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ЯДЕРНАЯ ФИЗИКА
DOI: 10.5862/JPM.237.6 UDC 539.125.5
Yu.P. Braginetz12, Ya.A. BerdnikovV.V. Fedorov1, I.A. Kuznetsov2, M.V. LasitsaL2, S.Yu. Semenikhin2, E.O. VezhlevL2, V.V. Voronin12
1 Peter the Great St. Petersburg Polytechnic University 2 Petersburg Nuclear Physics Institute
CRYSTAL ACCELERATION EFFECT FOR COLD NEUTRONS IN THE VICINITY OF THE BRAGG RESONANCE
A new mechanism of neutron acceleration is studied experimentally in detail for cold neutrons passing through the accelerated perfect crystal with the energies close to the Bragg one. The effect arises due to the following reason. The crystal refraction index (neutron-crystal interaction potential) for neutron in the vicinity of the Bragg resonance sharply depends on the parameter of deviation from the exact Bragg condition, i.e. on the crystal-neutron relative velocity. Therefore the neutrons enter into accelerated crystal with one neutron-crystal interaction potential and exit with the other potential. Neutron kinetic energy cannot vary inside the crystal due to its homogeneity. So after passage through such a crystal neutrons will be accelerated or decelerated because of the different energy change at the entrance and exit crystal boundaries.
NEUTRON ACCELERATION, PERFECT CRYSTAL, NEUTRON DIFFRACTION, ACCELERATED CRYSTAL.
1. Introduction
The possibility to control the energy of neutron beams is of great interest because
of the wide neutron applications in various
scientific fields from material science to nuclear physics, particle physics and astrophysics. The acceleration effect for neutrons scattered by exited isomeric nuclei was first predicted in 1959 [1] and was discovered experimentally in 1980 [2, 3]. The acceleration of neutrons in an inversely populated medium [4, 5] turned out to be very important in processes of stellar nucleosynthesis. In Ref. [6] acceleration of neutrons by vibrationally excited nitrogen molecules was observed.
Acceleration of neutrons in the uniform magnetic field by means of radio-frequency flipper is well-known and successfully used in physical experiments (see, e.g., Ref. [7]). The
phenomenon of neutron acceleration in a strong alternating magnetic field (of amplitude ~ 0.4 T) was observed in Ref. [8]. The acceleration of neutrons in a weak alternating magnetic field (of 0.1—1.0 mT) was measured using anomalous behaviour of the velocity dispersion for neutrons, moving in a crystal close to the Bragg directions [9]. The foundations of the neutron acceleration in a laser radiation field were considered in Ref. [10].
Also acceleration and deceleration of neutrons by reflection from moving mirror [11, 12] or by Doppler-shifted Bragg diffraction from a moving crystal [13, 14] are well-known and used in experiments with ultracold neutrons.
Recently a new interest has arised in the acceleration of neutrons, passing through accelerating media [15, 16]. This effect was first observed by the authors of Ref. [17] and was described in detail in Ref. [18]. It was noted in
Ref. [18] that "the observed effect was a manifestation of quite a general phenomenon — the accelerated medium effect (AME) inherent to waves and particles of different nature". In Ref. [19], the acceleration and deceleration of neutrons were observed by applying a specific time-of-flight method. In Ref. [20], some new special features of the effect for a birefringent medium were discussed with the applications to neutron spin optics and evolution of flavor states of neutrino, propagating through a free space. The acceleration of the samples in the mentioned experiments reached several tens of g units, and the value of the energy transfer AEn to a neutron with energy En
(AEn * 2(Av/Vn)En[(1 - n)/n])
fell within the range of (2-6)-10-10 eV [18] for ultracold neutrons (UCN), so up to now AME was observed only for UCN and by only one research group (see Refs. [18, 20]). Here vn is a neutron velosity, Av is a value of a relative neutron-matter velocity variation during the neutron time-of-flight through the sample, n is the refraction index for a neutron.
