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Energy--angle differential and total probabilities of positron creation in slow supercritical collisions of two identical heavy nuclei are calculated beyond the monopole approximation. The time-dependent Dirac equation (TDDE) for positrons is solved using the generalized pseudospectral method in modified prolate spheroidal coordinates, which are well-suited for description of close collisions in two-center quantum systems. In the frame of reference where the quasimolecular axis is fixed, the rotational coupling term is added to the Hamiltonian. Unlike our previous calculations, we do not discard this term and retain it when solving the TDDE. Both three-dimensional angle-resolved and angle-integrated energy distributions of outgoing positrons are obtained. Three-dimensional angle-resolved distributions exhibit a high degree of isotropy. For the collision energies in the interval 6 to 8 MeV/u, the influence of the rotational coupling on the distributions and total positron creation probabilities is quite small.

The problem of orbital collapse of the $5g$ and $6f$ electrons in atoms of superheavy elements (SHE) is considered. Previously, the presence of the orbital collapse was established for the $4f$ and $5f$ elements of the periodic table. Because of the large centrifugal term for the $f$ and $g$ electrons, the effective radial potential has two wells, one narrow and deep and the other wide but shallow. Depending on the external parameters, the electron can be either localized in the outer well with low binding energy and large average radius or in the inner one with higher energy and smaller radius. In this work, we demonstrate the existence of the orbital collapse for the $5g$ electrons when changing the total angular momentum $J$ of the atom. We also found that for some SHE elements, two different solutions of the same Dirac-Fock equations may coexist, with the $5g$ electron localized either in the inner or outer well. In both cases, the radial wave functions are nodeless. The problem of the dual-state coexistence is studied by the configuration-interaction method in the Dirac-Fock-Sturm orbital basis as well., Comment: 8 pages, 2 figures

We present a theoretical and computational study of positron supercritical resonances in systems consisting of two highly-charged bare nuclei. The resonance positions and widths depending on the internuclear separation are calculated with the help of the complex-scaling generalized pseudospectral method in modified prolate spheroidal coordinates. The results are applied to estimate the probability of spontaneous positron creation in slow U$^{92+}$--U$^{92+}$ and Cm$^{96+}$--Cm$^{96+}$ collisions.

Positron creation probabilities as well as energy and angular distributions of outgoing positrons in slow collisions of two identical heavy nuclei are obtained within the two-center approach beyond the monopole approximation. The time-dependent Dirac equation for positron wave functions is solved with the help of the generalized pseudospectral method in modified prolate spheroidal coordinates adapted for variable internuclear separation. Depending on the nuclear charge, the results are obtained for both subcritical and supercritical regimes of the positron creation. The signatures of transition to the supercritical regime in the total positron creation probabilities and energy spectra are discussed. The angular distributions of emitted positrons demonstrate a high degree of isotropy.

The problem of spontaneous vacuum decay in low-energy collisions of heavy nuclei is considered beyond the scope of the monopole approximation. The time-dependent Dirac equation is solved in a rotating coordinate system with $z$-axis directed along the internuclear line and the origin placed at the center of mass. The probabilities of electron-positron pair creation and the positron energy spectra are calculated in the approximation neglecting the rotational coupling. The two-center potential is expanded over spherical harmonics and the convergence with respect to the number of terms in this expansion is studied. The results show that taking into account the two-center potential instead of its spherically symmetric part preserves all the signatures of the transition to the supercritical regime that have been found in the framework of the monopole approximation and even enhances some of them., Comment: 8 pages, 4 figures, 1 table

Recently, a high energy superconducting (SC) \epem linear collider (LC) with energy recovery (ERLC) have been proposed where twin RF structures are used to avoid parasitic collisions within linacs. Such a collider can operate in a duty cycle (DC) or in a continuous (CW) modes (if sufficient power) with a luminosity of ${\cal O}(10^{36})$ \cms at $2E_0=250-500$ GeV. In this paper, I note that the luminosity at the ERLC operating in duty cycle mode does not depend on the accelerating gradient (at the same total power), but only slightly changes as $L \propto \sqrt{Q}$. So, the ERLC can work at maximum available acceleration gradients. The article also considers $e^-e^-$ twin collider with energy recovery and estimates the achievable luminosity. Such an $e^-e^-$ collider is much simpler than $e^+e^-$ one, because beam recirculation is not required, can have $L$ well above $10^{36}$ cm$^{-2}$s$^{-1}$. It also has a fairly rich physics program., Comment: 6 pages, 2 figures

The process of elastic scattering of photons (light-by-light scattering) attracts a lot of attention in the last years. It goes via the loop and all charged particles contributes to its cross section. Theoretical prediction of the cross section have existed for more than half a century, there are various accelerators with real and virtual photons, but only recently this process was discovered at the LHC in ion-ion collisions. Hopes for further study of this process are associated with high-luminosity $e^+e^-$ colliders (SuperKEKb, FCC, ILC, CLIC) and gamma-gamma colliders based on the Compton scattering of laser photons on electrons. In this article, we show that there is very serious background processes when the final pair of photons is created in the annihilation of real and virtual $e^+$ and $e^-$, and the remaining products fly away from the detector at small angles.

