Conclusion. 109m Ag isomer showed that there is no such broadening. Because one can hardly

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1 Conclusion This small book presents a description of the results of studies performed over many years by our research group, which, in the best period, included 15 physicists and laboratory assistants and technicians, but which now diminished to five scientists without any subsidiary personnel. Nonetheless, we were able to create experimental devices, even in the last, especially hard, years, relying on our own efforts exclusively, and to obtain unique results by using this equipment. Here, I would like to remind briefly the main that we have done and which I have described in this book. First, this is, of course, a series of studies devoted to exploring magnetic-field-perturbed angular distributions of resonantly scattered gamma rays. We were able to prove experimentally the correctness of the theoretical predictions according to which the result of such a perturbation depends on the shape of the spectrum of scattered gamma rays and explained this effect by the dependence of the mean lifetime of the participant nucleus in an excited state on this shape. A detailed analysis of this situation led to the conclusion that nuclear processes of gamma-ray emission and absorption are of a protracted character. This point of view, albeit possibly in a less explicit form, existed earlier (see the argument of Dr. E.B. Bogomol nyi above in explaining the difference between the excitation of nuclei by gamma rays of narrow and wide spectrum), but it turned out to be quite unexpected for the overwhelming majority of physicists (and not only experimenters) with whom I discussed this problem. The results of our experiments devoted to the gamma-resonant excitation of long-lived isomeric states of nuclei proved to be even more important. Until recently, the common point of view was (has been to date for many) that the minimum gamma-line width accessible to measurement is about to ev. Even in diamagnetic substances, the widths of narrower gamma lines should increase up to such values because of the dipole-dipole interaction of nuclear magnetic moments with the magnetic moments of neighboring nuclei and conduction electrons. Paradoxically as it might seem, our experiments with the 109m Ag isomer showed that there is no such broadening. Because one can hardly believe that quantum electrodynamics, which is a highly reliable theory, could lead to an incorrect result in this case, it only remains to think that some as-yet-unknown special features of nuclear radiative processes are responsible for this. An attempt at explaining this situation by a possible averaging of dipole-dipole interaction energy, Springer International Publishing Switzerland 2015 A.V. Davydov, Advances in Gamma Ray Resonant Scattering and Absorption, Springer Tracts in Modern Physics 261, DOI /

2 188 Conclusion which changes quickly in magnitude and sign, over the mean lifetime of the excited state of the nucleus involved raised serious objections of theorists. The second hypothesis that we proposed was that the radiating nucleus and the gamma wave emitted by it are both insensitive to external effects as long as the radiative process lasts. In support of this hypothesis, we put forward the argument that, if this was not so, it would be impossible to observe gamma lines of natural width, but one sometimes observes them. Of course, a much more profound analysis is required for explaining this anomaly conclusively. It is also worth mentioning that our group designed and manufactured a gravitational gamma spectrometer, which is an instrument belonging to quite a new type and which is simple in underlying idea and in design and was made from improvised materials. By using this spectrometer, we were able to measure the shape of the gamma resonance in the long-lived 109m Ag isomer, thereby improving the resolving power of gamma spectrometry by about eight orders of magnitude in relation to that of Mössbauer spectrometers dealing with gamma rays of the 57 Fe nuclide. This result confirms fully earlier data demonstrating that the 109m Ag Mössbauer gamma line does not undergo a large broadening that could be caused by dipole-dipole interaction. Our observation of resonant annihilation-photon scattering on nuclei is the most important point in the remaining part of the book since this process permits developing a new method for studying Fermi surfaces of metals. The discovery of manifestations of binding energies of atomic electrons in the spectra of scattered gamma radiation is yet another important result. Last but not least, I gratefully acknowledge that some experiments with the 109m Ag isomer received support from the Russian Foundation for Basic Research and from INTAS.

