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Three-nucleon system on a translationally invariant nuclear single
particle picture
H. Kamada, W. Gloeckle, J. Golak, Kyushu Institute of Technology, JapanRuhr-Universiteat Bochum, Germany
Jagiellonian University, Poland
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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.
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single particle ansatz
Total wave function is given as
where R is the function of the coordinates ui defined by
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3-boson system
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3-boson system
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Direct scheme (3D)
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ー
ー
ー
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potential
０．６ｆｍ
－５７ＭｅＶ
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Percentage of component
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Fitting the wave function
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Function R
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Algorism
k=1
k=2
k=3
k=4
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Gauss model for calibration
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Gauss model
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Lagrangian for MT-V potential
Ｌ＝０．８８４％ Ｓｑｒｔ（Ｌ）＝９．４０％
Faddeev Solution
Single particle picture
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Gauss model
MT-V
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Wave function
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Fitting wave function
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Difference
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Original
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Result
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Correlation function
Solid line = ResultDotted line =Original
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Correlation function 2
Solid line = ResultDotted line =Original
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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.
