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论散射过程相分析中的不定性问题

黄念宁

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论散射过程相分析中的不定性问题

黄念宁

ON THE PROBLEM OF AMBIGUITY IN THE PHASE SHIFT ANALYSIS OF SCATTERING PROCESSES

HUANG NIEN-NING
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  • 从散射过程的相分析中存在不同的相移的选取所必须满足的条件出发,在本工作中,讨论了任意自旋粒子的弹性散射过程的相分析中的不定性问题。给出了全部不同的相的集合之间的变换矩阵,其中所含的实参数由二阶代数方程组决定,因此相分析中的不定性问题化为解这些代数方程的实根的问题。指出此实根的组数之半即为相分析中不同选取的组数。这样,相分析中的运动学不定性问题已完全解决。当道自旋为1/2时,只存在两组不同的相移,当道自旋为1时,也只有两组不同的相移,因此证明了,已知的南氏不定性是这样的自旋值下的全部不定性。在道自旋为3/2时,给出了四给不同的相移。因此除已找出的相移间的变换外,还存在两种新的变换。物理上说,相分析中的不定性相应于自旋的某种运动,它保持自旋张量在动量方向的分量不变,且表征此种运动的参量取一定数值。从讨论中得出,道自旋为整数的情况和为半整数的情况,相移的变换矩阵中所含的实参数所满足的代数方程组具有十分不同的性质,因此实根的组数也不同。这表示,道自旋为整数和为半整数的情况的相移的不同选取的组数也完全不同。一般的推测是,道自旋为整数的情况时的相移不同选取要比为半整数时的少很多。
    Starting from the conditions which should be satisfied by the existence of different choice in the phase shift analysis, in this paper the general ambiguity in the analysis of elastic scattering of particles with arbitrary spins has been discussed. The transformation matrices among the different sets of phase shift are given, the real parameters involved are determined by the system of second order algebraic equations. The problem of ambiguity in the phase shift analysis therefore is reduced to the problem of finding the teal roots of those equations. The number of different sets of real roots is twice that of different phase shift choice. Therefore, the kinematical ambiguity in the phase shift analysis in general is solved. When the channel spin is 1/2, it has been shown that only two sets of phase shift exist; when the channel spin is 1, only two sets of phase shift are given also, therefore it has been shown that the Minami's ambiguity is the whole ambiguity in these cases. When the channel spin is 3/2, it has been found that there are four different sets of phase shift. Therefore, in addition to the known transformation there are two new transformation matrices in that case. In general, the ambiguity in the phase shift analysis corresponds to the motion of spin which conserves the components of spin-tensors in the direction of momentum, and the parameters which characterize those general spin motion take the fixed values. In our discussion it has been shown that the systems of algebraic equations which are satisfied by the real parameters in the transformation matrices in the whole integral spin cases are quite different from that in the half integral spin cases. Therefore, the numbers of real roots in those two cases are also different, this means that the numbers of different phase shift sets are quite different. From the properties of those algebraic equation it has been suggested that the ambiguity in the case of integer spin is much smaller than that in the case of half integer spin.
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出版历程
  • 收稿日期:  1962-05-25
  • 刊出日期:  2005-08-05

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