@Peter The energy of a photon is proportional to hf for all frequencies of the electromagnetic spectrum all the way from gamma down to the lowest possible frequencies conceivable. This is well bellow radio and audiofrequencies. Very low EM frequencies with very low photon energies are considered in the context of cosmology and the very old dilute universe with extreme red shifts. Wavelengths may approach the size of t.he observable universe... that is the "size" of the photon eventually approaches the size of the observable universe as I understand it.

Perhaps the simplest explanation of why photons are not detected at ordinary radio frequencies and lower is that thermal noise proportional to kTB completely masks the effects of quantization caused by very low photon energies. But already at high microwave frequencies this photon noise sets the ultimate limit of receiver sensitivity. At THz frequencies single photon detection is currently possible. But they are always hiding there...

Another matter is the mechanism at the size of what the photon interacts with. Antennas work down to very small sizes. The concept of an classical antenna fails when it can no longer have a meaningful geometry at the molecular level. At the molecular and atomic sizes other mechanisms become important as You well know.

Regarding Your question on antenna size - large antennas of course collect more photons - like parabolic reflectors and horns. But a resonant 1/4 wave antenna or dipole has a fixed size determined by the dielectric constant and the frequency. It will then couple best to the field and give the strongest signal at these dimensions.

I will try to give a simle and short reply, but I am not sure to succes.

the width of a photon is simply its diffraction pattern, the corresponding field is the one given by the maxwell equation (so depends on about every thing on the photon path source etc ...)

For visible light photons, the typical lenght of the variation of the pattern is far greater than orbitals of any electrons ( it is roughtly the wavelength). So as you wrote, when one photons hits a surface, any atoms from this surface can absorb the photon with a probability distribution corresponding to the diffraction pattern.

I hope it helps.

Romain, I do agree with your answer. I had not realized it would be related to diffraction, but intuitively, of course, it must. Rather diffraction depends on the photon's "size", and likely only via diffraction studies can the "width" be determined, empirically, to confirm any predictive math equations.

The relationship of the wavelength to 'width' is still tenuous in my mind. I had thought of that. But my readings have indicated photon wavelength has no associated width, which being physics is often counter intuitive, I accepted with a small grain of salt, as I found it published by more than several fellow scientists. I do agree the wavelength does effect the cross section size on a surface of atoms that will "see" the photon, and have a better probability of absorption. A long time ago, 10 years, I looked online for the related math, and found very little, though I did find some intriguing papers, of which my grain of salt was too large, for me to believe.

Thus, I posted here, in hopes of definitive discussion, and terms or papers or websites I might go to that would be expert on this topic. Best would be equations, as then I could crank out the answers over a range of frequencies. In a week I will have time to try another literature search based upon your input. Thanks Romain.

Peter

But a single photon doesn't have a diffraction pattern, only a multitude of photons have a diffraction pattern, or rather the illusion of one. A single photon has a point of impact, the wavelength refers to its probability of being deflected to strike a certain point not its actual physical dimensions, no? So what size is that single point of impact? Can it be measured?

In case You have not seen this regarding single photon electron scattering cross section:

http://en.wikipedia.org/wiki/Klein%E2%80%93Nishina_formula

The scattering or absorption process as far as I understand it, is a function of both the electrons and the photons cross section and energies. I don´t think diffraction is the best analogy to try to understand a single photon event intuitively. The Quantum probability distribution as in the sums over histories in quantum theory seems to me like a better way to get a feeling for the nature of the cross section, wich needs to be defined as a probability distibution. Particle diffraction as You may well know can be explained this way. In QED theory the strength of photon electron interaction is determined by the coupling constant = the fine structure constant which is a fundamental physical constant that can not be derived. That is essentially the same as the familiar e2/hc. The fine structure constant is a fundamental physical constant that can not be derived.

If the wavelength of a photon was roughly its size then the signal strength in antenna of a radio receiver (lambda in range [3m, 2 km]) should increase when you shorten the antenna, eventually to zero length. Clear absurd, isn't it?

Exactly the same question might be asked about phonons, quasi-particles not existing outside crystals (or magnons).

This article may be of interest:

http://nanoscience.bu.edu/nanophotonics05-files/papers/Pohl%20Optical%20Antennas.pdf

Like any EM radiation, the optimum absorption of the E field is in a 1/4 wave dipole antenna. This one way to define the "size" of the photon in a dielectric media with a certain dielectric constant.

This research on antenna based photovoltaic cells is a fairly hot research topic. Its very different from electron photon interaction.

The field strength in an E-field antenna is maximum at !/4 wavelegth. Coupling to the radiation decreases for smaller antennas.

