Precision measurement of the coherent neutron scattering length of 3He through neutron interferometry

Improved knowledge of the real part of the neutron scattering length of ³He is important for further development of nuclear few-body theory, as well as for a thorough understanding of neutron scattering off quantum liquids. The real part of the bound incoherent neutron scattering length b_i' has recently been measured directly with an experimental uncertainty of better than 1% by means of spin echo spectrometry. The uncertainty of the more fundamental bound multiplet scattering lengths b_±' is thus limited by today's 1.2% uncertainty of the spin-independent coherent part b_c'. Employing the skew-symmetric perfect crystal Si-interferometer at the S18 experimental site at ILL, Grenoble, we have re-measured the real part of the bound coherent neutron scattering length b_c' of ³He. Our result b_c' = 6.010(21)fm exhibits a significant deviation compared to the latest accepted value b_c' = 5.74(7)fm (H. Kaiser, H. Rauch, G. Badurek, W. Bauspiess, U. Bonse, Z. Phys. A 291, 231 (1979)). Including the known value of the incoherent neutron scattering length, we obtain new values for the real parts of the free singlet and triplet scattering lengths, a_-' = 7.573(30)fm and a₊' = 3.480(18)fm. Our result contravenes by more than 7 standard deviations the measurement of the same physical quantity that has recently been performed by a group at NIST in a very similar experiment (P.R. Huffman, D.L. Jacobson, K. Schoen, M. Arif, T.C. Black, W.M. Snow, S.A. Werner, Phys. Rev. C 70, 014004 (2004)) which yielded b_c' = 5.853(7)fm.     

Neutron interferometric measurement of the coherent scattering length of cobalt

A precise determination of the coherent scattering length of Co with a neutron interferometer yields a valueb _Co =2.53(5) fm. It agrees well with the value 2.5(1) fm measured by Moon from diffraction work, but there is a disagreement with a value proposed by Koester et al. based on the Christiansen filter method.     

How low-energy weak reactions can constrain three-nucleon forces and the neutron-neutron scattering length

We show that chiral symmetry and gauge invariance enforce relations between the short-distance physics that occurs in a number of electroweak and pionic reactions on light nuclei. Within chiral perturbation theory, this is manifested via the appearance of the same axial isovector two-body contact term in pi(-)d --> nngamma, p-wave pion production in NN collisions, tritium beta decay, pp fusion, nud scattering, and the hep reaction. Using a Gamow-Teller matrix element obtained from calculations of pp fusion as input, we compute the neutron spectrum obtained in pi(-)d --> nngamma. With the short-distance physics in this process controlled from pp --> de(=)nu(e), the theoretical uncertainty in the nn scattering length extracted from pi(-)d --> nngamma is reduced by a factor larger than 3, to approximately < or = 0.05 fm.     

Measurement of the coherent neutron scattering length of 3He by neutron interferometry

A precise determination of the coherent scattering length of ³He with a neutron interferometer yields a value a_c = 4.29 ± 0.04 fm. A comparison with varoous theoretical perdictions is made and its relation to the few-body problem is discussed. A combination with other experimental results yield as most probable values for the free singlet- and triplet scattering length a_s = 8.0 ± fm and a_t = 3.05 ± 0.07 fm, respectively.     

On measuring the neutron coherent scattering length with ultrahigh precision

We propose an order of magnitude improvement in the present five parts in 10⁵ precision of a nondispersive interferometric measurement of the neutron coherent scattering lengthb _c. For this purpose we make a judicious selection of the Bragg angle for the interferometer and the sample thickness. The precision is further improved by an optimal choice of the Bragg reflection (and a consequent neutron wavelength). By performing the experiment in vacuum, errors arising from possible variations in the pressure, composition or humidity of the ambient air can be eliminated. On attaining such precision, we ought to account for the neutron beam refraction at the sample-ambient interfaces, to infer the correctb _c from the observed phase. The formula for the phase used hitherto is approximate and would significantly overestimateb _c. The refractive index for neutrons can thus be determined to a phenomenal precision of a few parts in 10¹².     

pd scattering at 250 MeV and three-nucleon forces

We have measured angular distributions of the differential cross-section, the analyzingpower and all of the spin transfer coefficients K _y ^y, K _x ^x, K _z ^x, K _x ^z, and K _z ^z for the pd elastic scattering at 250 MeV. These are the first measurements of a complete set of proton polarization observables for pd elastic scattering at intermediate energies. The present data are compared with theoretical predictions based on exact solutions of the three-nucleon Faddeev equations and modern realistic nucleon-nucleon potentials combined with three-nucleon forces (3NF), namely the Tucson-Melbourne (TM) 2 -exchange model, a modification thereof (TM) closer to chiral symmetry, and the Urbana IX model.Received: 30 September 2002, Published online: 22 October 2003PACS: 21.45. + v Few-body systems - 21.30.-x Nuclear forces - 24.70. + s Polarization phenomena in reactions     

