A Kerma from neutron irradiation

[Ozymandiac]

TL;DR

Does the kinetic energy of an atom with net zero charge count towards kerma?

Hi all,

I have a question regarding kerma from a neutron source. I will be giving a lecture about this topic (and others), and was creating a figure to explain which interacties / energies contribute to kerma and which do not.

The definition of Kerma I use is taken from ICRU report 57:

In the figure (see below), a reference volume with mass dm is irradiated by neutrons. From top to bottom, there are four interactions of neutrons with nuclei. Kinetic energies are denoted with T. Secondary ionisation is shows as small black dots. The aim of the figure is to determine which energies are counted towards the calculation of kerma (and which aren't). My initial thought was that kerma would be: K = (T1+T2+T4+T6) / dm.

My questions are all very similar, because I am unsure how I have to interpret the word "charged" from the kerma definition.

• In the first interaction (counted from the top) I show an (n,p) reaction. Does the kinetic energy from the nucleus (T2) count towards kerma? Does the moving atom even ionize surrounding atoms? I suppose the atom has charge -1 for a split second (since a proton was scattered away), but that extra electron will be quickly dumped, right? After which the atom has 0 charge.
• In the second interaction I show neutron capture (n,gamma). The atom recoils with kinetic energy T4. Is T4 counted towards kerma? My initial response was yes, but since the atom is neutral it does not satisfy the above definition of kerma.
• In the third interaction I show elastic scattering (n, n'). As before: does T6 count towards kerma, since the atom has neutral charge?

I would be grateful for any help and discussion.

 

[Astronuc]

TL;DR: Does the kinetic energy of an atom with net zero charge count towards kerma?

The definition of Kerma I use is taken from ICRU report 57:

Kerma is an acronym for Kinetic Energy Released per unit MAss. It is a non-stochastic
quantity applicable to indirectly ionizing radiations, such as photons and neutrons. It quantifies
the average amount of energy transferred from the indirectly ionizing radiation to directly
ionizing radiation without concerns to what happens after this transfer. In the discussion that
follows we will limit ourselves to photons.

Ref: https://recherche-expertise.asnr.fr...s_sante/documentation/syllabus_chapitre_2.pdf

In the first interaction (counted from the top) I show an (n,p) reaction.

The nuclear recoil T₂ counts to the kerma. The kinetic energy of the incident neutron is transferred to the nucleus and proton. Now part of T₁ is impart to the material (dm) until the proton leaves the dm, so one has to account for the portion of the kinetic energy transferred from the proton. The remaining energy of the proton would be imparted to the media outside dm.

• In the second interaction I show neutron capture (n,gamma). The atom recoils with kinetic energy T4. Is T4 counted towards kerma? My initial response was yes, but since the atom is neutral it does not satisfy the above definition of kerma.
• In the third interaction I show elastic scattering (n, n'). As before: does T6 count towards kerma, since the atom has neutral charge?

T₄ and T₆ count towards kerma. Based on the diagram, the photon and neutron (n') do not interact with the media of dm, so hν₃ and T₅ are not transferred to the media in dm.

The (n,α) reaction occurs outside dm, so the nuclear recoil, T₈ would not contribute to kerma in dm, but some of the alpha particle kinetic energy of the alpha particle is transmitted in the media of dm, so one could have to consider the contribution of the appropriate fraction of T₇ lost in dm. Since, there is an interacting medium outside dm, as evidence by the (n,α) reaction, one would have to consider energy of particles energy dm due to external reactions.

One would divide a target into many dV or dm, where dm = ρ dV. The finer the incremental volume the better the resolution of gradients, but one has to count more incident particle histories (usually with a Monte Carlo code).

 

[Ozymandiac]

Ref: https://recherche-expertise.asnr.fr...s_sante/documentation/syllabus_chapitre_2.pdf


The nuclear recoil T₂ counts to the kerma. The kinetic energy of the incident neutron is transferred to the nucleus and proton. Now part of T₁ is impart to the material (dm) until the proton leaves the dm, so one has to account for the portion of the kinetic energy transferred from the proton. The remaining energy of the proton would be imparted to the media outside dm.


T₄ and T₆ count towards kerma. Based on the diagram, the photon and neutron (n') do not interact with the media of dm, so hν₃ and T₅ are not transferred to the media in dm.

The (n,α) reaction occurs outside dm, so the nuclear recoil, T₈ would not contribute to kerma in dm, but some of the alpha particle kinetic energy of the alpha particle is transmitted in the media of dm, so one could have to consider the contribution of the appropriate fraction of T₇ lost in dm. Since, there is an interacting medium outside dm, as evidence by the (n,α) reaction, one would have to consider energy of particles energy dm due to external reactions.

