Effective Range Corrections to Three-Body Recombination for Atoms with Large Scattering Length

Few-body systems with large scattering length a have universal properties that do not depend on the details of their interactions at short distances. The rate constant for three-body recombination of bosonic atoms of mass m into a shallow dimer scales as \hbar a^4/m times a log-periodic function of the scattering length. We calculate the leading and subleading corrections to the rate constant which are due to the effective range of the atoms and study the correlation between the rate constant and the atom-dimer scattering length. Our results are applied to 4He atoms as a test case.Comment: 6 pages, 2 figures, improved discussion, final versio

Spectral convexity for attractive SU(2N) fermions

We prove a general theorem on spectral convexity with respect to particle number for 2N degenerate components of fermions. The number of spatial dimensions is arbitrary, and the system may be uniform or constrained by an external potential. We assume only that the interactions are governed by an SU(2N)-invariant two-body potential whose Fourier transform is negative definite. The convexity result implies that the ground state is in a 2N-particle clustering phase. We discuss implications for light nuclei as well as asymmetric nuclear matter in neutron stars.Comment: 10 pages, 2 figures; references adde

The Four-Boson System with Short-Range Interactions

We consider the non-relativistic four-boson system with short-range forces and large scattering length in an effective quantum mechanics approach. We construct the effective interaction potential at leading order in the large scattering length and compute the four-body binding energies using the Yakubovsky equations. Cutoff independence of the four-body binding energies does not require the introduction of a four-body force. This suggests that two- and three-body interactions are sufficient to renormalize the four-body system. We apply the equations to 4He atoms and calculate the binding energy of the 4He tetramer. We observe a correlation between the trimer and tetramer binding energies similar to the Tjon line in nuclear physics. Over the range of binding energies relevant to 4He atoms, the correlation is approximately linear.Comment: 23 pages, revtex4, 5 PS figures, discussion expanded, results unchange

Adiabatic hyperspherical study of triatomic helium systems

The 4He3 system is studied using the adiabatic hyperspherical representation. We adopt the current state-of-the-art helium interaction potential including retardation and the nonadditive three-body term, to calculate all low-energy properties of the triatomic 4He system. The bound state energies of the 4He trimer are computed as well as the 4He+4He2 elastic scattering cross sections, the three-body recombination and collision induced dissociation rates at finite temperatures. We also treat the system that consists of two 4He and one 3He atoms, and compute the spectrum of the isotopic trimer 4He2 3He, the 3He+4He2 elastic scattering cross sections, the rates for three-body recombination and the collision induced dissociation rate at finite temperatures. The effects of retardation and the nonadditive three-body term are investigated. Retardation is found to be significant in some cases, while the three-body term plays only a minor role for these systems.Comment: 24 pages 6 figures Submitted to Physical Review

Dimer-atom scattering between two identical fermions and a third particle

We use the diagrammatic $T$-matrix approach to analyze the three-body scattering problem between two identical fermions and a third particle (which could be a different species of fermion or a boson). We calculate the s-wave dimer-atom scattering length for all mass ratios, and our results exactly match the results of Petrov. In particular, we list the exact dimer-atom scattering lengths for all available two-species Fermi-Fermi and Bose-Fermi mixtures. In addition, unlike that of the equal-mass particles case where the three-body scattering $T$-matrix decays monotonically as a function of the outgoing momentum, we show that, after an initial rapid drop, this function changes sign and becomes negative at large momenta and then decays slowly to zero when the mass ratio of the fermions to the third particle is higher than a critical value (around 6.5). As the mass ratio gets higher, modulations of the $T$-matrix become more apparent with multiple sign changes, related to the "fall of a particle to the center" phenomenon and to the emergence of three-body Efimov bound states.Comment: 6 pages, 3 figures, and 2 table

Three-boson problem near a narrow Feshbach resonance

We consider a three-boson system with resonant binary interactions and show that three-body observables depend only on the resonance width and the scattering length. The effect of narrow resonances is qualitatively different from that of wide resonances revealing novel physics of three-body collisions. We calculate the rate of three-body recombination to a weakly bound level and the atom-dimer scattering length and discuss implications for experiments on Bose-Einstein condensates and atom-molecule mixtures near Feshbach resonances.Comment: published versio