3 Index A Absorption coefficients, 108 Absorption operator, 6 Acoustic broadening, 81 Amplitude for the emission process, 30 Angular distribution, 23, 25, 43, 48, 52, 166, 167, 177 Angular distribution function, 15 Angular distribution of resonantly scattered gamma rays, 44 Angular-correlation function, 24 Angular-distribution function, 15 Annealing, 108 Annihilation photon, 141, 146, 149, 155, 161, 167, 182 Antimatter, 184 Associated Legendre function, 13, 16 Associated Legendre polynomial, 97 Atomic number, 156 B Background, 93, 160, 161 Beta decay, 155 Binding energy, 173, 175 Boltzmann constant, 169 Bremsstrahlung, 158, 175, 185 Broadening factor, 123, 127, 131, 132, 135, 138 Broadening of gamma lines, 80 Broadening of a Mössbauer gamma line, 82, 84, 94 C Coefficient of absorption, 151, 164, 185 Coefficient of internal conversion, 147 Coefficients of linear expansion, 106, 111, 119 Compaction, 113 Compaction of the materials, 106 Compton effect, 175 Conduction electrons, 141, 144, 167 Correlation function, 5, 19 Coulomb fragmentation, 176, 178 Cross section, 114 Cryostat, 87, 107 Crystallographic directions, 183 D D-functions, 7, 14, 20, 24 Decay, 109 Detector efficiency, 112 Differential cross section, 152, 153, 154, 161, 165 Diffusion, 109 Diffusion annealing, 108 Diffusion coefficient, 110 Dipole-dipole, 123 Dipole-dipole interactions, 124 Doppler effect, 177 E E2 and M1 multipoles, 10, 11, 22 Earth s magnetic field, 118 Efficiency, 59, 60, 120 Efficiency matrix, 9 Eigenfunction, 3 Elastic-scattering peaks, 151 Electric quadrupole interaction, 166 Electrolytic dissociation, 178 Electromagnetic oscillation, 28 Electron density, 84 Electron momentum, 143 Excited state, 25, 27, 36, 62, 93 Springer International Publishing Switzerland 2015 A.V. Davydov, Advances in Gamma Ray Resonant Scattering and Absorption, Springer Tracts in Modern Physics 261, DOI /

4 190 Index Exciting gamma radiation, 52 Exciting gamma rays, 62 Hyperfine interaction, 81 Hyperfine structure, 96 F Fermi energy, 81, 143 Fermi surface, 142, 170, 182 Fourier transform, 28, 29 Frequency characteristic, 28 Frequency distribution, 28 G Gamma beam, 106, 107, 117, 118, 122, 124, 128, 131 Gamma line, 22 Gamma ray absorption, 6 Gamma resonance, 139 Gamma source, 36, 37, 40, 42, 43, 45, 49, 52, 53, 81 83, 88, 101, 103, 106, 116, 135 Gamma transitions, 9 Gamma-beam, 39 Gamma-beam divergence, 131 Gamma-line broadening, 102 Gamma-ray absorption, 57 Gamma-ray intensity, 112, 116, 119 Gamma-ray resonant absorption, 22 Gamma-ray self-absorption, 85 Gamma-ray spectrum, 115 Gamma-ray yield, 111 Gaussian distributions, 162 Geomagnetic field, 90, 135 Germanium detector, 90 g-factor, 45 47, 57, 59, 60 Gravitational gamma spectrometer, 132, 136, 139 Gravitational gamma spectrometry, 127 Gravitational shift, 128 Gravitational shift of the gamma resonance, 115 Gravitational suppression of resonance conditions, 107 Gravitational waves, 139 Gravity, 84 Ground state, 6 H Half-life, 45, 141 Hamiltonian, 2 Helmholtz coils, 104, 107, 120, 123, 127, 135 Holes, 121 I Inclination angle, 136 Incoherently scattered gamma rays, 163 Interaction, 123 Internal magnetic field, 35, 55, 58 Internal-conversion coefficient, 87 Interstitials of the crystal lattice, 124 Irradiation, 83, 90, 154 Isomeric shift, 83, 139 Isomeric state, 140 Isotope, 151 J 3J coefficients, 9, 20, 23 K K-shell, 175 L Larmor frequency, 25, 177 Lattice heat capacity, 84 Legendre polynomials, 24, 49 Liquid nitrogen, 36, 53, 92 Liquid-helium temperature, 114 Long-lived nuclear isomeric states, 80 Lorentzian gamma line form, 5 M Magnetic field, 2 Magnetic hyperfine interaction, 62 Magnetic moment, 35, 42, 52, 178 Magnetic moments of nuclei, 1 Magnetic quantum number, 6, 97 Magnetic-field strength, 16, 20 Matrix element, 2, 17 Maximum-likelihood method, 50 Mean lifetime, 26, 59, 149, 165, 169 Mean lifetime of a nucleus, 29, 44 Mean lifetime of nuclei in an excited state, 25 Metzger, R.F., 35 Momentum projections, 145, 146 Momentum space, 145 Mössbauer absorption, 106 Mössbauer effect, 36, 48, 52, 59, 79, 102 Mössbauer emission, 99 Mössbauer excitation of nuclei, 27