Neutron-interferometric measurement of the coherent scattering length of the isotopes of silver

Employing a new measuring scheme with the D 18 Neutron Interferometer at the ILL, Grenoble, the thermal neutron coherent scattering lengthb _c for bound atoms of natural Ag,¹⁰⁷Ag and¹⁰⁹Ag have been measured at the wavelengthλ=1.8742 Å. The results, corrected for composition and density of the actual samples, are nat Ag:b _c =5.922 (7) fm¹⁰⁷Ag:¹⁰⁷ b _c =7.555 (11) fm¹⁰⁹Ag:¹⁰⁹ b _c =4.165 (11) fm The result is in agreement with an earlier value obtained with the interferometer for nat Ag (5.932 (6)) using a different measuring scheme and a totally different sample. For nat Ag and¹⁰⁷Ag the values determined interferometrically are ?0.05 and ?0.08 fm smaller, repectively, than those measured with the Christiansen filter method.     

New methods for interferometric neutron scattering lengths measurements

A skew symmetric neutron interferometer has been used for tests of a nondispersive and phase contrast variation measuring technique of scattering lengths and for the measurement of anomalous scattering lengths of strongly absorbing substances. The following bound coherent scattering lengths have been obtained: b_c(Pt)=9.60 ± 0.01 fm, b_c(Te) =5.6 ± 0.1 fm and as real parts of anomalous scattering lengths at λ=l.86Å: b_c(Sm) =0.7 ± 0.2 fm, b_c(Eu)=5.3 ± 0.3fm, b_c(Gd)=5.1 ±0.4 fm, b_c(Dy)=16.9 ± 0.3 fm.     

A precise measurement of the spin-dependent neutron scattering length of 3He

The poor knowledge of the spin-dependent neutron scattering length of ³He has until now handicapped nuclear four body theory and the interpretation of excitations in the quantum liquid. We have measured, for the first time directly, the real part of the bound incoherent neutron scattering length, b_i′ of ³He. A neutron spin echo spectrometer was used to detect pseudomagnetic precession of polarised neutrons passing through polarised ³He gas. Any absolute calibrations of sample and beam parameters were avoided using simple transmission measurements with non-polarised neutrons. The only a priory information required was the spin-dependent neutron absorption cross section of ³He. The result is b_i′ = -2.365(20) fm, which reduces the prior uncertainty by a factor 30. The corresponding new value of the bound incoherent scattering cross section is σ_i = 1.532(12) barn. Including the known value of the coherent neutron scattering length, we obtain new values for the real parts of the free triplet and singlet neutron scattering lengths, a_-′ = 7.370(58) fm and a₊′ = 3.278(53) fm.     

Three-nucleon forces and the three-nucleon systems

The basic principles and philosophy which have guided the area of few-nucleon physics are motivated and discussed. Recent advances have made it possible to solve accurately the Schrödinger (or Faddeev) equation for many of the configurations of the few-nucleon systems, A brief review is given of some of the results of these calculations, which also Indicate that one-pion exchange plays roughly the same role in binding these systems that it plays in electromagnetic meson-exchange currents. Finally, a qualitative discussion of chiral perturbation theory is presented, which highlights the role that chiral symmetry plays in the nuclear force. Three-body forces from different areas of physics are discussed, as well as the significance of three-nucleon forces in few-nucleon systems.Lectures held at the Indian Summer School on Electromagnetic and Weak Interactions of Particles with Nuclei, Sázava, Czechoslovakia, 6–11 September 1992The work of J. L. F. was performed under the auspices of the U. S. Department of Energy. The support of the Alexander von Humboldt-Stiftung is gratefully acknowledged. The author gratefully acknowledges discussions with B. Holstein, whose superb lectures on this topic introduced him to chiral perturbation theory.     

Measurement of coherent neutron scattering lengths of gases

With the neutron interferometer, measurements of the coherent neutron scattering lengths by various gases have been performed. We get the following numbers for the bound coherent scattering lengths for atoms (in fm):b _c (H) =?3.64(3),b _c (D)=6.55(8),b _c (He?3)=5.74(7),b _c (He)=3.26(3),b _c (N)=9.30(8),b _c (O)=5.83(5),b _c (Ne) =4.63(4),b _c (Ar)=2.07(2),b _c (Kr)=7.52(6),b _c (Xe)=4.69(4). In some cases greater accuracy is achieved in comparison with recommended values from the literature. The absolute values for hydrogen and deuterium measured with gaseous samples, are about 2% smaller than the values measured with liquids and other reference values.     

