WKB Treatment of Boson Hamiltonian of Inter-Nucleus Interaction

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Abstract
By treating the inter-nucleus interaction process in the framework of the generator coordinate method, we can obtain the Boson Hamiltonian for the relative motion, where the Boson operators are arranged in normal order. When the WKB approximation is applied to this Boson Hamiltonian by expanding the action S as S=S0+ ℏS1+ ⋯, we get for S0 the same equation as that obtained by the method of the moving wave packet. However, the local momentum should not be determined by this equation. This is because S1 contains the real part and therefore the local momentum should be calculated from S0+ ℏReS1. This renormalization from ReS1 is found to make the results similar to the WKB results obtained by utilizing the Wigner transforms of the non-local interactions of the resonating group method. The appearance of the renormalization by ReS1 is due to the normal ordering of the Boson operators which makes the Boson Hamiltonian contain the odd power terms of the momentum operator. References

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