Continuous Versus Average Cross Section
Cross sections depend strongly on the incoming particle speed. In the case of a beam with multiple particle speeds, the reaction rate R is integrated over the whole range of energy:
Where σ(E) is the continuous cross section, Φ(E) the differential flux and N the target atom density.
In order to obtain a formulation equivalent to the mono energetic case, an average cross section is defined:
Where Φ= Φ(E) dE is the integral flux.
Using the definition of the integral flux Φ and the average cross section σ, the same formulation as before is found:
Read more about this topic: Neutron Cross Section
Famous quotes containing the words continuous, average, cross and/or section:
“For good and evil, man is a free creative spirit. This produces the very queer world we live in, a world in continuous creation and therefore continuous change and insecurity.”
—Joyce Cary (1888–1957)
“Three million of such stones would be needed before the work was done. Three million stones of an average weight of 5,000 pounds, every stone cut precisely to fit into its destined place in the great pyramid. From the quarries they pulled the stones across the desert to the banks of the Nile. Never in the history of the world had so great a task been performed. Their faith gave them strength, and their joy gave them song.”
—William Faulkner (1897–1962)
“But soft, behold! lo where it comes again!
I’ll cross it though it blast me. Stay, illusion!”
—William Shakespeare (1564–1616)
“Socialite women meet socialite men and mate and breed socialite children so that we can fund small opera companies and ballet troupes because there is no government subsidy.”
—Sugar Rautbord, U.S. socialite fund-raiser and self-described “trash” novelist. As quoted in The Great Divide, book 2, section 7, by Studs Terkel (1988)