Experiments on electron bremsstrahlung when passing through narrow slits and their interpretation in terms of inverse photoelectric eﬀect
V.V. Demjanov Ushakov State Maritime Academy, Novorossiysk∗
(Dated: April 27, 2011)
In special experiments on slowing down soft electrons from the energy E1 at the entry of a narrow slit down to E2 < E1 in the exit there was drawn a conclusion that the source of the retardation radiation with the energy ∆E12 = E1 − E2 in the opening of the narrow slit is not the passing by electrons, but a radiation due to inverse photoelectric eﬀect of valence electrons in the stationary structure of the edge of the hole. Here we consider only central-axial ﬂight of electrons via a narrow slit (of the width < 0.2 µm) which generates quanta of light with the energy ∆E12. If with the aid of external electrodes inside a wider slit (> 2 µm) to create a ﬁeld with the same retardation potential ϕ = ∆E12 then despite of the same slowing down in it of central-axial ﬂying by electrons there will be observed no emission of light quanta with the energy ∆E12. This enables us to interpret in a diﬀerent way the mechanism of induced radiation of matter under quantum transitions in it of particles. It looks such that the ﬂying by electrons excites around themselves spherical zones of nonlinearity with radius ∼ 0.2 µm. The orbitals (with energies E1 and E2 < E1) of stationary valence electrons in the edge of the narrow oriﬁce (of the width < 0.2 µm), falling in these zones, in accord with the Ritz combination rule gives from the diﬀerence of terms ν1 = E1/h and ν2 = E2/h the observed in experiments monochromatic radiation of the frequency ν12 = ν1 − ν2. The passing of center-axial electrons via a wider gaps (> 2 µm) is not aﬀected by the nonlinearity zones of the orbitals of stationary valence electrons in the edge of the slit. Thence, despite of the dragging by the external ﬁeld of the diaphragm ϕ = ∆E12 in this case the ﬂying by electrons does not radiate at the frequency ν12 = ∆E12/h.
PACS numbers: 41.60.-m, 78.70.-g Keywords: electron bremsstrahlung, narrow slits, inverse photoelectric eﬀect, quantum transitions

1. CONVENTIONAL INTERPRETATION OF A PARTICLE’S QUANTUM TRANSITION

The micro-model, which treats the transition of an elementary particle from a stationary energy level E1 to a lower level E2, assumes that it is this particle that emits an electromagnetic (light) quantum of the energy ∆E12 = E1 − E2 and frequency [1]:

ν12 = (E1 − E2)/h = ∆E12/h.

(1)

However, there is no deﬁnite evidences that (1) is the radiation law of the very moving particle. Here we consider the radiation that arises when a preliminary accelerated particle uniformly moves towards a narrow slit in an opaque screen where it is hampered. The source of radiation in this scheme of macro-level observation is still the question of debate. Some believe that these are the ﬂying by electrons themselves that radiate in the course of their slowing down in the narrow slit. Others associate this radiation with the electrons of the material that the border of the slit is made of which are supposedly excited due to retardation of ﬂying by electrons [2]. There is especially emphasized in [2] that, by the logic of implementing action (1), a steadily moving particles does not radiate, while in case of ﬂight through narrow slits with the uniform velocity (VV−C = const)> c/n there arises a (Vavilov-Cherenkov) radiation. In the experiments performed by me with softer electrons (V1 VV−C) the conditions are speciﬁed when the source of the bremsstrahlung with the frequency ν12 incited by the center-axial ﬂying by electrons in narrow gaps (with width < 0.2 µm) is the inverse photo eﬀect of valence electrons of gap’s edge. Basing on the fact of the absence of the radiation with the frequency ν12 in the center-axial passing of the electrons through the slits wider than 2 µm there is suggested a nonconventional [3] interpretation of the processes of any emission arising in the ”nearby“ zone of a retarded, uniform or accelerated motion of an elementary particle.

