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Three-nucleon system on a translationally invariant nuclear single particle picture

Three-nucleon system on a translationally invariant nuclear single particle picture. H. Kamada, W. Gloeckle, J. Golak, Kyushu Institute of Technology, Japan Ruhr-Universiteat Bochum, Germany Jagiellonian University, Poland. motivation.

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Three-nucleon system on a translationally invariant nuclear single particle picture

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  1. Three-nucleon system on a translationally invariant nuclear single particle picture H. Kamada, W. Gloeckle, J. Golak, Kyushu Institute of Technology, Japan Ruhr-Universiteat Bochum, Germany Jagiellonian University, Poland

  2. motivation • The shell model has been applying a single particle product ansatz. • The Schroedinger equation for that Hamiltonian can be solved by few-body techniques, which will allow to check the validity or non-validity of the single particle product ansatz.

  3. single particle ansatz Total wave function is given as where R is the function of the coordinates ui defined by

  4. 3-boson system

  5. 3-boson system

  6. Direct scheme (3D)

  7. ー ー ー

  8. potential ０．６ｆｍ －５７ＭｅＶ

  9. Percentage of component

  10. Fitting the wave function

  11. Function R

  12. Algorism k=1 k=2 k=3 k=4

  13. Gauss model for calibration

  14. Gauss model

  15. Lagrangian for MT-V potential • Ｌ＝０．８８４％ • Ｓｑｒｔ（Ｌ）＝９．４０％ Single particle picture Faddeev Solution

  16. MT-V Gauss model

  17. Wave function

  18. Fitting wave function

  19. Difference

  20. Original

  21. Result

  22. Correlation function Solid line = Result Dotted line =Original

  23. Correlation function 2 Solid line = Result Dotted line =Original

  24. Summary and outlook • The wave function of single particle picture is obtained from the exact solution by minimizing the norm Lagrangian L. • L is minimized up to 0.00884. (0.884%) • The short range part of the wave function is destroyed but the volume factor x2y2 makes it hidden. * OUTLOOK • To apply the realistic NN potential • To extend 4N system • The short range part of the potential is modified by the low-k unitary transformation.

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