II-2. Nuclear Physics (Theory)

RIKENAccel.
Accel.Prog.
Prog. Rep.
Rep. 54
RIKEN
54(2021)(2021)

Structure of 12 C studied by the no-core Monte-Carlo shell model
T. Abe,∗1 P. Maris,∗2 T. Otsuka,∗1,∗3 N. Shimizu,∗4 Y. Utsuno,∗5,∗4 and J. P. Vary∗2
Carbon-12 is of particular importance in our life. Thisnucleus is produced by the triple-α reactions through thesecond 0+ state known as the Hoyle state. The properties of this state are still being investigated actively bothin the experimental and theoretical ways. On the theoretical side, ab initio approaches for low-energy nuclear
structure calculations have been developed rapidly in recent years, owing to recent computational and methodological developments. Here, we report the low-lyingstates of 12 C examined by the ab initio calculations inthe no-core Monte Carlo shell model (MCSM).1)
We have performed the large-scale calculations in theno-core shell-model (NCSM) method,2) applying theMCSM technique for conventional shell-model calculations.3–5) The no-core MCSM calculations have been
done with 100 basis states in the basis space of Nshell = 7
with the harmonic-oscillator energy of h̄ω = 20 MeV. We
have adopted the Daejeon16 N N interaction,6) which isbased on an N N interaction from chiral eﬀective ﬁeldtheory (χEFT).
Figure 1 shows preliminary results of the no-core
MCSM calculations in comparison with the experimental data.7) In Fig. 1, the absolute energies and transition strengths for three low-lying states are shown.
The no-core MCSM results with the Daejeon16 interaction provide a reasonable agreement with the experimental data for the ground 0+ and the ﬁrst-excited2+ states. The experimental ground-state energy is−92.16 MeV, while our result is −91.9 MeV and well
reproduces the no-core full-conﬁguration (NCFC, one ofthe other NCSM approaches) result with the same interaction of −92.9(1) MeV.6) The point-proton radius
for the ground state is ∼2.29 fm both in the no-core
MCSM and the NCFC methods, corresponding to theexperimental value of 2.33 fm. The excitation energyof the ﬁrst-excited 2+ state is 5.01 MeV in the no-core
MCSM and 4.57(15) MeV in the NCFC. These energies are also comparable with the experimental value of
4.44 MeV. The electric quadrupole and monopole transition strengths are also in reasonable agreement withthe experimental values.
The excitation energy of the second 0+ state, however,is higher than the experimental value by ∼3 MeV and thepoint-proton radius is 2.60 fm, which is smaller than thevalues by the phenomenological calculations, typicallylarger than 3 fm (see, for example, Ref. 8) and references
therein). It is because the Hoyle state is believed tohave the loosely-bound three-α-cluster structure and is∗1
∗2
∗3
∗4
∗5

RIKEN Nishina Center
Department of Physics and Astronomy, Iowa State University
Department of Physics, the University of Tokyo
Center for Nuclear Study, the University of Tokyo
Advanced Science Research Center, Japan Atomic Energy
AgencyDaejeon16 NN, Nshell = 7, hw = 20 MeV
w/o energy-variance extrapolationǆ;ϬͿсϭϬ͘ϳϵDĞsǆ;ϬͿсϳ͘ϲϱϰDĞs

;,ŽǇůĞͿD;ϬͿсϱ͘ϰ;ϮͿĞĨŵǆ;ϮͿсϰ͘ϰϯϵϴDĞsD;ϬͿсϱ͘ϳϲĞĨŵǆ;ϮͿсϱ͘ϬϭDĞs;ϮͿсϳ͘ϰϬĞĨŵ;ϮͿсϳ͘ϲ;ϰͿĞĨŵ;Ő͘Ɛ͘Ϳ

Fig. 1. Excitation spectra of 12 C. The right (left) side in theﬁgure shows no-core MCSM results (experimental data)with the red (black) color. The energy levels of three
low-lying states are shown by horizontal bars. The electric quadrupole and monopole transition strengths are denoted by arrows. The experimental data are taken fromRef. 7).

challenging to be described in the harmonic-oscillator
basis at least with the basis space employed here. It isawaited to extrapolate our results obtained in the ﬁnite
basis-space size into the inﬁnite basis-space-size limit soas to compare with the experimental values and also
the other theoretical calculations in more detail. Basedon our preliminary calculations, the investigation of theintrinsic structure of 12 C is currently underway, aiming
to elucidate the α-cluster structure in light-mass nuclear
systems from ﬁrst principles.
References

1) T. Abe, P. Maris, T. Otsuka, N. Shimizu, Y. Utsuno,J. P. Vary, Phys. Rev. C 86, 054301 (2012).
2) B. R. Barrett, P. Navrátil, J. P. Vary, Prog. Part. Nucl.
Phys. 69, 131 (2013).
3) T. Otsuka, M. Honma, T. Mizusaki, N. Shimizu, Y. Utsuno, Prog. Part. Nucl. Phys. 47, 319 (2001).
4) N. Shimizu, T. Abe, Y. Tsunoda, Y. Utsuno,
T. Yoshida, T. Mizusaki, M. Honma, T. Otsuka,
Prog. Theor. Exp. Phys. 2012, 01A205 (2012).
5) N. Shimizu, T. Abe, M. Honma, T. Otsuka, T. Togashi,
Y. Tsunoda, Y. Utsuno, T. Yoshida, Phys. Scr. 92, 063001(2017).
6) A. M. Shirokov, I. J. Shin, Y. Kim, M. Sosonkina,P. Maris, J. P. Vary, Phys. Lett. B761, 87 (2016).
7) F. Ajzenberg-Selove, Nucl. Phys. A 506, 1 (1990).
8) M. Chernykh, H. Feldmeier, T. Neﬀ, P. von NeumannCosel, A. Richter, Phys. Rev. Lett. 98, 032501 (2007).

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