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In the sequential microscopic theory of the nucleus, using the formalism of Green's functions (GF), it is necessary to consider the full amplitude of the interaction (scattering amplitude) $\Gamma$ [1,2], which contains the regular part of $\Gamma^r$. First of all, this is due to the inclusion of two-phonon configurations in addition to the 1p1h+phonon configurations [2], i.e. we are talking about the sequential consideration (in the language of GF) of two-phonon configurations.
The equation for the regular part of $\Gamma^r$ was obtained by A.B. Migdal [1] and, as far as we know, has never been studied quantitatively. To solve it, it is necessary to find the second free term $F_1$ containing the square of the phonon creation amplitude $g$ (the first free term is the well-known interaction F in the theory of finite Fermi systems [1])
We transformed both these equations for $g$ and $\Gamma^r$ in the approximation for the interaction of $F$ in the form of separable forces, see [3], with the parameters of these forces found by us for $^{208}Pb$ for $E2$ transitions, used the corresponding experimental data for $g$ and solved the equation for $\Gamma^r$. Calculations showed a rather unexpected result: the ratio of two free terms $F_1/F$ = -6.0, and the ratio $\Gamma^r/F$=-31.2. Apparently, these estimates mean that the microscopic theory of two-phonon nuclear excitations must be substantially refined.
- A. B. Migdal, Theory of Finite Fermi Systems and Application to Atomic Nuclei, Interscience Publishers, New York, 1967.
- S. P. Kamerdzhiev, M.I. Shitov, Phys. At. Nucl. 84 No.6, 804 (2021); 84 №5, 649 (2021); 85 №5, 425 (2022).
- V. G. Solovʹev, Theory of Atomic Nuclei, Quasi-particle and Phonons, Institute of Physics Pub., Bristol; Philadelphia, 1992.
| Section | Nuclear structure: theory and experiment |
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