PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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application of the dynamical theory to the neutron case has grown substantially. A concise review with focus on the work presented in this thesis is given in Chapter 2. Some excellent papers and reviews already exist on the theory for example, by Sears [67-68], Rauch and Petrascheck [1,69], Wagh and Rakhecha [4,70] and Klein and Werner [5]. Extension of the dynamical diffraction theory for magnetic case is provided by Stasis and Oberteuffer [69,71]. Many of the theoretical predictions of neutron dynamical diffraction have since been verified and exploited for applications. Knowles in 1956 showed that the intensity of neutron capture γ-radiation varies markedly close to a Bragg condition for CdSO 4 single crystals [72]. This was the first effect of dynamical diffractions of neutrons demonstrated experimentally. Thereafter, anomalous transmission of neutrons associated with α-branch of the dispersion surface was experimentally verified by Sippel et a1. [73] and Shilshtein et a1. [74] using InSb crystals. The angle amplification effect was exploited by Kikuta et a1. [75] and Zeilinger et al. [76] to measure small directional changes of a neutron beam resulting from prism refraction. In a TOF (time-of-flight) experiment, Shull [77] could also observe ‘anomalous’ speed reduction by a factor cos B within a single crystal. The effects of a finite curvature of the incident wavefront can be accounted for by using the spherical wave approach [78]. Shull and Oberteuffer [66,78] used the Laue collimator setup to measure the fringe shift with the displacement of the exit slit along the crystal face. The experiment [79] showed that the phenomenon ought to be described in terms of a spherical incident wave. The interest and activities in neutron dynamical diffraction theory and its applications, reached the crescendo with the successful operation of the 1st perfect-crystal neutron interferometer (IFM) by Rauch-Treimer-Bonse [80] in 1974 by exploiting the amplitude division of the neutron wave function in the symmetric Laue configuration. However, a perfect-crystal X-ray IFM [81] was conceived and realized 9 years earlier. The first neutron IFM was built by Maier-Leibnitz and 8
Springer though in 1962, that used the wavefront division. Biprism (refraction based) IFMs suffer from small beam separations (~ 60 μm) making measurements with samples placed in one of the interfering paths extremely difficult [82]. To overcome this, various IFMs based on amplitude division have been developed for different requirements [Chapter 3, 1,4,83-84]. Among these, the LLL IFM (both skew symmetric and symmetric case) is the most widely used. Neutron interferometry has been a testing bed for the concepts of quantum mechanics. Many of the hypotheses previously treated only in thought experiments have since been verified neutron interferometrically. Some of these landmark experiments include observation of 4π spinor periodicity [85-87] and gravitational phase shift measurement [88], separation of geometric and dynamical phases [89], observation of Aharonov-Anandan-Casher (AAC) [90-91] and scalar Aharonov-Bohm (AB) effects [92-93], confinement induced phase [94], coherence length measurements [95-96] and experiment for testing quantum contextuality with single neutrons [97]. These alongwith some other experiments and many more interesting proposals are well documented [1,4,98-107]. 1.3 Motivation and scope of the thesis With neutron optics lying at the very heart of every neutron instrument, it becomes challenging indeed to match new experimental requirements with better instruments and novel optical components. Single crystal neutron optics plays a pivotal role in development of some of the key components of neutron instruments. In this section, we describe some of the neutron optics issues needed to be resolved, present motivation for their solution and circumvent them through new optical devices coupled with novel ideas. This opens up new vistas for the many experiments which otherwise are not possible (Chapters 3-5). 9
Page 1: Studying neutron dynamical diffract
Page 4 and 5: DECLARATION I, hereby declare that
Page 6 and 7: ACKNOWLEDGEMENTS I sincerely, thank
Page 8 and 9: Fig.10 Boundary conditions on wave
Page 10 and 11: Fig.28 Theoretical curves for Si {1
Page 12 and 13: sample. Least-squares fit to the sa
Page 14 and 15: Fig.62 Interference contrast and av
Page 16 and 17: 3.4 Experimental 49 3.5 Results and
Page 18 and 19: SYNOPSIS The present thesis aims to
Page 20 and 21: analytic expressions for intensity
Page 22 and 23: Research A, 634 (2011) S41. [9] S.
