The development of a versatile field program for measuring tritium in “real-time”

Robust sample handling and liquid scintillation counting (LSC) procedures have been developed to routinely monitor tritium in the field relative to the 20,000 pCi/L drinking water standard. This procedure allows tritium to be monitored hourly during 24 hour drilling operations at depths in the saturated zone potentially contaminated by sub-surface nuclear weapons testing at the Nevada Test Site. Using retrofitted, shock hardened, vibration damped counters and strict analytical protocols, tritium may be measured rapidly in the field under hostile conditions. Concentration standards and dead tritium backgrounds are prepared weekly in a central laboratory and delivered to remote drilling locations where they are recounted daily as a check on counter efficiency and calibration. Portable LSC counters are located in trailers and powered off a battery pack and line filter fed by mobile generator. The samples are typically groundwaters mixed with drilling fluids returned after circulation through a drill string. Fluids are aerated and de-foamed, filtered, mixed with scintillation cocktail and dark adapted before counting. Real-time monitoring affords drilling and field personnel early warning against intercepting down-gradient plumes of radioactivity. For routine operations, the tritium activity may not exceed a 10,000 pCi/L threshold.     

Lehmer pairs of zeros,the de Bruijn-Newman constant Λ, and the Riemann Hypothesis

We give here a rigorous formulation for a pair of consecutive simple positive zeros of the functionH ₀ (which is closely related to the Riemann -function) to be a Lehmer pair of zeros ofH ₀. With this formulation, we establish that each such pair of zeros gives a lower bound for the de Bruijn-Newman constant (where the Riemann Hypothesis is equivalent to the assertion that 0). We also numerically obtain the following new lower bound for :