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Register a new userElastic $alpha$ transfer in the $^{16}$O+$^{12}$C scattering and its impact on the nuclear rainbow
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Elastic $^{16}$O+$^{12}$C scattering is known to exhibit the nuclear rainbow pattern at incident energies $E_text{lab}gtrsim 200$ MeV, with the Airy structure of the far-side scattering cross section clearly seen at medium and large angles. Such a rainbow pattern is well described by the deep real optical potential (OP) given by the double-folding model (DFM). At lower energies, the extensive elastic $^{16}$O+$^{12}$C scattering data show consistently that the nuclear rainbow pattern at backward angles is deteriorated by an oscillating enhancement of elastic cross section that is difficult to describe in the conventional optical model (OM). Given a significant $alpha$ spectroscopic factor predicted for the dissociation $^{16}$O$toalpha+^{12}$C by the shell model and $alpha$-cluster models, the contribution of the elastic $alpha$ transfer (or the core-core exchange) to the elastic $^{16}$O+$^{12}$C scattering should not be negligible and is expected to account for the enhanced elastic cross section at backward angles. To reveal the impact of the elastic $alpha$ transfer, a systematic coupled reaction channels analysis of the elastic $^{16}$O+$^{12}$C scattering has been performed, with the coupling between the elastic scattering and elastic $alpha$ transfer channels treated explicitly, using the real OP given by the DFM. We found that the elastic $alpha$ transfer enhances the near-side scattering significantly at backward angles, giving rise to an oscillating distortion of the smooth Airy structure. The dynamic polarization of the OP by the coupling between the elastic scattering and elastic $alpha$ transfer channels can be effectively taken into account in the OM calculation by an angular-momentum (or parity) dependent potential added to the imaginary OP, as suggested by Frahn and Hussein 40 years ago.
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The elastic scattering $^{16}$O$+^{12}$C angular distributions at $^{16}$O bombarding energies of 100.0, 115.9 and 124.0 MeV and their optical model description including the $alpha$-particle exchange contribution calculated in the Coupled Reaction Channel approach are presented. The angular distributions show not only the usual diffraction pattern but also, at larger angles, intermediate structure of refractive origin on which finer oscillations are superimposed. The large angle features can be consistently described including explicitly the elastic $alpha$-transfer process and using a refractive optical potential with a deep real part and a weakly absorptive imaginary part.
Inelastic $^{16}$O +$^{12}$C rainbow scattering to the $2^+$ (4.44 MeV) state of $^{12}$C was measured at the incident energies, $E_L$ = 170, 181, 200, 260 and 281 MeV. A systematic analysis of the experimental angular distributions was performed using the coupled channels method with an extended double folding potential derived from realistic wave functions for $^{12}$C and $^{16}$O calculated with a microscopic $alpha$ cluster model and a finite-range density-dependent nucleon-nucleon force.The coupled channels analysis of the measured inelastic scattering data shows consistently some Airy-like structure in the inelastic scattering cross sections for the first $2^+$ state of $^{12}$C, which is somewhat obscured and still not clearly visible in the measured data. The Airy minimum was identified from the analysis and the systematic energy evolution of the Airy structure was studied. The Airy minimum in inelastic scattering is found to be shifted backward compared with that in elastic scattering.
The molecular algebraic model based on three and four alpha clusters is used to describe the inelastic scattering of alpha particles populating low-lying states in $^{12}$C and $^{16}$O. Optical potentials and inelastic formfactors are obtained by folding densities and transition densities obtained within the molecular model. One-step and multi-step processes can be included in the reaction mechanism calculation. In spite of the simplicity of the approach the molecular model with rotations and vibrations provides a reliable description of reactions where $alpha$-cluster degrees of freedom are involved and good results are obtained for the excitation of several low-lying states. Within the same model we briefly discuss the expected selection rules for the $alpha$-transfer reactions from $^{12}$C and $^{16}$O.
The algebraic molecular model is used in $^{12}$C to construct densities and transition densities connecting low-lying states of the rotovibrational spectrum, first and foremost those belonging to the rotational bands based on the ground and the Hoyle states. These densities are then used as basic ingredients to calculate, besides electromagnetic transition probabilities, nuclear potentials and formfactors to describe elastic and inelastic $alpha$+$^{12}$C scattering processes. The calculated densities and transition densities are also compared with those obtained by directly solving the problem of three interacting alphas within a three-body approach where continuum effects, relevant in particular for the Hoyle state, are properly taken into account.
We present a new picture that the $alpha$-linear-chain structure for ${^{12}{rm C}}$ and ${^{16}{rm O}}$ has one-dimensional $alpha$ condensate character. The wave functions of linear-chain states which are described by superposing a large number of Brink wave functions have extremely large overlaps of nearly $100%$ with single Tohsaki-Horiuchi-Schuck-Ropke (THSR) wave functions, which were proposed to describe the $alpha$ condensed gas-like states. Although this new picture is different from the conventional idea of the spatial localization of $alpha$ clusters, the density distributions are shown to have localized $alpha$-clusters which is due to the inter-$alpha$ Pauli repulsion.
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