Email this article 
THE SEPARABLE FORCES APPROXIMATION IN THE GENERALIZED THEORY OF FINITE FERMI SYSTEMS
- Authors: Kovaleva Y.V.1, Shitov M.I.2, Kamerdzhiev S.P.2
-
Affiliations:
- Voronezh State University
- National Research Center “Kurchatov Institute”
- Issue: Vol 87, No 6 (2024)
- Pages: 451-459
- Section: ЯДРА. Теория
- URL: https://journals.rcsi.science/0044-0027/article/view/281906
- DOI: https://doi.org/10.31857/S0044002724060011
- EDN: https://elibrary.ru/HPICXI
- ID: 281906
Cite item
Full Text
Abstract
The separable forces approximation is applied for the first time to the generalized theory of finite Fermi systems (TFFS), which was developed in the works [1–4] in order to consistently account for complex configurations with phonons within the framework of the Green’s function method. Standard multipolemultipole forces are used, and for their quadrupole case, two parameters are adjusted according to the known quadrupole effective polarization charges, which are well known in the experiment and in the standard TFFS. It is shown that in this approximation, the equations of the standard TFFS for the vertex and the total amplitude are easily solved. A useful relationship has been obtained between effective quadrupole polarization charges and the parameters of separable forces, which describe the full amplitude in a separable form. As an application of our approach, the equation for the regular part of the Γ amplitude was studied for the first time. Both free terms of this equation are estimated and it is shown that the additional term containing the product of two phonon creation amplitudes is several times higher than the other free term, which is the effective interaction of TFFS, taken in a separable approximation. The obtained solutions of the equation for Γ lead to the conclusion that this value cannot be neglected. Since Γ naturally appears in the generalized TFFS to describe two-phonon excitations, this means that the theory of two-phonon excitations can become noticeably more complicated.
About the authors
Yu. V. Kovaleva
Voronezh State UniversityVoronezh, Russia
M. I. Shitov
National Research Center “Kurchatov Institute”
Email: kamerdzhiev_sp@nrcki.ru
Moscow, Russia
S. P. Kamerdzhiev
National Research Center “Kurchatov Institute”Moscow, Russia
References
- S. P. Kamerdzhiev and M. I. Shitov, Eur. Phys. J. A 56, 265 (2020).
- С. П. Камерджиев, М. И. Шитов, ЯФ 84, 410 (2021).
- S. Kamerdzhiev and M. Shitov, Phys. At. Nucl. 84, 804 (2021).
- С. П. Камерджиев, М. И. Шитов, ЯФ 85, 330 (2022).
- L. S. Kisslinger and R. A. Sorensen, Rеv. Mod. Phys. 35, 853 (1963).
- S. Gales, Ch. Stoyanov, and A. I. Vdovin, Phys. Rep. 166, 125 (1988).
- В. Г. Соловьев, Теория атомного ядра: квазичастицы и фононы (Энергоатомиздат, Москва, 1989).
- N. Ryezayeva, T. Hartmann, Y. Kalmykov, H. Lenske, P. von Neumann-Cosel, V. Yu. Ponomarev, A. Richter, A. Shevchenko, S. Volz, and J. Wambach, Phys. Rev. Lett. 89, 272502 (2002).
- J. Bryssinck, L. Govor, D. Belic, F. Bauwens, O. Beck, P. von Brentano, D. De Frenne, T. Eckert, C. Fransen, K. Govaert, R.-D. Herzberg, E. Jacobs, U. Kneissl, H. Maser, A. Nord, N. Pietralla, H. H. Pitz, V. Yu. Ponomarev, and V. Werner, Phys. Rev. C 59, 1930 (1999).
- N. Tsoneva, H. Lenske, and Ch. Stoyanov, Phys. Lett. B 586, 213 (2004).
- L. M. Donaldson, J. Carter, P. von Neumann-Cosel, V. O. Nesterenko, R. Neveling, P.-G. Reinhard, I. T. Usman, P. Adsley, C. A. Bertulani, J. W. Brummer, E. Z. Buthelezi, G. R. J. Cooper, R. W. Fearick, S. V. Fortsch, H. Fujita, et al., Phys. Rev. C 102, 064327 (2020).
- S. P. Kamerdzhiev, Sov. J. Nucl. Phys. 5, 971 (1967).
- А. Б. Мигдал, Теория конечных ферми-систем и свойства атомных ядер (Наука, Москва, 1967; Wiley, New York 1967).
- Sov. J. Nucl. Phys. 24, 367 (1976).
- Phys. At. Nucl. 79, 1030 (2016).
- С. П. Камерджиев, ЯФ 2, 415 (1965).
- С. П. Камерджиев, ЯФ 15, 676 (1972).
- M. Harakeh and A. van der Woude, Giant Resonances: Fundamental High-Frequency Modes of Nuclear Excitation (Oxford Univ. Press, Oxford, 2001).
Supplementary files
