Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 47 (2014)

RIKEN Accel. Prog. Rep. 00 (0)Giant monopole resonances in covariant finite-amplitude method†
H. Z. Liang,∗1 T. Nakatsukasa,∗1 Z. M. Niu,∗2 and J. Meng∗1,∗3
During the past decades, the covariant density functional theory has received widespread attention because it has successfully described many nuclear phenomena1) . In this report, we mainly focus on the recent progress in the self-consistent relativistic randomphase approximation (RPA) established by using theﬁnite-amplitude method (FAM).
The RPA is one of the leading theories applicable
to both low-lying excited states and giant resonances.
In the relativistic framework, quantitative RPA calculations were realized after recognizing the importanceof the Dirac sea. Subsequently, great eﬀorts on therelativistic RPA have been made. However, most investigations are essentially restricted within sphericalsymmetry. The conventional RPA calculations in thematrix form face a signiﬁcant computational challenge
when the number of particle-hole (ph) conﬁgurations
Nph becomes large.
The so-called ﬁnite-amplitude method was proposed
as a promising solution for this computational challenge2,3) . In this method, the eﬀects of residual interactions are numerically evaluated by considering a ﬁnite density deviation around the ground state. Thus,
the self-consistent RPA calculations become possible
with a slight extension of the static Hartree-Fock code.
Furthermore, by using the iterative methods, the com3
putation time linearly depends on Nph , instead of Nph,in the diagonalization scheme, which is crucial whenNph becomes large.
Work is in progress for developing the self-consistent
relativistic RPA by using both the iterative and matrix
FAM schemes, i.e., i-FAM and m-FAM, the detailed
formalism of which can be found in the original article† .
In Fig. 1, we show the isoscalar giant monopole resonances (ISGMR) in 208 Pb calculated with the relativistic parametrization DD-PC1. The eﬀects of the Diracsea and the rearrangement terms can be examined byswitching on or oﬀ the corresponding ph residual interactions.
First, the transition strengths calculated in the mFAM scheme with and without the Dirac sea are compared in the upper panel. It is found that the Dirac sea
shows profound eﬀects on the centroid energy, and theexperimental data4) is reproduced only when the Diracsea is taken into account. Although the eﬀects of theDirac sea cannot be isolated in the coordinate-space
representation, it can be clearly seen that the i-FAM
results are exactly above the m-FAM results that in†∗1∗2∗3Fig. 1. ISGMR in 208 Pb calculated using i-FAM and mFAM. The results calculated with and without the Diracsea and the rearrangement terms are compared. The
experimental centroid energy4) is denoted by the arrow.

clude the Dirac sea. This conﬁrms that these two FAM
schemes are equivalent and the eﬀects of Dirac sea canbe taken into account automatically and implicitly.
It is tedious to calculate the rearrangement terms
in the conventional RPA calculations; in contrast, inFAM, these terms can be simply taken into account by re-calculating the coupling strengths with newdensities. In the lower panel, the transition strengthsof ISGMR calculated using m-FAM with and without
the rearrangement terms are shown, together with thei-FAM results calculated without the rearrangement terms. The equivalency of these two FAM schemesis demonstrated once more. It is also found that therearrangement eﬀects on the centroid energies is quantitatively substantial.
References
1) J. Meng et al.: Prog. Part. Nucl. Phys. 57, 470 (2006).
2) T. Nakatsukasa, T. Inakura, and K. Yabana: Phys. Rev.
C 76, 024318 (2007).
3) T. Nakatsukasa: Prog. Theor. Exp. Phys. 2012, 01A207(2012).
4) D. H. Youngblood et al.: Phys. Rev. C 69, 034315(2004).

Condensed from the article in Phys. Rev. C 87, 054310(2013)RIKEN Nishina Center
School of Physics and Material Science, Anhui University
School of Physics, Peking University- 49 -1