∗Electronic address: e-mail: demjanov@nsma.ru

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2. RESULTS OF EXPERIMENTS

Early in 1970s, making experiments on scattering soft electrons with energies 0.3 ÷ 100 eV at narrow gaps [3], I disclosed an eﬀect by which in the central-axial ﬂight of electrons in the narrow slit the source of radiation appeared to be not the passing electrons themselves but the electrons of the atomic structure of the slit’s border. The idea of the experiment is presented at Fig.1.
A speeded up to the energy E1 electron moves in the laboratory vacuum with a uniform velocity V1 = const. When passing through a narrow slit with electrodes at the inlet and outlet, forming a two-electrode brake diaphragm (BD), the electron can lose (or gain, for a reverse potential at the electrode diaphragm) a part of the kinetic energy (up to level E2 < E1). Further on, it continues to move with a reduced (or increased) uniform velocity V2 = const to the viewing screen S. Matrix of semiconductor sensors (MSS) records the density distribution of the arrival of electrons to the plane of the screen. The speeds V1 and V2 were monitored by direct measurements of the ratio ∆Xi/∆ti (see Fig.1a), in which the interval ∆ti with measurement bases 0.2 ≤ ∆Xi ≤ 2 m has had the nanosecond scale (10 ≤ ∆ti ≤ 80 ns) with the resolution ∼ 5 ns.
In the experiments reported the attention is focused at two reasons why electrons may be slowed down in passing through narrow slits provided with a pair of electrodes of a brake diaphragm (BD) at the entry and exit (see Fig.1a). The ﬁrst reason is related with the retarding potential at electrodes of BD which is controlled in the experiment . The second reason is concerned with an electrodynamic interaction of a passing electron with the borders of the transit slit, and its consequences will be only the slowing down response. However, it became clear that with the accelerating potential at BD there are implemented modes of ﬂight both with the acceleration and slowing down depending on the width of the gap (see below).
Observing a positive diﬀerence V1 − V2 in velocities (i.e. the positive energy diﬀerence E1 − E2) after the passing by each electron the zone BD, the process of slowing down can be regarded as a quantum transition from level E1 to a lower level E2. Modern quantum theory holds that such a ”braking“ process (when E2 < E1) is always associated with the emission of a photon with frequency ν12 = (E1 − E2)/h. As might be expected, I registered in the opening of the slit the emission of light pulses having the frequency ν12 deﬁned by (1). Light’s pulses were recorded at the exit of the aperture of the narrow opening by means of the semiconductor photo-sensor (PS, Fig.1a), which was located at a distance of 10 µm from the edge of the outlet of BD and was connected to an ampliﬁer of photo-pulses (APP). However, an interesting thing was found. In the case of electrons passing through center of the slit (i.e. in the absence of a mechanical contact of the electron with the edge of the slit) at one and the same diﬀerence of brake energies E1 − E2 light pulses in the exit of the aperture arose only for very narrow slits (δX < 0.2 µm) and were absent in case of wide slits (δX > 2 µm).
Using this scheme special observations were carried out of only those light ﬂashes which arose from the electrons passed through the center of the slit depending on the width of the gap in the screen of BD and axial length δX of the slit’s tunnel (i.e. depending on the thickness of the right by Fig.1a electrode of BD). In the experiments there were taken all available in these years measures in order to identify the coupling of the excitations of brake photo pulses of frequency (1) especially with the electrons ﬂying along the central axis and thus having no mechanical core contact with the border of the slit. This relation was determined in particular by monitoring simultaneous emergence of pulses at the selector of central-axial electrons (SCAE) coming from the matrix of semiconductor sensors (MSS) and ampliﬁer of photo-pulses (APP) to the electronic coincidence circuit with the resolution ∼ 5 ns.
Thus, passing of electrons through the center of a “wide” slit (2 µm < δX < 50 µm, Fig.1c) in the range of braking potentials 1 < ∆E12 < 100 eV at BD exhibited no radiation from the aperture of the slit. In this event, it can be seen that electrons spend for travel in the braking zone BD the time 10−12s ≤ τslit ≤ 10−14s, losing the speed V1 − V2 = ∆V12 and, respectively, the energy E2 < E1 in the range 1 eV< (V12 − V22) · m/2 < 100 eV. On the other side, in the course of the central axial passage of electrons via narrow slits (δX ≤ 0.2 µm, Fig.1b) light pulses of the bremsstrahlung are always registered by the SCAE apparatus, what is more, they occur not only when there is a braking potential on the plates of the capacitor BD (| − Ubrake| = 0, Fig.1а), but also when it is absent (Ubrake = 0). While in the latter case the central-axial passage of electrons should take place with a constant speed. But even if we will reverse the sign of the braking potential (+Ubrake = 0), when the central-axial electrons should be accelerated (i.e. they do not radiate but absorb light quanta), the SCAE apparatus registers from the aperture of narrow slits (with critical radius rcrit ≤ 0.2 µm, Fig.1b) the same output of the pulses of light radiation of spectral composition (1) as in the case (Ubrake = 0).
In these experiments I was able to discover an interesting empirical regularity. Looking after photo-pulses at the exit hole of BD by means of the SCAE apparatus (see Fig.1a), I have found the disappearance of the radiation from the aperture of the outlet with the critical radius rcrit ∼ 0.2 µm at the axial lengths δXcrit of the slit’s tunnel getting longer of the following critical value:

δXcrit ≤ rcritE1/∆Ephotoeffect,

(2)