The single photon coherence length is also a way to define a size for the photon in its direction of travel. There is an interesting discussion with some references here: http://www.physicsforums.com/showthread.php?t=153755

I recently tried to measure the refractive index of a sparse layer distribution of dielectric spheres in water. Contrary to the idea that the light and matter field distributions constitute a mean-field average and therefore that an effective medium assumption can be made to infinite dilution, I have found that there is a limit to the dilution for this assumption to be safely applied. One fairly convincing (in my view of course!) explanation is that fundamental spatial modes of light (photons?) only have a transverse width equal to the inverse of the wavenumber. See if you like the ideas: http://dx.doi.org/10.1364/OL.38.003057

There is a superb treatment of (the wider context of) this question in Charles Joachain's 'Quantum Collision Theory' textbook

I want to thank everyone for causing me to rethink my question, the premise, and it's value. I wanted to respond to each poster (see below, not in any order), as I got value from each post. RG is a great place for value. My sense of understand physical reality has been honed tonight.

Difraction derived cross sections for photons would likely only be valid for that one situation, and not other measurement methods. This type of cross section measuring is true for all cross section determination methods for all particle types, including molecules. So, the dual nature of a photon, and single photon difraction, does not really 'effect' the difraction derived cross section experiment., at least as far as wavelength goes. The same applies for the sparse layer of dielectric spheres. That stated, these two ideas are quite interesting, as extremes must be examined to confirm the interpolation of results between the extremes, or when one goes to an extreme, do the physics change? Good points bearing well to the question. And quite clearly making the 'difraction measurement' not a fully valid way.

I see Scribd.com has a copy of Joachain's book. I will read it. Thanks.

The use of a quarter wavelength antenna could be a strong way, though I think the broadcasting and receiving of 'waves' in this case, is not applicable to higher frequencies, where the math changes to the 'particle' nature of light. Again, however, this extreme needs to be considered.

This direction leads me to another question I have, of the contemporary concensus on how light is different from radio, that is, different equations are 'better' predictors of behavior. It depends on the generation method, or receiving methods. A wire with accelerating electrons it, emits radio waves, and no one has gotten it to emit light, until the wire heats up, and then the method of light generation is from individual atoms, and not from free electrons. Terahertz microwave generation has been recently published on, I just read only the brief, not the full article. However, at the other extreme, recombination of an electron with a positive atom, can lead to a wide range of emitted frequencies, from xrays down to microwaves, and perhaps lower, just not really within the equipment's measuring range, below it's noise level.

Just a slight clarification to the posted info, a quarter wavelength antenna is not the only maximum field strength, as longer antennas, multiples of the full wavelength are the same field strength. I agree, the quarter wave antenna is the 'shortest' length that can 'best' receive and send that wavelength. Shorter antennas are less efficient, having higher signal loss/noise issues. Like you write, the coupling is key.

The signal strength in an ever shortening antenna, whose cross section is decreasing, would intersect/pickup fewer 'photons', so a counter to the strength increasing would be occuring. That's my first thought. The second, how do these two effects match in magnitude? My third thought was why is size connected to strength? Size is such a mis-used word in this entire thread. Wavelength is inversely related to energy level (strength?). So, in 'context' size would be inversely related to strength. I agree if wavelength was related to size by proportion or similar, then an absurdity does occur.

A quantum method using the fine coupling constant would seem to lead to a definitive photon size, if only quantum mechanics could be so interpreted. Given a single experimental setup, such likely could be achieved, and the probability distibution would likely provide a predictive method, to explore the extreme photon wavelengths. The Klein-Nishina formula had I read last year, and it assumes the photon is a point source. Well, I assume it does, as most QM does. I'd like the time to un-assume this point source idea, and crank the numbers to find a photon size, that works, and see how that extrapolates to the extremes.

Lattices and inerton radiation is a part of the growing pains of bleeding edge physics. There are many scientists making conjectures at these small scales, no one is the "lead". The idea of a holographic universe, reduceable to a digital form, has more than one proponent. ResearchGate I feel is created to be place where exposure to these 'radical' ideas is a cool thing. I like knowing of these very new theories, to compare and contrast them, to watch as history selects a winner, which is displaced in the far future. The Earth is the center of Universe lost to Kepler/Newton, who lost to Eisenstein, ... Only those scientists who do this type of compare and contrast have a chance of competing.

"Single photon coherence length" - Wow. What a thread at that URL. I had to skip some of the longer posts, as they went their own way, away from the original question. The answer involving QED has something distinct to offer my question. I'm comfortable with the 'fact' that a photon/particle travels by 'all' pathways, and so exists in quite a 'large space.' My question was clarified for a single experimental setup, striking a surface, which electron wil soak up the photon. Or put it another way, what surface cross section size equation is there to the photon wavelength? That QED will have a definite 'say' in answering my question is now obvious to me, and I will look into that.

To find my answer, I'm thinking I must design an experiment, and try it. I'm not sure such an answer would have any predictive value, so the experiment set up must include that. I'm putting on my thinking cap.

@Peter The energy of a photon is proportional to hf for all frequencies of the electromagnetic spectrum all the way from gamma down to the lowest possible frequencies conceivable. This is well bellow radio and audiofrequencies. Very low EM frequencies with very low photon energies are considered in the context of cosmology and the very old dilute universe with extreme red shifts. Wavelengths may approach the size of t.he observable universe... that is the "size" of the photon eventually approaches the size of the observable universe as I understand it.

