A unit commonly used at a nuclear reactor to indicate the reactivity of something in the core, in a relationship useful to changes in power of the reactor. The dollar ($) is equal to the reactivity of the object (ρ, expressed in Δk / k_{eff}) divided by the proportion of delayed neutrons that cause fission (β_{eff}). A cent is also used to represent 0.01 dollars. In order to explain what these terms mean, here is a basic lesson in nuclear physics in relation to reactivity.

The first value, Δk/k_{eff}, is the departure of a nuclear reactor from criticality. The denominator, k_{eff}, is a multiplication factor that tells you how fast your pool of neutrons is growing. k_{eff} is the ratio of neutrons in your reactor right at this instant to the number you had one generation ago, before those neutrons smashed into your fuel and created new neutrons. For uranium 235 (or ^{235}U), for example, every time an atom is activated by a neutron it spits out two neutrons, and a generation is the time it takes for all of the 'splitting' neutrons to hit uranium and create a new pool of 'split' neutrons. Of course, this is theory rather than practice; neutrons split constantly, so a generation is a type of approximation rather than a physically meaningful time. As well, not every neutron will be able to fission fuel; some escape, some are absorbed by other things in the reactor, and some are going the wrong speed(See: fast neutrons vs. thermal neutrons). In order to determine k_{eff} for a particular reactor, a number of different factors are taken into account, and not all of the values can be determined theoretically.

In the end, the important thing about k_{eff} is that it tells you how fast the neutron supply is growing or shrinking, or if the reactor is sustaining its neutrons by replacing them at the same rate that they are being absorbed or escaping. If k_{eff} is less than one, there are less neutrons every generation and the reactor is subcritical; if it equals 1, the reactor is critical and not changing, and if it is greater than one, the reactor is supercritical and power is increasing.

Δk is the distance that k_{eff} is from critical, or k_{eff} - 1. Mathematically, this means that the reactivity of a substance is 1 - 1/k_{eff}. An object can have positive or negative reactivity depending on what it does to a reactor when it is inserted into the core; adding something like fuel, which has a positive reactivity, increases the number of neutrons each generation, while borated carbon, a compound used in control rods with negative reactivity, will decrease the number of neutrons each generation.

β_{eff}, or *beta effective* is defined as the fraction of delayed neutrons that cause fission. A delayed neutron is one that is created from a fission product, not from a fission reaction. For example, when uranium fissions, one of its products is bromine-87, which decays into krypton-87, and krypton decays further into krypton-86 and spits out a neutron. This neutron is a delayed neutron, and while there aren't a lot of them in comparison to the rest of the neutrons from direct fission(also called prompt neutrons), they do help control the time of a neutron generation, and thus the speed a reactor goes to power.

In order to take into account all of these factors, the dollar as a unit of reactivity divides the orignal reactivity by the β_{eff}, getting a unit that takes into account the effect of delayed neutrons on the change in reactivity of the core. Like k_{eff}, β_{eff} must be calculated for a specific nuclear reactor. This unit is especially useful when discussing types of criticality and power increases; the higher dollar value the reactor core has, the faster its power is increasing, and the more the power increase is due to prompt neutrons rather than delayed neutrons.

So why a dollar? When the Manhattan Project was first underway, a lot of code words were created to talk about nuclear physics. Dollars and cents were a handy decimal system already in place, with a normal enough usage elsewhere to make talking about "fifty cents worth of fuel" less suspicious. The usage has become so regular that when operators talk about the reactivity of something in the core, they talk about its "worth."