Phonon-particle coupling effects in single-particle energies of semi-magic nuclei

Abstract

A method is presented to evaluate the particle-phonon coupling (PC) corrections to the single-particle energies (SPEs) in semi-magic nuclei. In such nuclei always there is a collective low-lying $2^{+}$ phonon, and a strong mixture of single-particle and particle-phonon states often occurs. As in magic nuclei, the so-called $g_L^2$ approximation, where $g_L$ is the vertex of the $L$-phonon creation, can be used for finding the PC correction $\delta {\Sigma }^{\mathrm{PC}}(\epsilon )$ to the initial mass operator ${\Sigma }_0$. In addition to the usual pole diagram, the phonon "tadpole" diagram is also taken into account. In semi-magic nuclei, the perturbation theory in $\delta {\Sigma }^{\mathrm{PC}}(\epsilon )$ with respect to ${\Sigma }_0$ is often invalid for finding the PC corrected SPEs. Instead, the Dyson equation with the mass operator $\Sigma (\epsilon )={\Sigma }_0+\delta {\Sigma }^{\mathrm{PC}}(\epsilon )$ is solved directly, without any use of the perturbation theory. Results for a chain of semi-magic Pb isotopes are presented.

6 pages, 4 figures, 3 tables; v2 -- small corrections in the text; to be published in JETP Letters

References in corpus (4)

• Covariant theory of particle-vibrational coupling and its effect on the single-particle spectrum
• Microscopic calculation and LDA of the spatial dependence of the pairing field with bare and induced interactions
• Spectroscopic properties of nuclear Skyrme energy density functionals
• Semi-microscopic model of pairing in nuclei

Cited by in corpus (5)

• Phonon-particle coupling effects in odd-even double mass differences of semi-magic nuclei
• The first self-consistent calculation of quadrupole moments of odd semi-magic nuclei accounting for phonon induced corrections
• Phonon-particle coupling effects in odd-even mass differences of semi-magic nuclei
• Including particle-vibration coupling in the Fayans functional. Odd-even mass differences of semi-magic nuclei
• Self-consistent account for phonon induced corrections to quadrupole moments of odd nuclei. Pole and non-pole diagrams