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Рис. 1: The scheme of passing soft electrons (a) in the experiment with narrow slits, formed by the holes in the right-hand electrode of brake diaphragm (BD). This electrode, with δX as its thickness, performs three function: 1) the slit with a variable (from 0.05 microns to 10 microns) distance rbord. between its boundaries; 2) the “spectrum analyzer” of emitted photo-pulses due to the inverse photoelectric eﬀect; 3) the plate of the capacitor of BD of retarding ﬁeld in the gap ∆X. The following abbreviations are used: APP − ampliﬁer of photo-pulses from photo-sensor (PS), SCAE − selector of central axial electrons registered by the sensor of electrons in the from of the matrix of photo-diodes (MPD). Energies of the nonlinearity zones around of the electrons: • − 2 ÷ 3 eV; • − 3 ÷ 5 eV; • − 5 ÷ 8 eV revealed by the right electrode of BD made, respectively, of CsAu, Ce, Ni. At insets b) and c) are shown two modes of observation; − the occurrence of electromagnetic radiation when passing of electrons ev1 through the center of “narrow” (b) slits (the width < 0.2 µm) in the opaque screen with BD (the electron does not touch the edges of the slit by the kernel of his dense body, but acts at it only by the high energy zone of his nonlinear Coulomb ﬁeld, lowering thus own velocity by ∆V = V1 − V2); − the absence of electromagnetic radiation when passing of electrons ev1 via the center of “wide” slits (width 1 µm) in opaque screen; in this event the passing through the center electron does not touch the edges of the slit neither by the kernel of his body nor by the high energy zone of his nonlinear Coulomb ﬁeld, but the braking potential of the capacitor ensures the same level (∆V ) of his slowing down.
where ∆Ephotoeffect is the work of photo-emission of light quanta from the material of the hole (in the right for Fig.1a electrode). One of the consequences of (2), found in the experiments, indicates that the length of the tunnel δXcrit in BD at which there ceases the generation at the hole’s exit of photo-pulses with the spectral energy ∆Ephotoeffect, is so times greater than the found by me independently value rbord. = rcrit as the energy E1 of accelerated electrons at the entry of the hole of BD is greater than the energy ∆Ephotoeffect of registered by means of SCAE photo-pulses. Besides the growth of E1 proportionally to length δXcrit of the tunnel there was found also, that in successive changing of materials, CsAu, Ce and Ni, for the right-hand (in Fig.1a) electrode the value of rcrit decreased from ∼ 0.3 µm to ∼ 0.1 µm. These empirical regularities can be useful for further theoretical constructs of the micro-model of combination-bremsstrahlung due to the inverse photoelectric eﬀect from edges of the narrow hole contactlessly (non-mechanically) incited by the center-ﬂying electrons.
Thus the analysis of the results of these experiments testiﬁes to that in the axial ﬂight of electrons through wide

