When dealing with matter in bulk, the reaction rate Ыаф is often written as Еф, where £ = Ncr and is known as the macroscopic cross-section. E (capital sigma) may be regarded as the total collision area presented by the target nuclei per unit volume of material. As it has dimensions (area/volume), m_1, £ may also be interpreted as the probability per metre of track length that a neutron will interact with the material.

Now the average distance that a neutron travels without interacting is known as the mean free path, X. It may readily be shown that the mean free path is the reciprocal of the macroscopic cross-section, i. e., X = l/Ee. The subscripts used for a are also used for X and £ as appropriate:

Xt, Xa, X$ … £[, Eat •••

1.3.3 Thermal neutrons

Neutrons in thermal equilibrium with the surrounding material are referred to as thermal neutrons. It may be shown, using the methods of the kinetic theory of gases, that the mean kinetic energy of thermal neu­trons in surroundings at a temperature of TK is given by:

1/2 mV2 = 3/2 kT

where m is the mass of the neutron

у is the mean neutron energy

к is the Boltzmann’s constant (1.38 x 10-‘ J/K)

Nuclear data are often given for the ‘standard’ temperature of 293 К (20°C). Calculation for thermal neutrons in surroundings at 293 К gives a mean ve­locity of 2200 m/s and corresponding kinetic energy of 0.025 eV. Thus for uranium 235 and for thermal neutrons at the ‘standard’ 2200 m/s we may write:

<Т( = О a +

= <7C + fff + <?e + Uj

690 = 101 + 579 + 10 + 0

The values for a are taken from Table 1.2.

Sometimes the term ‘slow neutron’ is used as if synonymous with ‘thermal neutron’ — this is not so. Also, thermal neutrons are sometimes regarded as being necessarily at 20°C — again this is not so. For example, neutrons in equilibrium with their sur­roundings at, say, 250°C or 500°C would be thermal neutrons with corresponding speed and energy values of (2940 m/s)/(0.045 eV) or (3570 m/s)/(0.067 eV) respectively.