We present the study of the decay $J/\psi \rightarrow \rho\pi$. The results are based on of 5.2~million $J/\psi$ events collected by the KEDR detector at the VEPP-4M collider. The branching fractions are measured to be $\B(J/\psi \rightarrow \rho\pi) = \big(2.072\pm 0.017 \pm 0.062 \big)\cdot 10^{-2}$ and $\B(J/\psi \rightarrow \pi^+\pi^-\pi^0) = \big(1.878 \pm 0.013 \pm 0.051 \big)\cdot 10^{-2}$, where the first uncertainties are statistical and the second systematic. Our results are more precise than the previous relative measurements.

We discuss the goals, the designs, the state of technical readiness, and the critical R&D needs of the accelerators that are currently under discussion as Higgs and electroweak factories. We also address the respective staging options enabling future energy-frontier colliders. The accelerators covered are based on many different techniques and approaches. They include several circular colliders, various linear colliders, colliders based on energy recovery linacs (ERLs), ERL-ring combinations, as well as gamma-gamma colliders. The linear colliders proposed consist of options for the International Linear Collider (ILC), for the Compact Linear Collider (CLIC), for the Cold Copper Collider (C^3), and for the more recent Higgs-Energy Lepton Collider (HELEN). ERLs are key components of the Recycling Linear e+e- Collider (ReLiC), of the Energy Recovery Linear Collider (ERLC), and of the Circular Energy Recovery Collider (CERC). Among the more conventional ring colliders, the following proposals are featured: the Future Circular Collider (FCC-ee), the Circular Electron Positron Collider (CEPC), the Electron Positron Circular Collider at Fermilab (EPCCF), and the Large Electron Positron collider $\#$3 (LEP-3). In addition, we consider the X-ray FEL based gamma-gamma Collider Higgs Factory (XCC) and the High-Energy High-Luminosity gamma-gamma collider (HE&HL gamma-gamma). Finally, a Higgs factory based on a circular muon collider is mentioned for completeness., Comment: Submitted to Snowmass 2021

Energy-recovery linacs (ERLs) have been emphasised by the recent (2020) update of the European Strategy for Particle Physics as one of the most promising technologies for the accelerator base of future high-energy physics. The current paper has been written as a base document to support and specify details of the recently published European roadmap for the development of energy-recovery linacs. The paper summarises the previous achievements on ERLs and the status of the field and its basic technology items. The main possible future contributions and applications of ERLs to particle and nuclear physics as well as industrial developments are presented. The paper includes a vision for the further future, beyond 2030, as well as a comparative data base for the main existing and forthcoming ERL facilities. A series of continuous innovations, such as on intense electron sources or high-quality superconducting cavity technology, will massively contribute to the development of accelerator physics at large. Industrial applications are potentially revolutionary and may carry the development of ERLs much further, establishing another shining example of the impact of particle physics on society and its technical foundation with a special view on sustaining nature.

Recently, a $\gamma\gamma$ collider based on the existing 17.5 GeV linac of the European XFEL has been proposed. High-energy photons will be generated by Compton scattering of laser photons with a wavelength of 0.5-1 $\mu$m on electrons. Such a photon collider covers the range of invariant masses $W_{\gamma\gamma} <12$ GeV. The physics program includes spectroscopy of $\mathit C$-even resonances ($c$-, $b$-quarkonia, 4-quark states, glueballs) in various $J^P$ states. Variable circular and linear polarizations will help in determining the quantum numbers. In this paper, we present a summary of measured and predicted two-photon widths of various resonances in the mass region 3-12 GeV and investigate the experimental possibility of observing these heavy two-photon resonances under the conditions of a large multi-hadron background. Registration of all final particles is assumed. The minimum values of $\Gamma_{\gamma\gamma}(W)$ are obtained at which resonances can be detected at a $5\sigma$ confidence level in one year of operation., Comment: 12 pages, 16 figures

