This book deals with one of the basic topics of quantum mechanics: the theory of angular momentum and irreducible tensors. Being rather versatile, the mathematical apparatus of this theory is widely used in atomic and molecular physics, in nuclear physics and elementary particle theory. It enables one to calculate atomic, molecular and nuclear structures, energies of ground and excited states, fine and hyperfine splittings, etc. The apparatus is also very handy for evaluating the probabilities of radiative transitions, cross sections of various processes such as elastic and nonelastic scattering, different decays and reactions (both chemical and nuclear) and for studying angular distributions and polarizations of particles.Today this apparatus is finding ever increasing use in solving practical problems relating to quantum chemistry, kinetics, plasma physics, quantum optics, radiophysics and astrophysics.The basic ideas of the theory of angular momentum were first put forward by M. Born, P. Dirac, W. Heisenberg and W. Pauli. However, the modern version of its mathematical apparatus was developed mainly in the works of E. Wigner, J. Racah, L. Biedenharn and others who applied group theoretical methods to problems in quantum mechanics. At present a number of good books on the theory of angular momentum have been already published. The general principles and results of the theory may be found in the books by M. Rose [31], A. Edmonds [16], U. Fano and G. Racah [18], A. P. Yutsis, I. B. Levinson and V. V. Vanagas [44], A. P. Yutsis and A. A. Bandzaitis [45], D. Brink and G. Satcher [9]. Nevertheless, many formulas and relationships essential for practical calculations have escaped these books and are either scattered in various editions, or included as appendices in papers discussing somewhat disparate topics, making them generally inaccessible. Even greater difficulties arise when one tries to use the results, as each author employs his own phase conventions, initial definitions and symbols.The authors of this book aimed at collecting and compiling ample material on the quantum theory of angular momentum within the framework of a single system of phases and definitions. This is why, in addition to the basic theoretical results, the book also includes a great number of formulas and relationships essential for practical applications.This edition is the translated version of our book published in the USSR in 1975. In the course of its preparation we have tried to comply with a number of suggestions from our readers. For instance, each chapter opens with a comprehensive listing of its contents to ease the search for information needed. We also included some new results relating to different aspects of angular momentum theory which have recently appeared in journals. Unfortunately the limited volume of the present book prevented us from covering all the aforementioned results. We offer sincere apologies to the authors whose results we failed to include.The monograph is a kind of handbook. Consequently the material is pres...

The electron–positron annihilation spectrum observed by SPI/INTEGRAL during deep Galactic Centre region exposure is reported. The line energy (510.954±0.075 keV) is consistent with the unshifted annihilation line. The width of the annihilation line is 2.37 ± 0.25 keV (full width at half‐maximum), while the strength of the ortho‐positronium continuum suggests that the dominant fraction of positrons (94 ± 6 per cent) form positronium before annihilation. Compared to the previous missions, these deep INTEGRAL observations provide the most stringent constraints on the line energy and width. Under the assumption of an annihilation in a single‐phase medium, these spectral parameters can be explained by a warm Te∼ 7000 to 4 × 104 K gas with degree of ionization larger than a few 10−2. One of the widespread phases of the interstellar medium (ISM) – warm (Te∼ 8000 K) and weakly ionized (degree of ionization ∼0.1) – satisfies these criteria. Other single‐phase solutions are also formally allowed by the data (e.g. cold, but substantially ionized ISM), but such solutions are believed to be astrophysically unimportant. The observed spectrum can also be explained by annihilation in a multiphase ISM. The fraction of positrons annihilating in a very hot (Te≥ 106 K) phase is constrained to be less than ∼8 per cent. Neither a moderately hot (Te≥ 105 K) ionized medium nor a very cold (Te≤ 103 K) neutral medium can make a dominant contribution to the observed annihilation spectrum. However, a combination of cold/neutral, warm/neutral and warm/ionized phases in comparable proportions could also be consistent with the data.

During the period Aug.23-Sept.24 2003, the INTEGRAL observatory performed an ultra deep survey of the Galactic Center region with a record sensitivity at energies higher than 20 keV. We have analized images of the Galactic Center region obtained with the ISGRI detector of the IBIS telescope (15-200 keV) and present here a catalog of detected sources. In total, 60 sources with a flux higher than 1.5 mCrab have been detected. 44 of them were earlier identified as Galactic binary systems, 3 are extragalactic objects. 2 new sources are discovered.

We analyse SPI/INTEGRAL data on the 511-keV line from the Galactic Centre, accumulated over ∼6 yr of observations. We decompose the X-ray and soft gamma-ray emission of the central part of the Milky Way into relatively compact 'bulge' and more extended 'disc' components and report their spectral properties. The bulge component shows a prominent 511-keV line and essentially no flux at 1.8 MeV, while the disc component on the contrary contains a prominent 1.8-MeV line and a very weak annihilation line.We show that the spectral shape of the annihilation radiation (the narrow 511-keV line and the associated ortho-positronium continuum) is surprisingly well described by a model of annihilation of hot positrons in a radiatively cooling interstellar medium (ISM). The model assumes that positrons are initially injected into a hot (∼10 6 K), volume-filling ISM, which is allowed to freely cool via radiative losses. The annihilation time in such a medium is longer than the cooling time for temperatures higher than a few 10 4 K. Thus, most of the positrons annihilate only after the gas has cooled down to ∼10 5 K, giving rise to annihilation emission characteristic of a warm, ionized ISM.

We present a detailed analysis of an H 2 -rich, extremely strong intervening damped Ly-α absorption system (DLA) at z abs = 2.786 towards the quasar J 0843+0221, observed with the Ultraviolet and Visual Echelle Spectrograph on the Very Large Telescope. The total column density of molecular (resp. atomic) hydrogen is log N(H 2 )=21.21 ± 0.02 (resp. log N(H i)=21.82 ± 0.11), making it to be the first case in quasar absorption line studies with H 2 column density as high as what is seen in 13 CO-selected clouds in the Milky-Way.We find that this system has one of the lowest metallicity detected among H 2 -bearing DLAs, with [Zn/H] = −1.52 +0.08 −0.10 . This can be the reason for the marked differences compared to systems with similar H 2 column densities in the local Universe: (i) the kinetic temperature, T ∼120 K, derived from the J = 0, 1 H 2 rotational levels is at least twice higher than expected; (ii) there is little dust extinction with A V < 0.1; (iii) no CO molecules are detected, putting a constraint on the X CO factor X CO > 2 × 10 23 cm −2 /(km/s K), in the very low metallicity gas. Low CO and high H 2 contents indicate that this system represents "CO-dark/faint" gas.We investigate the physical conditions in the H 2 -bearing gas using the fine-structure levels of C i, C ii, Si ii and the rotational levels of HD and H 2 . We find the number density to be about n ∼ 260 − 380 cm −3 , implying a high thermal pressure of 3 − 5 × 10 4 cm −3 K. We further identify a trend of increasing pressure with increasing total hydrogen column density. This independently supports the suggestion that extremely strong DLAs (with log N(H) ∼ 22) probe high-z galaxies at low impact parameters.