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Purpose. To study environmental crimes in the field of subsurface resources protection and provide their criminological characterization, namely, to determine criminological indicators reflecting the studied crime rate, dynamics and structure. Methodology. A system of general scientific and special methods and approaches ensuring an objective analysis of the studied issue, particularly, logical and dogmatic, systematic, documentary, and modeling and statistical analysis methods. Findings. We determined absolute, mean and relative indicators of environmental crimes in the field of subsurface resources protection in Ukraine during 2002–2021, their total recorded number (9118 crimes), annual average (456 crimes) and share in the overall crime structure over the past 20 years (0.1 %). The conclusion shows a significant growth of environmental crimes in the field of subsurface resources protection in the overall crime structure (from 0.01 to 0.24 %) due to a significantly higher increase in these crimes rate compared to the absolute overall crime rate. The calculated dynamics indicators showed wave-like changes in the recorded crimes number against their steady overall upward trend – over the twenty-year period analyzed, reported crimes of this category increased more than 14 times. Originality. Following a long-term statistical analysis, since illegal amber mining criminalization, the article provides the first criminological characterization of environmental crimes in the field of subsurface resources protection. Practical value. The authors substantiate their understanding of the essence of this crime category envisaged by Article 240 of Ukraine’s Criminal Code “Violation of the Rules for Subsurface Resources Protection or Use, Illegal Extraction of Mineral Resources” and Article 2401 of Ukraine’s Criminal Code “Illegal Mining, Sale, Acquisition, Transfer, Sending, Transportation, and Processing of Amber”. The calculated indicators of the rate, dynamics and structure of the studied crimes are of standalone significance for academic research and law enforcement activities and create an appropriate basis for the information provision of combating environmental crimes in the field of subsoil protection being a prerequisite for developing an appropriate system of specified crime prevention measures.

Purpose. The identification and hygienic assessment of main sources of natural exposure of the population of the city of Moscow. Ranking areas of the territory of the city according to the potential radon hazard. The elaboration of criteria for the radon hazard of the territory. Material and Methods. There are provided data of the radiation control of the territory of the city (g-spectrometry, the determination of the activity of natural radioactive substances, including samples of the soil and in lithological layers, the density of radon flux (DRF) from the soil), surveys of residential and public buildings for different purposes according to the content of the equivalent equilibrium volumetric activity of radon (EEVAR). Results. There is presented the analysis of materials concerning the evaluation of results of radiation control (the of 226Ra activity in different types of soils, the levels of the DRF from the soil, the concentration of radon in newly constructed and operated buildings, various premises) in administrative districts of Moscow. There was executed the comparison of the spatial distribution of the fields of DRF and EEVAR values in basements and premises of buildings exceeding 200 Bq/m3. There was performed the analysis of criteria of radon-dangerous of areas. Conclusion. There were substantiated criteria and zones of the aggravated radon danger within the city according to following indices: 226Ra content in soils, DRF on soil surfaces, EEVAR in premises, annual dose of the radiation. Performed long-term studies allowed to rank the territory of Moscow into various zones of the radon danger and allocate most dangerous areas (South-Eastern Administrative District, South Administrative District, South-Western Administrative District). There was obtained a map of the interrelationship of the spatial distribution of anomalous DRFs from the soil surface and elevated EEVA values in premises. Ranging of areas for the radon danger permits to significantly optimize the system of radiation control and measures for radiation protection of the population.

Materials on the work of interdepartmental expert councils for 2011-2014 are presented. The results of the analysis of the conditions and methodological approaches of the establishment by the expert councils of the causal connection of diseases, disability and death of citizens exposed to radiation factors due to the Chernobyl disaster are shown. Data on the number and structure of the taken measures are presented, and the place of the expertise in the system of post-emergency sanitary and hygienic measures is shown.

