.. _section-4.3:

Delayed-Neutron Precursors
--------------------------

The net rate of change of the delayed-neutron precursor population is
given by

(4.3‑1)

.. _eq-4.3-1:

.. math::

	{\dot{C}}_{\text{i}}\left( t \right) = \frac{\beta_{\text{i}}\phi\left( t \right)}{\Lambda} - \lambda_{\text{i}}C_{\text{i}}\left( t \right)

where :math:`\beta_{\text{i}}` is the effective delayed-neutron fraction for
precursor :math:`i`, and the initial, normalized steady precursor
population is given by

(4.3‑2)

.. _eq-4.3-2:

.. math::

	C_{\text{i}}\left( 0 \right) = \frac{\beta_{\text{i}}}{\lambda_{\text{i}}\Lambda}

In terms of the individual precursor delayed-neutron fractions, the
total effective delayed-neutron fraction is given as

(4.3‑3)

.. _eq-4.3-3:

.. math::

	\beta = \sum_{\text{i}}\beta_{\text{i}}

The number of delayed neutron precursors is entered in input variable
:sasinp:`NDELAY`, the effective delayed neutron
fractions are entered in input array :sasinp:`BETADN`, and the delayed neutron precursor 
decay constants are entered in input array :sasinp:`DECCON`. The prompt neutron
lifetime is entered in input variable :sasinp:`GENTIM`.