Graphical method for deriving an effective interaction with a new vertex function
- Senior Academy, Kyushu Institute of Technology, Kitakyushu 804-8550 (Japan)
- Department of Physics, Kyushu Institute of Technology, Kitakyushu 804-8550 (Japan)
- Faculty of Information Engineering, Fukuoka Institute of Technology, Fukuoka 811-0295 (Japan)
- Center for Nuclear Study (CNS), University of Tokyo, Wako Campus of RIKEN, Wako 351-0198 (Japan)
Introducing a new vertex function, Z(E), of an energy variable E, we derive a new equation for the effective interaction. The equation is obtained by replacing the Q box in the Krenciglowa-Kuo (KK) method with Z(E). This new approach can be viewed as an extension of the KK method. We show that this equation can be solved both in iterative and noniterative ways. We observe that the iteration procedure with Z(E) brings about fast convergence compared to the usual KK method. It is shown that, as in the KK approach, the procedure of calculating the effective interaction can be reduced to determining the true eigenvalues of the original Hamiltonian H and they can be obtained as the positions of intersections of graphs generated from Z(E). We find that this graphical method yields always precise results and reproduces any of the true eigenvalues of H. The calculation in the present approach can be made regardless of overlaps with the model space and energy differences between unperturbed energies and the eigenvalues of H. We find also that Z(E) is a well-behaved function of E and has no singularity. These characteristics of the present approach ensure stability in actual calculations and would be helpful to resolve some difficulties due to the presence of poles in the Q box. Performing test calculations, we verify numerically theoretical predictions made in the present approach.
- OSTI ID:
- 21499405
- Journal Information:
- Physical Review. C, Nuclear Physics, Vol. 83, Issue 2; Other Information: DOI: 10.1103/PhysRevC.83.024304; (c) 2011 American Institute of Physics; ISSN 0556-2813
- Country of Publication:
- United States
- Language:
- English
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