Low-energy three-body dynamics in binary quantum gases

The universal three-body dynamics in ultra-cold binary Fermi and Fermi-Bose mixtures is studied. Two identical fermions of the mass $m$ and a particle of the mass $m_1$ with the zero-range two-body interaction in the states of the total angular momentum L=1 are considered. Using the boundary condition model for the s-wave interaction of different particles, both eigenvalue and scattering problems are treated by solving hyper-radial equations, whose terms are derived analytically. The dependencies of the three-body binding energies on the mass ratio $m/m_1$ for the positive two-body scattering length are calculated; it is shown that the ground and excited states arise at $m/m_1 \ge \lambda_1 \approx 8.17260$ and $m/m_1 \ge \lambda_2 \approx 12.91743$, respectively. For m/m_1 \alt \lambda_1 and m/m_1 \alt \lambda_2, the relevant bound states turn to narrow resonances, whose positions and widths are calculated. The 2 + 1 elastic scattering and the three-body recombination near the three-body threshold are studied and it is shown that a two-hump structure in the mass-ratio dependencies of the cross sections is connected with arising of the bound states.Comment: 16 page

Partner symmetries and non-invariant solutions of four-dimensional heavenly equations

We extend our method of partner symmetries to the hyperbolic complex Monge-Amp\`ere equation and the second heavenly equation of Pleba\~nski. We show the existence of partner symmetries and derive the relations between them for both equations. For certain simple choices of partner symmetries the resulting differential constraints together with the original heavenly equations are transformed to systems of linear equations by an appropriate Legendre transformation. The solutions of these linear equations are generically non-invariant. As a consequence we obtain explicitly new classes of heavenly metrics without Killing vectors.Comment: 20 pages, 1 table, corrected typo

Universal low-energy properties of three two-dimensional particles

Universal low-energy properties are studied for three identical bosons confined in two dimensions. The short-range pair-wise interaction in the low-energy limit is described by means of the boundary condition model. The wave function is expanded in a set of eigenfunctions on the hypersphere and the system of hyper-radial equations is used to obtain analytical and numerical results. Within the framework of this method, exact analytical expressions are derived for the eigenpotentials and the coupling terms of hyper-radial equations. The derivation of the coupling terms is generally applicable to a variety of three-body problems provided the interaction is described by the boundary condition model. The asymptotic form of the total wave function at a small and a large hyper-radius $\rho$ is studied and the universal logarithmic dependence $\sim \ln^3 \rho$ in the vicinity of the triple-collision point is derived. Precise three-body binding energies and the $2 + 1$ scattering length are calculated.Comment: 30 pages with 13 figure

Three-alpha-cluster structure of the 0^+ states in ^{12}C and the effective alpha-alpha interactions

The $0^{+}$ states of $^{12}\mathrm{C}$ are considered within the framework of the microscopic three-$\alpha$-cluster model. The main attention is paid to accurate calculation of the width of the extremely narrow near-threshold $0^+_2$ state which plays a key role in stellar nucleosynthesis. It is shown that the $0^{+}_2$-state decays by means of the sequential mechanism ${^{12}\mathrm{C}} \to \alpha+{^8\mathrm{Be}} \to 3\alpha$. Calculations are performed for a number of effective $\alpha - \alpha$ potentials which are chosen to reproduce both energy and width of $^8\mathrm{Be}$. The parameters of the additional three-body potential are chosen to fix both the ground and excited state energies at the experimental values. The dependence of the width on the parameters of the effective $\alpha - \alpha$ potential is studied in order to impose restrictions on the potentials

Universal description of the rotational-vibrational spectrum of three particles with zero-range interactions

A comprehensive universal description of the rotational-vibrational spectrum for two identical particles of mass $m$ and the third particle of the mass $m_1$ in the zero-range limit of the interaction between different particles is given for arbitrary values of the mass ratio $m/m_1$ and the total angular momentum $L$. If the two-body scattering length is positive, a number of vibrational states is finite for $L_c(m/m_1) \le L \le L_b(m/m_1)$, zero for $L>L_b(m/m_1)$, and infinite for $L<L_c(m/m_1)$. If the two-body scattering length is negative, a number of states is either zero for $L \ge L_c(m/m_1)$ or infinite for $L<L_c(m/m_1)$. For a finite number of vibrational states, all the binding energies are described by the universal function $\epsilon_{LN}(m/m_1) = {\cal E}(\xi, \eta)$, where $\xi=\displaystyle\frac{N-1/2}{\sqrt{L(L + 1)}}$, $\eta=\displaystyle\sqrt{\frac{m}{m_1 L (L + 1)}}$,and $N$ is the vibrational quantum number. This scaling dependence is in agreement with the numerical calculations for $L > 2$ and only slightly deviates from those for $L = 1, 2$. The universal description implies that the critical values $L_c(m/m_1)$ and $L_b(m/m_1)$ increase as $0.401 \sqrt{m/m_1}$ and $0.563 \sqrt{m/m_1}$, respectively, while a number of vibrational states for $L \ge L_c(m/m_1)$ is within the range $N \le N_{max} \approx 1.1 \sqrt{L(L+1)}+1/2$

Consistent alpha-cluster description of the 12C (0^+_2) resonance

The near-threshold 12C (0^+_2) resonance provides unique possibility for fast helium burning in stars, as predicted by Hoyle to explain the observed abundance of elements in the Universe. Properties of this resonance are calculated within the framework of the alpha-cluster model whose two-body and three-body effective potentials are tuned to describe the alpha - alpha scattering data, the energies of the 0^+_1 and 0^+_2 states, and the 0^+_1-state root-mean-square radius. The extremely small width of the 0^+_2 state, the 0_2^+ to 0_1^+ monopole transition matrix element, and transition radius are found in remarkable agreement with the experimental data. The 0^+_2-state structure is described as a system of three alpha-particles oscillating between the ground-state-like configuration and the elongated chain configuration whose probability exceeds 0.9