A new bound state Δ method for finding an asymptotic normalization coefficient (ANC) is proposed. This is valid, while the standard effective-range function (ERF) Kl(k2) method does not work when the product of colliding particles charges increases. The denominator of the strict expression of the re-normalized scattering amplitude f˜l includes the factor dl(E)=Δl(E)+hr(E)−h(η) , where η=1/aBk , aB is the Bohr radius. In the physical region, the Coulomb term hr=Reh(η) . So an analytical continuation of hr(E) from the physical region to E≤0 can be found by fitting hr(E) for E≥0 . The related analytical continuation of h(η) consists in a simple sign change, E→−E , using an explicit dependence of h(η) on E . This is important that for E≤0 , abs(Δh)=abs(h−hr)=0 at E=0 , and it increases when abs(E) does. Thus, a new real equation, dl(−e)=0 , is obtained for a binding energy e . It is applied to find a residue W of f˜l at the bound state pole E=−e , the nuclear vertex constant (NVC) and (ANC). The Coulomb-nuclear phase shift δlcs , cotδlcs and a finite limit of the nuclear part Δl(k2) of Kl(k2) are also derived for an arbitrary orbital momentum l when E→0 . It is shown that cotδlcs has an essential singularity at zero energy, but Δl(k2) does not. The explicit finite limit of Δl(k2) when E→0 is found using the expression for Kl(k2) . These results are in agreement with those for the S -wave scattering, which are widely accepted. The ANCs for the ground and first excited bound states for the vertex Be7↔3He4He are calculated using the proposed new method, and are compared with those for the approximate method when dl(E)=Δl(E) proposed by Ramirez Suarez and Sparenberg (2017). The fit of Δl(E) is found from the experimental phase-shift input data and the additional equation dl(−e)=0 .

Recently a new $\Delta$ method for deducing the energy and asymptotic normalization coefficient (ANC) from phase-shift data has been formulated and applied to resonance states. This differs from the conventional effective-range function (ERF) method by fitting only the nuclear part of the ERF. It also differs from the method which was proposed for bound states by Ram\'irez Su\'arez and Sparenberg (see Ref. below) which also named the $\Delta$ method where a pole condition defines by the Eq. $\Delta_l=0$ ($\Delta_l$ is the function in the ERF determined only by the scattering phase shift). Here the standard pole condition, including the Coulomb part into the relate equation, is used for a resonant state. It has been shown that the ERF method does not work for large-charge colliding nuclei. Moreover, even for lower charges it is not clear that the results of the ERF method are accurately enough. The Coulomb part forms a background, which smooths an ERF energy dependence. Therefore, one needs to find when the ERF method becomes inaccurate and this requires recalculating some published results by the $\Delta$ method. This project has already been started in a recent paper for resonances in the $\alpha$-$\alpha$ scattering. Here this method is applied using the $\Delta_l$-function fittings to the experimental $p$-${}^4$He scattering phase-shift data in the $P_{3/2}$ and $P_{1/2}$ resonance states. The calculation results are compared with those obtained earlier by the ERF method. The main changes concern resonance energy and width., Comment: 7 pages, 1 figure, 1 table. This preprint differs from arXiv:2004.12855 by corrections of typos and adding 2 equations

Recently, a new $\Delta$ method for the calculation of asymptotic normalization coefficients (ANC) from phase-shift data has been formulated, proved and used for bound states. This method differs from the conventional one by fitting only the nuclear part of the effective-range function which includes a partial phase shift. It should be applied to large-charge nuclei when the conventional effective-range expansion or the Pad\'e-approximations using the effective-range function $K_l(k^2)$ fitting do not work. A typical example is the nucleus vertex $\alpha+^{12}$C $\longleftrightarrow ^{16}$O. Here we apply the $\Delta$ method, which totally excludes the effective-range function, to isolated resonance states. In fact, we return to the initial renormalized scattering amplitude with a denominator which defines the well-known pole condition. Concrete calculations are made for the resonances observed in the $^3$He-$^4$He, $\alpha$-$\alpha$, and $\alpha$-$^{12}$C collisions. We use the experimental phase-shift and resonant energy data including their uncertainties and find the ANC variations for the states considered. The corresponding results are in a good agreement with those for the $S$-matrix pole method which uses the differing formalism. The simple formula for narrow resonances given in the literature is used to check the deduced results. The related ANC function clearly depends on the resonance energy ($E_0$) and width ($\Gamma$), which is used to find the ANC uncertainty ($\Delta$ANC) through the energy ($\Delta E_0$) and the width ($\Delta\Gamma$) uncertainties.We also discuss the $\Delta$ method differences between bound and resonance states pole conditions., Comment: 9 pages, 3 figures and 3 table

