Normalization of Simulated histograms

Dear All!
I wanted to simulate Cs-137 and i am interested in 662 keV gamma line of it. I simulated Cs-137 and i got the spectrum shown in figure 1 where i didn’t get any 662 keV line so in order to get that, i simulated excited state of Ba-137 and as a result get spectrum shown in figure 2.

Now to do analysis i want to add both of them and to add them i want to normalize them first. But i’m confused at this step.

What i’m doing to Normalize Figure 1 is this: hist->Scale(1./hist->Integral())

And for figure 2 : hist->Scale(0.947/hist->Integral()) beacuse 662 keV line has a branching ratio of 94.70.

And then i’m adding them up. I am not sure whether i’m doing it right? Or is there any mistake in it. It would be great if you could help me with this.

Thank you!