Development of method approaches to the use of regression models for assessment of health effects of socio-economic risk factors in the system of socio-hygienic monitoring (experience of the Sverdlovsk region)

The analysis of socio-hygienic monitoring data showed statistically significant correlations between the mortality in working-age population and socio-economic indices (modern conveniences in homes, availability of medical aid, the portion of pensioners, and the level of unemployment) and also between their increases with account for the time lag. The highest (by module) coefficients of correlation between the increase in socio-econom ic risk factors and the change in the working-age mortality rate were found with the time lag of 1 year. For a more adequate decision making related to effects of socio-economic factors indicator rates in the sphere of securing sanitary and epidemiologic welfare of the population were identified.Проведенный анализ данных социально-гигиенического мониторинга показал наличие статистически значимых корреляционных связей между смертностью населения в трудоспособном возрасте и социально-экономическими показателями (степень благоустройства жилья, обеспеченность врачами, доля пенсионеров и уровень безработицы), а также между их приращениями с учетом временных сдвигов. Наибольшие (по модулю) коэффициенты корреляции между приращениями социально-экономических факторов риска и изменением показателя смертности в трудоспособном возрасте отмечены при временном сдвиге 1 год. Выявлены индикаторные показатели в сфере обеспечения санитарно-эпидемиологического благополучия населения для более адекватного принятия управленческих решений в связи с воздействием социально-экономических факторов

Bound states and scattering lengths of three two-component particles with zero-range interactions under one-dimensional confinement

The universal three-body dynamics in ultra-cold binary gases confined to one-dimensional motion are studied. The three-body binding energies and the (2 + 1)-scattering lengths are calculated for two identical particles of mass $m$ and a different one of mass $m_1$, which interactions is described in the low-energy limit by zero-range potentials. The critical values of the mass ratio $m/m_1$, at which the three-body states arise and the (2 + 1)-scattering length equals zero, are determined both for zero and infinite interaction strength $\lambda_1$ of the identical particles. A number of exact results are enlisted and asymptotic dependences both for $m/m_1 \to \infty$ and $\lambda_1 \to -\infty$ are derived. Combining the numerical and analytical results, a schematic diagram showing the number of the three-body bound states and the sign of the (2 + 1)-scattering length in the plane of the mass ratio and interaction-strength ratio is deduced. The results provide a description of the homogeneous and mixed phases of atoms and molecules in dilute binary quantum gases

Methodical approaches to assessing influence of climate variability and air pollution on the health of population in industrially developed cities of the Sverdlovsk region

We conducted an environmental epidemiological study of influence of such risk factors as high temperature, forest fires, and atmospheric inversions related to an abnormally stable anticyclone established in the territory of the European part of the Russian Federation in May-August 2010 on the population mortality. The impact of climate variability in the cities of Yekaterinburg, Nizhny Tagil, and Verkhnyaya Pyshma was assessed.Проведено эколого-эпидемиологическое исследование влияния на смертность населения факторов риска (высокая температура, лесные пожары и инверсионные процессы в атмосферном воздухе), связанных с действием на территории Европейской части Российской Федерации аномально стабильного антициклона в период с его зарождения (май 2010 года) до распада (август 2010 года). Оценено влияние изменчивости климата в городах Екатеринбург, Нижний Тагил и Верхняя Пышма

Coping Responses During the COVID-19 Pandemic: A Cross-Cultural Comparison of Russia, Kyrgyzstan, and Peru

Background. The COVID-19 pandemic has subjected people around the world to severe stress, evoking a variety of coping responses. Coping responses can be broadly classified into four strategies: 1) problem-focused coping; 2) emotion-focused coping; 3) socially supported coping; and 4) avoidance. While there is a wide variability of individual coping responses, to some extent they are also culturally specific. Objective. This study aimed to compare the differences in the prevalence and factor structure of coping responses during COVID-19 pandemic in three countries: Russia, Kyrgyzstan, and Peru. Design. The sample included 501 participants from Russia, 456 participants from Kyrgyzstan, and 354 participants from Peru. The mean age of participants was 28 years in Russia (SD = 13.5); 24 years in Kyrgyzstan (SD = 10.0); and 30 years in Peru (SD = 12.3). In Russia and Kyrgyzstan, coping strategies were assessed with an abbreviated Russian adaptation of the COPE (Coping Orientations to Problems Experienced) questionnaire. In Peru, coping responses were assessed using the Spanish version of the Brief COPE questionnaire. The average scores from fifteen COPE scales were used as the input data for linear modelling and factor analysis. Results. The coping scores varied substantially within each country. Differences between countries accounted for 17.7% of the total variability in religious coping; 15.8% in acceptance; 13.9% in mental disengagement; and less than 7% in the other coping strategies. No difference in the prevalence of coping responses was found between Russian and Kyrgyz participants after accounting for age and gender. In all three countries the coping responses were associated with the same four coping domains: problem-focused coping, socially supported coping, avoidance, and emotion-focused coping. Four factors explained up to 44% of the total variation in the COPE scores. Religious coping and mental disengagement were classified into different coping domains in the three countries. Conclusion. The results suggest that during the COVID-19 pandemic, people from different countries apply the full range of coping responses within the four universal coping strategies. Religious coping and mental disengagement differed the most across the countries, suggesting that some coping behaviors can take on different roles within the system of coping responses to stressful events. We attribute these differences to differing cultural and socioeconomic characteristics, and the different measures taken by governments in response to COVID-19. © 2020. Lomonosov Moscow State University. All Rights Reserved.is study was supported by Russian Foundation for Basic Research (Project No. 20-04-60394)