In slow collisions of two bare nuclei with the total charge number larger than the critical value, $Z_{\rm cr} \approx 173$, the initially neutral vacuum can spontaneously decay into the charged vacuum and two positrons. Detection of the spontaneous emission of positrons would be the direct evidence of this fundamental phenomenon. However, the spontaneous emission is generally masked by the dynamical positron emission, which is induced by a strong time-dependent electric field created by the colliding nuclei. In our recent paper [I.A. Maltsev et al., Phys. Rev. Lett. 123 , 113401 (2019)] it has been shown that the spontaneous pair production can be observed via measurements of the pair-production probabilities for a given set of nuclear trajectories. In the present paper, we have significantly advanced this study by exploring additional aspects of the process we are interested in. We calculate the positron energy spectra and find that these spectra can give a clear signature of the transition from the subcritical to the supercritical regime. It is found that focusing on a part of the positron spectrum, which accounts for the energy region where the spontaneously created positrons can contribute, allows to get a much stronger evidence of the transition to the supercritical mode, making it very well pronounced in collisions, for example, of two uranium nuclei. The possibility of extending this study to collisions of bare nuclei with neutral atoms is also considered. The probability of a vacancy in the lowest-energy state of a quasimolecule which is formed in collisions of a bare U nucleus with neutral U and Cm atoms has been calculated. The relatively large values of this probability make such collisions suitable for observing the vacuum decay.

中文翻译：

---

如何在超临界库仑场访问QED

在两个电荷总数大于临界值的裸核的缓慢碰撞中，$ Z _ {\ rm cr} \约173 $，最初的中性真空会自发地衰减为带电的真空和两个正电子。对正电子自发发射的检测将是这种基本现象的直接证据。但是，自发发射通常被动态正电子发射掩盖，动态正电子发射是由碰撞原子核产生的随时间变化的强电场诱导的。在我们最近的论文中[IA Maltsev等，Phys。莱特牧师 123，113401（2019）]已经显示，可以通过测量给定核轨迹集的成对产生概率来观察自发成对产生。在本文中，我们通过探索我们感兴趣的过程的其他方面，极大地推进了这项研究。我们计算了正电子能谱，发现这些能清晰地反映从亚临界到超临界状态的跃迁。我们发现，专注于一部分正电子谱，这说明了自发产生的正电子可以贡献能量的区域，这可以为过渡到超临界模式提供更强有力的证据，使其在碰撞中非常明显，例如，两个铀核。还考虑了将这项研究扩展到裸核与中性原子碰撞的可能性。计算了在裸U核与中性U和Cm原子碰撞中形成的准分子的最低能量状态中出现空位的可能性。