In the present paper, a new much more effective mechanism of acceleration effect is proposed [21], which has been tested and confirmed experimentally for cold neutrons passing through the accelerated perfect crystal. An energy transfer to a neutron in this case can be at the level of ~ 4-10-8 eV. This value in contrast to AME is determined by the amplitude Vg of the corresponding harmonic of the nuclear neutron-crystal periodic potential, but not by the value of a relative neutron-crystal velocity variation during the neutron time-of-flight through the crystal. For a cold neutron
[(1 - n)/n] * V0 / 2En ,
so AME in our case has an order
AEn * (Av/vn) V ~ 10-5, V0 ~ 10-13 eV
that is negligible in further consideration (V0 is zero harmonic of neutron-crystal interaction potential, i.e. averaged crystal potential).
The essence of the crystal acceleration effect is as follows. The crystal refraction index for neutrons in the vicinity of the Bragg resonance sharply depends on the crystal-neutron relative velocity (see further). The neutrons enter into
accelerated crystal with one potential of a neutron-crystal interaction and exit with the other potential, so the kinetic energy change at the crystal boundaries will differ, and neutrons will be accelerated or decelerated after passage through such a crystal, in this case the energy transfer to a neutron being at the level of ~ 4-10-8 eV.
Neutron wave function significantly modifies for neutrons moving through the crystal under conditions close to the Bragg ones. As a result neutrons concentrate on "nuclear" planes or between them [22, 23]. We take the term "nuclear" planes to mean the positions of maxima of periodic nuclear potential for corresponding system of crystallographic planes. The neutron-crystal interaction potential can be written as a sum (the reciprocal lattice vectors expansion) of harmonic potentials (harmonics) corresponding to all nuclear plane systems described by reciprocal lattice vector g normal to the given plane system, |g| = 2%/d (d is an interplanar distance):
V(r) = Yy/gx = V, + !2Vg cos(gr + <Pg). (1)
g g >0
Here Vg are the amplitudes of g-harmonics of the crystal nuclear potential, which are determined by neutron scattering amplitudes for crystal elementary cell (structural amplitudes). In general, Vg are complex values,
i.e. V = v exp m .
g g g
However, if the crystal is nonabsorbing and centrosymmetric, one can make all phases vanish at once, i.e. make all Vg real, putting the coordinate origin at the centre of symmetry. When neutron is moving through the crystal under conditions close to the Bragg ones for a plane system g, only one harmonic with amplitude Vg will be essential and should be taken into account. That is due to a very narrow width of the Bragg reflection of neutrons. For one harmonic, the origin of coordinates can be always placed at its maximum making Vg amplitude real. Just the same we can make with the crystal electric potential. So for centrosymmetric crystals the positions of «nuclear» and «electric» planes always coincide.
But if the center of symmetry is absent the maxima of electric potential for some
crystallographic planes will be shifted relative to the nuclear maxima. That will lead to gigantic electric fields, acting on the neutron inside the crystal [23—25], because the neutrons concentrate in the vicinities of the maxima and minima of nuclear potential where electric field is just nonzero in this case. So the whole class of new neutron optics phenomena arises (see, for example,Ref. [26]).
2. Neutron crystal optics
Interest in neutron optics in the perfect crystals has quickened in the past few years. It is caused first by new outstanding possibilities for studies of neutron fundamental properties and its interactions. The case in point is, for instance, a search for a neutron electric dipole moment, as well as a search for CP-violating pseudomagnetic forces due to exchange of a pseudoscalar axion-like particle, using neutron optics in the crystals [27—32]; these are now the most important tasks.
The admixture of the waves reflected by crystallographic planes to the neutron wave function significantly changes the pattern of neutron propagation in the crystal and leads to new phenomena, which manifest sharply defined resonance character with the Bragg (Darvin) width. For example, a small change of the neutron energy within this width (AE/E ~ 10-5 for thermal and cold neutrons) results in significant changing the neutron mean velocity in the crystal (the anomalous velocity dispersion), and so the sharp energy dependence of the neutron-traveltime through the crystal on neutron energy exhibits [33].
In the present paper we discuss one more phenomenon related to the change in the neutron wave function in the crystal, namely the resonant behavior of the neutron refractive index (i.e. kinetic energy of the neutron inside the crystal) depending on the difference of the initial and the Bragg neutron energies. If a neutron passes through the non-absorbing perfect crystal and Bragg conditions are not satisfied for any crystallographic planes, the neutron propagation through the crystal can be described by refractive index, which depends on the V0 amplitude of zero harmonic (average crystal potential). In this article, by a perfect crystal it is meant the crystal with the dispersion
of the interplanar distance much less than the intrinsic width of the Bragg reflection. But when the energy or velocity direction of a neutron approaches the Bragg values, the waves reflected by the corresponding plane system start arising. The amplitudes of these waves are determined by the corresponding Vg amplitudes of potential harmonics and by the deviations from the exact Bragg condition. When this deviation being more than the harmonic amplitude we can use the perturbation theory [28, 34]. In this case if the neutron has an initial energy equal to E0 and the wave vector k0 (E0 = Ak0/2m), its wave function inside the crystal will be written as
e,kr +
V.
