Physics of Atomic Nuclei

The paper presents a brief review of the scientific work performed by the authors in the field of quantum mechanics and atomic, laser, and mathematical physics. The following problems are considered: the semiclassical theory of tunneling and multiphoton ionization of atoms and ions in a strong electromagnetic field; generalization of the Keldysh ionization theory to the relativistic case; calculation of the Coulomb corrections to the ionization rate of atoms for arbitrary values of the adiabaticity parameter γ: from γ ≪ 1 (the adiabatic region) to γ ≫ 1, when the laser field changes its direction and magnitude many times during the time of flight of the electron through the barrier; the Lorentz ionization of atoms moving in a constant magnetic field; the WKB approximation and the imaginary time method for describing electron tunneling through a time-varying barrier; the Stark effect in a strong field; the energy spectrum of a hydrogen atom in a strong and superstrong magnetic field; quantization with account of the barrier transparency; creation of electron-positron pairs from vacuum in a constant electric or intense pulsed (laser) field and the dependence of the number of pairs on the intensity and frequency of the laser field; the Feynman method of disentanglement of noncommuting operators and its applications: transitions between atomic states in an alternating magnetic field (the Majorana problem); a quantum oscillator with time-dependent frequency; and a singular oscillator. The mathematical problems of quantum mechanics are considered: the fall of a particle to the center; modification of the Bohr-Sommerfeld quantization condition for potentials with a barrier and the Kramers matching conditions; divergence of perturbation series and their summation; eigenvalues of the Casimir operators for irreducible representations of Lie groups, including the SU(2), SU(3), and SU(6) groups, which are widely used in physics.

A correlation between the parameter β₂ and a half-life T_1/2 for oblate nuclei with sign β₂ < 0 and an anticorrelation for elongated nuclei sign β₂ > 0 are found. These analytical expressions for the function β₂(T_1/2) make it possible to calculate the shape parameters of β₂ nuclei if we know the half-lives T_1/2 for exotic nuclei for which this value is most accurately measured.

Within the QCD k_t-factorization approach, the cross sections for the processes of Higgs boson inclusive production and decay at LHC energies are derived. The calculus relies on transverse-momentum-dependent unintegrated gluon distribution functions in the proton obtained by numerically solving the Catani-Ciafaloni-Fiorani-Marchesini (CCFM) equation. On the whole, the ATLAS and CMS measurements of differential cross sections for the Higgs boson production at collision energies of 8 and 13 TeV are adequately reproduced. Our results demonstrate that, with the QCD k_t-factorization approach, higher order perturbative corrections are effectively taken into account. The dependence of the results obtained on the form of the unintegrated gluon distribution is investigated.

The results of calculation of two-point correlation functions of fermionic currents in a constant uniform magnetic field are presented. The off-diagonal correlation functions including the tensor current (namely, the scalar-tensor and pseudoscalar-tensor) are calculated in addition to the correlators of scalar, pseudoscalar, vector, and axial-vector fermionic currents. The tensor fermionic current is a part of the Pauli term in the Lagrangian, which is responsible for the electromagnetic interaction of the fermion through an anomalous magnetic moment. In particular, if we take this interaction into account, we modify the frequency of axion-photon oscillations. In the future, it is planned to investigate this feature in details.

The expressions for the transition form factors (TFFs) of pseudoscalar mesons are derived in the context of the anomaly sum rule approach based on the dispersion representation of the axial anomaly and hypothesis of the global quark-hadron duality. The obtained solutions take into account the π⁰-η-η′ mixing and the contribution of the gluon anomaly. It is shown that this method allows one to describe the TFFs for spacelike and timelike photon virtualities. The contribution of the gluon anomaly is estimated.

The problem of internal ionization in the beta decay of tritium due to the scattering of a β electron off a bound electron is discussed. The total probability of the process per a single decay event is calculated. The distributions over the momentum and the kinetic energy of a liberated electron are plotted. A correction to the β spectrum produced by internal ionization is determined. The identity of electrons is taken into account in all calculations. The results of calculations of the modified spectrum are of interest for the KATRIN experiment aimed at measuring the mass of an electron antineutrino. The high-luminosity source also makes it possible to search for keV-scale sterile neutrinos in the middle part of the β spectrum, where the internal ionization effect is significant.

