Springer Tracts in Modern Physics 261 Andrey V. Davydov Advances in Gamma Ray Resonant Scattering and Absorption Long-Lived Isomeric Nuclear States Springer Tracts in Modern Physics Volume 261 Honorary Editor G. Höhler, Karlsruhe, Germany Series editors Atsushi Fujimori, Tokyo, Japan Johann H. Kühn, Karlsruhe, Germany Thomas Müller, Karlsruhe, Germany Frank Steiner, Ulm, Germany William C. Stwalley, Storrs, CT, USA Joachim E. Trümper, Garching, Germany Peter Wölfle, Karlsruhe, Germany Ulrike Woggon, Berlin, Germany Springer Tracts in Modern Physics Springer Tracts in Modern Physics provides comprehensive and critical reviews of topics of current interest in physics. The following fields are emphasized: Elementary Particle Physics, Condensed Matter Physics, Light Matter Interaction, Atomic and Molecular Physics, Complex Systems, Fundamental Astrophysics. Suitable reviews of other fields can also be accepted. 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While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Preface This book was written by an experimenter. It summarizes the results of my fifty- year work at A.I. Alikhanov Institute of Theoretical and Experimental Physics on problems of gamma ray interaction with nuclei. I tried to reveal the physical meaning of these results, making the exposition as simple as possible and some- times resorting to arguments and derivations that could seem insufficiently strict, at least to orthodox theorists. The main part of the book addresses the problem of studying resonant gamma ray absorption and scattering by nuclei. These processes, which are essentially the simplest nuclear reactions, permit, if studied profoundly, revealing very interesting special features that are inherent in phenomena of gamma ray emission and absorption by nuclei, and which are seemingly of a general character. It is noteworthy that the concepts of the nature of the photon that are prevalent among the physics community are inaccurate in many respects, even sometimes erroneous. In particular, the assignment of a well-defined frequency ν to a photon of energy E = hν is an approximation because a monochromatic harmonic oscillation is infinite in time, but by no means does a photon, which is produced at specific instant, exist limited during time, ending up in absorption inside a detector or in some substance. This means that the Fourier frequency spectrum of a photon must have a finite width. Also, opinions on the particle-wave duality of the photon differ widely. Recently, an article of the present author where resonant gamma ray scattering on nuclei was considered and where a photon was shown to manifest a spatial and a time extent in this process was rejected by an authoritative Russian physics journal on the basis of reviewer’s evaluation. The argument of the reviewer was that the photon is a particle because it experiences photo-absorption even in very finely dispersed powders, and therefore cannot have extensive dimensions. Of course, the statement of the reviewer that, in processes like the photoelectric effect, photons behave as almost quasi point objects, not displaying wave properties, is correct. The same reveals in the behavior of photons in Compton scattering by electrons. However, the other processes exist in which the photon interacts with matter behaving itself like a wave of macroscopic size, not showing any particle property. In the monograph by Robert Wood “Physical Optics” [1], there is a description of an experiment where one observes light diffraction at a grating 3 cm v vi Preface long and measures the resolution of the grating. After covering half the grating with a screen, the resolution becomes lower by a factor of two. Since a stationary diffraction pattern arises owing to the interference of a photon with itself (the interference between of two photons cannot lead to a stationary pattern because of a stochastic character of the phase difference), this means that, under conditions of the experiment being discussed, photons have a size not smaller than 3 cm. Bragg scattering in crystals is yet another process of this type, but, here, it is gamma ray photons rather than optical photons behave as extended waves. In this process, each photon interacts with all crystal atoms within its absorption length, exhibiting no particle properties. A very convincing example is provided by an experiment of a 181 group headed by V.K. Voitovetsky [2], where gamma rays of the Ta nuclide were transmitted between the cogs of a rotating gear, the shape of the detected gamma line being measured with the aid of a Mössbauer spectrometer. It was found that, at a large number of gear revolutions per unit time such that the gap between the cogs traverses the gamma beam within 0.1 of the mean lifetime of source nuclei in the excited