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Laue diffraction method of a neutron EDM search. Project of the experiment

V.V. Voronin, V.V. Fedorov, E.G. Lapin, S.Yu. Semenikhin

Annotation

New experiment "DEDM" is proposed on a search for a neutron electric dipole moment (EDM) using Laue diffraction in a crystal without a center of symmetry. The value of the strong interplanar electric field affecting the neutron diffracted in such crystal can reach 109 V/cm. The calculated sensitivity of the experiment can be better than 10-26 e · cm for really existing quartz crystal and reach 10-27 e · cm for some other noncentrosymmetric crystals.

Existence of nonzero neutron EDM requires violation of both P and T invariances, so the new experimental limits on the EDM value would be of great importance for understanding the nature of the CP violation. The experiments for the search for the neutron EDM have been carried out in a half of century, and magnetic resonance method using ultracold neutron doesn't have concurrent last 25 years. So it is very important to develop the new methods for the neutron EDM search.

The main idea of this experiment is to use the strong interplanar electric field of noncentrosymmetric crystal for the neutron EDM search [1].

It is based on the new effects which was forecasted and recently observed [2]:

  1. Existence of a strong interplanar electric field Eg (up to 109 V/cm), acting on a neutron, diffracted by a crystal without a center of symmetry, during all time the neutron spends in crystal. Experimental value of the field turned out to be equal Eg=(2.1±0.12) · 108 V/cm for (110)-plane of quartz crystal and had coincided with the theoretical one. For the case of Laue diffraction, this field results in effect of depolarization of the diffraction neutron beam [3]. So large value of electric field essentially (on 5 order of value) reduces, in comparison with the UCN method, the requirements to a degree of shielding from exterior magnetic fields for achievement of the same level of precision.
  2. Essential increase of the time of neutron stay in crystal for Bragg angles close to π/2 for the Laue diffraction case [4]. The diffracted neutrons are moving along the crystallographic planes with the mean velocity v||=v · cos ΘB v · (π/2-ΘB) for ΘB ~ π/2, which can be decreased at least by an order compared with the total neutron velocity. Measured virtual velocity of neutron passage thought the quartz crystal for angle of diffraction equal to 87o was equal to (40±1) m/s (velocity of an incident neutron was 808 m/s), and corresponding time of neutron stay in crystal was (0.90±0.02) ms.

Thus, the value Eτ determining the sensitivity of a method to neutron EDM in our case can be 0.2 · 106 V s/cm.


The comparison with the UCN-method:


UCN method1) Laue diffraction method
E (kV/cm) 4.5 2.2 · 105
τ (c) 130 (v|| = 5-6 m/c) 0.9 · 10-3 (v|| = 39 m/c)
E · τ (kV c/cm) 585 200
N (neutron/c) 60 1 · 104
σD (e · cm)/day 6 · 10-25 1.5 · 10-25

1) P.G. Harris, C.A. Baker, K. Green, P. Iaydjiev, S. Ivanov, D.J.R. May, J.M. Pendlebury, D. Shiers, K.F. Smith, M. van der Grinten, P. Geltenbort. Phys. Rev. Lett. 1999, 82, 904.

Intensity of the Laue diffraction method was calculated for ILL cold neutron beam and crystal quartz 3,5x14x25 cm3 ((110) plane, Bragg angle 870).

Let us consider the physical base of the method. For the case of Laue diffraction, wave function of a neutron is a superposition of two kinds of Bloch waves ψ(1) and ψ(2), formed as a result of neutron interaction with the periodic nuclear potential of the system of crystallographic planes. For the case of noncentrosymmetric crystal, neutrons in the states ψ(1) and ψ(2) can be under influence of the strong interplanar electric fields of an opposite sign ±Eg. If the initial neutron spin is directed along neutron velocity, the Shwinger magnetic field ±HgS = 1 / c · [Eg x v] acting on the neutron will rotate the spin of states ψ(1) and ψ(2) in opposite directions, that results in a depolarization of the diffracted neutron beam. For plane (110) of quartz and crystal thickness 35mm the polarization of diffraction neutron beam becomes equal to zero. The preliminary measuring gives us a value about a few percent, while the initial polarization was about 90%. The presence of EDM gives in appearance of a component of polarization along HgS:

where D is a neutron EDM in 10-25 e · cm, τ - time of neutron stay in crystal, quantitative estimation is made for plane (110) of quartz L=35mm, ΘB = 870 (tg ΘB=20).

