Airy Minima Research Articles

Evidence for16O+16Ocluster bands in32S

Evidence for the existence of the lowest $N=24$ and $N=28$ cluster bands with the ${}^{16}\mathrm{O}{+}^{16}\mathrm{O}$ cluster structure in ${}^{32}\mathrm{S}$ is shown from the viewpoint of unified description of bound and scattering states of the ${}^{16}\mathrm{O}{+}^{16}\mathrm{O}$ system. The ${}^{16}\mathrm{O}{+}^{16}\mathrm{O}$ cluster band structure, the gross structure of the $90\ifmmode^\circ\else\textdegree\fi{}$ excitation function ${\mathrm{for}}^{16}\mathrm{O}{+}^{16}\mathrm{O}$ elastic scattering, and the Airy minima are understood in a unified way. The existence of the unobserved $N=26$ higher nodal band is predicted.

Refractive elastic scattering of carbon and oxygen nuclei: The mean field analysis and Airy structures

The experimental data on the $^{16}$O$+^{12}$C and $^{18}$O$+^{12}$C elastic scatterings and their optical model analysis are presented. Detailed and complete elastic angular distributions have been measured at the Strasbourg Vivitron accelerator at several energies covering the energy range between 5 and 10 MeV per nucleon. The elastic scattering angular distributions show the usual diffraction pattern and also, at larger angles, refractive effects in the form of nuclear rainbow and associated Airy structures. The optical model analysis unambiguously shows the evolution of the refractive scattering pattern. The observed structure, namely the Airy minima, can be consistently described by a nucleus-nucleus potential with a deep real part and a weakly absorptive imaginary part. The difference in absorption in the two systems is explained by an increased imaginary (mostly surface) part of the potential in the $^{18}$O$+^{12}$C system. The relation between the obtained potentials and those reported for the symmetrical $^{16}$O$+^{16}$O and $^{12}$C$+^{12}$C systems is drawn.

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.

New measurement of the refractive, elastic16O+12Cscattering at 132, 170, 200, 230, and 260 MeV incident energies

For the first time, differential cross section of the ${}^{16}\mathrm{O}{+}^{12}\mathrm{C}$ elastic scattering at ${E}_{\mathrm{lab}}=170,$ 200, 230, and 260 MeV has been measured over a wide angular range which covers both diffractive and refractive regions. In addition, the recent data at 132 MeV for this system have been remeasured with much better statistics. A well developed rainbow structure has been observed, where up to three Airy minima could be identified in each measured angular distribution. The optical model analysis of these data was done using the conventional Woods-Saxon shape for the optical potential as well as that given by the folding model. The Airy systematics enabled us to suggest a realistic family of the optical potential for the ${}^{16}\mathrm{O}{+}^{12}\mathrm{C}$ system, which consistently describes the new data as well as the data measured earlier at incident energies of 608 and 1503 MeV. Our results show that the ${}^{16}\mathrm{O}{+}^{12}\mathrm{C}$ system is a very suitable heavy-ion combination for the study of refractive phenomena, which can give important information on the nucleus-nucleus potential at small distances.

Airy minimum crossing θcm = 90° at Elab = 124 MeV for the [formula omitted] system

We have measured the elastic scattering angular distribution for the 16O + 16O system at E lab = 124 MeV, where a prominent minimum has been observed in the θ cm = 90° excitation function. The measured angular distribution shows modulated Airy structures at large angles with a dip at θ cm = 90°. It is concluded that the prominent minimum in the excitation function is due to an Airy minimum, most likely to be the third member, crossing 90° at that energy.

Observation of Airy oscillation for the 16O+ 16O system at Elab = 145 MeV

We have measured elastic scattering angular distribution at E lab= MeV for the 16O+ 16O system, for which nuclear rainbow scattering has been observed recently at E lab = 350 MeV. Analysis of the present data shows that the observed dip at θ cm ≅ 54° and the modulated peak at θ cm ≅62° are an Airy minimum and an Airy maximum, respectively. We found several discrete sets of optical potentials which fit the data. One of them provides a real volume integral which agrees with the previously proposed energy dependence.

Quasielastic scattering of 11Li and 11C from 12C at 60 MeV/nucleon.

The quasielastic scattering of the exotic ``halo'' nucleus $^{11}\mathrm{Li}$ on $^{12}\mathrm{C}$ has been studied at an energy of 60 MeV/nucleon and compared with that of the A=11 isobar $^{11}\mathrm{C}$. The prediction of enhanced refraction in the former system is confirmed, as is the need for very long-range absorption. No evidence is found for an Airy minimum in the far-side scattering.

The 90° excitation function for elastic 12C + 12C scattering : The importance of Airy elephants

The 90° excitation function for elastic 12C + 12C scattering, at laboratory energies between the Coulomb barrier and 130 MeV, exhibits a complex structure of peaks and valleys whose nature has remained an unsolved mystery for more than 20 years. The problem has primarily been caused by the difficulty of choosing from a plethora of discretely ambiguous optical potentials. However, data accumulated above 150 MeV over the last decade have determined unique potentials at these higher energies, and the requirement of continuity downward in energy has recently permitted the determination of a unique set of potentials for angular distributions at energies below 130 MeV, where the excitation-function data exist. These new potentials are used to provide a mean-field (i.e., nonresonant) interpretation of the structure in the 12C + 12C 90° excitation function between 70 and 130 MeV. Its most prominent minima are found to be Airy minima from nuclear rainbows, with the remaining structure arising primarily from more elementary optical phenomena related to Fraunhofer diffraction. These same potentials are also successful in explaining the details of excitation functions measured very recently at other angles by Morsad.

Analysis of an unusual potential ambiguity for [formula omitted] scattering

Woods-Saxon optical-potential fits to recent measurements of 16O+ 16O elastic scattering at 350 MeV have been interpreted as providing clear evidence for a nuclear rainbow. Three model-independent potentials have also recently been found to reproduce these data. Two of them were indeed found to be members of a rainbow series, in which a distinctive minimum near 44° is the first or second Airy minimum of a rainbow pattern, but the scattering by the third (shallower) potential was less easy to interpret. We show here that this potential achieves its fit to the data by a different and somewhat unconventional mechanisms. This serves as a reminder that ambiguities in interpretation can persist, even with as extensive and accurate a data set as this measurement provides.

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.