5. Dynamical neutron diffraction and a search for the electric dipole moment of neutron
The investigations on a dynamical diffraction of neutrons both in flat, and bent perfect single crystal were beginning in the laboratory from the work of O.I.Sumbaev [82] devoted to the discussion of the possibility to use the bent crystal as the neutron interferometer in 1981. Then the idea arose to use such an interferometer for observing the gravitational effect by precise measurements and the comparison of the Pendellosung pictures for two positions of the setup. The theory of the effect was advanced (O.I.Sumbaev,V.V.Fedorov) and the method for measurement of Pendellosung fringes in a neutron dynamical diffraction was proposed (O.I.Sumbaev) and developed (V.L.Alexeev). Soon the setup (similar to the shown in Fig. 20) for researching of a dynamical diffraction of neutrons was created (E.G.Lapin, E.K.Leushkin, V.L.Rumjantsev).
Using this setup the gravitational effect was first observed as the change of the contrast of Pendellosung picture (of a form as in Fig. 21) caused by the overturn of the whole setup due to gravitational field for neutrons diffracted in a single slightly bent crystal [83].
Then the investigations have changed their direction, when it have been understood (V.V.Fedorov, O.I.Sumbaev) that a strong crystal electric field, which acts on a neutron diffracting in a crystal without a centre of symmetry (considered earlier by V.V.Fedorov), can reach values more than 108 V/cm even for usual a-quartz crystals, used in the gravitational and other crystal diffraction experiments. Such great fields arise due to the shift (for crystals without centre of symmetry) of periodic crystal nuclear potential with respect to the electric one, and because of the neutron concentration on (or between) the maxima of nuclear potential, the neutron occurs in a strong interplanar electric field (Fig. 19).
Fig. 19. The electric field arose due to the diffracting neutron concentration on (or between) the "nuclear planes" of crystal and at the same time due to relative shift of electric and nuclear potentials for crystal without centre of symmetry
Fig. 20. Scheme of the setup for observing the Pendellosung picture for different spin orientation of a neutron. F is a flipper, D is a neutron detector, M is a beam monitor
This field was first measured (V.L.Alexeev, V.V.Fedorov, E.G.Lapin, E.K.Leushkin, V.L.Rumiantsev, O.I.S umbaev, V.V.Voronin) in the experiment on dynamical diffraction of the polarized neutrons in the perfect quartz crystal (Fig. 20) via the phase shift of the Pendellosung fringes (Fig. 21) accompanying the neutron spin flip, due to the Schwinger interaction of moving neutron with the interplanar electric field [84-86]. Obtained experimental value (2.1 ± 0.12)·108 V/cm had coincided with the theoretical one.
Such fields are more than four orders of magnitude higher than those used in the most sensitive now magnetic resonance method*, using the ultra cold neutrons (UCN method). It was a natural idea to use these crystal fields for searching the neutron EDM. However the value of the field turned out to be still unsufficient to reach the sensitivity of the UCN method , which is developed now in PNPI (V.M.Lobashev, A.P.Serebrov) and by ILL group (K.F.Smith, N.Crampin, J.M.Pendlebury, N.F. Ramsey et al.).
In 1990 an idea arose (V.V.Fedorov) to use Laue diffraction of polarized neutrons for EDM measurements with Bragg angles close to 90o that would essentially increase the time, the neutron spends in crystal under the strong electric field.
Fig. 21. Pendellosung oscillations of intensity as a function of the Bragg angle. ¯ mark the opposite spin projections on some direction.Q is an angle between this direction and that of Schwinger magnetic field HSg. A) Q = 90°, B) Q = 0°. The phase shift in B corresponds to electric field equal to
E110 = (2.10 ± 0.12)·108 V/cm. The absence of effect in A gives a raw estimation for EDM
A new two crystal diffraction method was proposed for this purpose in 1990 (V.V.Fedorov, V.V.Voronin, E.G.Lapin [87]). Moreover, it was shown [87], that for Laue diffraction case the sensitivity of the method may be increased more than by an order of magnitude for Bragg angles close to the direct one and may become comparable with that of the UCN method. Also the comprehensive theoretical study of dynamical neutron diffraction was carried out and some new results were obtained. In particular the effect of neutron depolarization was predicted for symmetric Laue diffraction of polarized neutrons in the noncentrosymmetric crystal. This effect was assumed as a basis for a new (more simple than two crystal one, but having some advantage over it) method of EDM searching, called the polarization method (V.V.Fedorov, V.V.Voronin, E.G.Lapin, O.I.Sumbaev. [88,89])
* Last experimental result of searching a neutron EDM by this method Dn6.3·10-26 excm at the 90% confidence level obtained at the ILL reactor by a collaboration of PNPI and ILL groups is not much better than previous approximately equal results of these groups received separately.
