Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 56 (2023)
RIKEN
Accel. Prog. Rep. 56 (2023)†Energy spectrum of 15
Ξ C and the ΞN two-body interaction
Y. Tanimura,∗1,∗2 H. Sagawa,∗3,∗4 T. -T. Sun,∗5 and E. Hiyama∗1,∗4Studying the interaction of the strangeness S = −2
sector is important in hypernuclear physics for a uniﬁed understanding of baryon-baryon interaction. To
this end, it is crucial to study the structure of doublestrangeness hypernuclei, such as double-Λ and Ξ hypernuclei.
In this work, we focused on new experimental data,
IRRAWADDY event,1) of a 15
Ξ C nucleus observed atBΞ = 6.27 ± 0.27 MeV. We estimate the strengths ofthe N Ξ interaction and give a consistent interpretation
for all the events1–4) of the Ξ hypernucleus including IRRAWADDY. In addition to our previous work
based on the relativistic mean-ﬁeld (RMF) model,5)
we introduce an N Ξ residual interaction and infer thatKINKA (BΞ = 8.00 ± 0.77 or 4.96 ± 0.77 MeV) andIRRAWADDY events1) are the ground-state spin doublet with the Ξ particle in the s orbit and that IBUKI(BΞ = 1.27 ± 0.21 MeV) and KISO (BΞ = 3.87 ± 0.21
or 1.03 ± 0.18 MeV) events2,4) are members of theexcited-state multiplets with the Ξ particle in the porbits.
To describe the 15
Ξ C nucleus and estimate its energy spectrum, we employ an RMF model and spinisospin dependent residual interaction. Within theRMF model, we adopt the PK1 parameter set6) for the
nucleon-meson couplings, while the coupling constantsin the hyperon sector are ﬁtted to roughly reproducethe observed spectrum. Moreover, the eﬀect of theresidual interaction is estimated by ﬁrst-order perturbation theory with the RMF wave functions taken as
the unperturbed states. The 14 N subsystem of the 15
Ξ Cnucleus is described as the p1/2 neutron and protonπcoupled to spin-parity Jnpnp = 1+ and isospin Tnp = 012on top of the inert C core. The Ξ particle is thencoupled to the nucleon pair to make the total quantum number J π T , where J π is the total spin-parity ofthe system, and T = 1/2 in the case of 15Ξ C.
We consider a residual interaction acting on s and pwaves. The s-wave interaction is given by∑(vσ Σi · ΣΞ + vτ ⃗τi · ⃗τΞVN Ξ =and ⃗τ are the isospin operators. The strength parameters of VN Ξ are ﬁxed based on the HAL QCD
ΞN potential.7) We further introduce a p-wave spindependent interaction given by∑←−→−vσp Σi · ΣΞ ∇ · δ(ri − rΞ ) ∇, (2)VNp Ξ =i∈nucleons

where vσp is a parameter to be optimized by the measured energies of IRRAWADDY and KINKA events.
Fig. 1(a) shows the energy spectrum of 15
Ξ C as afunction of vσp , which is obtained by assuming that theIRRAWADDY event is the ground state of 15
Ξ C. It isseen that vσp ∼ −150 MeV.fm5 and ∼100 MeV.fm5
give spectra consistent with all the experimental data.
Fig. 1(b) shows the energy spectrum obtained by assuming that the lower candidate of the KINKA eventis the ground state. In this case, vσp ∼ −150 MeV.fm5
and ∼125 MeV.fm5 give results consistent with thedata.
(a)Fig. 1. Estimated energy spectrum of 15
Ξ C nucleus as afunction of the p-wave spin-spin interaction strength vσp .
The energies of the levels labeled by the orbital occupied by the Ξ− particle, Ξlj , and the total spin parity,J π , are represented by lines. The experimental data ofBΞ− are shown by color bands.

i∈nucleons+ vστ Σi · ΣΞ⃗τi · ⃗τΞ )δ(ri − rΞ ),References(1)1) M. Yoshimoto et al., Prog. Theor. Expt. Phys. 2021,
073D02 (2021).
2) K. Nakazawa et al., Prog. Theor. Expt. Phys. 2015,
033D02 (2015)3) E. Hiyama et al., Annu. Rev. Nucl. Sci. 68, 131 (2018).
4) S. H. Hayakawa et al., Phys. Rev. Lett. 126, 062501(2021).
5) T. T. Sun et al., Phys. Rev. C 94, 064319 (2016).
6) W. H. Long et al., Phys. Rev. C 69, 034319 (2004).
7) K. Sasaki et al., Nucl. Phys. A 998, 121737 (2020).

where Σ is the spin operator acting on a Dirac spinor
†∗1
∗2
∗3
∗4
∗5(b)

Codensed from the article in Phys. Rev. C 105, 044324(2022)
Department of Physics, Tohoku University
Graduate Program on Physics for the Universe, Tohoku University
Center for Mathematics and Physics, the Univertysi of Aizu
RIKEN Nishina Center
School of Physics and Microelectronics, Zhengzhou Univeristy- 36 -