层子模型里介子的波函数和能级

本文利用Bethe-Salpeter型的方程处理了层子模型中的介子内部波函数,指出如果层子和反层子之间的作用可以用一个赝标型位阱来代表,那么0^-和1^-介子将满足相同的近似迳向波动方程,从而导致SU₆对称性。我们以前曾经证明赝标型位阱是唯一可以导致这个对称性的单一型位阱。我们的位阱是V=V₀+V₁,V₀代表一个超强的深位阱,它的作用是降低层子的原始质量M,使它的有效值M′变得很小,使得层子在强子内部的运动是相对论的。V₁代表数量级为1/M的简谐振子位阱,另外还引入一个张量力来解释自旋和轨道角动量相同态的能级分裂。我们得出基态和角动量激发态0^-和1^-介子的解,基本上解释了所有观察到的介子。我们的理论可以同样处理重子态,只要唯象位阱V₀只有介子的值的一半。

THE WAVE FUNCTION OF MESONS IN THE STRATON MODEL

An equation of the Bethe-Salpeter type is used to obtain the internal wave function of mesons. It is found that if the potential well between the straton and anti-straton is of the pseudo-scalar type, then the 0^- and 1^- mesons will satisfy the same approximate radial wave function, and thus lead to SU₆ symmetry. We have shown previously that pseudo-scalar potential is the only single type of potential which leads to this symmetry. The potential is V = V₀+ V₁, where V₀ represents a super-strong deep well, the effect of which is to reduce the very large mass M of the free straton to a small effective value. The motion of the straton inside the meson is therefore relativistic. V₁ represents a small potential of the order of 1/M of a simple harmonic oscillator. A tensor force is also introduced to account for the splitting of energy levels of the states with the same spin and orbital angular momentum. Our solutions for the ground and angular excited states of 0^- and 1^- mesons practically explain all the observed meson states. Our theory can apply equally to the baryon states if the phenomenological potential V₀ is reduced by a factor of 2.