A measurement of the neutron diffusion parameters of water at different temperatures by the pulsed method

TR Number



Journal Title

Journal ISSN

Volume Title


Virginia Polytechnic Institute


The neutron diffusion parameters of water and ice were measured by the pulsed source method at two temperatures; 1.0°C. and -19°C.

Neutron pulses were obtained at one millisecond intervals by modulating the beam in a Cockcroft-Walton type accelerator. The ₁H³(d,n)₂He⁴ reaction was used to generate neutrons.

The samples were contained in cylindrical aluminum cans covered with cadmium. The experiment was conducted inside a large paraffin block which served as a neutron shield and thermal insulator. The temperature of the samples was maintained constant to within ±1°C.

Neutrons leaving one surface of the sample were counted in a BF₃ proportional counter. The time distribution of these neutrons was recorded by an eighteen channel time analyzer. The width of each channel was 20 microseconds. The opening of the first channel was delayed 100 microseconds with respect to the start of the neutron burst to minimize harmonics in the neutron decay.

A geometric buckling was calculated for each sized sample from


where B² = geometric buckling

2.405 = first zero of Jo Bessel Functions

R = radios of cylinder

H = height of cylinder

∈ = extrapolation distance

The extrapolation distance ∈ was calculated from

∈ =0.71 λtr

where λtr = mean free path of neutrons in water

The extrapolation distance was assumed to vary as T½ where T is the temperature in degrees Kelvin.

The measured decay constants, α, were fitted by the method of least squares to a polynomial in B² of the form

α = (∑av) ÷ DoB² - CB⁴


a = the macroscopic absorption cross-section

v = the neutron velocity

Do = diffusion coefficient

C = diffusion cooling coefficient

The resultant values of (∑av) and Do for each temperature are below. The data did not permit a determination of C.

1.0°C. (∑av) = 4595 ± 365 sec⁻¹ Do = 29600 ± 840 cm²/sec

-19°C. (∑av) = 4355 ± 263 sec⁻¹ Do = 27050 ± 630 cm²/sec