Determining the ratio of the number of recoil electrons to the number of photoelectrons using a new method Determinación de la relación entre el número de electrones de retroceso y el número de fotoelectrones mediante un nuevo método

The problem in question is relevant due to discrepancy between the results of theoretical and known experimental studies of various interactions of ionizing emission photons with substances, in particular, photo effect and Compton scattering of these photons. The study aimed at carrying out specific measurements using a new method of simultaneously determining the ratio of the number of recoil electrons to the number of photoelectrons. Analysis of the results showed that there are significant discrepancies between theoretical calculations and experimental data. New values of simultaneously measured ratios of cross-sections for heavy atoms using a method invented by the author, and old measurements of these ratios for light atoms usingWilson cloud chamber, when compared with theoretical calculations, show that a significant (by one order and more) one-direction discrepancy is seen for X-ray and gamma emissions over a range of energies in question.It is shown that these discrepancies might be attributed to the fact that an atomic electron is in a free state for a while. Compton scattering occurs with a free electron; photo effect involves only bound electrons. Therefore, Compton scattering cross section is proportional to a period of time, during which electron was in a free state, whereas photo effect cross section is proportional to a time period, during which electron was in a bound state. The article materials might be helpful to perform both fundamental, and applied studies on interaction of light quanta with substance including modelling the phenomena under examination.


INTRODUCTION
Measuring electron streams in substances is relevant both for evaluating validity of light quanta-substance interaction theory and solving different applied problems (on determining electrical conductivity, for instance), including modelling of phenomena and processes under review. However, since methods of energy-dispersion registration of recoil electrons and photoelectrons, for example using Wilson cloud chamber, or electronic spectroscopy (Briggs, 1987;Lukyanova & Podolyako, 2004;Shpolskiy, 1950Shpolskiy, , 1974Thompson et al., 1985), in condensed media are challenging, it is a matter of priority to develop new experimental methods.
This study examines potential use of primary emission characteristic and incoherently scattered streams as a source of information about the above phenomena.It is shown that the ratio of mass coefficient of the primary emission incoherent scattering section to the mass coefficient of primary emission photoelectric absorption can be defined from simultaneously measured ratios of intensities of characteristic and incoherently scattered emissions in substance.

Results obtained by the known method
The first experiments on detecting recoil electrons when scattering gamma and X-rays in air were conducted by making use of Wilson cloud chamber (Shpolskiy, 1974). The results of measurements are listed in Table  1. where Nc/Npe is a ratio of the number of recoil electrons to the number of photoelectrons, /is a ratio of the primary emission incoherent scattering section coefficient to the primary emission photoelectric absorption coefficient . Here it is assumed that Nc/Npe = /. It is obvious that usingboth this method and electronic spectroscopy methods in solid substances, especially, in metals, is problematic. Indeed, it is almost impossible to single out and distinguish photoelectrons and recoil electrons against the background of "electron gas" deep in conductor.  As is evident, a discrepancy between the curves is of one order and more. It is clear that the experimental data are insufficient to ensure agreement of theory with experience.

New method
Many papers were devoted to studying and using spectral ratio method (Kosianov, 2005(Kosianov, , 2012Mamikonyan, 1976;Revenko, 2000). A large database of experimentally measured ratios of intensities of the characteristic and incoherently scattered X-ray and gamma emissions in various substances was built up. The author obtained the following expression (Kosianov, 2016;Morrison, 1967): where:  -fluorescence yield coefficient *;  н -mass coefficient of the primary radiation incoherent scattering cross section in sample; -anisotropy coefficient of incoherently scattered radiation angular distribution ;pktransition probability of an atom, excited to K-level with emission of the characteristic i-line radiation *; SK -value of K (or L) -absorption jump of the analyzed element *;  М mass coefficient of the primary radiation photoelectric absorption of the element [m 2 /kg]; *Dimensionless values And, the resulting expression (1) enables to obtain the desired ratio of the mass coefficient of the primary radiation incoherent scattering cross section to the mass coefficient of the primary radiation photoelectric absorption:

