Received a great answer on manually calculating this xenon pertubation. Is there anyone who can additionally provide a Python program that I can use so that I can change different unknows at the same time. Thanks$=\frac{[{}^{1^{*}}(m_{11}-{}_o{f}_{11})+{}^{2^{*}}(m_{21}-{}_0{f}_{21})]{}_0^1+[{}^{1^{*}}(m_{12}-{}_0{f}_{12})+{}^{2*}(m_{22}-{}_0{f}_{22})]{}_0^2}{({}^{*}{F}_{11}^0+{}^{2^{*}}{F}_{21}^0){}_0^1+({}^{1^{*}}{F}_{21}^0+{}^{2*}{F}_{22}^0){}_0^2}$

Now since $=\frac{1}{k},$ we have $d=-d\frac{k}{k^2}.$ And since for criticality we have $k=1,$ we then obtain for

$dk=,$ the following expression,

$k==-\frac{[{}^{1^{*}}(m_{11}-{}_0{f}_{11})+{}^{2^{*}}(m_{21}-{}_0{f}_{21})]{}_0^1+[{}^{1^{*}}(m_{12}-{}_0{f}_{12})+{}^{2^{*}}(m_{22}-{}_0{f}_{22})]{}_0^2}{({}^{1^{*}}{F}_{11}^0+{}^{2^{*}}{F}_{21}^0){}_0^1+({}^{1^{*}}{F}_{21}^0+{}^{2*}{F}_{22}^0){}_0^2}$

Now for the case of xenon poisoning the only perturbation is the

$m_{22}$ term.

$m_{11}=f_{11}=m_{21}=f_{21}=m_{12}=f_{12}=f_{22}=0$

$m_{22}={}_x^2$

$=-\frac{{}^{2^{*}}(r,z){}_x^2(r,z){}_0^2(r,z)rdrdz}{\{({}^{1*}(r,z)F_{11}^0+{}^{2^{*}}(r,z)F_{21}^0){}_0^1(r,z)+({}^{1^{*}}(r,z)F_{21}^0+{}^{2^{*}}(r,z)F_{22}^0){}_0^2(r,z)\}rdrdz}$

At this point it is worth noting that the denominator depends on

all of the group fluxes and so the $2$ Group model may be

inadequate. However, we can collapse a many group model to $2$

groups and get an effective first group.

Now Duderstadt & Hamilton give the steady state perturbation

number density for xenon as$,$

And as is well known the number density depends on the magnitude

of the flux. This is the issue.

The goal will be to develop a code that calculates Equation $1$ as a function of the reactor power

level