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holes (radius > 2 µm) with the decelerating ﬁeld formed by capacitor BD (see Fig.1a), despite of the retardation with the loss of the motion energy ∆E > ∆Ephotoeffect due to the braking potential | − Ubrake| = 0, they do not radiate light pulses. The questions arise, whether there is correct the conventional consideration [2], that the light is radiated by the particle itself experienced the quantum transition of bremsstrahlung and wasting the kinetic energy of motion E1(V1) to the level E2(V2) < E1(V1)? Whether the condition of light radiation from the aperture of the hole is the obligatory presence at the distances ≤ 200 nm from the passing by electron either the edge of narrow hole (as in my experiment) or of the atoms of any other substance?
3. DISCUSSION
The direct conclusion from the series of experiments thus performed is the insuﬃciency of the energy transition (“falling”) of a free electron from a high E1 to a lower E2 < E1 energy level in order that this electron was able to emit by itself a light pulse with the combinational frequency ν12 = (E1 − E2)/h. It turns out that a relatively free speeded up electron in the absence of interaction with electrons of the BD hole’s edge in the radius < 0.2 µm by itself, 0.2 µm away from the edges, does not radiate during the time of its dragging (slowing down) at the sharp ﬁeld gradient in vacuum.
Taking into account this result, the conventional view, that the slowing down the electrons is suﬃcient in order to induce their radiation, requires such a reﬁnement that another interpretation of the radiation process becomes inevitable. It is meant ﬁrst of all that the Ritz combination principle for the induced radiation is implemented neatly by (1). The point is that the diﬀerence combinations of the pairs of energies E1 and E2 in this principle requires the certainty of their magnitudes in the course of the all radiation process. According to (1), the constancy of the frequency ν12 in the course of radiation implies that during all the time period ∆t = t2 − t1 the diﬀerence ∆E12 = E1 − E2 is speciﬁed and ﬁxed.
In order that the emission of light quanta by the ﬂying electron itself occurred by the combination rule (∆E12 = E1 − E2) at a single as if anticipated mono-frequency (1) it should be exactly “known”, from the beginning t1(E1) to the end t2(E2) of the process, the energies E1 and E2 which are deterministically, but not probabilistically, associated with the body of the quantum oscillator. The very slowing down electron hardly can be a carrier of two energy states and two frequency terms ν1 = E1/h and ν2 = E2/h from which there is composed by the rule (1) the diﬀerence frequency ν12 = (E1 − E2)/h of the light quantum generated in the course of quantal transition.
The indeterminism of the problem of monic radiator has been noticed by scientist as early as in 1930ies, and since then the discussion on this subject keeps its actuality. The conventional explanation of how the particle experienced a quantum transition (falling down) from the energy level E1 to level E2 < E1 emits a quantum of light demands the explaining of an incredible phenomenon. Namely, how a closed on himself particle may “know” all the time in the course of the quantal transition the exact values of the energies E1 and E2 (in order to maintain the diﬀerence ∆E12 = E1 = E2 = const i.e. to ensure the monochromaticity of the radiation)? Since in the time of the transition it already abandoned the level E1 and, passing in the course of the retardation all the magnitudes Ei of the energy range E1 > Ei > E2, it did not yet come to level E2 and does not at all know what level it will fall at. The described above experiments have shown that a slowing down in vacuum particle (away from an interaction with other particles of the hole’s edge at the distance more than 0.2 µm as was above said) does not radiate by itself. The presence of the monochromatic retardation radiation out of the opening of narrow slits and incited by the pumping the radiation of quantum generators (with the level of monochromaticity ∆ν0.5/ν12 ∼ 10−8 ÷ 10−6 [4]) makes clear why the combination radiation (1) is implemented only when the binary combination ∆E12 = E1 = E2 = const is certainly realized. This enables me to put forward an alternative interpretation of the radiation induced in quantum transitions.
If, according to the above described experiment, the decelerated by the ﬁeld of a wide slit particle loses its energy, passing from the level E1 to level E2 < E1, but emits by itself nothing then consequently this energy is accumulated by the source of the retardation ﬁeld. When there is no retardation ﬁeld, the uniformly moving particle spends its energy for exciting (polarizing) around himself a nanometer zone of nonlinearity of ﬁne medium (physical vacuum, aether). In physical vacuum without particles the momentum and energy handed by the uniformly moving particle to nano-environment immediately are returned to it entirely and it, step by step, moves further according to conservation of its momentum.
Thus, in the course of the quantum transition there are seemingly formed around kinetically energetic particles excited nonlinearity regions of physical vacuum having radius up to ∼ 100 ÷ 200 nm. When such a particles enters to the zone of radius < 100÷200 nm of interaction of atoms with any medium, all respectable pairs of stationary particles of this medium (with energies of orbitals E1 = hν1 and E2 = hν2 occupied by valence electrons of the medium) start to take away actively the part of the energy of this polarized zone spending it on a nonlinear-combinational transformation of frequency terms ν1 and ν2. It is this combinational-transformational process that impedes the speeded up particle

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but not the presence in vacuum of a retardation ﬁeld which the uniformly moving particle is indeﬀrent to as an emitter. In the outcome, the nonlinear-combinational transformation of frequency terms by valence electrons of the medium are generated addition-subtraction combinations ν12 = ν1 ± ν2 and their harmonics [1]. Main harmonics of diﬀerence vibrations ν12 = ν1 − ν2 represent, ﬁrstly, the “implementations of Ritz combinations” and, secondly, they are the observed by us in experiments light pulses (quanta) of radiation by substances (in my experiment − due to inverse photo-eﬀect from the slit’s edge), which are incited by the combinational-transformational contactless retardation of passing by electrons in narrow slits. Supposedly, in other known means of pumping the nonlinearity of the medium take place similar processes of radiating monochromatic quanta of light generated not properly by the passing by electrons, but by the particles of stationary atoms of the medium getting into regions of nonlinearity that are excited by the retardation processes of the thrown to the upper energy valence level E1 of electrons by the "pumping".
[1] Landau L.D., Lifshitz E.M., Quantum mechanics (nonrelativistic theory) (Moscow: “Phizmatgiz”, 1963) 654 p. (in Russian). [2] Ginzburg V.L., The radiation of uniformly moving sources (Vavilov-Cherenkov eﬀects, transition radiation and some other
phenomena), UFN, v.171, No 10, p.1097 (2003) (in Russian). [3] Demjanov V.V., Aetherodynamical determinism of basic principles (Novorossiysk: NGMA, 2004) 568 p. (in Russian).
Experiments performed in order to reveal fundamental diﬀerences between the diﬀraction and interference of waves and electrons, arXiv 1002.3880v1 (2010). [4] Tables of physical quantities, Handbook, edited by Kikoin I.K., Moscow: “Atomizdat”, 1976, p.634 (in Russian).