Light Heavy-ion Systems Research Articles

ELASTIC AND INELASTIC ALPHA TRANSFER IN THE 16O+12C SCATTERING

The elastic scattering cross section measured at energies $E\lesssim 10$ MeV/nucleon for some light heavy-ion systems having two identical cores like \oc exhibits an enhanced oscillatory pattern at the backward angles. Such a pattern is known to be due to the transfer of the valence nucleon or cluster between the two identical cores. In particular, the elastic $\alpha$ transfer has been shown to originate directly from the core-exchange symmetry in the elastic \oc scattering. Given the strong transition strength of the $2^+_1$ state of $^{12}$C and its large overlap with the $^{16}$O ground state, it is natural to expect a similar $\alpha$ transfer process (or inelastic $\alpha$ transfer) to take place in the inelastic \oc scattering. The present work provides a realistic coupled channel description of the $\alpha$ transfer in the inelastic \oc scattering at low energies. Based on the results of the 4 coupled reaction-channels calculation, we show a significant contribution of the $\alpha$ transfer to the inelastic \oc scattering cross section at the backward angles. These results suggest that the explicit coupling to the $\alpha$ transfer channels is crucial in the studies of the elastic and inelastic scattering of a nucleus-nucleus system with the core-exchange symmetry.\Keywords{optical potential, coupled reaction channels, inelastic $\alpha$ transfer

Elastic and Inelastic Alpha Transfer in the \(^{16}\)O+\(^{12}\)C Scattering

The elastic scattering cross section measured at energies \(E\lesssim 10\) MeV/nucleon for some light heavy-ion systems having two identical cores like \(^{16}\)O+\(^{12}\)C exhibits an enhanced oscillatory pattern at the backward angles. Such a pattern is known to be due to the transfer of the valence nucleon or cluster between the two identical cores. In particular, the elastic \(\alpha\) transfer has been shown to originate directly from the core-exchange symmetry in the elastic \(^{16}\)O+\(^{12}\)C scattering. Given the strong transition strength of the $2^+_1$ state of $^{12}$C and its large overlap with the $^{16}$O ground state, it is natural to expect a similar \(\alpha\) transfer process (or inelastic \(\alpha\) transfer) to take place in the inelastic \(^{16}\)O+\(^{12}\)C scattering. The present work provides a realistic coupled channel description of the \(\alpha\) transfer in the inelastic \(^{16}\)O+\(^{12}\)C scattering at low energies. Based on the results of the 4 coupled reaction-channels calculation, we show a significant contribution of the \(\alpha\) transfer to the inelastic \(^{16}\)O+\(^{12}\)C scattering cross section at the backward angles. These results suggest that the explicit coupling to the \(\alpha\) transfer channels is crucial in the studies of the elastic and inelastic scattering of a nucleus-nucleus system with the core-exchange symmetry.

Elastic transfer and parity dependence of the nucleus-nucleus optical potential

Background: A recent coupled reaction channel (CRC) study shows that the enhanced oscillation of the elastic $^{16}$O+$^{12}$C cross section at backward angles is due mainly to the elastic $\alpha$ transfer or the core exchange. Such a process gives rise to a parity-dependent term in the total elastic $S$-matrix, an indication of the parity dependence of the $^{16}$O+$^{12}$C optical potential (OP). Purpose: To explicitly determine the core exchange potential (CEP) induced by the symmetric exchange of the two $^{12}$C cores in the elastic $^{16}$O+$^{12}$C scattering at $E_{\rm lab}= 132$ and 300 MeV, and explore its parity dependence. Method: $S$-matrix generated by CRC description of the elastic $^{16}$O+$^{12}$C scattering is used as the input for the inversion calculation to obtain the effective local OP that contains both the Wigner and Majorana terms. Results: The high-precision inversion results show a strong contribution by the complex Majorana term in the total OP of the $^{16}$O+$^{12}$C system, and thus provide for the first time a direct estimation of the parity-dependent CEP. Conclusions: The elastic $\alpha$ transfer or exchange of the two $^{12}$C cores in the $^{16}$O+$^{12}$C system gives rise to a complex parity dependence of the total OP. This should be a general feature of the OP for the light heavy-ion systems that contain two identical cores.

