Neutron vector

For the calculations discussed in ref. [Ra 85], and for those shown here, the proton vector densities were obtained by unfolding the single proton (free space) electric form factor from the nuclear charge densities [Fr 77, Si 70, Si 79]. The contributions to the apparent total nuclear charge density due to the neutron electric form factor and the nucleon magnetic form factor (in the case of Pb) were taken into account [Be 72b, Ra79]. The neutron vector densities used in the RIA predictions were assumed to be... 

The relativistic IA2 calculations as well as the RIA calculations at 650 MeV used the nuclear densities described in section 4.2. The NRDD calculations and the NR calculations based on the Paris-Hamburg g-matrix used the proton and neutron vector densities described in section 4.2. For the 200 MeV, full-folding predictions of ref. [Ar 90b], the proton and neutron density matrices were computed from Woods-Saxon single particle eigenstates, which were fitted to empirical charge density root-mean-square (rms) radii and single particle energies. 

In order to use the NRDD model to fit dfferential cross section data empirically, the neutron vector density, p y(r) in eq. (4.34), can be replaced by [Ra85]... 

A similar chi-square fitting procedure was carried out in ref. [Ra 85] using the RIA model, where the neutron vector density was parametrized as in eq. (5.1) and the neutron scalar density was obtained from eq. (4.35), where p y(0 this equation was replaced by p v"(r). This method of generating the scalar density prevented the neutron-proton density variation from affecting the very sensitive... 

The X-ray and neutron scattering processes provide relatively direct spatial information on atomic motions via detennination of the wave vector transferred between the photon/neutron and the sample this is a Fourier transfonn relationship between wave vectors in reciprocal space and position vectors in real space. Neutrons, by virtue of the possibility of resolving their energy transfers, can also give infonnation on the time dependence of the motions involved. 

Scattering experiments invoive processes in which incident particies (X-rays or neutrons) with wave vector ki (energy Ej interact with the sampie and emerge with wave vector kf (energy )), obeying the conservation iaws for momentum and energy,... 

Figure 4 Schematic vector diagrams illustrating the use of coherent inelastic neutron scattering to determine phonon dispersion relationships, (a) Scattering m real space (h) a scattering triangle illustrating the momentum transfer, Q, of the neutrons in relation to the reciprocal lattice vector of the sample t and the phonon wave vector, q. Heavy dots represent Bragg reflections.

A procedure commonly used to extract dynamic data directly from experimental incoherent neutron scattering profiles is described in Ref. 17. It is assumed that the atomic position vectors can be decomposed into two contributions, one due to diffusive motion, fi /t), and the other from vibrations, Uijt), i.e.. 

Why, then, is the magnetisation density used The answer is that the magnetisation density is important for certain approximations which are usually made in analysing neutron scattering experiments. In the standard polarised neutron diffraction (PND) experiment [5], only one parameter is measured - the so-called flipping ratio . It is impossible to determine a vector quantity like the magnetisation density from a single number, unless some assumptions are made. The assumptions usually made are ... 

Unlike these conventional techniques, NSE measures the neutron velocities of the incident and scattered neutrons using the Larmor precession of the neutron spin in an external magnetic field, whereby, the neutron spin vector acts like the hand of an internal clock, which is linked to each neutron and stores the result of the velocity measurement at the neutron itself. The velocity measurement is thus performed individually for each neutron. For this reason, the... 

Similar neutron diffractogram modifications have been al-ready observed several time during our studies concerning the structural proper-ties of confined molecular species (D2, Ar, N2, Kr, CD4, C2D6) in Silicalite-I zeolite. But for such a MFI type of framework porosity, characterized by a two dimensional micropore network, the intensity of the diffraction peaks (101) and (020), observed at small wave vector Q (A1) values, vanishes completely when increasing the confined phase loading ( as shown on figure 6, for the Ar / Silicalite-I system Ld. = 68 % ). 

For the calculation of the hydrodynamic thickness we divide the profile artificially into elementary layers, the result being independent of the division chosen provided it is sufficiently fine. The s.a.n.s. data is obtained as a function of Q, the wave vector (4it/A sin(0/2), where X is the neutron wavelength and 0 the scattering angle. The Q resolution corresponds in real space to a fraction of a bond length which is small enough for defining an elementary layer. 

Like electrons, some nuclei also have spin. Protons and neutrons also have spins of Thus, if a nucleus consists of p protons and n neutrons its total spin will be a vector sum of p + n spins of Each isotope will have its own spin value, but the laws governing the vector addition of nuclear spins are not known, and at the moment, nuclear spins are known only in terms of some empirical rules. 

One of the most powerful techniques by which protein-protein neighborhoods within the ribosomal particles can be elucidated is neutron scattering. When using this method to determine the relative positions of proteins in the 30 S subunit, the pardcle is reconstituted with two specific proteins that are deuterated whereas all other ribosomal components are in the protonated form (Moore, 1980). The subunits containing the two deuterated proteins give additional contributions to the scattering curves which provide information on the lengths of the vectors between the two deuterated proteins. 

The momentum transfer hQ, respectively the wave vector, is given by Q= k -kf where k and kf are the wave vectors of the incoming and outgoing (scattered) neutrons. They relate to the neutron wavelength k j=2Tt/Aij. The neutron momenta a.rep ij=m Vi f=fikif. Therefore ... 

Incoming/outgoing neutron wave vector Segment length Monomer length Bond length... 

FIG. 5.9 Phase angles in an acentric X-N analysis phase angle as calculated with spherical-atom form factors and neutron positional and thermal parameters tpx is the unknown phase of the X-ray structure factors which must be estimated for the calculation of the vector AF. Use of FX — FN introduces a large phase error. Source Coppens (1974). 

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