Parametric normalization for full-energy peak count rates obtained at different geometries

The Effective Interaction Depth (EID) law has been systematically studied and applied to parametric normalization for peak count rates obtained at different source-detector distances (S-D). The errors caused by EID normalization are less than 4% over the full range of S-D (from to several mm) for true coincidence-free -rays. Parametric corrections for the true coincidence (summing) effect are also established, based on simplified decay schemes and P/T ratio determinations. The total response of Ge detector for single-energy -rays (T) is clearly defined with scattering contributions from surroundings included. Errors from summing effect corrections are also less than 4%. The combined EID normalization and summing effect corrections give an error no greater than 5.7% for the worst situations (several mm S-D and cascade-crossover decay scheme), acceptable for most practical K₀ NAA.     

On small zeros of quadratic forms over finite fields (II)

Let be a quadratic form with integer coefficients and letp denote a prime. Cochrane^[1] proved that ifn≥4 then has a solution satisfying , where . The aim of the present paper is to generalize the above result to finite fields.