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

Farside-dominant quasinuclear rainbow in refractive α\alpha+α\alpha scattering

$\alpha$+$\alpha$ scattering has a long history since the first experiment by Rutherford and Chadwick in 1927 and has been studied thoroughly experimentally and theoretically. However, $\alpha$+$\alpha$ scattering has never been paid attention from the viewpoint of refractive scattering. I have successfully analyzed the experimental angular distributions in $\alpha$+$\alpha$ scattering systematically over a wide range of incident energies $E_L$=53.4 - 280 MeV using a phenomenological optical model with a deep real potential. The existence of a farside-dominant quasinuclear rainbow with no well-defined rainbow angle and no supernumerary bow in the lit side followed by the shadow, which is not a genuine rainbow but a refractive scattering from a marginally small droplet at high energies, is found for the first time in $\alpha$+$\alpha$ scattering. The refraction due to the deep potentials with an attractive core at short distances are discussed from the viewpoint of the Luneburg. The deep vs shallow problem of the potential and the nuclear rainbow scattering in inelastic channels are also discussed.Comment: 8 pages, 6 figure

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