ELSEVIER Physica B241 243(1998) 130 132

A new neutron interferometric method used to measure the scattering length of silicon

A. Ioffe a'b'*, D. Jacobson c, M. Ariff, M. Vrana d, S.A. Werner c, P. Fischer a, G. Greene f, F. Mezei a

Berlin Neutron Scattering Center, Hahn-Meitner-lnstitut, Glienicker Str. I00, 14109, Berlin, Germany b St. Petersburg Nuclear PItvsies Institute, Gatchina, Lenigrad distr. 188350, Russian Federation

National Institute (?/'Standards and Teehnologv. Gaithersburg, MD, 20899, USA d Nuclear Pl~vsics Institute ( f CAS, 20568 Rez near Prague, Czech Republic'

Department c?[' Physics and Ast~vnomv, Unil~ersitv o[" Missouri-Columbia. Columbia. MO 6521 I. USA Los Alamos National Laboratol T, Los Alamos, NM. USA

Abstract

The neutron interferometry technique provides a precise and direct way to measure the coherent scattering lengths b of low-energy neutrons, but its potential accuracy has not been fully realized in past experiments due to systematic sources of error. We have used a new method, which eliminates two of the main sources of error, to measure the scattering length of silicon to an accuracy of 0.005 %. The resulting value h = 4. 1507(2) fm is in agreement with the current accepted value, but has an error limit five times lower, it' 1998 Elsevier Science B.V. All rights reserved.

Keywords: Neutron interferometry; Coherent scattering length; Silicon

1. Introduction

The coherent scattering length b is the most important parameter characterizing the scattering of low-energy neutrons by nuclei in matter. An accurate knowledge of b for different isotopes is essential for the application of neutron scattering methods in condensed matter physics [1,2] and is crucial for a number of problems of fundamental physics [3,4]. We used a new 2-independent, N1

* Correspondence author. Fax: + 49 30 8062 2523: e-mail: ioffe@hmi.de.

method [5] to measure the scattering length of Si with an improved accuracy of a factor of five over the most accurate previous measurement of Shull and Oberteuffer, who achieved an accuracy of 0.03% [6]. The basic idea of the method [5] incor- porates a LLL neutron interferometer to measure the phase shift acquired in the sample not relative to the empty beam II (as it was proposed in the non-dispersive geometry [7]) but relative to the beam with the sample placed asymmetrically (Ac ~ At:). This is achieved by the transport of the sample parallel to the interferometer blades to positions 1 and 2 (Fig. 1). This leads to the differ- ence phase shift which may be expressed in terms of

0921-4526/98/$19.00 I ' 1998 Elsevier Science B.V. All rights reserved PII S 0 9 2 1 - 4 5 2 6 ( 9 7 ) 0 0 8 6 6 - 1

A. loffe et al. /Physica B 241-243 (1998) 130 132 131

LLL Interferometer.,~ ~o~. A~

position 2 .... / ~ poNtion 1 )~--Si

.Z,', /fl \ ~ ~ shifte

5 1 - - ~ \ \ 1 1 1

3 He detectors

sample ~-" 249=

q~

248~

, , I . . . . I . . . . [ . . . . [ . . . . I ' ,

!

,/ /

¢ /

/

'1 . . . . I . . . . I . . . . I . . . . I ' -1 0 1 2 3

(deg)

Fig. 2. Difference phase shift versus the misalignment angle c.

