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Physics of Atomic Nuclei

On the Width of γ-Line and the Photon Structure

Vladimir V Koltsov

Published Dec 1, 2022• 2 citations
Publisher

Abstract

The well-known narrowing of the Mössbaur γ-line with increasing age of the excited energy state ℏω0 of the emitter nucleus (the half-life is T1/2) and broadening of the γ-line with decreasing irradiation time of the absorber nucleus are analyzed. Taking into account the short time of emission of quantum transition energy – much less than T1/2, which can be seen, for example, from the duration of the γ-signal on the scintillator, the analysis leads to the idea of the structure of the γ-quantum (photon) as an electromagnetic wave of frequency ω0 that does not carry energy (0-wave), which is emitted by the nucleus from the moment of formation of the excited state to the quantum transition, with the energy quantum ℏω0 in the form of a short-term singularity on the “tail” of this 0-wave. A possible source of 0-waves can be virtual transitions of the nucleus from the excited state to the ground state and back before the emission of an energy quantum. Detection of 0-waves is possible due to changing the width of the γ‑line with additional irradiation of the absorber nuclei by resonant 0-waves. The possibility of predicting the future decay of an excited state by 0-waves detecting and the prospects of using 0-waves for information transmission are noted. The principle of a 0-wave generator without energy radiation is proposed.

DOI
10.1134/s1063778822110035

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The well-known narrowing of the Mössbaur γ-line with increasing age of the excited energy state ℏω0 of the emitter nucleus (the half-life is T1/2) and broadening of the γ-line with decreasing irradiation time of the absorber nucleus are analyzed. Taking into account the short time of emission of quantum transition energy – much less than T1/2, which can be seen, for example, from the duration of the γ-signal on the scintillator, the analysis leads to the idea of the structure of the γ-quantum (photon) as an electromagnetic wave of frequency ω0 that does not carry energy (0-wave), which is emitted by the nucleus from the moment of formation of the excited state to the quantum transition, with the energy quantum ℏω0 in the form of a short-term singularity on the “tail” of this 0-wave. A possible source of 0-waves can be virtual transitions of the nucleus from the excited state to the ground state and back before the emission of an energy quantum. Detection of 0-waves is possible due to changing the width of the γ‑line with additional irradiation of the absorber nuclei by resonant 0-waves. The possibility of predicting the future decay of an excited state by 0-waves detecting and the prospects of using 0-waves for information transmission are noted. The principle of a 0-wave generator without energy radiation is proposed.
We propose a technique for transforming the intensity of quasi-monochromatic recoilless radiation with a photon energy of 93.3 keV, emitted by radioactive Mössbauer sources 67Ga or 67Cu, into a sequence of short pulses with individually and independently controlled, on demand, the moments of appearance of pulses, as well as the peak intensity, duration and shape of each pulse. The technique is based on the transmission of recoilless (Mössbauer) 93.3-keV photons from the source through a medium containing resonantly absorbing 67Zn nuclei. The pulses are formed due to the rapid reciprocating movement of the source relative to the absorber at specified moments in time along the direction of photon propagation at a distance not exceeding half the radiation wavelength. The produced sequences of γ\gamma γ -ray pulses are similar to the digitization of information carried by electromagnetic waves. They can also be used to develop Mösbauer spectroscopy of the atomic and subatomic structures, as well as open novel opportunities for γ\gamma γ -ray quantum optics.
Due to the virtual photon exchange between atomic nuclei and the field of zero-point electromagnetic oscillations, some nuclei of a given sample are in a virtual excited state with the lifetime ∼ħ/ E , where E is the energy of nuclear level. For 57 Fe nuclei, whose first excited state has an energy of 14.4 keV, this time is equal to ∼4.6×10 −20 s. If a thin 57 Fe Mössbauer gamma-ray absorber is surrounded by a thick screen of the same atoms, the number of virtual excited nuclei in the absorber decreases and, at first glance, it should more strongly absorb Mössbauer gamma rays emitted by an external source and passing through the absorber. In this work, the ratio of the intensities of 14.4-keV gamma rays emitted by the 57 Fe nuclide and passing through the thin resonant absorber is measured in the absence and presence of the resonant screen around the absorber. Comparison shows that these ratios measured for the gamma source at rest and in the oscillating state differ by 0.00123±0.00075. This value should be treated as the upper limit for the desired effect under these experimental conditions.
Reversible coherent transients induced by a single photon in an ensemble of resonant particles are considered. It can be shown that a phase shift of a single photon wave packet produces its re-emission by these particles. As an example, the resonant interaction of a single gamma-photon with Mössbauer nuclei is theoretically analyzed. This example has interesting applications in such areas as information transmission and measuring of sub-angstrom vibrations of thin films for creating of sub-angstrom etalon displacements, which can be used for sensor calibration. We show that coherent transients that are governed by the time evolution of a population of nuclear excited states can be detected not only in the transmission of photons through resonant absorbers, but also directly in the time evolution of a population of nuclear excited states. These states experience radiative decay and also emit conversion electrons. The detection of conversion electrons provides information about the excited state population of nuclei located nearby the surface of the radiation incidence on the absorber. This is because of short mean free path (or escape depth) of these electrons in the bulk.
The spectrum of electromagnetic waves emitted by an oscillator trapped in an external potential well is studied. It is assumed that the natural frequency of the oscillator is much greater than the frequency of oscillations in the potential well. We consider the quantum model of emission with regard to the recoil effect. The highest intensity of the absorption and emission lines is observed on the natural frequency of the oscillator when the recoil energy is equal to the energy of the quantum of low-frequency (LF) oscillations in the potential well. A certain decrease in the amplitude of the emission and absorption lines is noted caused by the oscillations of the potential well due to, for example, the presence of the phonon spectrum. The relaxation times of the oscillator LF motion in the potential well, resulted from the phonon emission, are estimated. It is concluded that these processes have no influence on the observed features of the emission and absorption of high-frequency photons. This model can be applied to description of the emission and absorption of gamma rays in the crystal structures even in the presence of the phonon spectrum on condition that the relaxation time of the LF movements in the potential well is greater than the lifetime of the HF oscillator.
A method for obtaining the intensity distribution in a spectral line is derived from Dirac's quantum theory of the radiation field. The calculations are carried out for the case of emission from a first excited state (resonance line) and show that the intensity of frequency $\ensuremath{\nu}$ is, in this case, proportional to $\frac{1}{[4{\ensuremath{\pi}}^{2}{({\ensuremath{\nu}}_{0}\ensuremath{-}\ensuremath{\nu})}^{2}+{(A\ifmmode\cdot\else\textperiodcentered\fi{}2)}^{2}]}$ were AAA is the rate at which atoms are leaving the upper state and ${\ensuremath{\nu}}_{0}$ is the frequency of the transition. The half-width is therefore $\frac{1}{2\ensuremath{\pi}}$ times the Einstein probability coefficient for spontaneous transition to the lower state. The more general case where the lower state has a finite life time is not treated.A general method for the treatment of radiation problems, which is essentially Weyl's modification of Dirac's method, is briefly described.
We propose a technique of ultra-short $\ensuremath{\gamma}$-ray pulses production with a pulse duration much less than the natural lifetime of a nucleus excited state. The technique is based on compression of frequency modulated radiation of a Mossbauer source while propagating in a far-detuned resonant absorber. Numerical estimates for 57Fe{}^{57}\mathrm{Fe}57Fe 14.413 keV nuclear resonance energy show feasibility of experimental realization of the technique