Extensions of Variational Methods, II : Two Parameter Eigenvalue Problem for the Deuteron State

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概要

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• In the usual treatment of the deuteron problem, depths of both central and tensor potentials are to be determined so as to give the correct experimental values for the binding energy γ^2 and the electric quadrupole moment Q assuming a suitable function for the potential. We can consider these two depth values as "two parameter eigenvalue". In this connection the following approximate relation among Q, γ^2 and the mixing parameter ε of the D-state to the S-state is useful, tanε=-√<2>Qγ^2, γ^2=(binding energy of deuteron)×(nucleon mass)÷〓^2, which is shown to be accurate within 10 percents. The usual variational method is extended to this problem : We first find the stationary expressions for both depths of central and tensor potentials, and it is proved that the stationary requirement is equivalent to the fundamental equations of the deuteron state with specified mixing ratio ε. Actual applications are carried out for the square well potentials. The most advantageous point of the present method is that we can determine both depths simultaneously without resource to approximate method such as trial-and-error method. Lastly the variation principle corresponding to the Rayleigh-Ritz variational method is generalized to many parameter eigenvalue problem.

• 理論物理学刊行会の論文

著者

• Kikuta Takashi

  Department Of Physics University Of Tokyo

• Kikuta Takashi

  Department Of Physics Faculty Of Science University Of Tokyo

• KIKUTA Takashi

  Department of Physics, University of Tokyo

関連論文

• Effect of Hard Core on the Binding Energies of H^3 and He^3, I^*
• Extensions of Variational Methods, II : Two Parameter Eigenvalue Problem for the Deuteron State
• Convergence of Iterative Methods
• Extensions of Variational Methods, I : Super-Stationary Variational Method

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