1. Anomalous neutron Compton cross sections – model free approach and beyond Maciej Krzystyniak, PhD Frankfurter Allgemeine, 27 June 2004, Nr. 26

2. Inverted geometry spectrometer VESUVIO at ISIS, Rutherford Appleton Lab, UK Neutron source E 0, L 0  E 1, L 1 sample detector foil Time of flight measuring principle [J. Mayers and T. Abdul-Redah, J. Phys.: Cond. Matter 16, 4811 (2004) ] Large energy and momentum transfers, e. g. for hydrogen at  =65.7°: 7 eV <  < 90 eV 70 Å -1 < q < 200 Å -1

3. Convolution Approximation (CA) [see J. Mayers and T. Abdul-Redah, J. Phys.: Cond. Matter 16, 4811 (2004) ] -20-15-10-505101520 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 M(1)=1.0079 a. u. -100-80-60-40-20020406080100 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 M(2)=16 a. u -1000-800-600-400-20002004006008001000 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 M(3)=92.9 a. u. 0100200300400500600 -0.5 0 0.5 1 1.5 2 2.5 x 10 -3 TOF [us] Count Rate [arb. units] y M(1 ) y M(2 ) y M(3 ) Our aim: The determination of I M ~N M  M from the mass M at a given scattering angle .

4. How to obtain the scattering intensity regardless of the form of : nuclear momentum distribution, and; resolution function for a given scatterer with a mass M ? Model free NCS data reduction scheme (proposed by B. Dorner, ILL): (1)The TOF spectrum C(t) collected for a given fixed scattering angle  is normalized to a constant flux of the incoming neutrons with initial energies given by the spectrum I(E 0 ): C(t)  C norm (t) =C(t) / [E 0 I(E 0 )]. (2) The individual values of the TOF in C norm (t) are replaced by the corresponding values of the energy transfer  - without any Jacobian ! (3) The counts corresponding to a given mass M are multiplied point-wise by the corresponding mass dependent Jacobian of the transformation from the constant  scan into a fictitious constant q-scan: (a separate paper [B. Dorner, NIM B, in press]) (4) The signals C norm M (  ; q = const) are integrated over the respective  range to obtain the scattering intensities from different masses M.

5. Case of polyethylene NCS measurements:

6. New contact: ILL - Berlin

7. Krzystyniak and Dreismann (analytical proof, PRB 2005): =  q qq  with the West variable y M being the momentum p of the nucleus projected onto the scattering vector:

9. Conclusions and outlook: The scattering intensities derived from the Dorner scheme are independent on the form of the momentum distribution of the scatterer and the instrument resolution function; Both, Dorner scheme and CA are equivalent; There exist a third possible data reduction scheme: model independent treatment directly in the TOF space (paper in preparation); In order to compare the experimental results in model free schemes with theoretical prediction a transformation is needed from a constant scattering angle into constant momentum transfer scan; Is there an experimental scheme to gain the integrated intensities without the above transformation (a direct constant q-scan)? - YES (paper in preparation)