How to Observe the Vacuum Decay in Low-Energy Heavy-Ion Collisions

In slow collisions of two bare nuclei with the total charge larger than the critical value $Z_{\mathrm{cr}}\approx 173$, the initially neutral vacuum can spontaneously decay into the charged vacuum and two positrons. The detection of the spontaneous emission of positrons would be direct evidence of this fundamental phenomenon. However, the spontaneously produced particles are indistinguishable from the dynamical background in the positron spectra. We show that the vacuum decay can nevertheless be observed via impact-sensitive measurements of pair-production probabilities. The possibility of such an observation is demonstrated using numerical calculations of pair production in low-energy collisions of heavy nuclei.

Figure 1

Pair-production probability $P$ in the hypothetical head-on collision of bare nuclei with the modified dependence of the internuclear distance on time $R_{\alpha }(t)$, defined by Eq. (1), as a function of $\alpha$. The solid line shows the results for the Fr-Fr (subcritical) collision at $E=674.5\mathrm{MeV}$; the dashed line corresponds to the U-U (supercritical) collision at $E=740\mathrm{MeV}$. The results were obtained in Ref. [20].

Figure 2

The internuclear distance $R$ for U-U collision as a function of time for different values of the collision energy with the fixed distance of the closest approach $R_{\min }=16.5\mathrm{fm}$, $E_0$ is the energy of the head-on collision. The red horizontal line corresponds to the critical distance $R_{\mathrm{cr}}\approx 32.6\mathrm{fm}$ and indicates the border between subcritical and supercritical regimes.

Figure 3

The pair-production probability in the collision of two identical nuclei with $Z_1=Z_2=Z_{\mathrm{nucl}}$ as a function of the ratio $\eta =E/E_0$, where $E$ is the collision energy and $E_0$ is the energy of the head-on collision. The results for $Z_{\mathrm{nucl}}=96$ are multiplied by factor 0.5.

Figure 4

The total pair-production probability in U-U collision, and contributions from channels with $\kappa =\pm 1$ as functions of the ratio $\eta =E/E_0$, where $E$ is the collision energy and $E_0$ is the energy of the head-on collision.

Figure 5

The total pair-production probability in U-Cm collision as a function of the ratio $\eta =E/E_0$, where $E$ is the collision energy and $E_0$ is the energy of the head-on collision.

Figure 6

The derivative $dP/d\eta$ taken at $\eta =1$ as a function of $Z_{\mathrm{nucl}}$, where $\eta =E/E_0$, $E$ is the collision energy, $E_0$ is the energy of the head-on collision, $P$ is the pair-production probability, and $Z_{\mathrm{nucl}}$ is the charge of each colliding nucleus. The red vertical line marks the border between subcritical and supercritical domains.