Determination of the direction to a source of (anti)neutrinos is important for the physics of supernovae and of the Earth. Inverse beta decay reaction allows to reconstruct the direction to a source of antineutrinos. We present modern mathematical formalism and recent experimental data on antineutrino directionality.

The nonequilibrium equation of state is studied in the context of the hydrodynamic approach. The compression stage, the expansion stage, and the freeze-out stage of the hot spot formed during the collisions of heavy ions are considered. The energy spectra of protons and subthreshold pions produced in collisions of heavy ions are calculated with inclusion of the nuclear viscosity effects and compared with experimental data for various combinations of colliding nuclei with energies of several tens of MeV per nucleon.

Using the Geant4 software package, a numerical simulation of a neutron source of the time-offlight spectrometer GNEIS created on the basis of the SC-1000 synchrocyclotron with 1 GeV proton energy at the NRC Kurchatov Institute—PNPI (Gatchina) has been carried out. The influence of the structural features of the neutron source of the spectrometer on the spatial and energy distributions of neutrons has been studied. The intensity and spectral characteristics of the neutron flux in the range of 1–1000 MeV have been determined on the basis of the obtained information and detailed allowance for all elements of the neutron beam guide system. It is found that the best agreement between the experiment and calculation performed by means of Geant4 is observed when using the QGSP_INCLXX_HP model. In the neutron energy range of 1–200 MeV, the difference between the experimental and calculated shapes of the spectra is less than 25%.

In the PANDA experiment of the FAIR project, it is proposed to use internal targets based on the hydrogen isotopes that provide a monodisperse regime of flow generation of solid spherical pellets with the diameter from 15–40 µm with the frequency from several tens of to several hundred kilohertz. The process for generating the pellets in such facilities includes the cooling, liquefying, and disintegration into drops of the liquid hydrogen jet directed vertically downwards; freezing of the jet when expiring with acceleration into vacuum; and its transport through the vacuum path into the region of interaction with the antiproton beam. For the effective control of the systems of the setup and for the adjustment of generation of pellets, an automatization and control system is developed combining the devices for measurement and control of pellet parameters (temperature, pressure, hydrogen flow, and piezoelectric generator frequency) and the optical diagnostics in a unified computational network. For data exchange between the devices, the TCP/IP Sockets and Modbus TCP protocols are used.

The article presents a description of the ISNP/GNEIS testing facility with a neutron spectrum that reproduces the spectrum of atmospheric neutron radiation. The facility was developed at the Petersburg Nuclear Physics Institute (PNPI) of the National Research Center Kurchatov Institute in collaboration with the Institute of Space Device Engineering, a branch of JSC (Joint Stock Company) United Rocket and Space Corporation. The spallation neutron source of the facility is based on the 1-GeV SC-1000 proton synchrocyclotron at the PNPI. The internal neutron-production lead target produces 10-ns pulses of neutrons with a repetition rate of 45–50 Hz and an average neutron intensity of 3 × 10¹⁴ n/s (in the 4σ solid angle). In the irradiation area located at a distance of 36 m from the neutron source, a high-quality collimated neutron beam with a broad energy spectrum of 1–1000 MeV and a neutron flux of 4 × 10⁵ n/(cm² s) allows conducting accelerated single-event soft error testing of electronic components. In the course of the irradiation, the neutron energy spectrum and intensity and the spatial profile of the beam are controlled using a fission ionization chamber (beam monitor) and a position-sensitive multiwire proportional counter (beam profile meter). The data acquisition system of the ISNP/GNEIS facility utilizes 250 MS/s 12 bit CAEN waveform digitizers for the processing of signals from the monitor and profile meter by the neutron time-of-flight technique. In the report, parameters of the ISNP/GNEIS testing facility are discussed in comparison with analogous world-class facilities, as well as requirements and recommendations of the standards used in this field.

