Abstract
The paper presents a brief review of the results in the self-consistent theory of the anharmonic effects of the second and third orders in the phonon production amplitude, based on the quantum many-body theory. Numerical (for second-order effects) and theoretical analyses of new, i.e., three- and four-quasiparticle correlations in the ground state (backward-going graphs) in magic nuclei and in nuclei with pairing are given. A formula for the probability of transition between one- and two-phonon states is obtained and compared to the solution of a similar problem within the quasiparticle-phonon model. It is shown that the approach under consideration contains a number of new effects.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
A. Bohr and B. Mottelson, Nuclear Structure: Vol. 2. Nuclear Deformations (Benjamin, New York, 1974).
A. V. Avdeenkov and S. P. Kamerdzhiev, “Description of excitations in odd nonmagic nuclei by the Green’s function method,” Phys. Atom. Nucl. 62, 563–578 (1999).
I. Hamamoto, “Particle spectra and particle-vibration coupling in the Pb region,” Phys. Rep. 10, 63–105 (1974).
P. Ring and J. Speth, “Nuclear structure calculations with a density-dependent force in 208Pb,” Nucl. Phys. A 235, 315–351 (1974).
R. A. Broglia, R. Liotta, and V. Paar, “Quadrupole moments of the 21+ state of proton-closed-shell nuclei,” Phys. Lett. B 38, 480–484 (1972).
B. L. Birbrair, “Static quadrupole moments of first 2+ states of spherical nuclei in a schematic model,” Phys. Lett. B 32, 165–168 (1970).
D. Voitenkov, S. Kamerdzhiev, et al., “Self-consistent calculations of quadrupole moments of the first 2+ states in Sn and Pb isotopes,” Phys. Rev. C 85, 054 319 (2012).
V. G. Soloviev, Theory of Atomic Nuclei: Quasi-Particles and Phonons (Energoatomizdat, Moscow, 1989) [in Russian].
V. Yu. Ponomarev, Ch. Stoyanov, N. Tsoneva, and M. Grinberg, “Boson forbidden low-energy E1-transitions in spherical nuclei,” Nucl. Phys. A 635, 470–483 (1998).
A. P. Platonov, Sov. J. Nucl. Phys. 36, 491 (1982).
V. A. Khodel, “Anharmonic effects in nuclei in the quantum hydrodynamic description,” Sov. J. Nucl. Phys. 24, 367–377 (1976).
A. B. Migdal, The Theory of Finite Fermi Systems and The Properties of Nuclei (Nauka, Moscow, 1982).
V. A. Khodel and E. E. Saperstein, “Finite Fermi systems theory and self-consistency relations,” Phys. Rep. 92, 183–337 (1982).
S. P. Kamerdzhiev, D. F. Voitenkov, E. E. Sapershtein, S. V. Tolokonnikov, and M. I. Shitov, “Self-consistent description of EL transitions between one-phonon states in magic nuclei,” JETP Lett. 106, 139–144 (2017).
S. P. Kamerdzhiev and M. I. Shitov, “Third-order anharmonic effects in nuclear quantum many-body theory,” Pis’ma Zh. Eksp. Teor. Fiz. 109, 65–71 (2019) (in press).
S. P. Kamerdzhiev, D. A. Voitenkov, E. E. Sapershtein, and S. V. Tolokonnikov, “Self-consistent calculations of the quadrupole moments of the lowest 3– states in Sn and Pb isotopes,” JETP Lett. 108, 155–160 (2018).
ACKNOWLEDGMENTS
We are grateful to V.Yu. Ponomarev and V.A. Khodel for fruitful discussions.
Funding
This work was supported by the Russian Science Foundation, project no. 16-12-10155.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by E. Chernokozhin
Rights and permissions
About this article
Cite this article
Shitov, M.I., Kamerdzhiev, S.P. Second- and Third-Order Anharmonic Effects within the Quantum Many-Body Theory. Phys. Part. Nuclei 50, 544–549 (2019). https://doi.org/10.1134/S1063779619050216
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063779619050216