Angular correlation, spin alignment, and systematics of mis-matched 12C+12C inelastic scattering resonances

Abstract

Particle gamma-ray angular correlation measurements have been used to study the spin alignment and magnetic-substate population parameters for the 2 + 1 (4.443 MeV) state in 12 C, populated in the 12 C( 12 C, 12 C[0 + 2 ]) 12 C(2 + 1 ) inelastic scattering reaction in the vicinity of a prominent, narrow peak in the scattering excitation function. The data show a strong alignment of the spin with the orbital angular momentum, and suggest that the cross section peak corresponds to a spin 14 + resonance at E c.m. = 28.0 MeV. This energy is close to that where a strong peak is also observed in the 0 + 1 + 0 + 2 excitation function. A comparison between the data for these two channels lends some support to recent theoretical calculations of resonance behavior for angular-momentum-mismatched channels in 12 C + 12 C inelastic scattering.The study of resonance behavior in the 12 C + 12 C system has occupied nuclear physicists for the better part of four decades. The resonances observed in various 12 C + 12 C inelastic scattering channels display a rich variety of phenomena, ranging from very narrow resonances near the Coulomb barrier, to broader (1-2 MeV wide) structures at higher bombarding energies. The common, simple and perhaps naive interpretation of these phenomena is that they correspond to large-scale collective behavior in the 12 C + 12 C sys-

Cluster models from RGM to alpha condensation and beyond

“…[113] that, as far as ξ 1 is chosen as the coordinate of the internal one-particle density matrix, the form of the internal one-particle density matrix calculated with any kind of internal coordinate system becomes necessarily the same as the one obtained with the Jacobi coordinate system, namely the form given in Eq. (121). Here the (n − 2) internal coordinates other than ξ 1 should be chosen to be orthogonal to ξ 1 because the coordinate ξ 1 should be maximally independent from the other internal coordinates [113].…”

“…(121) and Y (r) is also given by Y (ξ 1 )/ξ 1 ∝ ⟨χ n−1 |χ n ⟩ ∝ exp(−ν 1 ξ 2 1 ). Thus it is very useful to compare, for the present Hoyle state of 3α system, the single-α S-wave orbit rφ(r) with the 8 Be(0 + ) + α reduced-width amplitude Y (r) which is shown in Fig.…”

“…+ 16 C(g.s.) [118][119][120][121][122][123][124]. Theoretically, an elaborate coupled channel calculation of the 12 C + 12 C system including not only 12 C(g.s.)…”