Fusion hindrance for the positive Q -value system C12+Si30

Background: The fusion reaction 12C+30Si is a link between heavier cases studied in recent years, and the light heavy-ion systems, e.g., 12C+12C, 16O+16O that have a prominent role in the dynamics of stellar evolution. 12C+30Si fusion itself is not a relevant process for astrophysics, but it is important to establish its behavior below the barrier, where couplings to low-lying collective modes and the hindrance phenomenon may determine the cross sections. The excitation function is presently completely unknown below the barrier for the 12C+30Si reaction, thus no reliable extrapolation into the astrophysical regime for the C+C and O+O cases can be performed. Purpose: Our aim was to carry out a complete measurement of the fusion excitation function of 12C+30Si from well below to above the Coulomb barrier, so as to clear up the consequence of couplings to low-lying states of 30Si, and whether the hindrance effect appears in this relatively light system which has a positive Q value for fusion. This would have consequences for the extrapolated behavior to even lighter systems. Methods: The inverse kinematics was used by sending 30Si beams delivered from the XTU Tandem accelerator of INFN-Laboratori Nazionali di Legnaro onto thin 12C (50μg/cm2) targets enriched to 99.9% in mass 12. The fusion evaporation residues (ER) were detected at very forward angles, following beam separation by means of an electrostatic deflector. Angular distributions of ER were measured at Ebeam=45, 59, and 80 MeV, and they were angle integrated to derive total fusion cross sections. Results: The fusion excitation function of 12C+30Si was measured with high statistical accuracy, covering more than five orders of magnitude down to a lowest cross section ≃3μb. The logarithmic slope and the S factor have been extracted and we have convincing phenomenological evidence of the hindrance effect. These results have been compared with the calculations performed within the model that considers a damping of the coupling strength well inside the Coulomb barrier. Conclusions: The experimental data are consistent with the coupled-channels calculations. A better fit is obtained by using the Yukawa-plus-exponential potential and a damping of the coupling strengths inside the barrier. The degree of hindrance is much smaller than the one in heavier systems. Also a phenomenological estimate reproduces quite closely the hindrance threshold for 12C+30Si, so that an extrapolation to the C+C and O+O cases can be reliably performed.

Experimental investigations of the sub-Coulomb 12C+12C and 12C+16O reactions

Cluster resonances in light heavy-ion systems like 12C+12C and 12C+16O may have a major impact on astrophysics stellar scenarios. Resonant radiative capture reactions have been studied for these systems at energies at and slightly below their Coulomb barriers to investigate the possible 12C-12C and 12C-16O molecular origin of the resonances. Spins have been attributed to the resonances and specificities of their γ-decay have been identified. At deep sub-barrier energies, a fusion cross section measurement using the particle-γ coincidence technique is discussed for the 12C+12C system. A new project is presented to possibly extend the 12C+12C S low-energy S factor study.

Sub- and near-barrier fusion reactions experimental results

Early data of sub-barrier fusion teached us that cross sections may strongly depend on the structure of colliding nuclei and on couplings to transfer channels. The influence of transfer is clearly indicated in the excitation functions of different nickel isotopes and various Ca+Zr systems. Fusion barrier distributions often yield the fingerprint of the relevant inelastic and transfer couplings. At lower energies, far below the barrier the slope of the excitation function keeps increasing in many cases, so that the cross sections are strongly over-predicted by standard coupled-channels (CC) calculations; this was named a hindrance effect.Furthermore, light heavy-ion systems show cross section oscillations above the Coulomb barrier. Recent experiments have been performed on the fusion of 28,30 Si+ 28,30 Si systems where all phenomena cited above show up. In particular regular oscillations that have been revealed above the barrier for 28 Si+ 28 Si and have been interpreted as the consequence of the strong channel couplings and/or the oblate deformation of 28 Si.

Fusion of28Si +28Si: oscillations above the barrier and the behavior down to 1μb

Fusion excitation functions of light heavy-ion systems show oscillatory structures above the Coulomb barrier, caused by resonances or due to the penetration of successive centrifugal barriers well separated in energy. In heavier systems, the amplitude of oscillations decreases and the peaks get nearer to each other. This makes the measurements very challenging.

Dynamics aspect of subbarrier fusion reaction in light heavy ion systems

Subbarrier fusion of the 7Li+12C reaction is studied using an antisymmetrized molecular dynamics model (AMD) with an after burner, GEMINI. In AMD, 7 Li shows an α + t structure at its ground state and it is significantly deformed. Simulations are made near the Coulomb barrier energies, i.e., Ecm = 3 — 8MeV. The total fusion cross section of the AMD + GEMINI calculations as a function of incident energy is compared to the experimental results and both are in good agreement at Ecm > 3MeV. The cross section for the different residue channels of the AMD + GEMINI at Ecm = 5MeV is also compared to the experimental results.