state, the measured width of the Mössbauer gamma line was much larger than that in the case of a very slow rotation of the gear. This obviously indicated that the gear cogs interrupted the spatially extended wave train of a photon because wave trains shorter than natural ones corresponded to gamma lines of width larger than the natural width. We would like to emphasize that, in no physics process, a photon demonstrates its wave and particle properties simulta- neously—either the former or the latter. After being involved in Bragg scattering in a crystal, a photon is recorded by a detector in an event of photo-absorption or Compton scattering; that is, the photon behaves as a particle that lost completely the wave properties that it has just revealed. However, this does not mean that the wave transformed into a particle immediately after Bragg scattering. If, instead of a detector, one places a second crystal on the path of a photon that experienced Bragg scattering, and if the Bragg conditions hold in this crystal, then the photon would be able to undergo Bragg scattering once again with a sizable probability—that is, to exhibit anew its wave properties. At the same time, a photon that has shown particle properties in an event of Compton scattering in a detector can thereupon interact in a wave manner with a crystal (under Bragg conditions other than those in the first case, because the photon energy changed after scattering), transforming from a particle into a wave again. The question of how and why such transformations occur is one of the most mysterious in modern physics. The ensuing exposition is organized as follows. In the first chapter, we consider theoretically the process of resonant gamma ray scattering by nuclei. We are interested in a question of how the angular distribution of resonantly scattered gamma rays depends on the perturbing action of magnetic fields. Solving this particular and seemingly trivial problem, we arrive at conclusions that give suffi- cient grounds to take a fresh look at some special features of processes involving gamma ray emission and absorption by nuclei. In the second chapter, we describe experiments performed by our group and devoted to measuring unperturbed and magnetic-field-perturbed angular distributions (ADs) of resonantly scattered gamma 182 191 rays of W and Ir. Those experiments confirmed the prediction of the theory Preface vii that the result of perturbing ADs depends on the width of the spectrum of gamma rays incident to a resonant gamma ray scatterer. At the end of this chapter, we show that important conclusions follows from the theoretical and experimental data described in it: the mean lifetime of nuclei in an excited state depends on the mode of its excitation, and processes of gamma ray emission and absorption by nuclei have a protracted character. In the third chapter, we consider in detail the problem of gamma resonant excitation of long-lived isomeric states of nuclei. Experimental investigations of this problem revealed a glaring contradiction between present-day theoretical predictions, which require, among other things, that the Mósbauer 109 gamma line emitted in the decay of Ag nuclei that were in the isomeric excited state characterized by an energy of 88.03 keV and a mean lifetime of 57 s must be broadened by five to six orders of magnitude in relation to the natural width, and the experimental results of three research groups (including ours), which obtained data indicating that the relative broadening of this gamma line does not exceed one to two orders of magnitude. So small a broadening of the Mósbauer gamma line of the 109m Ag isomer permitted implementing the idea of a gravitational gamma spec- trometer and directly measuring the profile of the Mósbauer gamma resonance in this isomer. The use of a traditional Mósbauer spectrometer for this purpose is technically impossible because this would require creating a device capable of -12 moving a gamma source with respect to the absorber at a velocity of about 10 cm/s; that is, it would be necessary to push it forward over a distance per second nearly equal to the diameter of the silver-atomic nucleus, and to measure simul- taneously this velocity by some method. The principle of operation of the gravi- 109m tational gamma spectrometer based on the Ag isomer is described in the fourth chapter. Its resolution is about eight orders of magnitude higher than the resolution 57 of usual Mósbauer spectrometers employing gamma rays of the Fe nuclide. In the next chapter, we describe our experiments devoted to exploring the resonant scattering of annihilation photons by nuclei, whereupon (in the last chapter) we show how one can use this phenomenon to study the shape of Fermi surfaces in metals. Some other experiments performed by our group