A new algorithm for the asymptotic nuclear coefficients calculation, which we call the $\mathrm{\ensuremath{\Delta}}$ method, is proved and developed. This method was proposed by Ram\'{\i}rez Su\'arez and Sparenberg (arXiv:1602.04082.) but no proof was given. We apply it to the bound state situated near the channel threshold when the Sommerfeld parameter is quite large within the experimental energy region. As a result, the value of the conventional effective-range function ${K}_{l}({k}^{2})$ is actually defined by the Coulomb term. One of the resulting effects is a wrong description of the energy behavior of the elastic scattering phase shift ${\ensuremath{\delta}}_{l}$ reproduced from the fitted total effective-range function ${K}_{l}({k}^{2})$. This leads to an improper value of the asymptotic normalization coefficient (ANC) value. No such problem arises if we fit only the nuclear term. The difference between the total effective-range function and the Coulomb part at real energies is the same as the nuclear term. Then we can proceed using just this $\mathrm{\ensuremath{\Delta}}$ method to calculate the pole position values and the ANC. We apply it to the vertices $^{4}\mathrm{He}+^{12}\mathrm{C}\ensuremath{\leftrightarrow}^{16}\mathrm{O}$ and $^{3}\mathrm{He}+^{4}\mathrm{He}\ensuremath{\leftrightarrow}^{7}\mathrm{Be}$. The calculated ANCs can be used to find the radiative capture reaction cross sections of the transfers to the $^{16}\mathrm{O}$ bound final states as well as to the $^{7}\mathrm{Be}$.

In the present work one- and two-channel approaches using the expansion of the effective-range function K(E) in powers of energy E are applied to obtain the asymptotic normalization coefficients (ANCs) and vertex constants (VCs) for the d + α system. The coefficients of the K(E) expansion are found by fitting the dα phase shifts. By analytic continuation of K(E) thus obtained to the corresponding poles the ANCs and VCs for D wave dα resonances with Jπ = 1+, 2+, 3+ are calculated for the first time. The 1+-resonance and the bound state of 6Li (Jπ = 1+) are considered jointly in the two-channel (S + D) effective-range approach and the ANCs and VCs for the ground 6Li state are found.

The general properties of the three-parametric Woods-Saxon potential and the two-parametric Hulthen and square-well potentials are studied by converting them to dimensionless scaling variables. The relations between the parameters of the potentials and such characteristics of a system as binding energies and the asymptotic normalization coefficients of wave functions are investigated.

We find the vertex constant for the synthesis α + α → 8Be and the corresponding asymptotic normalization coefficient of the Gamov wave function for 8Be in the ground state. We use modern data on the position and width of the narrow resonance of this state as well as the energy dependence of the αα scattering phase shift in the s-wave known from the literature. The effective-range theory was applied with the Coulomb interaction taken into account. The parameters of the standard effective-range function expansion up to the member with k4 (k being the relative momentum) were found.

The phase-shift-analysis data for the 3He4He scattering are analyzed using the effective-range theory, with the Coulomb interaction taken into account. We find both the renormalized nuclear vertex constants for the vertex 7Be → 3He + 4He in the ground (3/2−) and in the first excited (1/2−) bound states of 7Be, and the corresponding asymptotic normalization constants of the radial wave functions in these states. The results obtained can be used in an astrophysical S-factor calculation for radiative capture reaction 4He(3He, γ)7Be

3H and 3He nuclei are considered in a two-body model (3H = n + d; 3He = p + d). Two independent approaches are used: in the first, interaction is described by the folding potential, while NN potentials are taken in the Hulthen form with allowance for violations of isotopic invariance. The second approach features phenomenological Hulthen and Yukawa Nd potentials used as Nd interaction. In both approaches, the binding energies, vertex constants, and asymptotic normalization coefficients in the N+d channel are calculated.

A new method is proposed for finding the resonance parameters of a nuclear system, obtained from the phase shift analysis of elastic scattering data, by means of a pole representation of an S-matrix in complex momentum space is proposed. This method is based on the expansion of the potential phase shift into a Taylor series within the area of real momentum near the resonance pole. The coefficients of the expansion and resonance parameters are determined by fitting the analytical expression for the experimental phase shift. The proposed method provides reliable values of the energy and width of broad resonances.

