Analysis of heavy ion reactions using projection operators

Abstract

A projection operator method based on the Feshbach doorway approach is developed for low-energy heavy-ion scattering. Applications to "C+"C and "C+"0are made with doorways taken as quasibound or virtual states of the reduced mass coupled to 2+ and 3 vibrations. For "C+"C the elastic differential cross section at 90' c.m. is calculated. For "C+"0 we calculate the ratio of the differential cross section to the Rutherford cross section at a range of angles between 90' and 160' c.m. In both cases the calculations agree well with experiment by producing both the gross and intermediate molecular structure. The conditions under which intermediate structure can be expected are discussed. NUCLEAR REACTIONS C+ C elastic scattering, E =10-30 MeV c.m. , C + i60 elastic scattering, E=18-26 MeV c.m. , projection operator intermediate structure theory, calculated 0 (90') for ' C+ C and 0/0~th (90'-160', increments of 10') for C+ O.

Projection Operator Treatment for Sub-Coulomb Widths

“…More extensive derivations can be found elsewhere. 7,14 The state |ψ of the system satisfies the Schroedinger equation,…”

“…1,2 The method proposed has resulted in identifying various resonances and extracting resonance parameters. [3][4][5][6][7][8][9][10] While the method has been successful at energies above the Coulomb barrier, at low energies, such as those found in α-decay, the sub-Coulomb resonances are difficult to handle by modern projection operator formalisms. More important is the fact that the widths obtained for α-decay are in some cases an order of magnitude larger than those obtained experimentally.…”

Particle decay of resonant state generated by direct reaction

“…In order to study these highly excited continuum states in connection with reaction theory, improved treatments of resonance formula are necessary and many papers have been published in this direction [7][8][9][10][11]. The purpose of this paper is to give a theoretical tool to treat these states.…”