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Register a new user$(Zalpha)^{4}$ order of the polarization operator in Coulomb field at low energy
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We derive the low-energy expansion of $(Zalpha) ^{2}$ and $(Zalpha) ^{4}$ terms of the polarization operator in the Coulomb field. Physical applications such as the low-energy Delbr{u}ck scattering and magnetic loop contribution to the $g$ factor of the bound electron are considered.
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We study nonlinear trident in laser pulses in the high-energy limit, where the initial electron experiences, in its rest frame, an electromagnetic field strength above Schwingers critical field. At lower energies the dominant contribution comes from the two-step part, but in the high-energy limit the dominant contribution comes instead from the one-step term. We obtain new approximations that explain the relation between the high-energy limit of trident and pair production by a Coulomb field, as well as the role of the Weizsacker-Williams approximation and why it does not agree with the high-$chi$ limit of the locally-constant-field approximation. We also show that the next-to-leading order in the large-$a_0$ expansion is, in the high-energy limit, nonlocal and is numerically very important even for quite large $a_0$. We show that the small-$a_0$ perturbation series has a finite radius of convergence, but using Pade-conformal methods we obtain resummations that go beyond the radius of convergence and have a large numerical overlap with the large-$a_0$ approximation. We use Borel-Pade-conformal methods to resum the small-$chi$ expansion and obtain a high precision up to very large $chi$. We also use newer resummation methods based on hypergeometric/Meijer-G and confluent hypergeometric functions.
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.
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