Superconducting technology makes it possible to build a high energy $e^+e^-$ linear collider with energy recovery (ERLC) and reusable beams. To avoid parasitic collisions inside the linacs, a twin (dual) LC is proposed. In this article, I consider the principle scheme of the collider and estimate the achievable luminosity, which is limited by collision effects and available power. Such a collider can operate in a duty cycle (DC) and in a continuous (CW) modes, if sufficient power. With current SC Nb technology ($T=1.8$ K, $f_{\rm RF}=1.3$ GHz, used for ILC) and with power $P= 100$ MW, a luminosity $L \sim 0.33 \times10^{36}\,\rm cm^{-2}s^{-1}$ is possible at the Higgs factory with $2E_0=250$ GeV. Using superconductors operating at 4.5 K with high $Q_0$ values, such as Nb$_3$Sn, and $f_{\rm RF}=0.65$ GHz, the luminosity can reach $L \sim 1.4 \times10^{36} \,\rm cm^{-2}s^{-1}$ at $2E_0=250$ GeV (with P=100 MW) and $L \sim 0.8 \times 10^{36}\,\rm cm^{-2}s^{-1}$ at $2E_0=500$ GeV (with P=150 MW), which is almost two orders of magnitude greater than at the ILC, where the beams are used only once. This technology requires additional efforts to obtain the required parameters and reliably operation. Such a collider would be the best machine for precision Higgs studies, including the measurement of Higgs self-coupling., Comment: Talk presented at the International Workshop on Future Linear Colliders (LCWS2021), 15-18 March 2021. C21-03-15.1

The relative center-of-mass energy spread at $e^+e^-$ colliders is about $10^{-3}$, which is much larger than the widths of narrow resonances J/$\psi$, $\psi$(2S), $\Upsilon$(1S), $\Upsilon$(2S), $\Upsilon$(3S) mesons, tauonium and some others. It's reduction would significantly increase the resonance production rates and open up great opportunities in the search for new physics. In this paper, we propose a new monochromatization method for colliders with a large crossing angle (which can provide a high luminosity). The contribution of the beam energy spread to the spread of the center-of-mass energy is canceled by introducing an appropriate energy-angle correlation at the interaction point; $\sigma_W/W \sim (0.5-1)10^{-5}$ appears possible., Comment: 8 pages, 2 figures

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., Comment: 18 pages, 22 figures, 1 table Minor corrections, results unchanged

We propose and demonstrate that a gamma-gamma collider with W_gg < 12 GeV can be added to the European XFEL with a minimal disruption to its main program. High-energy photons will be obtained by Compton scattering of 0.5 micron laser photons on the existing 17.5 GeV electron beams. Such a gamma-gamma collider would be an excellent place for the development and application of modern technologies: powerful lasers, optical cavities, superconducting linacs, and low-emittance electron sources -- as well as training the next generation of accelerator physicists and engineers. The physics program would include spectroscopy of C=+ resonances in various J^P states b\bar{b}, c\bar{c}, four-quark states, quark molecules and other exotica) in a mass range barely scratched by past and not covered by any current or planned experiments. Variable circular and linear polarizations will help in the determination of quantum numbers and measurement of polarization components of the gamma-gamma cross section (\sigma_\perp, \sigma_\parallel, \sigma_0, \sigma_2)., Comment: 8 pages, 4 figures

Wavefunction-splitting or mask method, widely used in the non-relativistic calculations of the photoelectron angular distributions, is extended to the relativistic domain within the dipole approximation. Since the closed-form expressions for the relativistic Volkov states are not available within the dipole approximation, we build such states numerically solving a single second-order differential equation. We calculate the photoelectron energy spectra and angular distributions for highly charged ions under different ionization regimes with both the direct and the relativistic mask methods. We show that the relativistic mask method works very well and reproduces the electron energy and angular distributions calculated by the direct method in the energy range where both methods can be used. On the other hand, the relativistic mask method can be applied for longer laser pulses and/or higher photoelectron energies where the direct method may have difficulties.

We calculate two-dimensional photoelectron momentum distributions and energy spectra after multiphoton ionization of Li atoms subject to intense laser fields in one-photon Rabi-flopping regime. The time-dependent Schr\"{o}dinger equation is solved within the single-active-electron approximation using a model potential which reproduces accurately the binding energies and dipole matrix elements of the Li atom. Interaction with the external electromagnetic field is treated within the dipole approximation. We show that the Rabi oscillations of the population between the ground $2s$ state and the excited $2p$ state in the one-photon resonance regime are reflected in the energy spectra of emitted photoelectrons which manifest interference structures with minima. Transformations of the interference structures in the photoelectron energy spectra caused by the variation of the laser peak intensity and pulse duration are analyzed.

Approximate scaling laws with respect to the nuclear charge are introduced for the time-dependent Dirac equation describing hydrogen-like ions subject to laser fields within the dipole approximation. In particular, scaling relations with respect to the laser wavelengths and peak intensities are discussed. The validity of the scaling relations is investigated for two-, three-, four-, and five-photon ionization of hydrogen-like ions with the nuclear charges ranging from $Z=1$ to $92$ by solving the corresponding time-dependent Dirac equations adopting the properly scaled laser parameters. Good agreement is found and thus the approximate scaling relations are shown to capture the dominant effect of the response of highly-charged ions to intense laser fields compared to the one of atomic hydrogen. On the other hand, the remaining differences are shown to allow for the identification and quantification of additional, purely relativistic effects in light-matter interaction.

