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...

We investigate the double K-shell ionization of heliumlike ions caused by the absorption of a single photon with energies being much smaller than the rest energy of an electron. In the near-threshold region, differential and total cross sections of the process are calculated for light ions, taking into account the leading orders of the 1/Z and ␣Z expansions. QED perturbation theory with respect to the parameter 1/Z exhibits a fast convergence in the entire nonrelativistic domain for moderate nuclear charge numbers Zу2. Going beyond the electric dipole approximation leads to a forward/backward asymmetry in the angular distributions for the ejected electrons with respect to the incident photon beam. A comparison of theoretical predictions for the ratio of double-to-single photoionization cross sections with available experimental data for a number of neutral atoms is also presented.

A new, simplified apparatus has been developed for fatigue-testing fibres using the technique of biaxial rotation over a pin. This involves the tension-compression of fibres which are rotated whilst bent over a pin. The angle through which the fibre is bent during a fatigue test can be altered, and the effect of this on fatigue life and fracture morphology has been investigated.To remedy this situation a prototype singlc-station tester, operating on a similar principle but with the jaw shafts aligned parallel, has been constructed (figure 2). This greatly facilitates the gearing of the apparatus and allows a number

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Upconversion nanoparticles have attracted considerable attention as luminescent markers for bioimaging and sensing due to their capability to convert near-infrared (NIR) excitation into visible or NIR luminescence. However, the wavelength of about 970 nm is commonly used for the upconversion luminescence excitation, where the strong absorption of water is observed, which can lead to laser-induced overheating effects. One of the strategies for avoiding such laser-induced heating involves shifting the excitation into shorter wavelengths region. However, the influence of wavelength change on luminescent images quality has not been investigated yet. In this work, we compare wavelengths of 920, 940 and 970 nm for upconversion luminescence excitation in the thickness of biological tissues in terms of detected signal intensity and obtained image quality (contrast and signal-to-background ratio). Studies on biological tissue phantoms with various scattering and absorbing properties were performed to analyze the influence of optical parameters on the depth and contrast of the images obtained under 920–970 nm excitation. It was shown that at the same power the excitation wavelength shift reduces the detected signal intensity and the resulting image contrast. Visualization of biological tissue samples using shorter excitation wavelengths 920 and 940 nm also reduces signal-to-background ratio (S/B) of the obtained images. The S/B of the obtained images amounted to 2, 6 and 8 for 920, 940 and 970 nm, respectively. It was demonstrated that pulse-periodic excitation mode is preferable for obtaining high quality luminescent images of biological tissues deep layers and minimize overheating. Short pulse durations (duty cycle 20%) don’t result in heating even for 1 W cm−2 pumping power density and allow obtaining high luminescence intensity, which provides good images quality.