Geant4 Version: 11.4.0
Hello everyone,
We have encountered what we think is a bug in how internal conversion (IC) is handled in some 0+ to 0+ transitions when simulating radioactive decay in Geant4. These de-excitations are gamma-forbidden and thus proceed via IC.
We observed the symptoms when simulating the beta-minus decay of Pa-234m to U-234 (from the decay chain of U-238). According to ENSDF, we expect gamma-rays and intensities of 766 keV (0.317%) and 1001 keV (0.842%) from this decay. However, we observe higher intensities in both cases, about 0.95% (766 keV) and 0.91% (1001 keV). This result can be replicated by using the rdecay01 example with /gun/ion 91 234 0 73.920, using the attached macro.
test_pa234m.mac.txt (794 Bytes)
The Pa-234m decay can populate the 0+ states U234[809.907] and U234[1044.536]. Both states can transition to a lower 0+ state via IC or to a lower non-0+ state via gamma decay.
For U234[809.907], the PhotonEvaporation6.1.2 entry is:
7 - 809.907 1e-10 0.0 2
1 766.4089 100 4 0 0.0187 0.7155 0.1208 0.07509 0.01621 0.02888 0.02016 0.004614 5.543e-05 3.119e-05 0.01863
0 809.907 1e-20 1 0 2.7e+22 0.8387 0.1517 0.009666 0 0 0 0 0 0 0
In other words, a very small (1e-20) relative gamma intensity for the 809 keV 0+ to 0+ transition, to “only” allow IC. The very large (2.7e+22) IC coefficient results in a combined relative IC and gamma intensity of 1e-20 * (1 + 2.7e+22) = 270. This matches ENSDF.
However, when this information is read in G4LevelReader.cc, the IC coefficient (fAlpha) is limited (line 355):
fAlpha = std::min(std::max(fAlpha,0.f), fAlphaMax);
Here, fAlphaMax is (line 63):
fAlphaMax = (G4float)1.e15;
The result is a capped IC coefficient of 1e15, making the relative IC and gamma intensity 1e-20 * (1 + 2.7e+15) = 2.7e-5, much smaller than the expected 270. So, almost no IC occurs and the competing gamma transition intensity (766 keV) is too large (as observed).
For U234[1044.536], the PhotonEvaporation6.1.2 entry is:
18 - 1044.536 0 0.0 4
9 192.796 0.067 4 0 0.847 0.1911 0.04915 0.3608 0.1802 0.01336 0.09676 0.05136 0.0007377 0.0003811 0.05605
7 234.629 1e-20 1 0 1.153e+12 0.833 0.1613 0.005763 0 0 0 0 0 0 0
6 258.248 8.6 2 0 0.0548 0.7925 0.104 0.03159 0.02109 0.02392 0.007916 0.005611 0.0001889 0.000206 0.013
1 1001.0379 100 4 0 0.01107 0.7541 0.1236 0.051 0.009555 0.02936 0.01368 0.002712 2.926e-05 1.871e-05 0.01589
Here, the 234.629 keV 0+ to 0+ transition has relative IC and gamma intensity of 1e-20 * (1 + 1.153e+12) = 1.153e-8. This is much smaller than the value in ENSDF, which is 10.4. So, almost no IC occurs and the competing gamma transition intensity (1001 keV) is too large (as observed).
I think a solution could be:
In G4LevelReader.cc, change fAlphaMax = (G4float)1.e15; to 1.e25.
In PhotonEvaporation6.1.2/z92.a234, change 1.153e+12 to 1.04e+21.
It seems IC for this specific decay (Pa-234m) has been given attention in the past (I found Bugzilla reports 1967, 2076, 2170, and a Geant4 forum topic). But unfortunately a part of the problem seems to remain.
This could be an issue for other 0+ to 0+ transitions. I searched quickly and found other 0+ to 0+ transitions where the IC coefficient is large and gets capped (e.g. Th230[634.919]).
I can create a bug report in Bugzilla if this explanation sounds reasonable.
Thanks for your time.