Neutron velocity

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... 

The energy transfer AE and co can be determined by measurement of the neutron velocities Vi and Vf. Note that for all problems discussed in this article i f and therefore ... 

Even slow motions of molecules cause neutron velocity changes that are large enough to be detectable, in particular NSE is able to resolve changes Avof the order of 10" v,. 

The velocity distribution in a neutron gas at equilibrium is subject to the laws of the kinetic theory of gases. The neutron velocities at equilibrium obey the Maxwell distribution... 

Silvery-white lustrous metal face-centered cubic crystal structure ductile ferromagnetic density 8.908 g/cm at 20°C hardness 3.8 Mohs melts at 1,455°C vaporizes at 2,730°C electrical resistivity 6.97 microhm-cm at 20°C total emissivity 0.045, 0.060 and 0.190 erg/s.cm2 at 25, 100 and 1,000°C, respectively modulus of elasticity (tension) 206.0x10 MPa, modulus of elasticity (shear) 73.6x10 MPa Poisson s ratio 0.30 thermal neutron cross section (for neutron velocity of 2,200 m/s) absorption 4.5 barns, reaction cross section 17.5 barns insoluble in water dissolves in dilute nitric acid shghtly soluble in dilute HCl and H2SO4 insoluble in ammonia solution. Thermochemical Properties... 

E. Melkonian, Slow neutron velocity spectrometer studies of 02, N2A, H2, H20, and seven hydrocarbons. Phys. Rev. 76, 1750 (1949) J.L. Russell, J.M. Neill, J.R. Brown, total cross section measurements in H20, General Atomic Div. Reports No.7581 (1966) K. Heinloth, Subthermal neutron scattering on H20, CH202 AND C6H6. Zeitschrift fuer Physik 163, 218 (1961)... 

A correction for TDS, that is, the inelastic phonon scattering, is a difficult problem not yet satisfactorily solved. A proper correction can only be made if the elastic constants of the crystal are known, although an empirical method has been suggested. TDS is inversely correlated with the bulk modulus, thus for soft molecular crystals at room temperature it can be as high as 20-30% of the Bragg intensity, while a much smaller percentage for hard inorganic solids. The effect of no correction is to underestimate the ADP. For neutrons, the problem is even more complicated since the TDS correction will depend on the neutron velocity relative to the velocity of sound in the crystal. ... 

Upe Cross section, bams (at 2200 m s neutron velocity) for Fe Cross section, bams (at X ta is the activation time (s)... 

The energy and momentum of the neutron are related through the neutron velocity. We evaluate the energy and momentum of a neutron, of mass 1.67 xlO kg, travelling with a speed, v = 1000 m s. ... 

This need is met by appropriate shielding. The same process of moderation found at the heart of the source is again exploited but this is now followed by adsorption. Most materials have a l/(neutron velocity) dependence to their absorption cross section and slower neutrons are more readily absorbed. (The 1/v dependence simply comes fi"om the fact that the slower the neutron, the longer it spends near an absorbing nucleus). 

Since the mass of the neutron (w , kg) is known, as are the neutron flight distances d, m), for an elastic scattering (diffraction) process the flight time t, ps) determines the neutron velocity (v ) and hence its energy E, cm ) since (cf Eq. 2.21)... 

Here it is convenient to recall the expression for the de Broglie wavelength. A, of a neutron and the related neutron momentum vector, k. Readers should familiarise themselves with aspects of the manipulation of k ( 2.3). The neutron velocity is v. 

Here, ko and k are the neutron velocities before and after the scattering process. Looking at Eq. (2.75) immediately reveals the relation to G(r, t). The double differential scattering cross-section is directly related to the Fourier transform of the van Hove pair correlation function, which is given by... 

Figure 2.12 (a) Schematic diagram illustrating the principle of neutron wavelength selection on a continuous neutron source by use of mechanical choppers and the neutron time of flight, (b) Curved slot rotor another design for neutron velocity selection. 

For low energy ("slow") neutrons (< 1 MeV) the cross-section is also larger than the value, and decreases as the velocity increases this relation, n relationship between the cross-section and the neutron velocity can be understood in wave mechanical terms since the wavelength associated with the neutron increases with a decrease in velocity. According to the matter-wave hypothesis ( 10.4) the wavelength associated with a moving particle is X = h/ mv) which can be written ... 

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