5 Index 191 Mössbauer gamma line, 57, 90, 118 Mössbauer resonance width, 45 Mössbauer resonant absorption, 118 Mössbauer resonant scattering, 42 Mössbauer scattering of gamma rays, 35 Multipolarity, 97 Multipole-mixing parameter, 11, 50, 177 Multipole-mixing ratios, 1 N Narrow spectral line, 29 Natural width, 44, 52, 124 Natural width of the excited nuclear state, 5, 168 Nihilation photons, 143 Nuclear radius, 82 Nuclear resonant scattering, 158 Nuclide, 148 O Orthogonality, 23 Oscillation amplitude, 28 P Pair production, 153, 165 Pair-production cross section, 164 Parent nuclide, 93 Parity, 4 Peak of elastic processes, 158 Peak of elastic-scattering processes, 161 Peak of the total absorption, 151 Perturbation of the angular distribution, 28 Perturbed angular distributions of resonantly scattered gamma rays, 57 Phase characteristic, 28 Phase space, 144 Photoelectric effect, 175 Photomultiplier tube, 158 Polarization of radiation, 169 Positron annihilation, 141 Positron thermalization, 141 Precipitation, 108 Protracted character of nuclear radiative processes, 32 Q Quadrupole interaction, 82 Quantization axis, 16, 17, 20 Quantum number, 8, 36 Quasimonochromatic line, 26 R Radiation parameters, 7 Radioactive atoms, 111 Rayleigh scattering, 40, 57, 152, 155, 157, 158, 161, 164, 168, 175, 184 Real width, 45 Recoil, 36, 166 Recoil energy, 185 Recoil of the emitting nucleus, 27 Recoilless gamma-ray emission, 48, 79, 85, 90 Reduced matrix element, 4, 10, 11 Resonance filter, 28, 29 Resonance frequency, 29 Resonant absorber, 80 Resonant absorption, 103 Resonant absorption of gamma rays, 100 Resonant gamma-ray absorption, 39, 85, 114, 117, 119, 122, 128, 140 Resonant gamma-ray scattering, 30, 35, 176 Resonant scatterer, 148 Resonant scattering, 90, 169 Resonant scattering of annihilation photons, 173 Resonant-absorption cross section, 115, 124, 132 Resonant-absorption probability, 100 Resonantly scattered photons, 56 Resonant-scattering, 1 Resonant-scattering cross section, 149, 164 Rotation matrix, 3 S Scatterer, 17, 22, 36, 38, 39, 43, 45, 50, 55, 59 Scattering angles, 25, 38, 48, 55, 153, 156 Scattering plane, 1, 25 Scintillation counter, 40, 79, 158 Single crystal, 182 Single-crystal gamma source, 118 Spectral distribution, 30 Spectrum of annihilation photon, 147, 148, 153 Spectrum of annihilation radiation, 143, 169 Spherical harmonics, 12 Spin, 3 Statistical factor, 148 T Taylor series, 29 Thermal-diffusion, 112

6 192 Index Thermal-diffusion annealing, 101 Thermal-neutron flux, 154 Total-absorption peaks, 169, 173 Total cross section, 166 Tunguska meteorite, 184 V Very wide spectrum, 32 W Wave vectors, 2 Wavelength, 115 Weak magnetic fields, 25, 27 Wigner 3J coefficient, 3 Wigner 6J coefficient, 8 X X-ray, 40, 55, 103, 108, 110, 112, 114, 120, 121 χ 2 criterion, 42, 55, 60, 131, 135, 162 Z Zeeman component, 98 Zeeman hyperfine structure, 100 Zeeman splitting, 90, 123

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