_'k„r
Ek - EK
= e
1 - — e'gr AB
(2)
where
AbB - Ekg)/Vg =2(Ek - EB)/Vg
is the dimensionless parameter of deviation from the exact Bragg condition for some g system of planes; k, kg = k + g are the wave vectors of incident and reflected waves inside the crystal with the mean refraction index taken into account; Ek and Ek are the unperturbed neutron kinetic energies' in states | k) and
lk g X
Ek =
h2k2 /2m = h2k2 / 2m - V0, Ek = h2k/2m;
EB = g2 /(8m sin2 9B)
is the neutron energy that corresponds to exact Bragg condition. The presence of reflected wave with the amplitude equal to 1/AB leads to localization of neutron density in the crystal on (or between) reflecting planes depending on the sign of AB :
| r) |2= 1 - -^cos(gr). (3)
AB
The concentration of neutron density in the vicinity of maxima or minima of nuclear potential, as in the case of Laue diffraction, leads to additional changing the neutron kinetic energy Ek and, respectively, the value of the wave vector and the refractive index n inside the crystal depending on the magnitude of this concentration, i.e. on deviation parameter AB from the Bragg condition. Notice that the
neutron refraction index n is determined as usual:
n2 = 1 - Ek / E0.
Averaging the potential over the wave function (2), using (3), one gets
h2k2 1 EE = w * = E - y + v _ (4)
E 2m E Vo +^ AB' (4)
The last term in Eq. (4) increases infinitely approaching the Bragg condition (Ek = Ek ), so it becomes incorrect (and the perturbation theory is inapplicable as well) already for
E, - \ ~ y,'
The precise fulfilment of the Bragg condition
Ek - Ekg = 0
means the equality of energies for two neutron states with momenta Wk and h( k + g), i.e. the neutron energy level Ek becomes doubly degenerated. Amplitudes of these neutron states become comparable in value, and one should solve well-known two-level problem that corresponds to the two-wave approximation of the dynamic diffraction theory. The result is the following. Neutrons with the energies within Bragg (Darwin) width |Ek — EB| < Vg/2 cannot penetrate into the working K3 crystal (Fig. 1), they will completely reflect from the crystal entrance face which is parallel to the crystal-lographic planes. So only the neutrons with |Ek — EB| >y/2 (AB > 1) can pass through this crystal and can be accelerated. Using expansion of the exact two wave dispersion equation over 1/AB one can get the following result for the kinetic energy of neutron after its entrance into the crystal:
E - К + Vg
Д2 +1
(5)
The last term in Eq.(5) describes the additional potential neutron energy due to neutron localization. It significantly changes with small variation of neutron energy within the Bragg reflection width AB = 1, i.e. in the narrow energy range
EB - Vs < Ek < EB + Vg.
For thermal and cold neutrons
Vg / Eb = 10-5. The V amplitude value itself is comparable to that of the mean crystal potential V0. Hence changing the incident neutron energy in the vicinity of Eb, one can observe a well-defined resonance-type energy dependence of the neutron refraction index in the crystal. For example, for (110) plane of quartz Vg =4 • 10-8eV, V0 = 10-7eV and Eb = = 3.2 • 10-3eV for diffraction angle close to n/2.
It is worth to notice that in our case the Eq. (4) can also be quite good approximation, the infinities can be removed by overaging over neutron spectrum within AB ~ 2, because it is formed by two crystals K1 and K2. When AB = 0 for the central part of the spectrum only the left and the right wings, having opposite potentials connected with the neutron concentration, can penetrate to the crystal so that averaged potential for this neutrons will be zero as in accordance with Eq. (5).
3. Experimental setup
Our experiment was carried out at the horizontal neutron beam of the WWR-M reactor (PNPI, Gatchina, Leningrad Region, Russia). The energy change of a neutron passed through the accelerating crystal near to the Bragg condition was measured.