Local approximations for polarization potentials

We discuss the derivation of an equivalent polarization potential independent of angular momentum $l$ for use in the optical Schr\"odinger equation that describes the elastic scattering of heavy ions. Three different methods are used for this purpose. Application of our theory to the low energy scattering of light heavy-ion systems at near-barrier energies is made. It is found that the notion of an $l$-independent polarization potential has some validity but cannot be a good substitute for the $l$-dependent local equivalent Feshbach polarization potential.

Expectations forC12andO16induced fusion cross sections at energies of astrophysical interest

The extrapolations of cross sections for fusion reactions involving $^{12}\mathrm{C}$ and $^{16}\mathrm{O}$ nuclei down to energies relevant for explosive stellar burning have been reexamined. Based on a systematic study of fusion in heavier systems, it is expected that a suppression of the fusion process will also be present in these light heavy-ion systems at extreme sub-barrier energies due to the saturation properties of nuclear matter. Previous phenomenological extrapolations of the $S$ factor for light heavy-ion fusion based on optical model calculations may therefore have overestimated the corresponding reaction rates. A new ``recipe'' is proposed to extrapolate $S$ factors for light heavy-ion reactions to low energies taking the hindrance behavior into account. It is based on a fit to the logarithmic derivative of the experimental cross section which is much less sensitive to overall normalization discrepancies between different data sets than other approaches. This method, therefore, represents a significant improvement over other extrapolations. The impact on the astrophysical reaction rates is discussed.

Nuclear Orbiting At Low Energy Nuclear Collisions

The emissions of projectile-like fragments from light and medium heavy ion reactions have been discussed. In the case of certain nuclear reactions, such as, 24Mg+16O, 28Si+12C etc. among light heavy ion systems and 16O+89Y, 16O+93Nb etc. among medium heavy ion systems, both a 1 / sin θ c . m . angular distribution for projectile-like fragments and strong entrance channel dependence favoring breakup into the entrance channel with large excitation energy have been observed. We think these observations imply the formation of a long-lived orbiting dinuclear complex where the nuclei maintain their identities and nucleon exchange between them is highly suppressed. The analysis of fragment spectra show that the projectile-like fragments coming from such an orbiting dinuclear complex give significantly lower temperature compared to that of the respective compound nucleus.

Airy structure in inelastic light-ion and light heavy-ion scattering

We suggest that the transparency displayed by some light heavy-ion systems, such as $^{16}\mathrm{O}+^{16}\mathrm{O}$, $^{16}\mathrm{O}+^{12}\mathrm{C}$, or $^{12}\mathrm{C}+^{12}\mathrm{C}$, which manifests itself by the emergence of Airy structure in the elastic scattering angular distributions and excitation functions, could also have observable consequences in some inelastic channels. Indeed benchmark calculations for the $\ensuremath{\alpha}+^{40}\mathrm{C}\mathrm{a}$ light-ion system, where a similar mechanism dominates elastic scattering at low energy, reveals the persistence in inelastic scattering of the interference mechanism between the barrier-wave and internal-wave components of the scattering amplitude which underlies the Airy structure in the elastic channel. These calculations seem to point to new phase rules between the elastic and inelastic angular distributions.

Interpretation of airy minima in 16O+16O and 16O+12C elastic scattering in terms of a barrier-wave/internal-wave decomposition

The observation of refractive effects in 16O+16O and 16O+12C elastic scattering data has definitively established the fact that the optical potential for some light heavy-ion systems is relatively transparent and that its real part is deep. Most of the interpretations of the rainbow features of these data rely on the so-called nearside-farside decomposition of the scattering amplitude. Starting from recent optical model analyses of 16O+16O and 16O+12C elastic scattering around 100 MeV incident energy as an example, we present an alternative interpretation based on the barrier-wave/internal-wave decomposition first proposed by Brink and Takigawa. This method, which complements the nearside-farside approach, demonstrates clearly the exceptional transparency of the 16O+16O, and to a lesser extent 16O+12C, interactions at the investigated energies and makes possible the extraction of the two contributions whose interference explains the Airy oscillations seen in the farside amplitude.

Detailed study and mean field interpretation of16O+12Celastic scattering at seven medium energies

Detailed measurements of the elastic scattering of ${}^{16}\mathrm{O}$ ions from ${}^{12}\mathrm{C}$ have been carried out at seven energies from 62 to 124 MeV, at center-of-mass angles from about $10\ifmmode^\circ\else\textdegree\fi{}$ to about $145\ifmmode^\circ\else\textdegree\fi{}.$ A coherent optical model analysis of these data has been performed using both the Woods-Saxon and the folding-model potentials. The extracted results are consistent with analyses of data at higher energies for this and similar light heavy-ion systems. Some model-independent spline forms for the real potentials were also investigated.

