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Relativistic mean-field description of the dynamics of giant resonances
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Relativistic mean-field description of
the dynamics of giant resonances
D. Vretenar a, P. Ring b, G.A. Lalazissis b, and N.Paar a
a Physics Department, Faculty of Science,
University of Zagreb, Croatia
b Physik-Department der Technischen Universita?t Mu?nchen,
D-85748 Garching, Germany
February 9, 2008
Abstract
The relativistic mean-field theory provides a framework in which
the nuclear many-body problem is described as a self-consistent sys-
tem of nucleons and mesons. In the mean-field approximation, the
self-consistent time evolution of the nuclear system describes the dy-
namics of collective motion: nuclear compressibility from monopole
resonances, regular and chaotic dynamics of isoscalar and isovector
collective vibrations.
1 The relativistic mean field model
Relativistic mean-field (RMF) models have been successfully applied in cal-
culations of nuclear matter and properties of finite nuclei throughout the pe-
riodic table. In the self-consistent mean-field approximation, detailed calcu-
lations have been performed for a variety of nuclear structure phenomena [1].
1
In this work we present applications of RMF to the dynamics of collective vi-
brations in spherical nuclei. In relativistic quantum hadrodynamics [2], the
nucleus is described as a system of Dirac nucleons which interact through
the exchange of virtual mesons and photons. The Lagrangian density of the
model is
L = ψ? (iγ · ? ?m)ψ +
1
2
(?σ)2 ? U(σ)
?
1
4
?μν?
μν +
1
2
m2ωω
2 ?
1
4
~Rμν~R
μν +
1
2
m2ρ~ρ
2 ?
1
4
FμνF
μν
? gσψ?σψ ? gωψ?γ · ωψ ? gρψ?γ · ~ρ~τψ ? eψ?γ ·A
(1? τ3)
2
ψ . (1)
The Dirac spinor ψ denotes the nucleon with mass m. mσ, mω, and mρ are
the masses of the σ-meson, the ω-meson, and the ρ-meson, and gσ, gω, and
gρ are the corresponding coupling constants for the mesons to the nucleon.
U(σ) denotes the nonlinear σ self-interaction, and ?μν , ~Rμν , and F μν are
field tensors [1, 2]. The coupled equations of motion ar
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