If a neutron moves through the accelerating crystal, then the parameter of deviation from the Bragg condition and correspondingly the mean potential of neutron-crystal interaction will be time-dependent (see Eq. (5)). As a result, the refractive index will vary during a neutron travel in the crystal. Correspondingly the changes in the neutron kinetic energies at the entrance and the exit surfaces of the crystal will differ. Therefore, one should observe either acceleration or deceleration of the neutron passing through such a crystal, because the kinetic energy Ek of the neutron inside the crystal does not change because of the crystal homogeneity. It should be noticed that it does not matter in which way a change in the parameter of deviation from the Bragg condition occurs over a time interval of the neutron propagation through the crystal. For example, instead of variation of the relative neutron-crystal velocity one can vary the crystal temperature or deform the crystal by squeezing.
Fig. 1. Scheme of the experimental setup:
K1 is the monochromator; K2 is the crystal-analyzer; K3 is the working crystal; PG are the mosaic crystals of pyrolytic graphite; T1, T2, T3 are the crystal temperatures; n is the neutron beam; (002), (110) are the reflecting planes; v(t) is the time-dependent speed of crystal K3; D is a neutron detector inside a neutron shield S
Both actions will cause a change in the crystal interplanar dimensions and so to the shift of the Bragg energy. The crystal movement was chosen due to the convenience of its realization (the above-mentioned accelerated medium effect [18] is negligible in this case). Numerical estimations show that for the quartz crystal plane (110) the Bragg width in the neutronvelocity units is equal to AvB = 9 mm / s, i.e. if the crystal velocity changes by 9 mm/s over the time interval of neutron transit through the crystal, the deviation from the Bragg condition will vary by one Bragg width.
The scheme of our experimental setup is shown in Fig. 1. Preselected neutron beam (the beam size is about 3^1 cm), reflected by the mosaic crystal of pyrolytic graphite (PG) with reflecting plane (002), falls on the monochromator K1 made from perfect quartz crystal. Reflected by K1 highly monoenergetic (within Darwin width) neutrons pass through the working crystal K3 (the size is 5^5^10 cm) and then are reflected by the crystal-analyzer K2. The second PG crystal redirects these reflected neutrons to the detector. The quartz crystals K1, K and K3 with the same working reflecting planes (110) were arranged to have
their plane orientations in the parallel directions. The diffraction angle was close to the right one: 0B= 89° (k « 4.9 A). Scanning over the Bragg wave length performed by varying temperature difference T21 = T2 — T1 between crystals K and K1, the temperature T3 of the crystal K3 being a reference one. An example of a scanning curve is shown in Fig. 2, when the crystal K3 is absent. We have scanned the shape of neutron reflex from the K1 crystal changing T21 and so the relative interplanar distance for the K crystal-analyzer. The width of this convolution scanning curve is close to that calculated (solid line) for two perfect crystals.
There was a possibility to vary the temperature of the crystal K3 and so its interplanar distance too. Also we could move it in the direction parallel to the reciprocal lattice vector g for the working plane. To carry out an experiment, the crystal was set in harmonic motion by a piezoelectric motor. The frequency of crystal vibration was vc = 4.5 kHz and the period tc = 222 (is. Vibration amplitude reached a value of 0.15 (m. The crystal length was L = 5 cm and neutron time-of-flight through the crystal was Tn = 62 (s that was about a quarter of the crystal vibration period.
N, 1/s
o-l----,--,--.-,
-4 -2 0 2 4
T2V K
Fig. 2.The experimental (symbols) and the calculated (solid line) two-crystal reflection curves.
They reach their maxima when interplanar distances for K1 and K2 crystals (see Fig. 1) coincide (T21 = T2 — Tl = 0); N is the neutron intensity. The width W(in Kelvin) corresponds to Ad/d = 1.8-10-5
(in d units of the interplanar distance)
If the speed of the working crystal K3 depends on time as
v(t) = v0 • sin ra t, (6)
the deviation from the Bragg condition for neutrons moving through that crystal will also depend on time in the same way:
Ab(t ) = A Bo + 4 — |B v(t), (7)
0 vn Vg
where vn is the speed of incident neutrons, A is the deviation from the Bragg condition
Bo
for resting crystal at v(t) = 0. This deviation A is determined by the T difference of
B0 13
temperatures (interplanar distances) between K1 and K3 crystals T13 = T1 — T3. So further we will use this temperature difference T13 as a parameter of deviation from the Bragg condition for neutrons passing the resting K3 crystal. The relationship between parameters A and T, is
B0 13
given by the expression
EB
g
(8)
where aL = 1.3 -10
is the linear thermal expansion coefficient for a quartz crystal in the direction perpendicular to crystallographic planes.