with gamma rays are discussed at the end of this book along with the ideas of experiments that have yet to be conducted. Some of the experiments described here were performed by methods that seem obsolete from the modern point of view, but I deemed it necessary to tell about them because they were an inalienable link in the chain of experiments that led to important conclusions both in what is concerned with the dependence of the mean lifetime of nuclei in an excited state on the method of excitation and in what is concerned with the duration of nuclear radiative processes. One comment on the notation used is in order. Vector quantities appearing in some equations are printed in boldface. viii Preface Acknowledgments It is my pleasant duty to record here the benefit of working over many tens of years side by side with Yury Denisovich Bayukov, Yury Nikolaevich Isaev, and Mark Mikhailovich Korotkov, who are members of our research group and who made an invaluable contribution to the implementation of the experiments described in this book. I am also indebted to my son Professor V.A. Davydov for valuable advice and help in solving some mathematical problems, and to my second son Anton, my wife Nina Mikhailovna, and to the scientist from our group Yuri B. Novozhilov for their very valuable help in the preparation of this book for printing. I would also thank the assistance of ITEP library A.A. Alekhina, E.V. Sandrakova, and O.M. Kuz’mina, the assistance of JINR library V.M. Smirnova and the head of library of Physical Faculty of Moscow State University V.M. Zuev for their help in the search for translation in English versions of the papers from Russian journals. Special thanks are due to Professor F.S. Dzheparov; the corresponding members of Russian Academy of Sciences Yu.G. Abov, M.V. Danilov, and B.L. Ioffe; and Academician L.B. Okun. Over many years, I have had the opportunity of discussing with them problems considered in this book. I am grateful to Doctor N.V. Lazarev for his interest in the work on this book and for his help in translating it. I will always mourn the untimely death of the collaborators of our group Vladilen Grigor’evich Alpatov, Gavriil Romanovich Kartashov, Vadim Mikhailovich Samoylov, Galina Eugen’evna Bizina, Mikhail Georgievich Gavrilov, Gennadiy Victorovich Rotter, and Yury Ivanovich Nekrasov and cherish memory of their selfless work, which ensured the success of our experiments. I recall with gratitude my first supervisor Professor N.A. Burgov, who introduced me in the realms of resonant gamma ray scattering, and the first director of ITEP Academician A.I. Alikhanov, whose permanent attention to our work and support were invaluable. I nourish warmest recollections of Professor A.L. Suvorov, who was ITEP’s director until his untimely death in 2005. His support of our investigations was a great help to us all, and his attitude to me personally was highly benevolent. A.V. Davydov References 1. R.W. Wood, Physical Optics (The MacMillan Company, New York, 1934) 2. V.K. Voitovetsky, I.L. Korsunsky, Yu.F. Pazhin et al., Phys. At. Nucl. 38, 394 (1983) Contents 1 Theory of the Resonant Scattering of Gamma Rays by Nuclei in a Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 ADRSG Function for the Case Where the Magnetic Field Is Perpendicular to the Plane of Gamma-Ray Scattering . . . . . . . 2 1.3 Angular Distribution in the Case Where Magnetic-Field Directions Are Distributed Chaotically Over the Scatterer Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.4 Some Particular Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2 Experimental Study of Resonant Gamma-Ray Scattering . . . . . . . . 35 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.2 Measurement of the Angular Distribution of 100.1 keV Gamma 182 Rays Resonantly Scattered by W Nuclei . . . . . . . . . . . . . . . . 36 182 2.3 Measurement of the Magnetic Moment of the W Nucleus + in the 2 Excited State at 100.1 keV . . . . . . . . . . . . . . . . . . . . 42 2.4 Measurement of the Unperturbed Angular Distribution 191 of Gamma Rays Resonantly Scattered by Ir Nuclei . . . . . . . . 47 2.5 Measurements of Magnetic-Field-Perturbed Angular Distributions of 129.4 keV Gamma Rays Resonantly 191 Scattered by Ir Nuclei in an Ir–Fe Alloy . . . . . . . . . . . . . . . . 52 2.6 Some Special Features of Gamma-Radiation Processes as Suggested by the Foregoing Analysis . . . . . . . . . . . . . . . . . . 69 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3 Problem of the Resonant Excitation of Long-Lived Nuclear Isomeric States. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.1 Small Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.2 Physical Reasons Behind Expected Difficulties in Performing Mössbauer Experiments with Long-Lived Isomers . . . . . . . . . . . 80 ix