Diffusion Parameters of Thermal Neutrons in Water

A method is described for the determination of neutron diffusion parameters by measurements of the decay of thermal neutrons in a finite moderator with a pulsed-neutron source and a time analyzer. In the theory for the method one takes into account the "diffusion cooling" effect, which decreases the temperature of thermal neutrons below the temperature of the moderator. Measurements are reported on a cylindrical geometry, involving between 1 and 4 liters of distilled water. Analysis of the result yields a value of 0.333 ±0.003 barns for the neutron-proton capture cross section, in good agreement with other measurements, and $(36\mathrm{}340\pm 750)[1-(0.20\pm 0.04\left){{\kappa }_0}^2\right]$ ${\mathrm{cm}}^2$/sec for the diffusion constant of thermal neutrons in water. The term involving the "buckling" ${{\kappa }_0}^2$ of the geometry is due to the diffusion cooling effect. The value of the diffusion constant for ${{\kappa }_0}^2=0\mathrm{}$ leads to a value for the diffusion length in excellent agreement with the result of other measurements. The diffusion cooling effect is larger by a factor of 3.5 than the theoretical value, calculated for the model of a monatomic gas.