Internal electron positron production


I’m interested in the decay of the first excited state of Zr-90. It is the source of the tiny positron branch in the decay of Y-90 and can be used for PET imaging. ENSDF only has the isomeric transition listed in the table for the isotope. Nickles et al (IEEE 2004) says that the 0+ -> 0+ nuclear level is constrained to decay by 2 gamma emission, internal conversion and internal e-/e+ decay. This is where the positron enters the picture. I’ve searched the G4 documentation and found that double beta decay is not modeled. I did note that there is e+/e- pair production modules with G4 EM physics lists but I think this production event is modeled from high energy gammas.

Anyone know if I’m correct about the assumptions I’ve made about these physics processes within G4/TOPAS? Anyone know a theoretical physicist that can help me with modeling this Zr-90 e-/e+ decay? I would like to get the kinematics as correct as I can since I want to study PET imaging of this reaction in detail. I thought to fake the events using F-18 as the e+ source and then adding a tabulated bremsstrahlung spectrum but I worry about spectrum differences between the F-18 and Zr-90 e+ decays that might be clinically relevant since the Zr-90 e+ is such a small signal.

I did find the BxDecay0 program by the BxCppDev group which is a C++ port of Vladmir Tretyak’s Fortran code. I’m trying to contact the authors about the code systems. Most of the theoretical work is on double beta decay with and without neutrinos and I would just like to help my old experimentalist mind wrap around it better.

Any help with this is greatly appreciated!



William A Dezarn, PhD
Medical Physicist
Radiation Oncology
Wake Forest University School of Medicine
Winston-Salem NC USA

1 Like

Hi Andy,

I don’t know if this topic is still relevant to you, but I don’t see why Zr-90 radioactive decay shouldn’t be correctly simulated in G4. The process of radioactive decay is included in G4RadioactiveDecay class, and as long as the list of decays in the data base is correct it should results in a correct decay chain. Why you don’t give it a try and just check products of Zr-90 simulated decay?

You don’t need a pair production physics for your problem, I think you are confusing two different things. Geant4 does not simulate double beta neutrino-less decay, as it is a hypothetical process possible only if neutrinos are Majorana particles. The standard \beta\beta decay should be covered. Group of Vladimir Tretyak is searching for double beta neutrinoless process. This is not relevant for your problem.

However, I suppose that the branching ratio for Zr-90 decay into \beta\beta is very small (I haven’t checked). Isn’t it a clinical problem? It will results in huge doses for patients and low sensitivity for PET coincidence detection.


Hi Weronika,
I have learned a lot about the specific decay I was interested in since I asked the question. Let me go back and be more specific at this point. I’m interested in Y-90 decay as used in radionuclide therapies, liver microspheres to be more exact. And even more specifically I’m interested in the Y-90 decay branch to the 1st excited state of Zr-90. When I first read in Nickles et al about the internal e-/e+ production as one of the decay states I incorrectly assumed this would be modeled as double beta decay. With more reading and talking with others this decay really is an E0 electromagnetic transition. Since it is a 0±>0+ transition angular momentum selection rules prohibit a first order single photon decay. Going to second order decay transitions leads to the two particle states that can be modeled by the Dirac theory. I found a couple of references last month that discuss the theory some but I’ve got more work to do to understand it completely. I also dug down into the G4 code and data tables and I don’t think it handles the second order transitions. The papers I found have e- and e+ spectra detailed in them when I really need to do a simulation. Let me know if you want the references I found and I’ll be glad to share them!
Thanks for the help! Later,

Hello Andy,

If this or similar rare decay is not implemented inside Geant4 it is possible to add user code. In particular, you may implement your own primary generator for this state of Zr-90 with known e+e- spectra.