One would divide a target into many dV or dm, where dm = ρ dV. The finer the incremental volume the better the resolution of gradients, but one has to count more incident particle histories (usually with a Monte Carlo code).

Dear Astronuc,

Thank you very much for your reply. I think there are a couple of points that require some further discussion, and some questions of mine that remain unanswered.

You quote a definition from a source that seems perfectly respectable to me. However, my original post includes a definition from the International Commission on Radiation Units & Measurements (ICRU). As far as I am aware, this is "the" definition. The second reason that I included the ICRU definition, is because it is included in the textbook that my students will receive. Finally, most of my questions relate to a very specific word in the ICRU definition ("charged").

I thought it might be useful to list the 8 energies and see how we align.

1. T1: you seem to say that only part of T1 is counted towards kerma (but I might have misunderstood your wording). I would say that T1 is counted in full towards kerma. It is irrelevant where the proton goes and if any ionisation occur outside reference mass dm. Only the initial kinetic energy is relevant. As you quoted in your definition of kerma: "without concerns to what happens after this transfer."
2. T2: see T4.
3. hν3: does not count towards kerma. We are agreed here.
4. T4: I am still unsure how to explain how this counts towards kerma, because the recoiling atom has net zero charge. It does not seem to satisfy the ICRU definition.
5. T5: does not count towards kerma. We are agreed here.
6. T6: see T4.
7. T7: does not count towards kerma. We are agreed here.
8. T8: does not count towards kerma. We are agreed here.

Again, very grateful for your thoughts.

O.

 

[Astronuc]

Considering the definition of kerma (kinetic energy released in matter) = "the sum of the initial kinetic energies of all the charged ionising particles liberated by uncharged ionising particles in a volume element of mass dm." Other definitions replace 'uncharged' with 'indirectly', but it means the same. So photons and scattered neutrons (n') do not count for the neutron kerma in the volume dm.

On the other hand, one must consider the radiative kerma (or kerma from the photons) in addition to the neutron kerma, if the secondary neutral particles interact within the volume associated with mass dm.

Atoms are considered charged since as they are displaced from the lattice, their electrons interact with other electrons causing atoms to be ionized. It's more clear that a proton and alpha particle are charged, but so is the nucleus. When a proton leaves the nucleus, the Coulomb force binding the electrons is reduced, so the atom (of Z-1) loses an electron, and likely the proton will affect one or two electrons on the order of femtoseconds.

Depending on the incident neutron energy, the displaced atoms collides with other atoms causing a 'displacement cascade'. https://en.wikipedia.org/wiki/Collision_cascade

So, in the (n,p) case, all of the incident neutron energy T(n), which is absorbed by the atom (nucleus) and partioned between the recoiled atom and proton. So, T(n) = T₁ + T₂.

For the (n,γ) and (n,n'), some of the incident neutron kinetic energy is not transferred to the nucleus, but rather some energy excites an internal state in the nucleus which then decays by photon emission (radiative capture) with energy hν₃ (so T₄ counts for kerma), or the neutron scatters losing some energy T₆ (which counts as kerma) to the nucleus but retains some kinetic energy T₅.

In the case of the (n,α) example, the neutron interaction happens outside the volume associated with dm, so it does not count in that volume, but would count in the volume dV in which the interaction takes place.
See page 2 (after the title page) of this presentation.
https://www-nds.iaea.org/nrdc/wksp_2014/present/simakov.pdf
When it comes to absorbed dose, then one has to apply kerma factors.

The example presented is for neutrons (indirectly or uncharged (i.e., neutral) ionizing by virtue of the atomic displacements).

There is a similar treatment for photons, which interact primarily with atomic electrons by virture of Rayleigh scattering, photoelectron effect (i.e., complete 'absorption' of the photon) and Compton scattering. Then there are photonuclear reactions: pair (e⁺, e^-) production, photoneutron production, and for U and transuranic nuclei, photofission, if the photon energy is sufficient. Photoneutron and photofission compete.

To calculation heating and absorbed dose, one has to consider the energy deposition of the secondary particles.

I'm particularly interested in radiative capture and photonuclear reactions in structural materials with respect to cumulative atomic displacements, which affect thermomechanical and some thermophysical properties, as well as the photonuclear reactions in structural materials and nuclear fuel systems.

I like the following video that explains KERMA and other terms like TERMA and KERMA_c