Vol. 48 (2017)

ACTA PHYSICA POLONICA B

No 10

η–NUCLEUS INTERACTION FROM THE d + d
REACTION AROUND THE η-PRODUCTION
THRESHOLD∗
Satoru Hirenzaki
Department of Physics, Nara Women’s University, Nara, Japan

Natsumi Ikeno
Department of Life and Environmental Agricultural Sciences, Tottori University
Tottori, Japan(Received September 12, 2017)
We have developed a theoretical model to evaluate the formation rateof the η-mesic nucleus in the d + d fusion reaction and show the calculated
results. We have compared our results with existing data of the d + d →η + α.
DOI:10.5506/APhysPolB.48.1787

1. Introduction
Recently, the new experiments of the d + d → (η + α) → X reaction havebeen proposed and performed at WASA-at-COSY [1–7]. In the experiments,the formation cross section of the η-mesic nucleus in the α particle in the d+dfusion reaction is planned to be measured by observing the emitted particles
from the decay of the η-mesic nucleus below the η-production threshold. InRefs. [6, 7], the upper limits of the bound state production are reported forthe d + d → 3 He + n + π 0 and d + d → 3 He + p + π − reactions. There werealso the data of η-production reaction d + d → η + α above the threshold[8–10], which are expected to provide the valuable information on the reaction mechanism.
In this paper, we show the numerical results for the formation crosssection of the η bound states in the d + d reaction evaluated by a theoreticalmodel developed in Ref. [11].
∗Presented at the 2nd Jagiellonian Symposium on Fundamental and Applied Subatomic Physics, Kraków, Poland, June 3–11, 2017.

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S. Hirenzaki, N. Ikeno2. Brief description of the model
We have developed a theoretical model to evaluate the formation rate ofthe η-mesic nucleus in the fusion reactions d + d → η + α [11]. In this model,
we have calculated the cross sections of the diagram shown in Fig. 1 andobtain the contributions of the conversion part and escape part separately
in addition to the total cross section by Green’s function method.

Fig. 1. The schematic diagram of the d + d → η + α reaction.

For the numerical evalaution, we assume the η–α optical potential has
the following form:ρα (r)Uopt (r) = (V0 + iW0 ),(1)ρα (0)
where V0 and W0 are the parameters to determine the potential strength
at the center of the α particle. The density of the α particle, ρα (r), is
assumed to have Gaussian form with the range parameter which reproduce
the R.M.S radius of α to be 1.681 fm. As the practical form of the reaction
form factor F , in this article we assume the Gaussian as
3/2

F (~p ) = (2π)

22p0 π

3/4p~ 2exp − 2p0and treat p0 as a phenomenological parameter.


,(2)

η–Nucleus Interaction from the d + d Reaction Around the η-Production . . . 1789

3. Numerical results
In Fig. 2, we show the calculated results for (V0 , W0 ) = −(30, 5), −(30, 20)
and −(30, 40) MeV cases with p0 = 500 MeV/c. In these weak attractive
potential cases with V0 = −30 MeV, we find the step-like structure at thethreshold for weak absorptive case with W0 = −5 MeV, which again becomesless prominent for stronger absorptive potential with larger |W0 | value.

Fig. 2. Calculated cross sections of the d + d → (η + α) → X reaction for the formation of the η–α bound systems plotted as functions of the η excited energy Eη −mη .
The parameters of the η–α optical potential are (V0 , W0 ) = −(30, 5), −(30, 20), and−(30, 40) MeV, and the p0 parameter is fixed to be p0 = 500 MeV/c. The solid lines
indicate the total cross sections σ, and the dashed lines the conversion parts σconv .

In Fig. 3, we show the calculated escape parts of the spectra with experimental data for V0 = −30 MeV cases with different strength of theabsorptive potential. The calculated results are scaled to fit the experimental data. The agreement between calculated results and the data above thethreshold seems reasonably good in these cases. As we can see from Fig. 3,
the shape of the escape part is relatively insensitive to the value of the potential parameter W0 and, in this case, it could be difficult to distinguishthe potentials only from the escape part.
To compare our calculated results with the data in the subthreshold region, we need to take into account the observed final states in the actualexperiments. In the experiments, since the η meson cannot be emitted in thesubthreshold region, the pion, nucleon, and residual three-nucleon systems
are mainly considered to be observed as the final state of the one-nucleon

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S. Hirenzaki, N. Ikeno

Fig. 3. Calculated escape part σesc in Fig. 2 is plotted with the experimental dataof the d + d → η + α reaction indicated by black squares [8], black circles [9],and open circles [10]. The parameters of the η–α optical potential are (V0 , W0 ) =−(30, 5), −(30, 20), and −(30, 40) MeV and the p0 parameter is fixed to be p0 =500 MeV/c. The line is roughly fitted to data by eye.

η-meson absorption decay of η–α bound states. Thus, we show in Fig. 4 thecalculated conversion parts of the spectra which correspond to theη-absorption processes.

Fig. 4. Calculated conversion part of cross sections of the d + d → (η + α) → X
reaction scaled by the same factor used in Fig. 3 plotted as functions of the η
excited energy Eη − mη . The flat contributions are subtracted. The parametersof the η–α optical potential are (V0 , W0 ) = −(30, 5), −(30, 20), and −(30, 40) MeV,and the p0 parameter is fixed to be p0 = 500 MeV/c.

η–Nucleus Interaction from the d + d Reaction Around the η-Production . . . 1791

4. Summary
We have developed a theoretical model to evaluate the formation rate ofthe η–α bound states in the d + d fusion reaction. Because of the difficulties
due to the large momentum transfer which is unavoidable to produce η mesonin the fusion reaction, we formulate the model in a phenomenological way.
We have shown the numerical results for the cases with the weak attractive
potential cases.
We have found that the data of η production above threshold provide
important information on the absolute strength of the reaction by comparing
them with the escape part of the calculated results.
The upper limit of the formation cross section of the η-mesic nucleus reported in Refs. [6, 7] also provides the important information on the strengthof the η–nucleus interaction. We would like to stress here that simultaneous
fit to both data of d + d → η + α and d + d → (η + α) → X using our model
make it possible to provide valuable information on η–nucleus interaction.
The details of this work will be reported in Ref. [11].
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