The effect of the neutron energy change
after passing through the crystal boundaries is determined by variation of the crystal velocity and so the averaged potential (5) is done during the neutron time-of-flight through the accelerated crystal:
AE (O = Vg
AB(t2)
AB(ti)
AB&) + 1 AB(ti) + 1
1 - A2
4EB
(9)
(1 + A B„)2
Av(to),
where Av(t0) = v(t0) - v(t0 + Tn); t0 is the entry time of the neutron into the crystal, Tn is the neutron time-of-flight through the crystal. Notice once more that the neutron kinetic energy (wave vectors) inside the crystal cannot change because of homogeneity of the averaged crystal potential.
The change (9) of neutron energy (as well as the wavelength) after accelerated crystal results in a shift of the scanning-curve maximum (see Fig. 2). This maximum will be found for some other temperature difference T21 of the K2 and K1 crystals. Such variations of the scanning curve, depending on temperature and movement of the K3 crystal, were studied to find how the crystal acceleration effects. Time-of-flight technique was used for this purpose.
n
The main systematic error of this experiment associates with the dependence of the neutron transmission through the K3 crystal on the deviation from the Bragg condition in this crystal, that results in the spectrum distortion for neutrons passed through the crystal. Therefore, the position and the shape of the scanning curve can change for neutrons passed even through the resting K3 crystal, when the acceleration effect is absent. Examples of the neutron intensity distribution over the wavelength after such passage through the resting K3 crystal with different deviations T31 from the Bragg condition are shown in Fig. 3. It is evident that both intensity of transmitted neutrons and maximum position of the scanning curve can change in different ways. In particular, for T31 = 0 K the neutrons after reflection from K1 crystal cannot penetrate into K3 crystal. They will be completely reflected (due to the exact Bragg condition) and cannot reach the K2 crystal. So the last will reflect only background neutrons. In the other case, for T31 >> 5 K, crystal behaves as a homogeneous medium and practically does not distort the spectrum. In an intermediate case, the spectrum
will be distorted, because the neutron K3 crystal reflectivity (and so its transmittance) sharply depends on the neutron wavelength.
However, unlike the sought crystal acceleration effect (9), the curve distortion is determined only by the deviation from the exact Bragg condition at the entry time t0 of neutron to crystal, but not by variation of the deviation during the time-of-flight through the crystal.
So the position Es(t0) of the maximum and the maximum intensity N(t0) of the scanning curve (see Fig. 2) in the absence of the crystal acceleration effect will be some functions of deviation AB(t0), depending on the crystal speed v(t0) :
Es (to) = F (Ab(to)), (10)
N (to) = G (Ab(to)).
(11)
For further consideration and comparison with the experimental results expressions (10) and (11) can be expanded by Taylor series over v(t0) about the point v(t0) = 0 (i.e. AB (t0) = AB). Taking into account that the crystal spee0 d was significantly less than the
M 1/s
ou -25 4 \
2015 I ? J
f' J fi ' V3 \ V
10 u 1 VM ■ M \ » v * A 1
R d / ; i Ot
n i'v i/ A
r I r i r r -1
-3
-2
-1
T , K
21
Fig. 3. Two-crystal scanning curves for neutrons passed through immovable working crystal with different deviations T31 from the Bragg energy. T31, K: 0 (1), +1.5 (2), —1.5 (3), > 5 (4). The arrows
point to exact Bragg positions for K3 crystal
typical Bragg widths, it is enough to leave expansion terms up to the second order over
Es(i0) = A + B • v(t0) + C • v(t0)2, (12) N(to) = No + N1 • v(to) + N2 • v(to)2, (13)
where A, B, C, N0, N1 and N2 are the free parameters depending on AB to be found from experiment.