Explicit expressions of the vertex constant for the decay of a nucleus into two charged particles for an arbitrary orbital momentum $l$ are derived for the standard expansion of the effective-range function $K_l(k^2)$, as well as when the function $K_0(k^2)$ has a pole. As physical examples, we consider the bound state of the nucleus ${}^3\rm{He}$ and the resonant states of the nuclei ${^2}$He and ${^3}$He in the s-wave, and those of ${}^5\rm{He}$ and ${}^5\rm{Li}$ in the p-wave. For the systems $Np$ and $Nd$ the pole trajectories are constructed in the complex planes of the momentum and of the renormalized vertex constant. They correspond to a transition from the resonance state to the virtual state while the Coulomb forces gradually decrease to zero., Comment: 17 pages, 5 figures

In view of projected experiments on the production of relativistic hypernuclei and the investigation of reactions induced by them, the characteristics of the hypernucleus and low-energy parameters of the Λ 5 He hyperon scattering from 4He were calculated. The interaction of the Λ hyperon and the α particle is described by the effective Λα potential in two different forms. The root-mean-square radius of the Λ hyperon in the Λ 5 He hypernucleus, the vertex constant for the Λ 5 He ↔ 4He + Λ process, and the corresponding asymptotic normalization coefficient of the Λ 5 He wave function were calculated by solving the radial Schrodinger equation. The scattering length and the effective radius for the scattering of Λ from 4He were calculated by two methods. The calculated characteristics turn out to be sensitive to the form of the Λα potential.

Trajectories for the S-wave pole of the scattering amplitude are constructed in the complex planes of the resonance momentum and of the renormalized vertex constant squared. They correspond to transitions from the resonance states to the virtual states of the singlet deuteron and the doublet triton while the Coulomb interaction gradually decreases to zero. The effective-range theory and a Yukawa-potential model are used. Physical reasons for the differences between the corresponding trajectories for Np and Nd systems are found. The results obtained explain why the resonances in the doublet Nd scattering are more difficult to detect in experiments in comparison with the well-studied singlet NN resonances.

A method has been developed for calculating the off-shell wave function by solving the inhomogeneous Schrodinger equation with allowance for the nuclear and Coulomb interactions. The off-shell wave function makes it possible to construct the off-shell scattering amplitude in order to solve the problems for three or more particles. An important application of the method is the Trojan Horse calculations of nuclear reactions that are important in nuclear astrophysics. Specific calculations are performed for neutron and proton scattering on the 7Be nucleus. The Woods-Saxon potential is used and the spin-orbital interaction is taken into account.

The regularization of the normalization integral for the resonant wave function, proposed by Zeldovich, is valid only when |Reqres| > |Imqres|. A new normalization procedure is proposed and implemented, which is valid when this condition fails. First, an arbitrarily normalized vertex function g(k) is calculated using the formula with the potential V(r) in the integrand. This Fourier integral converges for a potential with the asymptotics V(r) → constr−nexp(−μr) if |Imqres| < μ/2. Then the function g(k) is normalized using the generalized normalization rule, which is independent of the resonance pole position. The proposed method is approved by the example of calculation for a virtual triton.

The characteristics of bound states of hypernuclei were calculated in [1] in a wide range of mass numbers within the potential model for three different potentials. In this study, the phase shifts and low-energy parameters for scattering of Λ hyperons from core nuclei, considered in [1], have been calculated for the same potentials. The calculated scattering lengths and effective radii are compared with their values found in [1] on the basis of the data on the binding energies and vertex constants of hypernuclei.

Experimental data and theoretical model describing superradiance from the LaF 3 crystal doped with impurity praseodymium ions are presented in cases of non-resonator and resonator generation. The spiky structure of superradiance is registered and studied. When the crystal is placed inside a resonator, a new channel of energy removal by superradiance related to the resonator mode appears; the old non-resonator channels are preserved, as well. It has been found that the duration of superradiance in each channel decreases, and there arises a modulation independent of the length of resonator. These new peculiarities of superradiance induced by the presence of resonator have been explained on the basis of the developed simple mean-field theory.

In the paper, an original neural network algorithm for analysis of time series is presented. This algorithm allows predicting the occurrence of a certain event and finding a time interval to which a phenomenon (a precursor or a cause of the event) belongs. The characteristics of the algorithm functioning are investigated applied to the study of the solar-terrestrial relationship.

Explicit expressions for the virtual a → b + c decay vertex constant (or the asymptotic normalization factor) for charged particles b and c are obtained for the first time using the effective range function K(k2) for the standard effective range expansion and for the case where K(k2) has a pole. The bound and resonant states of the 2He nucleus and the resonant states of the 2He and 8Be nuclei are considered as physical examples. A trajectory in the complex momentum plane is constructed for the transition from the resonant state to the virtual state while the Coulomb interaction gradually decreases.

