Surface Transparent Potentials Research Articles

Transfer reactions at high energy and ambiguities in heavy-ion potentials

The smaller impact parameters that contribute to transfer reactions between heavy ions at high energies make them more sensitive to different types of optical potentials than is the case at lower energies. This may allow one to distinguish between potentials that otherwise generate similar elastic scattering cross sections within the limited angular region over which typical elastic data are available. We cite as evidence results for nucleon transfers induced by18O +28Si at 352 MeV which rule out surface transparent potentials.

Surface transparency inC12elastic scattering fromCa40,42,48

Angular distributions between 3 and 110 degrees in the laboratory system were measured for the elastic scattering of $^{12}\mathrm{C}$ from $^{40,42,48}\mathrm{Ca}$ at 51.0, 49.9, and 47.2 MeV, respectively. Pronounced oscillations were observed in the $^{12}\mathrm{C}$ + $^{40}\mathrm{Ca}$ angular distribution. Weaker oscillations were observed in the $^{12}\mathrm{C}$ + $^{42}\mathrm{Ca}$ angular distributions while none were seen in $^{12}\mathrm{C}$ + $^{48}\mathrm{Ca}$. An optical-model analysis was performed using Woods-Saxon and folded potentials. Surface transparent potentials were found to parametrize the oscillatory structure of the forward-angle data of $^{12}\mathrm{C}$ + $^{40}\mathrm{Ca}$. Stronger surface absorption in the $^{12}\mathrm{C}$ + $^{42,48}\mathrm{Ca}$ imaginary potentials apparently weakens or washes out any forward-angle oscillations. Optical potentials that fit forward-angle data of $^{12}\mathrm{C}$ + $^{40}\mathrm{Ca}$ also predict oscillatory structure in the excitation function at 180\ifmmode^\circ\else\textdegree\fi{}.NUCLEAR REACTIONS $^{40}\mathrm{Ca}$($^{12}\mathrm{C}$, $^{12}\mathrm{C}$)$^{40}\mathrm{Ca}$, $E=51$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$, measured $\ensuremath{\sigma}(E,\ensuremath{\theta}=180\ifmmode^\circ\else\textdegree\fi{})$. $^{42}\mathrm{Ca}$($^{12}\mathrm{C}$, $^{12}\mathrm{C}$)$^{42}\mathrm{Ca}$, $E=49.9$ MeV; $^{48}\mathrm{Ca}$($^{12}\mathrm{C}$, $^{12}\mathrm{C}$)$^{48}\mathrm{Ca}$, $E=47.2$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$.

Semiclassical analysis of the scattering of 16O by 28Si

Semiclassical analysis of the optical potentials which fit the recent Stony Brook-BNL 16 O + 28 Si scattering data, shows that the scattering mechanism of these potentials at backward angles is essentially the same. Neither the reflection from the sharp surface of the surface transparent potential used by Dehnhard and Shkolnik, Golin and Kahana, nor the modified form factor in the potential used by Lee and Chan is essential to fit the angular distribution. Based on the uniform approximation, we derive analytic formula to understand the angular distribution at backward angles and to understand the oscillatory structure in the 180° excitation functions.

Total fusion cross section for theO16+O16system

Total fusion cross sections ${\ensuremath{\sigma}}_{F}$ have been measured for $^{16}\mathrm{O}$+$^{16}\mathrm{O}$ at bombarding energies 27-66 MeV using the $E\ensuremath{-}\ensuremath{\Delta}E$ or the time-of-flight techniques. The fusion excitation function shows oscillations in agreement with the resonances produced in the total reaction cross section by a surface-transparent potential. The results are compared to those obtained via the $\ensuremath{\gamma}$-ray technique and the importance of direct decay to ground states is discussed. Mass and total angular distributions are well reproduced by statistical model calculations which take angular momentum into account explicity. Barrier and critical parameters are extracted from the average energy behavior of ${\ensuremath{\sigma}}_{F}$. No evidence for shell effects as predicted by Glas and Mosel is found on the measured fusion cross sections.NUCLEAR REACTIONS Complete fusion, $^{16}\mathrm{O}$+$^{16}\mathrm{O}$, ${E}_{\mathrm{lab}}=27\ensuremath{-}66$ MeV; measured fusion excitation function; statistical model analysis; extracted barrier and critical parameters.

A wave propagation matrix method in semiclassical theory

A wave propagation matrix method is used to derive the semiclassical formulae of the multi-turning-point problem. A phase shift matrix and a barrier transformation matrix are introduced to describe the process of a particle travelling through a potential well and crossing a potential barrier respectively. The wave propagation matrix is given by the products of phase shift matrices and barrier transformation matrices. We then apply the method to study scattering by surface transparent potentials and the Bloch wave in solids.