As it follows from Eq. (9), the crystal acceleration effect contains a term phase-shifted with respect to the false effect (12) by the value of raxn /2. This shift is approximately equal to n/4 for our experimental conditions. Furthermore, the presence of acceleration effect does not change the intensity of the line, but gives its additional shift. Thus there is a phase shift between time dependencies of Nexv (to) = N (to) and Eexp (t0) = Es (t0) + AE(t0)
that represents the crystal acceleration effect. 4. Results and discussion
An example of experimental dependence of the line positions on its maximal intensity E ( N ) is shown in Fig. 4. In the absence of
the acceleration effect it should be observed a bijection between the maximum positions and the intensities shown by a dashed line. The presence of the neutron energy change after passage through the accelerating crystal leads to dependence Eexp (Nexp) described with a closed curve like Lissajous figure, where the figure square is determined by the crystal acceleration effect. Curved arrows in Fig. 4 show the sweep direction over time. The relation between a line shift in units of the crystal temperature and a change in the neutron energy is given by the following expression:
(14)
AE
2EB • aLAT.
The splitting marked by arrows in Fig. 4 corresponds to AE = 5 neV.
Examples of the time dependencies of the scanning curve maximum position are shown in Fig. 5 for different deviations T13 from the Bragg condition. Those are the results of fitting the experimental curves under the assumption that the maximum position is determined by a sum of two effects: see formulae (12) and (9).
Dependence of the maximum value for an energy change (9) due to the acceleration effect on
E , a.u.
exp5 0.10
0.05-
0.00
-0.05 -
-0.10
Л __|2_f
■ щ s I I J ^Ябп \
\ \ ,0.0fi\ s \ r N N v П
4 \ 4 1 1 1
2000
2500
3000
3500
N , a.u.
Fig. 4.The plots of the line positions versus its maximum intensities Eex (N ). The initial deviation from the Bragg condition for the working crystal T13 = +1.5 K. Numbers inside the experimental points correspond to the channel numbers of the time spectrum. Solid curve is the result of fitting the experimental data; the dashed line indicates a bijection between the maximum positions and the intensities; curved arrows show the sweep direction over time
0.2
0.1
« 0.0
-0.1
■ / A y \ 1 J
J J-i ^ \ i vA \ \ \ i L !'■ 2 ! y, i / \ /kr>-A. \ i i i i
s V\ I ] i x / ui' 4 / / \ ■ m 1 ^ •—
- ■ 1
0 4 8 12 16
t0, a.u.
Fig. 5. The experimental dependence of the line position on the entry time t0 of neutrons into the crystal for various T13 — initial deviations from the Bragg condition; T31 , K: +1.0 (1), —1.5 (2), —2.5 (3). Horizontal axis t0 in time-of-flight (TOF) channel units. One channel is equal to 25.6 ^s
Fig. 6. The experimental (symbols) magnitude of energy variation of a neutron passed through the accelerating crystal as a function of the deviation from the Bragg condition for incident beam, and this function approximation (solid and dashed lines); measurements were carried out at two different crystal oscillation amplitudes, corresponding to v0 = 1.5 mm/s (1) and 3.0 mm/s (2)
the deviation from the neutron Bragg energy for the working crystal (temperature difference T13) is shown in Fig. 6. Measurements were carried out at two different crystal oscillation amplitudes, corresponding to v0 = 3.0 mm / s and
v0 = 1.5 mm / s (see Eq. (6)). Curves show the results of approximating the experimental points by the theoretical curve (9). Thus, one can see that the neutron energy change after passage through the accelerating crystal can reach ~20 neV.
■6 -3 0 3 6
(E^EJ/Ev It)"5
Fig. 7. The behaviour of the interaction potential E0 - Ek (see Eq. (5)) of neutrons with the crystal in the vicinity of the Bragg energy.
Calculated and reconstructed from Fig. 6 curves coincide in error limits; the curves for different v0 (v0 = 1.5 mm/s (1) and v0 = 3.0 mm/s (2)) coinside also (vertical bars show the scale of the experimental error)
The mean potential energy of a neutron-crystal interaction (see Eq. (5)) can be obtained from the experimental dependence shown in Fig. 6, because that is actually a derivative of function (5) (see Eq. (6)). One should take into account that far from the Bragg condition the correction to the mean interaction potential due to the presence of g-harmonic V tends to zero (see Eq. (4)), and so neutron refraction will be determined only by the average potential V0. The result of the interaction potential reconstruction for neutrons moving in a crystal with energies close to the Bragg one is shown in Fig. 7. It is easy to see that the relative change of the neutron energy by several units of 10-5 leads to the variation of the interaction neutron-crystal potential by ±20 %.