Investigation of nematic order by coherent neutron scattering

The mathematical relationship between the orientational order parameters and the coherent neutron scattering cross section for a nematic liquid crystal is given. For deuterated para-azoxyanisole the single-molecule part of the cross section is evaluated within the meanfield approximation and combined with experimental results to give information about molecular orientational order in terms of P ₂, P ₄ and P ₆. Both P ₂ and P ₄ are found necessary for describing the molecular order. Discrepancies between experimental and theoretical results are interpreted as possibly reflecting the inadequacy of the meanfield theory of Maier and Saupe.     

Investigation of nematic order by coherent neutron scattering

The mathematical relationship between the orientational order parameters and the coherent neutron scattering cross section for a nematic liquid crystal is given. For deuterated para-azoxyanisole the single-molecule part of the cross section is evaluated within the meanfield approximation and combined with experimental results to give information about molecular orientational order in terms of P ₂, P ₄ and P ₆. Both P ₂ and P ₄ are found necessary for describing the molecular order. Discrepancies between experimental and theoretical results are interpreted as possibly reflecting the inadequacy of the meanfield theory of Maier and Saupe.     

Compact fibre-based coherent anti-Stokes Raman scattering spectroscopy and interferometric coherent anti-Stokes Raman scattering from a single femtosecond fibre-laser oscillator

We demonstrate a new approach to CARS spectroscopy by efficiently synthesizing synchronized narrow-bandwidth (less than 10 cm⁻¹) pump and Stokes pulses (frequency difference continuously tunable upto ≈3000 cm⁻¹) based on spectral compression together with second harmonic generation (in periodically-poled nonlinear crystals) of femtosecond pulses emitted by a single compact Er-fibre oscillator. For a far better signal to non-resonant background contrast, interferometric CARS (I-CARS) is demonstrated and CARS signal enhancement upto three orders of magnitude is achieved by constructive interference with an auxiliary local oscillator at anti-Stokes field, also synthesized by spectral compression of pulses emitted from the same fibre oscillator.     

Precise measurement of dp elastic scattering at 270 MeV and three-nucleon force effects

The cross section, the deuteron vector A(d)(y) and tensor analyzing powers A(ij), the polarization transfer coefficients K(y('))(ij), and the induced polarization P(y(')) were measured for the dp elastic scattering at 270 MeV. The cross section and A(d)(y) are well reproduced by Faddeev calculations with modern data-equivalent nucleon-nucleon forces plus the Tucson-Melbourne three-nucleon force. In contrast, A(ij), K(y('))(ij), or P(y(')) are not described by such calculations. These facts indicate the deficiencies in the spin dependence of the Tucson-Melbourne force and call for extended three-nucleon force models.     

Determination of the phonon spectrum from coherent neutron scattering by polycrystals

As proposed by Bredovet al. [2, 3] the phonon spectrum can be obtained approximately from coherent neutron scattering by polycrystals if suitable averages over scattering angles are considered. The accuracy of this method is estimated by comparison with analytical results for simple lattice models (discussed here in particular for Aluminium). The errors are about 5% for low order moments and about 50% near van Hove singularities for “cold” neutrons (wavelength of the order of the nearest-neighbour-distance).     

Determination of the elastic constants by coherent neutron scattering in polycrystals

It is shown that elastic constants which usually can be determined in single crystals only may be measured in polycrystals by inelastic coherent neutron scattering. Measurements are reported for polycrystalline samples of aluminium, copper and stainless steel. The method is best suited for the determination of the elastic constants connected with transverse phonons.     

Determination of the neutron scattering length of208Pb by the neutron interferometry method

The coherent scattering length of²⁰⁸Pb was measured by means of the neutron interferometry method and the value ofb _c =9.494(29) fm was obtained.     

Binary scattering and breakup in the three-nucleon system

We present the further development of the three-particle formalism for differential Faddeev equations. The asymptotic boundary conditions in the hyperspherical adiabatic representation have been constructed. We prove that these conditions are asymptotically equivalent to the standard Merkuriev boundary conditions. With these boundary conditions we have formulated the boundary-value problem for Faddeev equations which has the property that the binary channel and the breakup channel are explicitly orthogonal. The effective numerical scheme for solving the formulated boundary-value problem is given.     

Birefringent neutron prisms for spin echo scattering angle measurement

In the first decade of the 19th century, an English chemist, William Wollaston, invented an arrangement of birefringent prisms that splits a beam of light into two spatially separated beams with orthogonal polarizations. We have constructed similar devices for neutrons using triangular cross-section solenoids and employed them for Spin Echo Scattering Angle Measurement (SESAME). A key difference between birefringent neutron prisms and their optical analogues is that it is hard to embed the former in a medium which has absolutely no birefringence because this implies the removal of all magnetic fields. We have overcome this problem by using the symmetry properties of the Wollaston neutron prisms and of the overall spin echo arrangement. These symmetries cause a cancellation of Larmor phase aberrations and provide robust coding of neutron scattering angles with simple equipment.