RIKEN Accel. Prog. Rep. 50 (2017)

Research Activities 1991–2016

Gaussian Expansion Method and its application to nuclear physics
with strangenessE. Hiyama ∗1
In physics, there are a lot of important and interesting problems to solve the Schrödinger equation forfew-body systems with high accuracy. Therefore, it isvery important to develop methods for such problems.
As one of the calculation methods, in the 1980s, theGaussian Expansion Method (GEM), which is one of
the ab initio variational methods for few-body systems,
was proposed by Kamimura, who performed nonadiabatic three-body calculations of muonic moleculesand muon-atomic collision.1)
This method was successfully applied to threenucleon bound states such as the 3 H and 3 He systems,
unstable nuclei, and antiprotonic helium atoms. Whenone proceeds to four-body systems, the calculation of
the Hamiltonian matrix elements becomes rather laborious. In order to make the four-body calculation
tractable even for complicated interactions, the inﬁnitesimally shifted Gaussian lobe basis function has
been proposed. GEM with the technique of inﬁnitesimally shifted Gaussians has been applied to various
three-, four-, and ﬁve-body calculations in hypernuclei;
the four-nucleon systems; and ultracold-atom systems.
As shown in Fig. 1, we have been studying many
subjects in various research ﬁelds of physics using themore developed GEM. The strategy for such studies
is as follows. We have been applying GEM to various research ﬁelds, such as (1) hypernuclear physics,(2) ultracold-atom physics, (3) the physics of unstable nuclei, etc. and have contributed to each researchﬁeld. As a feedback of the numerical eﬀorts for thecontributions, we have been able to develop the calculation method GEM further at the center and thenapply the developed GEM to a new ﬁeld, which has
not been studied previously by the present laboratory.
As a project in the laboratory, we have been repeating
this type of research cycle under this strategy.
In my laboratory, we have been focusing on hypernuclear physics. Here, I mention some highlights ofour studies in hypernuclear physics.
One of the main goals in hypernuclear physics isto understand the baryon-baryon interaction. The
baryon-baryon interaction is fundamental and important for the study of nuclear physics.
In order to obtain information on the baryon-baryon
interaction, it is important to study the structure ofhypernuclei.
Since I started our laboratory in 2008, our laboratory mainly studied the charge symmetry breaking(CSB) eﬀect between Λ and neutron, and Λ and pro∗1Fig. 1. Research strategy program in the strangeness nuclear physics laboratory.

ton by studying A = 7 Λ hypernuclei, 7Λ He, 7Λ Li(T = 1)
and 7Λ Be.2) We found that, if there is a large CSB effect in s-shell Λ hypernuclei between 4Λ H and 4Λ He, weneed an odd-state CSB eﬀect with opposite sign withan even-state CSB for A = 7 hypernuclei. Anotherhot topic in hypernuclear physics is to obtain ΛN-ΣNcoupling. For this study, in 2014, the nnΛ system wasobserved as a bound state at GSI.3) For this purpose,
we studied the nnΛ system by taking ΛN-ΣN coupling
explicitly to produce the binding energies of 3Λ H, 4Λ H,and 4Λ He. We do not ﬁnd any bound state for the nnΛsystem, which contradicts the data obtained at GSI.
Therefore, we need to perform a conﬁrmation experiment at GSI. We also studied the strangeness S = −2system, which is the entrance to the multi-strangenessworld. Especially, the observation of the “Hida” event
was reported in an emulsion experiment.4) We studied
this event within the framework of the α+α+n+Λ+Λ
ﬁve-body problem. The observed Hida event can beinterpreted to be the ground state. When our calculated binding energy is compared with the experimental value of 20.83 MeV with a large uncertainty of σ =1.27 MeV, we can say at least that our result does notcontradict the data within 2σ.
References
1) E. Hiyama, Y. Kino, M. Kamimura, Prog. Part. Nucl.
Phys. 51, 223 (2003).
2) E. Hiyama, Y. Yamamoto, T. Motoba, M. Kamimura,Phys. Rev. C 80, 054321 (2009).
3) J. K. Ahn et al., Phys. Rev. C 88, 014003 (2013).
4) C. Rappold et al., Phys. Rev. C 88, 041001(R) (2013).

Associate Chief Scientist/Chief Scientist of Strangeness Nuclear Physics Laboratory (2008–present)

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