氘氚自旋极化碰撞的相对论动力学
Spin-polarized collision of deuterium and tritium: Relativistic Kinematics
摘要：
本文研究了氘与氚自旋极化碰撞产生${}^4$ He和中子的相对论运动学。在狭义相对论的范围内，我们应用四个动量守恒和内禀自旋守恒，这导致了一个由十个方程组成的系统。我们施加初始条件，使得氘沿着x轴移动，氚在坐标原点处静止，并且氘的经典自旋矢量（自旋幅度= 1）沿着+z轴，而氚的经典自旋矢量（自旋幅度= 1/2）沿着$-$ z轴。我们扩展到二阶速度守恒方程，我们解决他们的中子，它的单位自旋取向矢量的速度分量，和${}^4$ He核的速度分量，作为入射氘能量的函数。我们发现，这个解析解与十个（未展开）方程的数值解非常吻合。对于给定的氘能量，我们发现有两个解决方案，每个解决方案有一个独特的速度为发射的中子和氦核。这两个解决方案是相互关联的反射在平面上垂直于氘自旋，并包含初始氘速度矢量。
英文摘要：
We investigate the relativistic kinematics of the spin-polarized collision of deuterium incident on tritium, producing ${}^4$He and a neutron. Within the context of special relativity, we apply the conservation of four momentum and the conservation of intrinsic spin, which leads to a system of ten equations. We impose initial conditions such that the deuterium is moving along the x-axis, the tritium is stationary at the origin of coordinates, and the classical spin vector of the deuterium (spin magnitude = 1) is along the +z-axis, while the classical spin vector for tritium (spin magnitude = 1/2) is along the $-$z-axis. We expand the ten conservation equations to second order in velocities and we solve them for the velocity components of the neutron, its unit-spin-orientation vector, and the velocity components of the ${}^4$He nucleus, as a function of the incident deuterium energy. We find that this analytic solution agrees closely with the numerical solution of the ten (unexpanded) equations. For a given energy of deuterium, we find that there are two solutions, each solution having a unique velocity for the emitted neutron and helium nucleus. The two solutions are related to each other by reflection in the plane perpendicular to the deuterium spin and containing the initial deuterium velocity vector.
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