2. Experiment

Fig. 1. Top view of interferometer setup.

the near non-dispersive phase difference Aq$(r,, 7) (see Ref. [5] for details):

2NbDd O(e,, 7) - A4bl(e, 7) - A4>z(e, 7) ~ ~ {2 + (Ae,) 2

[1 + 2cotZ(0B)]}. (1)

Here, Ae, = e - Co (Ae<< 1 ) and A7 = 7 - ?'o are the angles of horizontal and vertical misalignment of the sample surfaces w.r.t, the Bragg planes, d is the interferometer Bragg plane spacing, OR is the Bragg angle, N is the atomic density in the sample and D is the sample thickness. Since O(e,, 7) depends quadratically on Ae, the error due to misalignment is greatly reduced when e approaches Co. It follows from Eq. (1) that for Ae ~ 0.2" the resulting error in b is only 0.005% (for 0B = 30°). In contrast to this the non-dispersive geometry [7] is extremely sensi- tive to horizontal misalignment, because A4b(c, 7) is linearly dependent on Aa. To achieve the same accuracy in the measurement of b, Ae must be less than 6 arc sec.

Thus, the procedure [5] used here greatly re- duces or eliminates the errors due to dispersion and alignment. Due to this fact the coherent scattering length is only determined by the sample thickness D and atomic density N.

The experiment was performed at both the neu- tron interferometry facilities at the NIST and the HMI, which operate with (1 1 1) and (2 2 0) LLL interferometers at different wavelengths (0.271 and 0.198 nm, respectively) using the same sample made from perfect crystal Si (Wacker Siltronic). The sam- ple thickness was measured by the H M | to be, D = 0.30053(2)cm. Similarly, the thickness was mea- sured at the NIST Gauge Block Interferometer Facility which found D = 0.300527(15)cm. From these measurements a homogeneous area of the sample was selected by a Cd mask with a 6 mm x 6 mm square opening, placed over the sample.

The non-dispersive phase shift Aq$(c, 7) was ob- tained by fits to interferograms (intensity versus 8) when the sample was placed at positions 1 and 2 (Fig. 1). This sequence was repeated for various settings of e, holding the tilt I' fixed from which O(c) was obtained (Fig. 2). The angle of the perfect alignment (c = ~0) of the sample was determined within the accuracy of 0.05" by a quadratic fit to O(e) (Eq. (1)). The same procedure was carried out for the tilt 7- The values for b were obtained from measuring O(Eo, 7o). The main errors in the values for b were due to statistical uncertainties of about 0.006%. The systematic alignment errors were much smaller and were about 0.0002%. An addi- tional correction factor due to the displacement of air was also included. The values for N and d for

132 A. h~ffb et aL / Phvsica B 241 243 (1998) 130 132

experimental temperatures 19°C (NIST) and 26 'C (HMI) were adjusted from the crystal lattice con- stant of Si, a = 543101.993 fm at 22.5"C.

Two values obtained for b were b - -4 .15041 (21)fro (NIST) and b= 4 .15102 (21 ) fm (HMI). The final value for the coherent scattering length of Si is b = 4.1507(2)fm was obtained by averaging the results from the two experiments. This new value is in reasonable agreement with the accepted value 4.149(1) [6], but has an error limit five times lower.

Acknowledgements

We would like to thank Dr. T. Doiron (NIST) for measuring the sample thickness and Prof. H. Rauch (Vienna) for the providing the interferometer

crystal for HM 1. Support of BENSC and European Commission, T M R Programme, Network contract E R B F M R X C T - 0 0 5 7 "Neut ron Optics" is kindly acknowledged.

References

[1] G.E. Bacon~ in: Neutron Diffraction, Clarendon Press, Oxford, 1979.

[2] H. Rauch, Proc. Summer School on Neutron Physics, Zuoz, Switzerland, 1996.

[3] L. Koester, in: Neutron Physics, Springer Tracts in Modern Physics, vol. 80, Springer, Berlin, 1977, p. 1.

[4] A. Iofl'e, M. Vrana, V. Zabiyakin, J. Phys. Soc. Japan, (Suppl.) A 65 (1996} 82.

[5] A. loffe, M. Vrana, Phys. Lett. A (1997), in press. [6] C.G. Shull, J.A. Oberteuffer, Phys. Rev. Lett. 29 (1972) 871. [7] H. Rauch, E. Seidl, D. Tuppinger, D. Petrascheck, R.

Scherm, Z. Phys. B 69 (1987) 313.