Theoretical Discussions And Verifications Of The Quantum Design Of A Multiple Internal Reflections Method

In nuclear physics,the decay and fusion processes of nuclei are often used to study nuclear structures and the mechanisms of nuclear reactions.These processes are usually described as quantum processes that incident or emitted particles tunnel through potential barriers.Different methods were developed to solve problems with complicated potentials,among which WKB method is widely used.However,the WKB method is semi-classical and its scope of application is narrow.A new multiple internal reflection method,MIR method for short,was developed which can be applied for any potential barrier.Its computational accuacy is adjustable.A very small error can be achieved theoretically.At present,related papers which have been published mainly studied practical applications of the MIR method while the method's theoretical verifications are neglected.This thesis,with three main parts,focuses on the proving of our method.First,we outline the basic concepts of nuclear reactions and theoretical models of ?-decay and ?-fusion processes.This part of work is the backgrounds of the related papers.Second,we analyse idealizations,principles,cross-section formula in fusion processes of the MIR method.Third,one-dimensionally,for N rectangular barriers,N=0,1,2,…,we develop specific solutions in MIR method.Besides,we work out results in each case by the Transfer Matrix method.By comparing results given by two different methods,we prove our MIR method in part.At last,we suggest a work plan for complete provement.Theoretical discussions and verifications of the method's quantum design are necessary before applying such a new method.