Range Corrections to Three-Body Observables near a Feshbach Resonance

A non-relativistic system of three identical particles will display a rich set of universal features known as Efimov physics if the scattering length a is much larger than the range l of the underlying two-body interaction. An appropriate effective theory facilitates the derivation of both results in the |a| goes to infinity limit and finite-l/a corrections to observables of interest. Here we use such an effective-theory treatment to consider the impact of corrections linear in the two-body effective range, r_s on the three-boson bound-state spectrum and recombination rate for |a| much greater than |r_s|. We do this by first deriving results appropriate to the strict limit |a| goes to infinity in coordinate space. We then extend these results to finite a using once-subtracted momentum-space integral equations. We also discuss the implications of our results for experiments that probe three-body recombination in Bose-Einstein condensates near a Feshbach resonance.Comment: 28 pages, 3 figure

Survey of the world practice of implementing energy-efficient technologies in terms of mining enterprises

Purpose is the analysis of world practice of applying the best available techniques to increase energy saving and energy efficiency of mining enterprises being the important factor of the economic development. Methods. The research methodology is based on the scientific approaches: historical-evolutionary, interdisciplinary, integration, process, and situational. Methods of retrospective, categorical, and system analysis as well as modeling have been applied. The analysis was performed on the basis of both initial information sources (original texts of legislative documents, strategies) and material of the international analytical organizations (International Energy Agency, World Bank) as well as the data of official statistical records. Findings. For the first time, different variants of the best available techniques in Japan, the USA, and the EU have been analyzed as well as the role of a state in applying institutional measures of energy efficiency support, including mining complex, and prospects of its use in the Russian Federation. It has been determined that energy efficiency is the effective and economically feasible tool in reaching sustainable development of the national economy. It has been demonstrated that energy saving and increased energy efficiency may reduce the needs in investment, raise industrial competitiveness and consumer welfare as well as improve environmental protection owing to the reduced greenhouse gas emissions and decreased air pollution. Energy efficiency growth has direct effect upon the industrial competitiveness; it can be achieved by means of innovations. Originality. Emphasis has been put on the key scientific and technical aspects and approaches stimulating increased energy efficiency in the developed countries under the effect of strong, coordinated, and consistent national policy in different sectors of economy. Practical implications. The carried-out analysis is useful in terms of the innovative and technological development of different industries of the Russian Federation in the context of its complicated cooperation with European countries and the USA, dependence on foreign technologies, and limited access to them.Мета. Аналіз світового досвіду використання найкращих доступних технологій для підвищення енергозбереження та енергетичної ефективності гірничодобувних підприємств, які є важливими факторами інноваційного розвитку і економіки. Методика. В основі методології дослідження застосовані наукові підходи: історико-еволюційний, міждисциплінарний, інтеграційний, процесний і ситуаційний. Використано методики ретроспективного, категоріального, системного аналізу, моделювання. Аналіз виконувався на основі як первинних інформаційних джерел (оригінальні тексти законодавства, стратегій), так і на основі матеріалів міжнародних аналітичних організацій (Міжнародного енергетичного агентства, Світового банку), а також даних офіційного статистичного обліку. Результати. Вперше проаналізовані різні варіанти найкращих доступних технологій в Японії, США, ЄС, роль держави у застосуванні інституційних заходів підтримки енергоефективності, в тому числі у гірничодобувному комплексі, а також перспективи їх використання у Російській Федерації. Визначено, що енергоефективність є дієвим і рентабельним інструментом досягнення сталого розвитку економіки країни в цілому. Показано, що енергозбереження та підвищення енергоефективності може знижувати потребу в інвестиціях, збільшити конкурентоспроможність промисловості й добробут споживача, а також покращувати охорону навколишнього середовища, завдяки зниженню викидів парникових газів та зменшенню забруднення повітря. Підвищення енергоефективності безпосередньо впливає на конкурентоспроможність промисловості та може бути досягнуто за рахунок інновацій. Наукова новизна. Виділено ключові науково-технічні асп екти й підходи, що стимулюють підвищення енергоефективності в розвинених зарубіжних країнах під впливом сильної, скоординованої та послідовної політики держави у різних секторах економіки. Практична значимість. Проведений аналіз корисний у побудові інноваційного та технологічного розвитку різних галузей Російської Федерації в умовах її непростої взаємодії з країнами Європи і США, залежно від зарубіжних технологій та обмеженого доступу до них.Цель. Анализ мирового опыта использования наилучших доступных технологий для повышения энергосбережения и повышение энергетической эффективности горнодобывающих предприятий, которые являются важными факторами развития экономики. Методика. В основе методологии исследования применены научные подходы: историко-эволюционный, междисциплинарный, интеграционный, процессный и ситуационный. Использованы методики ретроспективного, категориального, системного анализа, моделирования. Анализ выполнялся на основе как первичных информационных источников (оригинальные тексты законодательства, стратегий), так и на основе материалов международных аналитических организаций (Международного энергетического агентства, Всемирного банка), а также данных официального статистического учета. Результаты. Впервые проанализированы различные варианты наилучших доступных технологий в Японии, США, ЕС, а также роль государства в применении институциональных мер поддержки энергоэффективности, в том числе в горнодобывающем комплексе, перспективы его использования в Российской Федерации. Определено, что энергоэффективность является действенным и рентабельным инструментом достижения устойчивого развития экономики страны в целом. Показано, что энергосбережение и повышение энергоэффективности может снижать потребность в инвестициях, увеличить конкурентоспособность промышленности и благосостояние потребителя, а также улучшать охрану окружающей среды, благодаря снижению выбросов парниковых газов и уменьшению загрязнения воздуха. Повышение энергоэффективности напрямую влияет на конкурентоспособность промышленности и может быть достигнуто за счет инноваций. Научная новизна. Выделены ключевые научно-технические аспекты и подходы, стимулирующие повышение энергоэффективности в развитых зарубежных странах под влиянием сильной, скоординированной и последовательной политики государства в различных секторах экономики. Практическая значимость. Проведенный анализ полезен в построении инновационного и технологического развития различных отраслей Российской Федерации в условиях ее непростого взаимодействия со странами Европы и США, зависимости от зарубежных технологий и ограниченного доступа к ним.This article was prepared as a part of the project section of the government contract as requested by the Ministry of Science and Higher Education of the Russian Federation on the subject formulated as “Development of Methodological Principles and Organizational Economic Mechanism of Strategic Management of Economic Security in Russia” (Assignment No. 26.3913.2017/4.6)

