Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 51 (2018)

Interplay between isoscalar and isovector correlations
in neutron-rich nuclei†
I. Hamamoto∗1,∗2 and H. Sagawa∗1,∗3
The interplay between isoscalar (IS) and isovector(IV) correlations has been an attractive and centrally
placed topic in the study of nuclear structure. In theanalysis of scattering data by IS particles such as α particles it is often assumed that IS particles excite only
IS strength. This assumption is generally incorrect ifN̸=Z for the target nuclei. For example, in nuclei withneutron excess, IS operators excite IS moments, butthe strong neutron-proton forces may tend to maintain the local ratio of neutrons to protons. Then, thepresence of neutron excess N>Z implies that IV moments may also be excited by IS particles.1) The exchange of the above roles of IS and IV excitations inthe response is expected to be true as well. That is, IVoperators may produce IS moments generally in nuclei
with N̸=Z except for the case in which the IS moment
corresponds to the center of mass motion.
To study this issue, we employ the self-consistent
Hartree-Fock (HF) plus the random-phase approximation (RPA) with Skyrme interactions in neuronrich oxygen isoyopes, simultaneously including both
IS and IV interactions. The RPA response function
is estimated in coordinate space to properly take into
account the continuum eﬀect for the IS compression
dipole (ISCD) operator:2))∑(
5ri3 − ⟨r2 ⟩ri Y1µ (r̂i ).
(1)
Dµλ=1, τ =0 =3i

5006dB(dipole)/dEx (fm /MeV)

22∗1∗2∗3−IS and IV interactions
IS interaction only300200100001020Ex (MeV)

3040Fig. 1. RPA strength of the isoscalar compression dipole(ISCD) of 22 O calculated using the SLy4 interaction asa function of excitation energy (Ex). The solid curve
expresses the strength obtained by including both IS
and IV interactions in RPA, while the dotted curve expresses the strength obtained by including only the ISinteraction.

be understood in the manner above (b). An example
is the broad peak around 18.5 MeV in the solid curve.
The IS peaks around 14.0 and 18.5 MeVn have no trivial corresponding peaks in the dotted curve. The samebehavior is also found in the response for the IV dipole
operator interchanging the roles of IV and IS correlations; the IV dipole peak appears at approximately
14 MeV only when both IS and IV interactions areincluded in the RPA response. We may call the relatively broad peak around Ex = 14 MeV pigmy resonance with both isoScalar and isoVector correlations(“iS-iV pigmy resonance”). The pigmy resonance isinterpreted as neither the IS strength induced by astrong IV peak nor the IV strength induced by a strong
IS peak, owing to the presence of neutron excess. It
is a relatively broad resonance having an energy much
lower than the energies of both IVD GR and ISCD
GR, but it gathers the collectivity of low-lying IS andIV strengths. The strong neutron-proton interaction
can be responsible for controlling the isospin structureof normal modes. In this study, it is explicitly shownthat in the scattering by isoscalar (isovector) particles
on N̸=Z even-even nuclei isovector (isoscalar) strengthin addition to isoscalar (isovector) strength may be
populated.

Figure 1 shows the calculated RPA strength for theISCD operator. We note the following points. (a) Wevery often obtain a large portion of ISCD strength inan energy interval several MeV above the threshold.
This large strength appearing at an energy much lower
than the energy of the ISCD giant resonance (GR),which is recognized as a very broad “resonance” foundfor Ex>24 MeV in Fig. 1, originates from the possible presence of occupied weakly bound low-ℓ neutron
orbits together with the strong r-dependence (r3 ) ofthe ISCD operator. (b) When IV interaction is included on top of IS interaction, the heights of many
lower-lying IS peaks become lower and the peak energies may shift to slightly higher energies via the IVcomponents contained in those IS peaks because of therepulsive nature of the IV interaction. (c) There aresome peaks denoted by the solid curve, which may not†O SLy4

IS compression 1

400References

Condensed from the article in Phys. Rev. C96, 064312(2017)RIKEN Nishina Center
Division of Mathematical Physics, Lund Institute of Technology at the University of Lund
Center for Mathematics and Physics, University of Aizu

1) A. Bohr, B. R. Mottelson, Nuclear Structure (Benjamin,Reading, MA, 1975).
2) I. Hamamoto, H. Sagawa, X. Z. Zhang, Phys. Rev. C
57, R1064 (1998).

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