Abstract
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.
Highlights
After the foundations of quantum field theory were formulated in the early 1930s, it was shown that the theory predicts the spontaneous creation of electron-positron pairs by a constant uniform electric field if the strength of the field is comparable to or greater than a critical value, Ecr 1⁄4 m2ec3=ðjejħÞ ≈ 1.3 × 1016 V=cm, [1,2,3]
The methods described in the previous section are employed for the calculations of the total pair-creation probabilities and positron spectra
We have studied possible scenarios to access QED in the supercritical Coulomb field which can be created by heavy nuclei in low-energy collisions near the Coulomb barrier
Summary
After the foundations of quantum field theory were formulated in the early 1930s, it was shown that the theory predicts the spontaneous creation of electron-positron pairs by a constant uniform electric field if the strength of the field is comparable to or greater than a critical value, Ecr 1⁄4 m2ec3=ðjejħÞ ≈ 1.3 × 1016 V=cm, [1,2,3]. Despite the aforementioned conclusions by the Frankfurt group, one could expect, that the detailed study of quantum dynamics of the electron-positron field in lowenergy heavy-ion collisions would allow to find some signatures which indicate the principal difference between the subcritical and the supercritical regimes. To carry out these studies, first of all it was necessary to develop the theoretical and computational methods beyond the approximation made by the Frankfurt group. The relativistic units (ħ 1⁄4 c 1⁄4 1) and the Heaviside charge unit (α 1⁄4 e2=ð4πÞ, e < 0) are used throughout the paper
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