Measure of the spatial size for the monopole excitation in proton scattering

Abstract

We formulate a scattering radius, which will be demonstrated to be a good measure of the spatial size of a general exclusive reaction. The scattering radius is presented in a framework of the partial-wave expansion method in a general two-body scattering problem. A microscopic coupled-channel calculation is performed for proton scattering by 12 C in the range of the proton's incident energy, E p = 29.95-200 MeV, and the scattering radii are evaluated for elastic scattering and inelastic scattering, going to the Hoyle 0 + 2 state with a well-developed 3α structure. A prominent enhancement of the scattering radius is clearly confirmed in the 3α final channel in comparison to the elastic channel. The scattering radius is also calculated for excitation to the giant monopole resonance (GMR) in a microscopic coupled-channel framework. The scattering radius for the 3α excitation is much more enhanced than the scattering radius for the GMR excitation. The proton's incident-energy dependence of the scattering radius is also investigated, and the energy systematics strongly suggest that the scattering radius can characterize the spatial size of a reaction area, which is determined by the matter radius of a nucleus excited to a final state.

Evidence of enhanced threeαradius inα+12C inelastic scattering

“…The radius of the final-state production, which is called the scattering radius (R S C ), is simply obtained according to the classical relation ofL = kR S C . R S C naturally goes to the matter radius of a target nucleus in the high energy limit of the proton elastic scattering [6,13,18]. The results ofL and R S C for the 2 + 1 and 2 + 2 states are summarized in table 1.…”

“…3 clearly means that the production area of the 2 + 2 state is more extended than the area of the 2 + 1 production. The distribution in the L-space can be transformed into a size of the production area of the final state by applying the method of the scattering radius [13]. In this method, the effective orbital spinL for the transition of 0 + → 2 + 1,2 is derived according to the following expression:…”

“…Thus, the cross sections are calculated for each of J, which are called the partial cross section. The distribution of the partial cross sections are used to characterize the spatial size for the final state production [13].…”

“…We believe that it is still important to consider a relation between an inelastic scattering and the size of the coupling potential. Recently, we have formulated the method of scattering radius, which can characterize a spatial size of the reaction area or a size of the coupling potential for the individual exit channels in a general exclusive reactions [13]. In this method, the angle-integrated cross section decomposed into each of the incident partial wave are used to measure the spatial size for the production area of the final channel.…”

Spatial measure of reaction size in proton scattering

“…[5], for instance, a diffraction radius of the Hoyle state in 12 C is speculated from the diffraction pattern observed in the differential cross section in the high energy proton scattering. In fact, a sign of an enhanced radius is confirmed for the Hoyle state of 12 C. a e-mail: itomk@kansai-u.ac.jp Recently, we have proposed the method of the scattering radius on the basis of a partial wave decomposition of a coupled-channel problem [6]. The scattering radius is considered to characterize a spatial size of the reaction area for exclusive reactions.…”