RESNUCLEI results after irradiation

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1

Dear FLUKA experts,
I am trying to study activation of niobium.
In the following file I defined a 1mm1mm2mm niobium cube,
irradiated by mono-energetic, 10 MeV neutrons, for one minute, and score the activation products at different times after irradiation.
When I look at the activation products, I do not understand the time evolution of the products and their isomers.
Please refer to the table below, regarding two isotopes pairs - 93Mo and 93mMo, and 94Nb and 94mNb.

Isotope Half life Activity at the end of irradiation (Bq) Activity after 1 hour (Bq)
93Mo 4 ky 2.1e-4 2.3e-4
93mMo 6.85 h 960 870
94Nb 20.4 ky 2.1e-4 2.2e-2
94mNb 6.26 m 2.9e6 3745

I have several questions:

  1. To the best of my understanding, FLUKA assumes 50%-50% production rate between the radionuclide and its isomer. For 93Mo we have two isomers - 93mMo and 93nMo. Does the production yield is divided equally between all three products (meaning 33.33 % for each), or there is a 50%-50% production yield between the isotope and all its isomers, and then an equal production probability (meaning 50% chance for 93Mo, 25% for 93mMo, and 25% for 93nMo)?

  2. Once we obtain the activation products, how does FLUKA decay the products? When I consider the table, I see that the activities of the isomers decay as expected, but the buildup rate for the non-metastable states is several orders of magnitude lower then expected, since the those metastable states should decay to the non-metastable state. Due to they long half life, all of the produced activity should be present, with negligible decay.

  3. If FLUKA does not consider the decay products that are created after irradiation and just decays the products analyticity, why does the activity of the non-metastable isotopes increases after time?

Please refer to the attached files.
Thank you kindly in advance,
Hen Shukrun
activation.flair (19.6 KB)
activation.inp (2.5 KB)
q_42_tab.lis (10.9 KB)

3

Dear Hen,
thank you for your question!
Please allow me some time to look at your requests and I will then come back to you.

Best,
Giuseppe

4

Dear Hen,

Let me answer to your questions one by one:

With more isomers, is the production yield divided equally between all products?

In the case of n possible isomers for a specific isotope, FLUKA will subdivide equally between them the production rate: each will be created as 1/n fraction of the total production rate. You can prove it yourself with small changes in your input. For example, changing the target material to Hf, you can check the production rate of 177Hf and its two metastables states (177m1Hf and 177m2Hf). In order to compute the production rate, you can add a RESNUCLEi card without an associated DCYSCORE card. As result, you will see all three states have the identical production rate.

The build-up rate for the non-metastable states is several orders of magnitude lower then expected

Doing a quick run with the input you provide, I can see that the results for 93Mo and its isomer have high uncertainty, I will focus then only on 94Nb. I am adding the results from the same short run in the table below:

Isotope T1/2 A0 (Bq) A1h (Bq)
94Nb 20.4 kyear 2.1651E-02 (3 %) 2.3404E-02 (3 %)
94mNb 6.26 min 3.0061E+06 (3 %) 3.927E+03 (3 %)

I am assuming there is a typo in the A0 result you are reporting for 94Nb.
Focusing now on the values, one should pay attention to the fact that they are expressed as Activity (Bq), so not as radionuclide’s concentration. Therefore, considering the decay chain of 94mNb, an exponential decrease of the metastable’s activity is expected, as you correctly say, and it is noted in the results. For the ground state, the activity build-up should follow the Bateman equation:

image

Computing analytically the activity for the ground state after 1 hour, summing the remaining activity of 94Nb directly produced by the neutron beam to the result from the Bateman equation, I get a value of A1h (94Nb) = 2.3404E-02 Bq, which is identical to the result of RESNUCLEi.

Why does the activity of the non-metastable isotopes increases after time

FLUKA does considered the decay products, and as said in the answer before, the activity 94Nb builds up due to the decay of 94mNb.

I hope this help you. Let me know if more clarifications are needed.
Best,
Giuseppe

5

Dear @gmazzola,
Thank you kindly for your detailed answers, this clears up my confusion.

Regards,
Hen

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