Energy, keV
where anisotropy coefficient of incoherently scattered radiation angular distribution -is  , for angles = =45° and,thus, for scattering angle  =90°, and energies from 10 keV to 100 keV, varies from 0.4 to 0.2; transition probability of an atom, excited to K -level with i-line characteristic radiation emissionp K ≥ 0,9 (Morrison, 1967), fluorescence yield for Kseries can be calculated by Stephenson formula (Heitler, 1956): where Z -atomic number of an element, b = 1,127* 10 -6 ; The obtained expression (2) allows to determine a ratio of mass coefficient of the primary radiation incoherent scattering cross section to mass coefficient of the primary radiation photoelectric absorption using experimentally measured ratios of intensities ofcharacteristic and incoherently scattered radiation of the known energy in a given substance, and hence a required ratio of the number of recoil electrons to the number of photoelectrons.

Results obtained with a new method
The author was the first to obtain a ratio of mass coefficient of the primary radiation incoherent scattering cross section to mass coefficient of photoelectric absorption in heavy metals, molybdenum, and tungsten.
Synthesis and statistical analysis of a number of experimental data (Kosianov, 2005)  For comparison, Table 2 contains the appropriate ratios, obtained on the basis of theoretical calculations (Losev, 1969).  It follows from the above comparison that the conclusions about substantial discrepancy between theoretical and experimental data are confirmed.
In the modern atomic physics, an electron is taken in a bound state with binding energy En, where quantum number n can vary from 1 to  and E = 0, i.e. the electron becomes free. Any transition from one bound state to another E2 E1 can be represented as E2 E E1, i.e., through a free state. Since the transition time cannot be zero (violation of conservation laws) tf> 0, i.e., for some time, the electron will be in a free state. The contemporary theory of atom is based on quantum mechanics and solves the steady-state Schrödinger equation for describing atom. Interaction of electron with light (xray or gamma radiation) is considered as a quantum effect, whereas interaction of electron with a nucleus is considered in terms of continuum theory as the motion of a particle in a continuous and stationary central field (Fig. 2). But if this interaction is also considered as a result of single collisions of electron (and hence, of the nucleus) with quanta from their total electromagnetic field, the picture will fundamentally change (Fig.  3). Electron will be in a free state over some period of timet free , and in a bound state over t bound period, withtfree=N tfree, wheretfreeis a time period between two successive interactions of electron with the nucleus tbound=N tbound, respectively, wheretboundis a length of one interaction, N is the number of interaction nodes, withN  Z, sinceN F Z (Z is the number of protons in the nucleus).
Let us examine Compton scattering and photo effect using Feynman's diagrams (Fig.4, 5). Compton scattering occurs on a free electron, photo effect involves only bounded electrons.. Therefore, the incoherent scattering section is нtf/Т, whereas the photo effect section is petb/Т, where T is a period of electron revolution. This is a reason why there is such a serious underestimation of incoherent scattering section in theory, where an orbital electron is always taken as bounded, therefore, photo effect section is considerably overestimated. As can be seen in the figure, Thus, there is an explanation provided for a discrepancy between experimentally and theoretically determined ratios of the corresponding values (by one order and more).

CONCLUSIONS
The author was the first to determine the ratios of the number of recoil electrons to the number of photoelectrons according to experimentally measured ratios of intensities of characteristic and incoherently scattered gamma radiation taking into account matrix effect on molybdenum and tungsten atoms. New results of simultaneously measured ratios of sections for heavy atoms with a method developed by the author, and old measurements of these ratios for light atoms using Wilson cloud chamber, when compared with the results of theoretical calculations, show that there is a significant (by one order and more) one-direction discrepancy for X-ray and gamma emissions over a range of energies in question. Hence, theoretically calculated values of incoherent scattering sections are substantially underestimated, and the values of photo effect sections are, on the contrary, overestimated.