On the correlation between the binding energies of the triton and the alpha-particle

We consider the correlation between the binding energies of the triton and the alpha-particle which is empirically observed in calculations employing different phenomenological nucleon-nucleon interactions. Using an effective quantum mechanics approach for short-range interactions with large scattering length |a| >> l, where l is the natural low-energy length scale, we construct the effective interaction potential at leading order in l/|a|. In order to renormalize the four-nucleon system, it is sufficient to include a SU(4)-symmetric one-parameter three-nucleon interaction in addition to the S-wave nucleon-nucleon interactions. The absence of a four-nucleon force at this order explains the empirically observed correlation between the binding energies of the triton and the alpha-particle. We calculate this correlation and obtain a prediction for the alpha-particle binding energy. Corrections to our results are suppressed by l/|a|.Comment: 4 pages, 1 ps figure, references update

Collective Excitations of Strongly Interacting Fermi Gases of Atoms in a Harmonic Trap

The zero-temperature properties of a dilute two-component Fermi gas in the BCS-BEC crossover are investigated. On the basis of a generalization of the Hylleraas-Undheim method, we construct rigorous upper bounds to the collective frequencies for the radial and the axial breathing mode of the Fermi gas under harmonic confinement in the framework of the hydrodynamic theory. The bounds are compared to experimental data for trapped vapors of Li6 atoms.Comment: 11 pages, 2 figure