Gribakin G F, Ludlow J
Department of Applied Mathematics and Theoretical Physics, Queen's University, Belfast BT7 1NN, Northern Ireland.
Phys Rev Lett. 2002 Apr 22;88(16):163202. doi: 10.1103/PhysRevLett.88.163202. Epub 2002 Apr 5.
The behavior of the positron- 2 gamma annihilation rate on an atomic target near the positronium (Ps) formation threshold is determined. When the positron energy epsilon approaches the threshold epsilon(thr) from below, the effective number of electrons contributing to the annihilation, Z(eff), grows as Z(eff) approximately A/square root of [epsilon(thr)-epsilon], where A is related to the size of the Ps formation cross section, sigma(Ps) approximately B square root of [epsilon-epsilon(thr)], by A = B square root of [2 epsilon(thr)]/32 pi (in atomic units). Taking account of the finite Ps lifetime eliminates the singularity in Z(eff) and shows that close to threshold the positron annihilation cross section is identical to the para-Ps formation cross section.
确定了正电子 - 2γ湮灭率在接近正电子素（Ps）形成阈值的原子靶上的行为。当正电子能量ε从下方接近阈值ε(thr)时，对湮灭有贡献的有效电子数Z(eff)增长，其增长方式为Z(eff)近似于A / √[ε(thr) - ε]，其中A与Ps形成截面σ(Ps)的大小相关，σ(Ps)近似于B√[ε - ε(thr)]，且A = B√[2ε(thr)] / 32π（以原子单位计）。考虑到Ps的有限寿命消除了Z(eff)中的奇点，并表明在接近阈值时正电子湮灭截面与仲正电子素形成截面相同。