The polarization due to neutron EDM PZ, marked by green, will have the different sign for two crystal positions marked by blue and red in a picture, while residual polarization has the same sign. So the difference of the Z component of polarization for blue and red crystal positions is a neutron EDM. It is necessary to note that feature of the setup is a low sensitivity to changing of an exterior magnetic field, because all the components of the vector of neutron beam polarization after the crystal are close to zero and its rotation by an external magnetic field does not change the measured values, also zero final polarization essentially reduces the sensitivity of the experimental setup to the direction and efficiency of polarization analysis.

Scheme of the proposed experimental is similar with the one for the 3-D spin analysis and is shown in the following picture:

The calculation have shown, that the statistical sensitivity of the experiment for the cold neutron beam of ILL reactor and really existing quartz crystal (250x140x35 mm3) are ~1 · 10-25 e · cm/day.

There are two main false effects which can simulate the neutron EDM and lead to the systematic errors:
  • The time dependence of the incident neutron spin orientation and its correlation with the crystal position;
  • Difference of the two channels of the polarization analysis (red and blue).
To eliminate these effects it is proposed the next:
  • To equip the setup by the system of polarization analysis and registration of the direct non-diffracted neutron beam D0. In fact, it will be a neutron on-line "magnetometer" and its sensitivity is much higher, than precision of the main experiment due to greater intensity of the direct neutron beam than the diffracted one. Flipping of polarization of direct and diffracted neutron beams occurs at the same time by the π-flipper.
  • As it was shown in the preliminary experiment, the direct diffraction beam consists of not only (110)-reflection but also of a few other reflections with the zero electric field [24]. It is proposed to use this background reflection as "zero" experiment, i.e. as on-line test of identity of two channels of the polarization analysis. For this purpose, the setup is equipped by the system of monochromators. The first pair of monochromators (M1, M2) selects (110)-reflection (angle Θ1, λ ≈ 4.8 Å), the second (M3, M4) - (101)-reflection (angle Θ1, λ ≈ 4.8 Å).

The preliminary calculation has shown that the nonuniformity of the direction and efficiency of polarization analysis over the neutron beams on the level ~10-3 can result in a systematic uncertainties corresponding to neutron EDM about 10-27 e · cm. In more detail of the experiment see [5].

Parameters of the some noncentrosymmetric crystals suitable for neutron EDM search

Crystal Symmetry group hkl d, (Å) Eg,109 V/cm τa, ms Eg · τa, (kV · s/cm)
α-quartz (SiO2) 32(D63) 111 2.236 0.23 1.0 230
110 2.457 0.20
220
Bi12GeO20 I23 433 1.739 0.52 0.9 468
312 2.711 0.24
216
BaTiO3 4mm 004 1.008 0.96 0.03 30
002 2.016 0.57
17
PbTiO3 4mm 41-1 0.923 1.78 0.03 53
002 2.075 1.42
43
BeO 6mm 011 2.06 0.54 7.0 3700
201 1.13 0.65
4500
LiTaO3 3m -444 1.061 1.38 0.003 4
006 2.297 0.92
3


View of the DEDM setup


View of the DEDM setup

Unit of the crystal


Unit of the crystal (DEDM setup)

References:


  1. V.V. Fedorov, V.V. Voronin, E.G. Lapin, O.I. Sumbaev. Physica B, 1997, 234-236, 8-9.
  2. V.V. Fedorov, E.G. Lapin, S.Yu. Semenikhin, V.V. Voronin. Physica B, 2001, 297 (1-4), 293-298.
  3. V.V. Voronin, E.G. Lapin, S.Yu. Semenikhin, V.V. Fedorov, JETP Letters, 2000, 72, (N.6), 308-311.
  4. V.V. Voronin, E.G. Lapin, S.Yu. Semenikhin, V.V. Fedorov, JETP Letters, 2000, 71 (2), 76-79.
  5. V.V. Fedorov, E.G. Lapin, S.Yu. Semenikhin, V.V. Voronin, Preprint PNPI-2451, Gatchina, 2001, 26.








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