The vertex constants, asymptotic normalization coefficients, and mean-square radii for a number of Λ hypernuclei have been calculated in a wide range of mass numbers. Interaction of a Λ hyperon with a core nucleus was described by the Woods-Saxon, Hulten, and Yukawa potentials. Geometric parameters of the Woods-Saxon potential were taken from the data in the literature, and the interaction force was fitted to the experimental binding energy of the ground state of this hypernucleus. The parameters of the Hulthen and Yukawa potentials were chosen so as to reproduce simultaneously the binding energy of the hyperon and its mean-square radius calculated with the Woods-Saxon potential. Within the effective-radius approximation, the low-energy parameters for hyperon scattering by the core nucleus are expressed in terms of vertex constants and the numerical values of these parameters are determined.

Asymptotic normalization coefficients (ANCs) are fundamental nuclear constants playing an important role in nuclear physics and astrophysics. We derive a new useful relationship between ANC of the Gamow radial wave function and the renormalized (due to the Coulomb interaction) Coulomb-nuclear partial scattering amplitude. We use an analytical approximation in the form of a series for the nonresonant part of the phase shift which can be analytically continued to the point of an isolated resonance pole in the complex plane of the momentum. Earlier, this method which we call the $S$-matrix pole method was used by us to find the resonance pole energy. We find the corresponding fitting parameters for the $^5\rm{He},\,^5\rm{Li}$, and $^{16}\rm{O}$ concrete resonance states. Additionally, based on the theory of the effective range, we calculate the parameters of the $p_{3/2}$ and $p_{1/2}$ resonance states of the nuclei $^5\rm{He}$ and $^5\rm{Li}$ and compare them with the results obtained by the $S$-matrix pole method. ANC values are found which can be used to calculate the reaction rate through the $^{16}\rm{O}$ resonances which lie slightly above the threshold for the $\alpha^{12}\rm{C}$ channel., Comment: 8 pages, 3 tables, 5 figures

In Y2SiO5:Pr3+ nanocrystals, an ordered phase is observed in the 1D2 luminescence decay curves of Pr3+ ions at their anomalously low concentration (0.5 at %). This effect is caused by the predominant accumulation of activator ions near the nanocrystal surface, which provides relaxation of the elastic strains arising as a result of the misfit between the ionic radii of Pr3+ and Y3+. The concentration quenching of Pr3+ luminescence is due to cooperative cross relaxation.

Parameters of the effective-range function K(k2) having a pole are found from the results that were obtained by calculating the S-wave phase shifts for doublet proton-deuteron scattering and the binding energies of three-nucleon nuclei on the basis of Faddeev equations and within the N/D method and which are known from the literature. The convergence of the expansion of K(k2) in powers of the momentum is studied. The energy of the proton-deuteron resonance corresponding to the virtual triton state is calculated.

The parameters of the generalized effective-range function K(k{sup 2}) having a pole are found by using the results that were obtained by calculating the S-wave phase shift {delta}(E) for doublet nd scattering and the triton binding energy on the basis of Faddeev equations and within the N/D method and which were presented in the literature. The convergence of the expansion of K(k{sup 2}) in powers of momentum is studied. The binding energy of the virtual triton and the residues of the partial-wave scattering amplitudes at the poles corresponding to the bound and virtual states are calculated. Correlations between the binding energies of the bound and virtual states of the triton, on one hand, and the doublet scattering length for nd interaction, on the other hand, are considered. The function K(k{sup 2}) is also calculated within a two-body model featuring various potentials.

The spiky structure of the spontaneous emission from praseodymium ions in the LaF3 lattice on the 3P0-3H6 transition under coherent pulsed excitation of the adjacent 3H4-3P0 transition has been studied experimentally and theoretically. The experimental results are in good agreement with the theoretical conclusions based on analysis of the emission dynamics of an excited ensemble of three-level systems in the mean field approximation. The generation of a spiky structure is interpreted as the emission of a cnoidal wave pulse. The recorded random pattern of time intervals between the spikes reflects the sensitivity of the cnoidal wave period to fluctuations in the system. The developed theory has been found to be related to models of deterministic chaotic dynamics.

The concept of power plant for a fast ignition heavy-ion fusion (FIHIF) is being developed. The characteristics of super-high-energy-ion driver are described. The scenario of 750 MJ fusion yield target compression and detonation is evaluated. The data on reactor chamber response to energy fluxes generated by microexplosion are given. The energy conversion thermal scheme and power plant output parameters are presented.

