Formulation of effective interaction in terms of the non-perturbative and analytic box

17th International Conference on Recent Progress in Many-Body Theories

Okamoto, R.^1 ; Suzuki, K.^1 ; Kumagai, H.^2 ; Matsuzaki, M.^3

Senior Academy, Kyushu Institute of Technology, Kitakyushu 804-8550, Japan^1

Faculty of Information Engineering, Fukuoka Institute of Technology, Fukuoka 811-0295, Japan^2

Department of Physics, Fukuoka University of Education, Munakata, Fukuoka 811-4192, Japan^3

关键词: Central problems;    Effective interactions;    Energy dependent;    Many-body systems;    Non-perturbative solutions;    Practical method;    Quantum mechanical;    Recursion methods;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/529/1/012021/pdf
DOI  :  10.1088/1742-6596/529/1/012021

来源: IOP

【 摘 要 】

One of the useful and practical methods for solving quantum-mechanical many-body systems is to recast the full problem into a form of the effective interaction acting within a model space of tractable size. Many of the effective-interaction theories in nuclear physics have been formulated by use of the so called Q box introduced by Kuo et al. It has been one of the central problems how to calculate the Q box accurately and efficiently. Introducing new basis states, the Hamiltonian is transformed to a block-tridiagonal form in terms of suhmatrices with small dimension. With the transformed Hamiltonian we derive a recursion method of calculating the Q box non-perturbatively and analytically. The Q box given in this study corresponds to a non-perturbative solution for the energy-dependent Hamiltonian interaction which is often referred to as the Bloch-IIorowitz or the Feshbach form. The present approach has a possibility of resolving many of the theoretical and practical| difficulties encountered in the calculation of effective-interaction and/or Hamiltonian.