to the Blair phase rule. In this quasiclassical limit the spin of the excited state is left precessing about the recoil direction. In order to quantify some of the results the authors derive an analytic expression based on the Hahne prescription for the inelastic radial integrals in which they employ the McIntyre parametrisation of the elastic S matrix. The consequences of an angular momentum mismatch on the polarisation of the excited state and on the symmetry angle for its subsequent gamma decay are discussed in terms of nearside and farside components and they study in particular the phenomenon of the rapid reverse rotation of this symmetry angle.

A nearside-farside analysis of deep inelastic reactions

Continuum multi-step direct-reaction theory is combined with a decomposition of the scattering amplitude into its near-and farside components. It is possible with these techniques to explain, in a quantum-mechanical framework, the increased importance of negative-angle scattering for large energy losses in deep inelastic collisions.