On the Scattering Problem in Pseudo-scalar Meson in Pseudo-vector Coupling

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概要

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• The theoretical investigation of meson nucleon scattering given by Brueckner which fits very well with the experimental data is based on the phenomenological considerations with the mixed use of weak and strong coupling theories. The weak coupling treatment was abandoned owing to its failure to explain the well known scattering data even qualitatively. These weak coupling calculations are Born approximation. The well known threshold rise of the cross-section is given by pseudo scalar meson with pseudo-vector coupling, but there is no securence that the Born approximation is allowed. In the weak coupling case, the effective-scattering Hamiltonian can be easily obtained by a canonical transformation (for example, assuming the coupling to be weak, retain only second order term), but if one regards this as a "potential" which causes the scattering of meson, the singularity of this "potential" is so strong that the Born approximation do nothing, and just as in the theory of nuclear force one should solve the problem exactly with this "potential". (The word "potential" does not mean that the meson scattering can be represented by potential scattering; we call the quantity which appears in place of potential as "potential".) We now perform a calculation firstly deriving the "potential" under the weak coupling assumption and then solve the dynamical problem of the system correctly (not in Born approximation) for the problem of meson-nucleon scattering. This is just the way taken up to date in the meson theory of nuclear force, i.e., deriving the nuclear potential under the weak coupling assumption and solve the Schroedinger equation with this potential exactly; we want to perform the same procedure in the meson-nucleon scattering. The "potential" derived from pseudo-scalar meson with pseudo-vector coupling is very singular and changes its sign and magnitude for different total isotopic spin and angular-momentum of the system. It is seen that the virtual level resonance takes place for I=3 / 2 and J=3 / 2 state. The conclusion is roughly the same as the theory by Brueckner. The divergences appear many places but can be summed up to the effective coupling constant aside from the position of virtual level.

• 理論物理学刊行会の論文

著者

• Sawada Katuro

  Department Of Physics Tokyo University

• Sawada Katuro

  Department Of Applied Physics Tokyo University Of Education

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