| Budget Amount *help |
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1989: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1988: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1987: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Research Abstract |
The aim of this project is to develop a method of coupled channels based on 3- and 4- body models of nuclear reactions involving rearrangement and break up of particles by extending the methods of Coupled Discretized Continuum Channels (CDCC) and Coupled Rearrangement Channels (CRC) which we have successfully developed in recent years.
We first investigated the foundations of CDCC itself, taking (p,n)-nucleus system as an example, in order to put the project on a solid basis. Detailed theoretical and numerical investigations proved convergence of CDCC wave functions to correct 3-body model wave functions within a region of configuration space which is limited but wide enough in practice. Thus, the validity of CDCC was established in the realistic case investigated. We then go on to also clarify the relation of CDCC with the method of connected kernels, including the Faddeev theory, which lead us to propose iterative improvements of CDCC.
We applied CRC, another pillar of the project, to
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investigation of the foundation of DWBA for rearrangement processes, testing whether DWBA, with suitable modification of the disoretizing potentials, can reproduce CRC for (d,p) reactions. The result was negative. This leaves a serious problem on the foundation of DWBA for rearrangement process.
We applied CRC also to the calculation of the ground states of ^3H and ^3He. A variational method was used with trial wave functions with components of all the rearranged channels radial wave functions of which were expanded in Gaussian type basis functions. The results reproduced the most advanced Faddeev calculations in the binding energies and the asymptotic amplitudes of the s- and d-states wave functions. The method has the advantage over the Faddeev theory in much faster convergence with respect to the extension of the angular momentum model space, no difficulty with Coulomb potentials, and capability of dealing with 4-body systems. Finally, we combined CDCC and CRC to study the reaction (d,mu) + t -> (t,mu) + d which is of great importance in the muon catalyzed fusion reaction of deuteron and triton. Break up of the mu-mesic atoms as well as transfer of mu were taken into account in the coupled channels calculation. A variational method of Kohn-Hulthen type was used in the calculation including the total angular momentum up to 4. The experimental cross section of the ground state transition in the incident energy range 0.0001 - 10eV was well reproduced. Transitions to excited states are being investigated with step-by-step integration of the coupled integro-differential equations. The same method is being developed for coupled channels calculation of general nuclear reactions involving both break up and rearrangement processes. Less
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