But only the experimental study of the dynamical Laue diffraction of neutrons in a noncentrosymmetric crystal for Bragg angles close to 90° can answer the question on the actual sensitivity of the diffraction method to the neutron EDM. For experimental study of the mentioned diffraction phenomena some exotic scheme of the setup (see Fig. 22) using the direct diffraction beam for measurements was proposed [88,89].
Fig. 22. The neutrons inside the crystal are moving along the crystallographic planes almost perpendicular to the incidence direction (it leads in particular to the essential time delay of neutron in crystal). The spins of moving neutron for two Bloch neutron states (concentrated on and between "nuclear planes") will rotate in opposite direction under opposite fields. When the angles become equal to p/2, the both diffracted neutron beams will be depolarized entirely. For 110 plane of a-quartz that will take place at the crystal thickness L0 = 3.5 cm. The existence of EDM will lead to a slight polarization along Schwinger magnetic field
Recently in 1999 the pilot setup was created and the first experimental results were obtained (V.V.Voronin, E.G.Lapin, S.Yu.Semenikhin, V.V.Fedorov) [90-92]. As all the reflecting planes, for which the Bragg conditions are satisfied, give the contributions (see Fig. 23) into the direct diffraction beam, the time of flight method was proposed (V.V.Voronin) to select the neutrons diffracted at the necessary system of crystallographic planes. The obtained results are as follows:
Fig. 23. Example of time-of-flight spectrum of direct diffraction beam for quartz crystal (Bragg angle QB = 75° for (110) reflection). Here nt is the order number of the TOF channel. The width of the TOF channel is equal » 51.2ms. N is the number of accumulated events. The total accumulation time for the whole spectrum is 5 h. The different peaks correspond to different systems of crystallographic planes. The peak from (110) planes is visibly moving with respect to the other ones when its Bragg angle approaches 90°
Fig. 24. The time-of-flight dependence on the Bragg angle for neutrons diffracted by (110) plane of quartz crystal. A and B are the two crystal positions with the same Bragg angles but anti-parallel to each other. The value nt is a number of time channel, propor-tional to total time of flight, tL is a delay time in crystal
3. The predicted effect of depolarization of a neutron beam was first experimentally observed for the case of Laue diffraction in noncentrosymmetric a-quartz crystal [90,92]. It has been experimentally demonstrated that the effect, (and the interplanar electric field, affecting a neutron, accordingly) does not depend on the Bragg angle (see Fig. 25) and coincides with the theoretical predictions and with the results of the previous experiments. This confirms the feasibility to increase more than an order of magnitude the sensitivity of the method to neutron EDM for the angles of diffraction close to 90°. For the Bragg angle equal 87° the sensitivity of the method to neutron EDM is increased approximately twenty times as compared with 45°.
4. It is experimentally shown that the value Et that determines the sensitivity of the method to the neutron EDM in our case is »0.2·106 V·s/cm [90-92] (for Bragg angle equal to 87°), which is comparable with that of the UCN method (» 0.6·106 V·s/cm in the last ILL experiment).
Fig. 25. Dependence of the neutron spin rotation angle DFS (due to the Schwinger interaction of magnetic moment of moving neutron with the crystal electric field) on the tan-gent of the Bragg angle for (110) plane of quartz crystal with the thickness L = 3.5cm. A and B correspond to two crystal positions. These data give the estimation for EDM Dn < 10-22 excm .
Using the obtained experimental results, the project of experiment on a search for the neutron EDM by such a crystal-diffraction polarization method (DEDM) is proposed with the sensitivity »1·10-25e·cm/day. This sensitivity is obtainable for really existing a-quartz crystal. The use of other crystal with a greater electric fields can improve the sensitivity up to a level »1·10 -26e·cm/day.