The present work continues a series of the KEDR measurements of the $R$ value that started in 2010 at the VEPP-4M $e^+e^-$ collider. By combining new data with our previous results in this energy range we measured the values of $R_{\text{uds}}$ and $R$ at nine center-of-mass energies between 3.08 and 3.72 GeV. The total accuracy is about or better than $2.6\%$ at most of energy points with a systematic uncertainty of about $1.9\%$. Together with the previous precise $R$ measurement at KEDR in the energy range 1.84-3.05 GeV, it constitutes the most detailed high-precision $R$ measurement near the charmonium production threshold., Comment: arXiv admin note: text overlap with arXiv:1610.02827 and substantial text overlap with arXiv:1510.02667

The product of the electronic width of the $\psi(2S)$ meson and the branching fraction of its decay to the muon pair was measured in the $e^{+}e^{-} \to \psi(2S) \to \mu^{+}\mu^{-}$ process using nine data sets corresponding to an integrated luminosity of about 6.5 pb$^{-1}$ collected with the KEDR detector at the VEPP-4M electron-positron collider: \[ \Gamma_{ee}\times\mathcal{B}_{\mu\mu} = 19.3 \pm 0.3 \pm 0.5 ~\text{eV}. \] Adding the previous KEDR results on hadronic and leptonic channels, the values of the $\psi(2S)$ electronic width were obtained under two assumptions: either with the assumption of lepton universality \[ \Gamma_{ee} = 2.279 \pm 0.015 \pm 0.042 ~\text{keV} \] or without it, summing up hadronic and three independent leptonic channels: \[ \Gamma_{ee} = 2.282 \pm 0.015 \pm 0.042 ~\text{keV}. \]

At this time, the design of the International Linear Collider (ILC) is optimized for e+e- collisions; the photon collider (gamma-gamma and gamma-electron) is considered as an option. Unexpected discoveries, such as the diphoton excess F(750 GeV) seen at the LHC, could strongly motivate the construction of a photon collider. In order to enable the gamma-gamma collision option, the ILC design should be compatible with it from the very beginning. In this paper, we discuss the problem of the beam crossing angle. In the ILC technical design, this angle is 14 mrad, which is just enough to provide enough space for the final quadrupoles and outgoing beams. For gamma-gamma collisions, the crossing angle must be larger because the low-energy electrons that result from multiple Compton scattering get large disruption angles in collisions with the opposing electron beam and some deflection in the solenoidal detector field. For a 2E=500 GeV collider, the required crossing angle is about 25 mrad. In this paper, we consider the factors that determine the crossing angle as well as its minimum permissible value that does not yet cause a considerable reduction of the gamma-gamma luminosity. It is shown that the best solution is to increase the laser wavelength from the current 1 \mum (which is optimal for 2E=500 GeV) to 2 \mum as this makes possible achieving high gamma-gamma luminosities at a crossing angle of 20 mrad, which is also quite comfortable for e+e- collisions, does not cause any degradation of the e+e- luminosity and opens the possibility for a more energetic future collider in the same tunnel (e.g., CLIC). Moreover, the 2 \mum wavelength is optimal for a 2E = 1 TeV collider, e.g., a possible ILC energy upgrade. Please consider this paper an appeal to increase the ILC crossing angle from 14 to 20 mrad., Comment: Talk presented at the International Workshop on Future Linear Colliders (LCWS2017), Strasbourg, France, 23-27 October 2017. C17-10-23.2. 12 pages, 11 figures

The product of the electronic width of the $J/\psi$ meson and the branching fractions of its decay to hadrons and electrons has been measured using the KEDR detector at the VEPP-4M $e^+e^-$ collider. The obtained values are: $\Gamma_{ee}(J/\psi) = 5.550 \pm 0.056 \pm 0.089 \, \text{keV}, $ $\Gamma_{ee}(J/\psi) \cdot \mathcal{B}_\text{hadrons}(J/\psi) = 4.884 \pm 0.048 \pm 0.078 \, \text{keV}, $ $\Gamma_{ee}(J/\psi) \cdot \mathcal{B}_{ee}(J/\psi) = 0.3331 \pm 0.0066 \pm 0.0040 \, \text{keV}.$ The uncertainties shown are statistical and systematic, respectively. Using the result presented and the world-average value of the electronic branching fraction, one obtains the total width of the $J/\psi$ meson: $\Gamma = 92.94 \pm 1.83 \, \text{keV}.$ These results are consistent with the previous experiments., Comment: 19 pages, 13 figures