Forward glory and the determination of the nuclear forward amplitude from heavy-ion elastic scattering

doi:10.1016/0375-9474(85)90445-2

Nuclear Physics A

Volume 441, Issue 4, 19 August 1985, Pages 733-756

https://doi.org/10.1016/0375-9474(85)90445-2 Get rights and content

Abstract

It is shown that a forward glory phenomenon is present in the elastic scattering angular distribution of heavy ions. The general properties of the glory determine the conditions under which it is possible to obtain both the amplitude and phase of the nuclear forward amplitude ƒ_N(0) from elastic angular distributions. Examples are given which show that even in strongly absorbing systems this amplitude is relatively large and can be easily measured. It is demonstrated that the knowledge of ƒ_N(0) provides a unique piece of information on the origin of the backward rise and of the resonances observed in heavy-ion-induced reactions.

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Cited by (20)

Nuclear forward glory scattering with stable and unstable nuclei; how to deduce σ<inf>r</inf> and f<inf>N</inf> (0<sup>o</sup>)?
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Citation Excerpt :
(iii) In particle physics, one type of phenomenological model based on the tunneling of surface waves is very consistent with observations of high-energy proton–proton scattering. As far as particle physics is concerned (i.e. high-energy nucleon–nucleon scattering), the concept of tunneling associated with surface waves has been exploited to describe hadronic diffraction [202,203]. In elastic collisions, hadrons (elementary particles that interact via the strong force) can be treated as extended objects in that there is a domain of interaction with a characteristic shape and size (in the center-of-mass system).
A detailed qualitative summary of the optical rainbow is provided at several complementary levels of description, including geometrical optics (ray theory), the Airy approximation, Mie scattering theory, the complex angular momentum (CAM) method, and catastrophe theory. The phenomenon known commonly as the glory is also discussed from both physical and mathematical points of view: backward glories, rainbow-glories and forward glories. While both rainbows and glories result from scattering of the incident radiation, the primary rainbow arises from scattering at about 138° from the forward direction, whereas the (backward) glory is associated with scattering very close to the backward direction. In fact, it is a more complex phenomenon physically than the rainbow, involving a variety of different effects (including surface waves) associated with the scattering droplet. Both sets of optical phenomena—rainbows and glories—have their counterparts in atomic, molecular and nuclear scattering, and these are addressed also. The conceptual foundations for understanding rainbows, glories and their associated features range from classical geometrical optics, through quantum mechanics (in particular scattering from a square well potential; the associated Regge poles and scattering amplitude functions) to diffraction catastrophes. Both the scalar and the electromagnetic scattering problems are reviewed, the latter providing details about the polarization of the rainbow that the scalar problem cannot address. The basis for the complex angular momentum (CAM) theory (used in both types of scattering problem) is a modification of the Watson transform, developed by Watson in the early part of this century in the study of radio wave diffraction around the earth. This modified Watson transform enables a valuable and accurate approximation to be made to the Mie partial-wave series, which while exact, converges very slowly at high frequencies. The theory and many applications of the CAM method were developed in a fundamental series of papers by Nussenzveig and co-workers (including an important interpretation based on the concept of tunneling), but many other contributions have been made to the understanding of these beautiful phenomena, including descriptions in terms of so-called diffraction catastrophes. The rainbow is a fine example of an observable event which may be described at many levels of mathematical sophistication using distinct mathematical approaches, and in so doing the connections between several seemingly unrelated areas within physics become evident.
Glory "in the shadow of the rainbow"
1999, Nuclear Physics A
We show that the angular distribution of the nuclear scattering amplitude behaves like the zeroth-order Bessel function with a fixed frequency at extremely forward angles even if there exists no genuine forward glory scattering. A semiclassical interpretation of this behaviour is provided in terms of the effect of scattering in the shadow of the nuclear rainbow. We also argue that the bombarding energy dependence of the amplitude of the sum-of-difference cross section at very small angles provides a possibility to judge whether genuine forward nuclear glory scattering is taking place or not.
Measurements of the total reaction cross section using the sum-of-differences method
1998, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
A precise measurement of the total reaction cross sections in a model independent way was made using the sum-of-differences (SOD) method in ¹²C, ¹³C, ¹⁵N, ¹⁶O+²⁸Si elastic scattering at incident energies much higher than the Coulomb barrier. Cross Sections have been measured in an angular range of θ_lab=0.6°∼2.0° with high accuracy. The scattering amplitudes at θ=0° and the total reaction cross sections were deduced from the present observation by the SOD method. These total reaction cross sections were compared with the results obtained from optical model analyses. Furthermore, it was shown that the contribution of the complete-fusion process to the total-reaction cross section in the ¹²C+²⁸Si scattering system was 75% at E_cm=45.5 MeV.
Forward nuclear glory scattering of a halo nucleus
1996, Nuclear Physics A
We show that characteristics of the elastic scattering of a halo nucleus manifest themselves in the forward nuclear glory scattering. Using the analysis of the sum of difference cross section, we demonstrate that the nuclear scattering amplitude at extremely forward angles is strongly enhanced compared with that in the scattering of stable nuclei if the projectile in heavy-ion collisions is a halo nucleus. Another characteristic is that the first glory minimum shifts towards a smaller angle. This can be seen if one can choose a scattering system, where the Coulomb rainbow angle is larger than the first glory minimum.
Energy levels of light nuclei A = 11-12
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Forward glory and the determination of the nuclear forward amplitude from heavy-ion elastic scattering

Abstract

Ann. of Phys.

Prog. Part. Nucl. Phys.

Nucl. Phys.

Phys. Lett.

Phys. Lett.

Lett. Nuovo Cim.

Nuovo Cim.

Phys. Rev.

Z. Phys.

Z. Phys.

Z. Phys.

Phys. Rev.

Phys. Lett.

Phys. Rev.

Phys. Rev.

Phys. Rev. Lett.

Phys. Rev. Lett.

Phys. Rev. Lett.

Phys. Rev.

Z. Phys.

Phys. Rev.

Phys. Rev.