Up to now, the nuclear power density `ft`

(W/cm³) was calculated from the fission neutron source `sf`

(neutr/cm³/s) by (1) where `κ/ν`

(**skn**) is tabulated along with the other neutronic properties.

Actually, __and__ the delayed neutron emitted by subsequent decay of radioactive fission product emitters

We remind (2) the balance equation of precursor

For stationary condition, (4) applies, which implies (5).

`sf`

represents the total "potential" fission neutron source which includes the prompt neutrons emitted at fission time, `cj`

generated at fission time.
We remind (2) the balance equation of precursor

`cj`

with decay constant `λj`

.
For stationary condition, (4) applies, which implies (5).

A strict mathematical similitude may be established between the delayed neutron precursors and the power decay fission product (FP) emitters. The concentration **j** with decay constant

(8) holds for steady-sate.;

`cyj`

(the added "`y`

" stands for power deca"Y") satisfies (7), where `βyj`

is the number of FP emitters of type `λyj`

.
(8) holds for steady-sate.;

The power density

At steady-state, from (8) and (9) , we obtain (10) which shows that if we set (11),

The actual__instant__ power.

In (13),

For

`fyj`

deposited by emitters `yj`

decay is proportional (factor `μ`

) to the decay rate (9).
At steady-state, from (8) and (9) , we obtain (10) which shows that if we set (11),

`fyj`

could be interpreted as well as the steady-state ratio of `cyj`

generated decay power `fyj`

to the total potential power `ft`

.
The actual

`fyj`

in transient condition is (12), and `f`

(13) the actual In (13),

`βyp`

is the prompt (major) fraction.
For

`yj`

emitters with time constant (`1/ λyj`

) much larger than the application duration, the contribution of those emitters should more conveniently be approximated by a constant part `βy0 ft0`

of the initial power. At steady state, `f=ft=ft0`

and (8) holds.Conceiving the power decay model as a strict analogy to the delayed neutron model allows taking profit of the existing coding. However, as power production is no longer synchronous whith neutron flux, modeling the interaction between neutronic and power effects (for example, the power feedback to reactivity) is more complicated

Power decay model is activated under **Lstcy** and **Lstcyj** lists. (

`be=β, am=λ`

).For most of the transients at power, the effect of decay power is just reflected by a small time lagging and smoothing of power production behind the neutron flux and the activation of the effect is not worthwhile; the normal model is probably conservative.

For safety evaluation of the core immediately after shutdown however, the residual power depends of previous reactor operation history and the delayed neutron produced by remaining precursors may contribute to some fission power. Then the decay power model is necessary.

The prompt fraction

`beyp`

must not be entered: it is calculated from `bey0`

and the `behj`

by means of (14).