Physicists of St Petersburg University, together with their foreign colleagues, have demonstrated that in the course of experiments with measuring the number of positronic particles appearing due to a low-energy collision of heavy ions it is possible to witness the evidence of the vacuum decay in supercritical Coulomb fields.

 Almost right after the basis of the quantum field theory had been laid in the 1930s, it was noticed that the theory predicts spontaneous production of electron-positron pairs by a uniform electrical field, as long as the field intensity equals or exceeds some (very big) critical data value. Whereas in theory this phenomenon was studied in a large number of works, its experimental detection was considered impossible due to the practical infeasibility of the necessary field intensity. There were certain hopes that the development of laser technologies would make the experimental detection possible. However, in the coming decades reaching the required field intensity with the help of lasers is very unlikely.    

The results of the research are published in the Physical Review Letters.

An alternative approach to studying the physics of vacuum in the presence of a supercritical field was suggested fifty years ago in the works of the Soviet physicists, Semyon Gerstein, Yakov Zeldovich, Vladimir Popov, and at the same time, independently, in the works of a German group of scientists headed by Walter Greiner. In these works, it was shown that in the field of a bare nucleus with a charge higher than the critical value of 173, vacuum becomes unstable. This can result in the spontaneous production of positrons. That is, changing from subcritical behaviour to supercritical, the original neutral vacuum breaks down to charged vacuum and two positrons.  

fiziki tablica

The graph shows the derivative of the possibility of positron production from the energy of collision of bare nucleuses with the same charge Z=Z=Z2 for trajectories with the fixed minimal nucleuses approximation, Rmin=16.5 fermi.  The red vertical line separates subcritical and supercritical regimes. Decreasing of the function dP/dη with the increasing of Z suggests the breaking down of the original neutral vacuum into charged vacuum and two positrons.


Given that there are no nucleuses with such large charges (the charge of the heaviest discovered element, Oganesson, equals 118), the only way to create the supercritical field is to collide nucleuses with the total charge exceeding the critical value (Z1+Z2>173). Efforts to observe experimentally this effect, undertaken around thirty years ago in the GSI Helmholtz Centre for Heavy Ion Research in Darmstadt (Germany), proved unsuccessful.

Moreover, the leading German theoretical study group worked on this problem under the supervision of Greiner for more than 20 years. They arrived at a conclusion that vacuum decay can only be experimentally observed if colliding nucleuses adhere for some time due to nuclear force. Such adhesion is necessary due to the small amount of time of the existence of the supercritical field during the atomic recoil. This results in it being impossible to witness the spontaneous production of positrons alongside the large dynamic (induced) production of positrons; which in turn occurs both in subcritical and supercritical fields (as opposed to spontaneous). However, the scientists have not managed to discover any evidence of nucleuses adhesion in such collisions so far.

Throughout the ten years of working on the problem I did not believe nucleuses adhesion in such collisions was possible.

Professor of the department of quantum mechanics of St Petersburg University, Vladimir Shabaev

‘Our main target was to manage to discover visible data attesting to a quality difference between subcritical and supercritical conditions. But to fulfil this idea we were to develop new methods of measuring the electron-positron field of low-energy collisions of heavy ions; which would allow us to go beyond the approximations used by the Greiner study group,’ said Vladimir Shabaev, professor of the department of quantum mechanics of St Petersburg University. Vladimir Shabaev pointed out that this great work was implemented by both experienced scientists and young members of the department, including students and post graduate students. The new developed methods enable the evaluation of the role of the effects, which were not considered before, and to start studying the more sophisticated nuances of quantum dynamics of the processes in question.

‘As a result of the research, we succeeded in showing that while measuring the amount of positrons produced through the low-energy collision of two bare nucleuses or a bare nucleus and a neutral atom in certain experiment conditions (real world conditions) it is possible to single out the contribution of spontaneous production of positrons to the process. This indicates the decay of the vacuum and the supercritical Coulomb field. No adhesion of nucleuses is required for it. This work attracted a lot of attention of experimentalists, and will without doubt influence the scientific research programmes of mega installations in Germany (FAIR) and China (HIAF). I look forward to a similar project being launched in Russia. During his visit to St Petersburg University this June, Yuri Oganessian told us that there are possibilities for such projects in Dubna,’ Vladimir Shabaev explained.

‘In conclusion I would like to underline,’ Vladimir Shabaev continued, ‘that despite scientists from different countries working on the research, the leading role belongs to the members of the department of quantum mechanics of St Petersburg University. Apart from me, these are the young members of the department, Ilia Maltsev and Yury Kozhedub, and post graduate students Roman Popov and Dmitry Tumakov. Finally, I would like to note that this research, as are many other projects of the last decade, would have been impossible without the financial support of St Petersburg University through competitive selection for the activities 1 and 2.’