A semiclassical study of optical potentials: Potential resonances

The semiclassical method is used to analyze various optical potentials. Resonances in an optical potential appear as the interference between the ware reflected from the external barrier and the wave reflected from the interior part of the potential. The interference causes a dip in the amplitude of the total S-matrix and is related to the zero of the S-matrix. Optical potentials are analyzed in this framework. We found that (i) the enhanced backward angle cross section can be interpreted as being due to a single potential resonance only when the absorption is weak, (ii) the Regge pole parametrization studied by McVoy in his surface transparent potential represents the surface transparent property of the potential - it has nothing to do with a potential resonance - and (iii) the anomalous large angle scattering (ALAS) of α- 40Ca is due to the coherent contribution of many partial waves. The method is also useful to analyze the scattering by optical potentials in general.

Long life potential resonances in 16O 12C scattering from an l-dependent absorptive potential

A semiclassical theory is applied to elucidating essential features of 16O 12C scattering from an l-dependent absorptive potential. Long life potential resonances do occur for surface partial waves and cause an enhanced backangle differential cross section and a typical interference pattern at intermediate angles. The almost constant frequency of the backangle oscillation is, however, essentially due to the narrow l-window characteristic of surface transparent potentials.

Surface transparent potentials and a coupled-channel Born-approximation study of diffractive behavior in heavy-ion induced reactions

Coupled channel explanations, which have been offered for the diffractive behavior observed in the differential ground state-ground state cross sections of ($^{16}\mathrm{O}$, $^{18}\mathrm{O}$) reactions on Ni isotopes, are in apparent disagreement with data for transfer to the $^{18}\mathrm{O}$(${2}^{+}$) state. A study of available quasielastic reaction data, elastic, inelastic, and transfer suggests the surface-transparent potentials both can better describe the optical phenomena observed in the angular shapes and can minimize effects due to coupled channels. As a byproduct a description, which does not require a large $^{18}\mathrm{O}$($2_{1}^{}{}_{}{}^{+}$) quadrupole moment, is obtained for the troublesome angular distribution in $^{18}\mathrm{O}$ + $^{58}\mathrm{Ni}$ inelastic scattering.[NUCLEAR REACTIONS CCBA analysis ($^{16}\mathrm{O}$, $^{18}\mathrm{O}$) reaction on Ni isotopes and all related quasielastic processes. Dependence on optical potentials examined.]

Optical potential for 12C + 28Si scattering

12C + 28Si elastic scattering angular distributions are smooth functions, relatively easily fit by optical potential predictions, at laboratory bombarding energies, E 1 ab , within ≈ 10 MeV of the Coulomb barrier (i.e. up to E 1 ab ≈ 27 MeV). Between E 1 ab = 27 and 36 MeV the angular distributions show pronounced oscillatory structure which is not easily fit with an optical potential. No optical potential has been found to give a very good account of all the angular distributions simultaneously; the best simultaneous fit to all the data was achieved with a surface-transparent potential whose real and imaginary well depths are energy dependent.

Surface transparency of optical potentials deduced from heavy-ion scattering studies

The elastic and inelastic cross-sections of 16,18O and 12C scattered from targets of even-even Ge and Ni isotopes have been measured over an angular range 12.5°–100° (laboratory angle) at E 16,180 = 56 MeV and E 12C = 48 MeV. By simultaneously fitting the angular distributions for the ground state (0 +) and first-excited level (2 +) using a coupled-equations search routine, we have been able to determine the optical potential parameters almost uniquely. The optical potentials so obtained exhibit two characteristic features: (1) the well depth of the imaginary part of the potential is larger than the well depth of the real part and (2) the radius and diffuseness of the imaginary part are respectively smaller than those of the real part. In addition, the deflection function corresponding to such surface transparent potentials displays a significant minimum at the grazing angular momentum.

Physical Basis for Enhanced Forward Cross Sections in Heavy-Ion Reactions

Calculations show that indirect transitions can explain the forward cross section observed in some experiments, in particular $^{60}\mathrm{Ni}$($^{18}\mathrm{O}$, $^{16}\mathrm{O}$). Normal optical potentials which fit elastic and inelastic data are used in the analysis. An earlier analysis in terms of a surface transparent potential is shown to depend sensitively on a scaling factor that was introduced to simulate recoil effects. However when recoil is properly taken into account it is found that the surface transparent potential does not reproduce the data.

Exact finite-range coupled-channels Born approximation analysis ofC13-induced reactions

Different descriptions of the reaction $^{28}\mathrm{Si}$ ($^{13}\mathrm{C}$, $^{12}\mathrm{C}$) $^{29}\mathrm{Si}$ at 36 MeV leading to the ground and first excited states of $^{29}\mathrm{Si}$ are examined. Sensitivity of the reaction cross section to various families of optical parameters is investigated and the so-called "surface transparent potential" is used as an alternate treatment. Exact finite-range distorted-wave Born approximation and coupled-channels Born approximation analyses of the reaction are performed, showing that the coupled-channels Born approximation analysis, even in its presently restricted form, leads to an improvement over the distorted-wave Born approximation predictions.NUCLEAR REACTIONS $^{28}\mathrm{Si}$ ($^{13}\mathrm{C}$, $^{12}\mathrm{C}$) calculated cross sections using exact finiterange CCBA with "surface transparent potential."