Similarity between nuclear rainbow and meteorological rainbow -- evidence for nuclear ripples

We present evidence for the nuclear ripples superimposed on the Airy structure of the nuclear rainbow, which is similar to the meteorological rainbow. The mechanism of the nuclear ripples is also similar to that of the meteorological rainbow, which is caused by the interference between the externally reflective waves and refractive waves. The nuclear ripple structure was confirmed by analyzing the elastic angular distribution in $^{16}$O+$^{12}$C rainbow scattering at $E_L$=115.9 MeV using the coupled channels method by taking account of coupling to the excited states of $^{12}$C and $^{16}$O with a double folding model derived from a density-dependent effective nucleon-nucleon force with realistic wave functions for $^{12}$C and $^{16}$O. The coupling to the excited states plays the role of creating the external reflection.Comment: 6 pages, 6 figure

Evidence for a secondary bow in Newton's zero-order nuclear rainbow

Rainbows are generally considered to be caused by static refraction and reflection. A primary and a secondary rainbow appear due to refraction and internal reflection in a raindrop as explained by Newton. The quantum nuclear rainbow, which is generated by refraction in the nucleus droplet, only has a "primary" rainbow. Here we show for the first time evidence for the existence of a secondary nuclear rainbow generated dynamically by coupling to an excited state without internal reflection. This has been demonstrated for experimental $^{16}$O+$^{12}$C scattering using the coupled channel method with an extended double folding potential derived from microscopic realistic wave functions for $^{12}$C and $^{16}$O.Comment: 5 pages, 4 figure

Emergence of a secondary rainbow and the dynamical polarization potential for ¹⁶O on ¹²C at 330 MeV

Background: It was shown recently that an anomaly in the elastic scattering of 16O on 12C at around 300 MeV is resolved by including within the scattering model the inelastic excitation of specific collective excitations of both nuclei, leading to a secondary rainbow. There is very little systematic knowledge concerning the contribution of collective excitations to the interaction between nuclei, particularly in the overlap region when neither interacting nuclei are light nuclei. Purpose: Our goals are to study the dynamic polarization potential (DPP) generated by channel coupling that has been experimentally validated for a case (16O on 12C at around 300 MeV) where scattering is sensitive to the nuclear potential over a wide radial range; to exhibit evidence of the nonlocality due to collective coupling; to validate, or otherwise invalidate, the representation of the DPP by uniform renormalizing folding models or global potentials. Methods: S-matrix to potential, SL → V (r), inversion yields local potentials that reproduce the elastic channel S matrix of coupled channel calculations. Subtracting the elastic channel uncoupled potential yields a local L-independent representation of the DPP. The dependence of the DPP on the nature of the coupled states and other parameters can be studied. Results: Local DPPs were found due to the excitation of 12C and the combined excitation of 16O and 12C. The radial forms were different for the two cases, but each were very different from a uniform renormalization of the potential. The full coupling led to a 10% increase in the volume integral of the real potential. Evidence for the nonlocality of the underlying formal DPP and for the effect of direct coupling between the collective states is presented. Conclusions: The local DPP generating the secondary rainbow has been identified. In general, DPPs have forms that depend on the nature of the specific excitations generating them, but, as in this case, they cannot be represented by a uniform renormalization of a global model or folding model potential. The method employed herein is a useful tool for further exploration of the contribution of collective excitations to internuclear potentials, concerning which there is still remarkably little general information

Supersolidity of α\alpha cluster structure in 40^{40}Ca

$\alpha$ cluster structure in nuclei has been long understood based on the geometrical configuration picture. By using the spatially localized Brink $\alpha$ cluster model in the generator coordinate method, it is shown that the $\alpha$ cluster structure has the apparently opposing duality of crystallinity and condensation, a property of supersolids. To study the condensation aspects of the $\alpha$ cluster structure a field theoretical superfluid cluster model (SCM) is introduced, in which the order parameter of condensation is incorporated by treating rigorously the Nambu-Goldstone mode due to spontaneous symmetry breaking of the global phase. The $\alpha$ cluster structure of $^{40}$Ca, which has been understood in the crystallinity picture, is studied by the SCM with ten $\alpha$ clusters. It is found that the $\alpha$ cluster structure of $^{40}$Ca is reproduced by the SCM in addition to $^{12}$C reported in a previous paper, which gives support to the duality of the $\alpha$ cluster structure. The emergence of the mysterious $0^+$ state at the lowest excitation energy near the $\alpha$ threshold energy is understood to be a manifestation of the Nambu-Goldstone zero mode, a soft mode, due to the condensation aspect of the duality similar to the Hoyle state in $^{12}$C. The duality of $\alpha$ cluster structure with incompatible crystallinity and coherent wave nature due to condensation is the consequence of the Pauli principle, which causes clustering.Comment: 12 pages, 8 figure