Page 24 and 25: spallation sources yield peak neutr
Page 26 and 27: SU(2) phase, and separation of geom
Page 28 and 29: [33-34,48]. The bi-refracting natur
Page 32 and 33: I. One of the major disadvantages o
Page 34 and 35: nuclear physics very important as i
Page 36 and 37: potential for most nuclei in spite
Page 38 and 39: Due to the rapid strides made latel
Page 40 and 41: for a positive value of b c i.e. fo
Page 42 and 43: k b k O H . ni sin( B S) . (18)
Page 44 and 45: factor exp(-W). The centre, θ C ,
Page 46 and 47: exploiting multiple successive iden
Page 48 and 49: We shall confine our discussion hen
Page 50 and 51: The depth Z is measured from the in
Page 52 and 53: wings (large-y regions). The freque
Page 54 and 55: expressed as T(y, t )R(y, t )R(
Page 56 and 57: studies. With such beams, the and
Page 58 and 59: CHAPTER 3 Neutron forward diffracti
Page 60 and 61: eing the separation of points M and
Page 62 and 63: 3.1 Neutron forward diffraction Con
Page 64 and 65: excited by the incident wave (Fig.1
Page 66 and 67: Therefore, the forward diffracted i
Page 68 and 69: Fig.15 Calculated cr and I O for a
Page 70 and 71: (1 I ) D tan b . ID cot( B S)
Page 72 and 73: Fig.18 Experimental layout to measu
Page 74 and 75: Fig.20 Bragg reflection intensity f
Page 76 and 77: fraction I O through the Bragg pris
Page 78 and 79: Fig.22 Experimental (points) and th
Page 80 and 81:
Table 2: Observed deflection sensit
Page 82 and 83:
total reflectivity domain. These ar
Page 84 and 85:
Here the term C() accounts for the
Page 86 and 87:
Fig.28 Theoretical curves for Si {1
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I H (θ H ) peaks of 0.18 height an
Page 90 and 91:
other with a compression factor lim
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an overall compression factor of 14
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4.3 Experimental 4.3.1 Bragg prism
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4.3.2 Experiment The experiment was
Page 98 and 99:
Fig.38 Bragg reflection rocking cur
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4.4 Applications of novel SUSANS se
Page 102 and 103:
Fig.42 First Q ~ 10 -6 Å -1 SUSANS
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2 (1) -(δk i .Δ i ) /2 Γ (Δ) =
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2 I( ) A( ) . (76) The least squa
Page 108 and 109:
Fig.46 Analyser rocking curve for a
Page 110 and 111:
This instrument was also employed t
Page 112 and 113:
Fig.48 Theoretical flat-topped angu
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difference between the two neutron
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Fig.52 Phase dispersion in a 26.5 m
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the beam and remains visible up to
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cos bc 4NDd1 1 2cot 2 III 2 2
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yield about an order of magnitude r
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The refractive index, n = (1-Nb c
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with a white, and hence high-intens
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proposed dual sample. The dual samp
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The experiment was performed with =
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Fig.59 Typical interferograms for p
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Fig.63 Path I, II and I-II phases d
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Fig.65 Average intensity with the s
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Fig.69 New metrological mapping of
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Si at 26.2 o C, applying a correcti
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selected asymmetric Bragg prism may
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III. High precision determination o
Page 146 and 147:
REFERENCES [1] H. Rauch and S. Wern
Page 148 and 149:
[36] J. S. Nico and W. M. Snow, Ann
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[67] V. F. Sears, Can. J. Phys., 56
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[97] A. Cabello, S. Filipp, H. Rauc
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[127] A. Ioffe, D. L. Jacobson, M.
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2009, (Grenoble, France, 2010) 3-15
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PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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