Dissipative processes in light heavy ion collisions

The characteristics of the dissipative processes in the collisions of light heavy ion systems at incident energies below 10 MeV/nucleon have been studied. The correlations between different experimental observables show similar trends as those known at much heavier systems and semiempirical relationships are established starting from assumptions on the nature of the microscopic mechanisms. The charge equilibration process in light systems is also studied.

Barrier and internal wave contributions to the quantum probability density and flux in light heavy-ion elastic scattering

We investigate the properties of the optical model wave function for light heavy-ion systems where absorption is incomplete, such as $\ensuremath{\alpha}{+}^{40}$Ca and $\ensuremath{\alpha}{+}^{16}$O around 30 MeV incident energy. Strong focusing effects are predicted to occur well inside the nucleus where the probability density can reach values much higher than that of the incident wave. This focusing is shown to be correlated with the presence at back angles of a strong enhancement in the elastic cross section, the so-called ALAS (anomalous large angle scattering) phenomenon; this is substantiated by calculations of the quantum probability flux and of classical trajectories. To clarify this mechanism, we decompose the scattering wave function and the associated probability flux into their barrier and internal wave contributions within a fully quantal calculation. Finally, a calculation of the divergence of the quantum flux shows that when absorption is incomplete, the focal region gives a sizable contribution to nonelastic processes.

Hints of a nearside nuclear rainbow in pion scattering from 208Pb at 291 MeV?

The scattering of π ±+ 208 Pb at 291 MeV can be described by an optical potential with a repulsive real part which is strong enough by itself to sustain a nuclear rainbow in the nearside scattering. We examine this in detail, using a semiclassical analysis, and find that including a physically realistic amount of absorption completely changes the nature of the scattering so that the rainbow language is no longer appropriate. We compare the pion case with the scattering of light heavy-ion systems which appeat to suffer comparable absorption, yet for which the rainbow language remains significant and useful. We conclude that, in fact, the pion scattering is better characterized as strong absorption scattering than is the case for the heavy ions.

The extended optical model with dispersion relation for the fusion of light heavy-ion systems

Fusion excitation functions were calculated for light heavy-ion systems in the whole measured energy range. The calculations were performed by using the extended optical model for fusion which was applied with success for above-Coulomb-barrier energies. This model is based on the separate absorptive potential for fusion. The modification of the extended optical-model potential in the sub-barrier region occurs in its real and imaginary energy-dependent parts through the dispersion relation. The effect of the critical angular-momentum cut-off has been obtained by the decrease of W fus( E) at the high-energy region. A very good description of the experimental fusion cross sections were obtained for the following systems: 12C+ 12C, 12C+ 14N, 12C+ 16O, and 16O+ 16O. A detailed discussion of the parameters of the model is presented.

Competition between the fusion-fission and deep-inelastic orbiting mechanisms in the35Cl +12C reaction

The binary decay properties of the47V nucleus, produced in the35Cl +12C reaction, have been investigated at the35Cl bombarding energiesE lab = 180 and 200 MeV by means of a kinematical coincidence technique. Binary reaction products show full energy equilibration and a characteristic 1/sin(θ cm) angular distribution. The elemental distribution of the fully-damped products is asymmetric, similar to what has previously been observed in the decay of the56Ni nucleus. Comparison with theoretical model predictions suggests the occurrence of a fusion-fission rather than orbiting process. Moreover the calculations performed using the Extended Hauser-Feshbach Method reproduce well the experimental fission yields. A general discussion of orbiting and fusionfission experimental data of light heavy-ion systems is presented in the framework of the calculated number of available open channels for these systems.

Chaos in heavy-ion dynamics at low energy

We discuss the quantum analog of classical chaotic scattering in the case of a collision between a deformed and a spherical nucleus. In agreement with previous investigations on model potentials, a firm correspondence between classical and quantal scattering is established; when wild oscillations in the classical deflection function are predicted, sharp irregular quantal fluctuations in the excitation functions and angular distributions appear. This behaviour occurs around the centrifugal barrier and for deformed light nuclei. Both in classical and quantum dynamics coexistence of regular and irregular motion is obtained. Chaotic scattering could be the natural explanation of those fluctuations observed in the experimental cross sections as a function of energy and scattering angle for light heavy-ion systems.