5. Summary
The features of refraction of a neutron wave moving in a crystal close to the Bragg condition has been studied. The energy dependence of the refractive index was shown to exhibit an evident resonance shape in the vicinity of the Bragg energy with the corresponding Bragg (Darwin) width (for thermal and cold neutrons AE / E = 10-5). The variation of the interaction potential of the neutron with the crystal in this energy range can reach about ±20 %.
The resonance behaviour of the neutron-crystal interaction potential results in one more new phenomenon. That is the neutron acceleration, which is found experimentally for neutrons passed through the accelerating perfect crystal for neutron energies, close to the Bragg one. The effect arises due to a change in the parameter of deviation from the exact Bragg condition during the neutron time-of-flight through the accelerating crystal. As a result the refraction index for neutron changes as well and so does the velocity of the outgoing neutron.
This crystal acceleration effect has been observed for the first time. One should take this phenomenon into account in precision neutron optical experiments such as mentioned above, because the neutron refraction index is determined not only by averaged crystal potential, but also by its harmonics, which have the same order of value as the average potential itself.
Acknowledgment
The authors are thankful to the staff of WWR-M reactor (PNPI, Gatchina) for efforts to maintain performance of this apparatus.
This work was supported by Ministry of Science and Education of the Russian Federation (program 3.329.2014/K).
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THE AUTHORS
BRAGINETZ Yulia P.
Peter the Great St. Petersburg Polytechnic University 29 Politechnicheskaya St., St. Petersburg, 195251, Russian Federation Petersburg Nuclear Physics Institute
Orlova Roscha, Gatchina, 188300, Leningrad Oblast, Russian Federation aiver@pnpi.spb.ru
BERDNIKOV Yaroslav A.
Peter the Great St. Petersburg Polytechnic University
29 Politechnicheskaya St., St. Petersburg, 195251, Russian Federation
berdnikov@spbstu.ru
FEDOROV Valery V.
Peter the Great St. Petersburg Polytechnic University 29 Politechnicheskaya St., St. Petersburg, 195251, Russian Federation Petersburg Nuclear Physics Institute
Orlova Roscha, Gatchina, 188300, Leningrad Oblast, Russian Federation vfedorov@pnpi.spb.ru
KUZNETSOV Igor A.
Petersburg Nuclear Physics Institute
Orlova Roscha, Gatchina, 188300, Leningrad Oblast, Russian Federation ikuz@pnpi.spb.ru
LASITSA Michael V.
Peter the Great St. Petersburg Polytechnic University 29 Politechnicheskaya St., St. Petersburg, 195251, Russian Federation Petersburg Nuclear Physics Institute
Orlova Roscha, Gatchina, 188300, Leningrad Oblast, Russian Federation mishlas1@gmail.com
SEMENIKHIN Sergey Yu.
Petersburg Nuclear Physics Institute
OrlovaRoscha, Gatchina, 188300, Leningrad Oblast, Russian Federation ssy@pnpi.spb.ru
VEZHLEV Egor O.
Peter the Great St. Petersburg Polytechnic University 29 Politechnicheskaya St., St. Petersburg, 195251, Russian Federation Petersburg Nuclear Physics Institute
Orlova Roscha, Gatchina, 188300, Leningrad Oblast, Russian Federation evezhlev@gmail.com
VORONIN Vladimir V.
Peter the Great St. Petersburg Polytechnic University 29 Politechnicheskaya St., St. Petersburg, 195251, Russian Federation Petersburg Nuclear Physics Institute
Orlova Roscha, Gatchina, 188300, Leningrad Oblast, Russian Federation vvv@pnpi.spb.ru
Брагинец Ю.П., Бердников Я.А., Федоров В.В., Кузнецов И.А., Ласица М.В., Семенихин С.Ю., Вежлев Е.О., Воронин В.В. ЭФФЕКТ УСКОРЕНИЯ ХОЛОДНЫХ НЕЙТРОНОВ В КРИСТАЛЛЕ ВБЛИЗИ БРЭГГОВСКОГО РЕЗОНАНСА.