A technique for correcting experimental data from a position-sensitive neutron detector with an active layer of solid boron-10, where the charge division method is used to determine the coordinate, is proposed. This technique relies on the signal amplitude loss in a distributed resistance circuit. Each resistance is connected to two adjacent wires of the anode (or to two adjacent strips of the cathode) of the detector. This readout method is simple to implement and does not require complex and expensive electronics. However, unlike the distributed delay line method, it requires that the nonlinear dependence of the coordinate both on the ratio of the measured amplitudes and on the sum of these amplitudes be taken into account when the neutron coordinate is calculated. Test measurements with a signal generator were conducted to determine the dependence of coordinates on the ratio of pulse amplitudes from two ends of the distributed resistance. This dependence is approximated by a third-order polynomial. At the same time, the coefficients of this polynomial depend on the sum of amplitudes of pulses at the outputs of two amplifiers connected to the two ends of the distributed resistance. The amplitude dependences of these coefficients are also approximated by third-order polynomials. Thus, the spatial resolution of the detector depends on the signal amplitudes and on the coordinate itself. It is possible to determine the signal amplitudes and neutron coordinates more accurately by correcting the data. The procedure also improves the integral uniformity of the coordinate distribution. Following the application of the proposed correction, the spatial resolution of the neutron detector improved from 2 to 1.5 mm along the x axis.

A method for reconstruction of the volume density distribution in dynamic targets from their proton radiography image is considered. The reconstruction can be carried out using the inverse Abel transform under the assumption that the studied object and processes have radial symmetry. To increase the accuracy of reconstructed data, algorithms for correction of basic types of distortions of proton radiography images are proposed. The results of processing experimental data obtained on proton radiography facilities PUMA at ITEP and PRIOR at GSI are presented.

A signal kinematical region is analyzed by the Higgs Boson Working Group (HWW) within the framework of a study of the Standard Model Higgs boson properties in the H → WW* → evεv decay channel in the ATLAS experiment on the Large Hadron Collider (LHC). The analysis is based on the full statistics of proton-proton collision data during exposures in 2015–2016 at the center-of-mass energy of 13 TeV. As compared to our previous analysis, the reconstruction software is updated and the simulation accuracy of backgrounds is improved. Events taken at low and high LHC luminosity are studied separately. In addition, the kinematics at the later stages of event selection is investigated in detail and systematic uncertainties are fully estimated. It is shown that the Monte Carlo modeling satisfactorily describes the experimental data at different selection stages. Kinematic distributions for hadron jets are studied also in the Z-boson control region, where the acquired data reach the order of ten million events. As compared to the previous investigation, the modeling accuracy of Z and background processes is noticeably improved, and events at low and high LHC luminosities are studied separately. Furthermore, all systematic uncertainties related to jets are estimated as well. As a whole, good agreement between experimental results and Monte Carlo simulation data is observed. No problems that would be caused by high luminosity are observed.

The possibility of observing the stimulated de-excitation of nuclear isomers (SDENI) in plasma (plasma lifetime ∼1.5 ps, temperature of electrons ∼ 10 keV) formed by the impact of a high-power laser pulse (∼10¹⁸ W cm⁻²) on a target is studied experimentally. Preliminary experiments are carried out with the ^110mAg (T_1/2 = 250 days) and ^186mRe (T_1/2 = 2 × 10⁵ years) isomers. A weak SDENI effect is observed only for the ^110mAg isomer on a platinum backing.

Processes of accumulation of radionuclides in the cooling circuit water of the Cyclone 18/9-HC cyclotron were studied under proton irradiation of the Nirta Fluor target. It is shown that the nature of the water activation reactions in the cooling circuit and the equivalent dose rate from the equipment of the system significantly depend on the dose accumulated by the target. The main source of radionuclides in the cooling circuit water is the ¹⁶O(n,p)¹⁶N reaction. In targets with high absorbed radiation doses associated with deformation of the target entrance window, the proton-induced ¹⁴N(p,α)¹¹C and ¹⁸O(p,n)¹⁸F reactions take place. Fluoride ¹⁸F⁻, carbonate ¹¹CO₃²⁻, and hydrocarbonate H¹¹CO₃⁻ anions formed in these reactions precipitate on the ion-exchange resin during the circulation of water in the cooling circuit. It has been ascertained that the average annual radiation exposure dose for the cyclotron operator from the water activation products in the cooling circuit does not exceed 1% of the annual staff exposure limit. Recommendations are given for the application of engineering barriers in the design and reconstruction of nuclear medicine facilities for the case of water leaks from the cyclotron cooling circuit.