Two algorithms for the automatic determination of flaw parameters during ultrasonic testing of welded joints with a high level of structural background noises are considered. The experimental data collected in the course of automated ultrasonic testing (AUT) using Avgur series with coherent processing of data (Avgur 4.2 and Avgur 5 systems) and the results of the assessment of nondestructive testing data are used. The first algorithm is used to identify zones where flaws may be located. This algorithm is applied after running AUT in the “search” mode. If the parameters of the algorithm application are selected properly, this algorithm makes it possible to determine the coordinates and the conventional length of the identified flaws. The second processing algorithm is intended to determine the flaw’s actual length and height. For its operations the algorithm uses the images obtained from coherent data processing. Results of testing methods for automatic (computer) determination of flaw parameters are cited. These results are obtained by the Avgur system during testing of austenite welded joints in stainless-steel pipes with a diameter of 325 mm and in perlite-steel pipes of various diameters.

The S-wave phase shift δ(E) for the spin-doublet nd scattering at low energy E is calculated in the framework of the two-body approach. The effective-range-theory formula k cot δ = (1+k2/k 0 2 )−1(−1/α+C2k2+C4k4) is used to obtain approximate analytical results with different potentials. The corresponding coefficients C2 and C4 are obtained from our previous calculations of the asymptotic normalization parameter function C t 2 (aκ), where κ is the triton wave number and a is the doublet nd scattering length. The model reasonably describes δ(E), the results being quite sensitive to the choice of the effective nd potential.

The main properties of infrared stimulated electronic Raman scattering (SERS) at the 62 S 1/2-72 S 1/2, 3/2 transitions in cesium atoms are studied theoretically and experimentally as functions of the atomic concentration, which was varied from 1011 to 1016 cm−3. It is found that the efficiency of generation of Stokes radiation strongly depends on one-photon absorption of the pump radiation tuned near frequencies of the 62 S 1/2-72 P 1/2, 3/2 transitions. By using the equation for the density matrix, which describes the evolution of a three-level system, the theory of resonance excitation of IR radiation upon one-photon absorption at an adjacent transition is developed. The theory describes well the main features of IR SERS in alkali-metal vapors.

Solar wind plasma and magnetic field observations from multiple spacecraft can be used to separate temporal and spatial variations and to determine the accuracy of predictions of solar wind conditions near Earth based on distant-spacecraft measurements. The study of correlations between the ion fluxes measured by three spatially separated spacecraft (IMP 8, WIND and INTERBALL-1) was one of the first steps in this direction. This paper describes a complex multifactor analysis of different physical, geometrical, and statistical parameters that control such correlations (considered separately and in combination). A linear-regression and an artificial neural network techniques are used for this analysis. The analysis is applied to an extensive array of correlation coefficients for the ion flux in the solar wind and provides estimates of the relative significance of the factors that control these correlation coefficients. The study shows that the most influential parameters are the solar wind density and the standard deviations of solar wind density, solar wind velocity and interplanetary magnetic field. This set of parameters permits us to develop a sufficiently accurate (with a relative error of less than a few per cent) quantitative model for the correlation between the ion fluxes measured on two spatially separated spacecraft.

The asymptotic normalization constant C T 2 for the triton is calculated within a two-body model for potentials characterized by a Yukawa-type short-distance behavior and the long-distance asymptotic behavior V(r)→const×r −νexp(−μr), where ν=0, 1, 2. It is shown that C T 2 decreases monotonically with increasing ν and that it smoothly decreases with increasing a 2 κ, where a 2 is the doublet scattering length and κ is the triton wave number. This behavior is consistent with effective-range theory taking into account the pole of κ cot δ and with the general trend of Faddeev calculations. It is established, however, that some calculations reported previously and performed on the basis of the N/D method yield, on the contrary, a sharp growth of C T 2 . The results of the calculation of the form factor for the T → d+n vertex are compared with the results of the well-known three-body calculation.

It is shown on the basis of studies of the optical spectra and luminescence decay of nonequivalent Pr3+ optical centers in the Y2SiO5 crystal that the occupation of the nonequivalent cation sites of the crystal lattice by the activator ions is irregular. For excitation in the region of the optical transitions 3H4→1D2in the temperature interval 6–80 K there is no transfer of electronic excitation energy between Pr3+ ions localized in different cation sites. The luminescence decay law of the Pr3+ optical centers is determined by the concentration of activator ions and has a complicated non-single-exponential character; the quenching of the luminescence of the Pr3+ ions is due to the formation of dimers of these ions. © 2002 American Institute of Physics.