Проведено детальное исследование нового механизма ускорения холодных нейтронов, прошедших через ускоренный совершенный кристалл с энергиями, близкими к брэгговским. Эффект возникает по следующей причине. Коэффициент преломления нейтронов в кристалле (и соответственно потенциал взаимодействия нейтрона с кристаллом) резонансно зависят от параметра отклонения от условия Брэгга, т. е. от скорости нейтрона относительно движущегося кристалла, так что нейтрон входит в ускоренный кристалл при одном значении потенциала взаимодействия, а выходит при другом. Следовательно, изменения кинетической энергии нейтрона на входной и выходной гранях кристалла будут разными. А поскольку кинетическая энергия нейтронов внутри кристалла не может измениться вследствие его однородности, то после прохождения границ кристалла нейтроны будут либо ускорившимися, либо замедлившимися.
УСКОРЕНИЕ НЕЙТРОНА, ИДЕАЛЬНЫЙ КРИСТАЛЛ, НЕЙТРОННАЯ ДИФРАКЦИЯ, УСКОРЕННЫЙ КРИСТАЛЛ.
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СВЕДЕНИЯ ОБ АВТОРАх
БРАГИНЕц Юлия Петровна — младший научный сотрудник кафедры экспериментальной ядерной физики Санкт-Петербургского политехнического университета Петра Великого; младший научный сотрудник Петербургского института ядерной физики им. Б.П. Константинова. 195251, Российская Федерация, г. Санкт-Петербург, Политехническая ул., 29 188300, Ленинградская область, Гатчина, Орлова Роща aiver@pnpi.spb.ru
БЕРДНИКОВ Ярослав Александрович — доктор физико-математических наук, заведующий кафедрой экспериментальной ядерной физики Санкт-Петербургского политехнического университета Петра Великого.
195251, Российская Федерация, г. Санкт-Петербург, Политехническая ул., 29 berdnikov@spbstu.ru
ФЕДОРОВ Валерий Васильевич — доктор физико-математических наук, главный научный сотрудник кафедры экспериментальной ядерной физики Санкт-Петербургского политехнического университета Петра Великого; заведующий лабораторией Петербургского института ядерной физики им. Б.П. Константинова.
195251, Российская Федерация, г. Санкт-Петербург, Политехническая ул., 29 188300, Ленинградская область, Гатчина, Орлова Роща vfedorov@pnpi.spb.ru
КУЗНЕцОВ Игорь Алексеевич — кандидат физико-математических наук, старший научный сотрудник Петербургского института ядерной физики им. Б.П. Константинова. 188300, Ленинградская область, Гатчина, Орлова Роща ikuz@pnpi.spb.ru
ЛАСИцА Михаил Владимирович — лаборант кафедры экспериментальной ядерной физики Санкт-Петербургского политехнического университета Петра Великого; старший лаборант Петербургского института ядерной физики им. Б.П. Константинова.
195251, Российская Федерация, г. Санкт-Петербург, Политехническая ул., 29 188300, Ленинградская область, Гатчина, Орлова Роща mishlas1@gmail.com
СЕМЕНИХИН Сергей Юрьевич — кандидат физико-математических наук, научный сотрудник Петербургского института ядерной физики им. Б.П. Константинова.
188300, Российская Федерация, Ленинградская область, Гатчина, Орлова Роща ssy@pnpi.spb.ru
ВЕжЛЕВ Егор Олегович — кандидат физико-математических наук, старший научный сотрудник кафедры экспериментальной ядерной физики Санкт-Петербургского политехнического университета Петра Великого; младший научный сотрудник Петербургского института ядерной физики им. Б.П. Константинова.
195251, Российская Федерация, г. Санкт-Петербург, Политехническая ул., 29 188300, Ленинградская область, Гатчина, Орлова Роща evezhlev@gmail.com
ВОРОНИН Владимир Владимирович — доктор физико-математических наук, ведущий научный сотрудник кафедры экспериментальной ядерной физики Санкт-Петербургского политехнического университета Петра Великого; заместитель директора по научной работе Петербургского института ядерной физики им. Б.П. Константинова.
195251, Российская Федерация, г. Санкт-Петербург, Политехническая ул., 29
188300, Ленинградская область, Гатчина, Орлова Роща
vvv@pnpi.spb.ru
© Санкт-Петербургский политехнический университет Петра Великого, 2016
