An accompanied Long Range Potential in NN interaction ~Efimov-like structure~ Shinsho Oryu Department of Physics, Tokyo University of Science APFB11, August 22, 2011 Sungkyunkwan University (SKKU) , Seoul Korea

The two-body potential reduction has the energy dependence.

Energy sequence sequence reversed

Bohr radius

Numerical calculation by Schroedinger equation: MeV fm Our analytic prediction fits to the numerical solution.

It is known that a pion-transfer creates an attractive short range Yukawa potential, however, it missed out the long range potential accompanied with.

Conclusion and discussion 1) In the present calculation, only the pion-transfer AGS-Born term is adopted. The pion-nucleon form factors are taken as a constant, but leading terms are taken into account. Therefore, the results are qualitatively correct. However, the detailed calculation will be presented before long. Our predictions are not observed yet, for the binding energy lesser than 50keV, for the phase shift lesser than 50keV. idea that the nuclear force is short range.

Proton-proton phase shift

3) The present theory will complement the stereotype idea that the NN-interaction is a short range. 4) The long range force is created by the particle transfer structure. This phenomena will appear in the other few-body systems. 5) The results will contribute to the study for the neutron rich nucleus and halo problem in the light nucleus. 6) In the zero energy bound state, the n-p probability will distribute up to the atomic region. 7) The phenomena will contribute to the nuclear fusion.

Three-body Efimov states Three-body break up threshold Two-body Present case Two-body threshold One-body

8) Zero energy bound states in NN systems could produce a special nuclear material which has a different phase from the well known nuclear matter. 9) If the nuclear material will be equilibrium in the universe, it could take a typical aspect with some heat radiation. 10) Classical three-body problem predicted new planets, however what we learn from the quantum three-body problem? 　 These phenomena could be one of them.

Yukawa predicted that a pion-transfer creates an attractive force, however, he missed out the fact that the long range potential accompanied with the Yukawa potential.

Accompanied potential in the many-body (three-body) system. The three-body point of view of the ionic bond. Since , then no accompanied potential. Zero mass particle transfer

Covalent bond： Accompanied potential exists, because

Nuclear force

Fourier tranceform to obtain ｒ-space rep. Energy dependent potential !! Laplace transform with weight gives an energy average.

Our NNπ-system Case of Hydrogen atom

The solution is the modified Bessel function The solution is the modified Bessel function. By the boundary condition, uncountable energy levels are obtained Uncountable energy levels are concentrated near at zero energy. Rms-radius incleases as far as the atomic-moleculer region，and affects the chemical reaction.

3) Thus the three-body calculation needs a special treatment 3) Thus the three-body calculation needs a special treatment. 4) Therefore we used the Fourier transformation of AGS-Born term to obtain the r-space three-body effective potential. 5) We obtained the r-space potential with the energy dependent range. 6) We introduced a typical average method for the energy dependence. The method is a kind of Laplace tranceformation. 7) We found that the Yukawa type potential plus the long range potential.

Possibility of new fusion １）confinement by laser cooling D2 molecule ２）excitement of deuteron to zero energy states which have long life time. 3）constituent nucleons extend to the molecular orbit, and make singlet deuteron D*-molecule. 4）D*2 molecule loses energy and down to the helium ground state.

尾立先生 ご質問の件、2HのLevelについては、 中性子分離エネルギーだけで、構造については 調べられていないのではないかと思います。 もしやと思い、ポリエチレン試料を、冷中性子で照射 したスペクトルを見てみました。 添付では、小さなGe結晶で測ったスペクトルです。 ノイズを切るために、50kevぐらいでDiscriminationしています。 これ以上下げると、検出器のDead Timeが多くなってしまいますので、 過去のデータでは、そこまで気にしていませんでした。 先生のご質問の問題を言い換えると、 1Hターゲットを照射して、得られたガンマ線スペクトルで、 2.2MeVガンマ線と、12.7keVガンマ線は、同時事象かどうか、 を調べることだと思います。 2.2MeVガンマ線にゲートをかけて、Coincidenceするガンマ線が 何か見えるだろうか、また、構造があれば、第一励起にいくパス がありますから、2224.57keV-12.7keV=2211.87keVにピークが現れるか、 ということになります。 検出器の分解能のせいで、2.2MeVのピークが2山やら、テールにコブ でもあれば、おやっ？ と思うのですが、手持ちのデータでは、はっきり しませんでした。

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