Perhaps the simplest explanation of why photons are not detected at ordinary radio frequencies and lower is that thermal noise proportional to kTB completely masks the effects of quantization caused by very low photon energies. But already at high microwave frequencies this photon noise sets the ultimate limit of receiver sensitivity. At THz frequencies single photon detection is currently possible. But they are always hiding there...

Another matter is the mechanism at the size of what the photon interacts with. Antennas work down to very small sizes. The concept of an classical antenna fails when it can no longer have a meaningful geometry at the molecular level. At the molecular and atomic sizes other mechanisms become important as You well know.

Regarding Your question on antenna size - large antennas of course collect more photons - like parabolic reflectors and horns. But a resonant 1/4 wave antenna or dipole has a fixed size determined by the dielectric constant and the frequency. It will then couple best to the field and give the strongest signal at these dimensions.

@Erik Interesting about the extreme low frequency. It makes sense to explore and attempt to measure at these wavelengths. If it can not be measured, does it exist? LOL A Marconi antenna 1/4th the length of the observable universe to send and receive ... to where? LOL. Gives me something to read up on. Thanks Erik.

Photons in the RF range would be identical to RF waves, due to QM duality. And Maxwell's equations. The generation method should not matter. I'd like to generate gamma rays with an RF method for research purposes. Easily said, harder to do with a straight piece of wire. Your noting 'classical' antenna size down to the nucleus size, where gamma rays are generated by decay events, is the other extreme. Does the classical antenna size fail at some size above this? Worthy of my looking into the recently announced tetrahertz RF generator. What size is it theorized to fail at?

Before I wrote my post on quarter wave antenna, I read about the comparison. It's a trick of wording, I think. 1/4 wave antenna 'couples' with a reflected image in the ground plane. A plane that has a degraded performance compared to either a half or full wave antenna. I wondered about the comparison, but found nothing definitive in my quick search. I believe Erik. Yes, the coupling may be strongest. "Signal strength" does not depend just on "coupling strength." Which is being talked about? The trick of wording needs more clarification. Sending a 'strong' signal from a small length of wire, unable to avoid melting at high amperages... compared to a longer, thicker antenna wire? Or receiving a greater number of photons? I ask, as I should know from the theoretical level, not just the intuitive one.

@Peter A link to VLF research: http://vlf.stanford.edu/

I do not know what the longest wavelength actually detected is, but I had friends at the university who used ton sized stacks of concrete steel reinforcement rods for H field VLF antennas in order to try to detect the lowest possible frequencies. Radio astronomy and geophysical phenomena are possible extreme VLF sources.

Visible light has a longer wavelength than atomic/molecular size. A search on "nano antennas" will yield plenty of information of direct dipole coupling to visible light photons. It seems uncertain at what wavelength this fails, but I guess the theoretical limit is probably somewhere in the Xray region.Making a physical antenna structure the "size" of the photon then becomes increasingly difficult. Gamma rays are likely out of bounds.

Wider resonant antenna structures generally tend to become more broadband. That is basic antenna theory. Matching also is a complicated field in itself. It is true that power matching not always gives optimum results. Noise matching and near field effects are other parameters affecting performance of a EM detector/antenna system. A good text on low noise reciever and antenna design usually describes these issues well. Also high Q of the system helps exclude noise. Noise temperature of the reciever front end is almost always the limiting factor of detectability.

Peter's initial question (see above) requires a classical-type answer which is fair enough given that we conceive of the world in this way. This does not mean that non-classical concepts cannot underlie our observations of course. So, taking the answer required, we need to describe a spatially constrained transverse EM field carried by our concept of the system that delivers energy in quanta as ‘clicks’ on a detector. When present in large numbers over short times or in low numbers over long times this conceived-of system needs to display diffraction phenomena and essentially all the classical observed properties predicted successfully by EM theories. Currently, the spatially constrained EM field is a postulate with no distinguishing experimental verification. Infinite transverse plane waves are the perfectly satisfactory starting point for observations not requiring detection of energy quanta. The Pilot Wave theory of de Broglie, extended and further formalised by Bohm is perhaps the most well developed postulate that seeks to combine the two aspects. Coupled with further postulates of the paths taken by the particles of such a postulate (paths of least time – Feymann) we can have an explanation for both ‘clicks’ and ‘diffraction’ as observations of the behaviour of, say, electrons or even C60. Bohm could not, however, fit the massless photon into the “de Broglie-Bohm” theory comfortably so we would need to go a bit further to adopt that route. Dr. Krashnoholovets begins his last post with a concept along similar lines perhaps (in my works the particle and its "wave" are two separate objects, which are bond in a special way. This "wave" is a cloud of excitations that the moving particle excites in the space). You may like to see why I have had to abandon the infinite plane wave approach in my own work after very careful consideration of my experimental results. Great care is needed to ensure that there is no alternative explanation for observations before moving away from traditional and successful theories. The paper referees are not responsible for asserting the correctness of any paper they allow through but within their realm of expertise they do have to assert that all reasonable alternative avenues have been explained. Thank you for posing a great question that deserves proper time spent on it.

@Erik ELF is niced expounded upon at Wikipedia.org. I've read about 10 articles there now. You may start at http://en.wikipedia.org/wiki/Extremely_low_frequency

Apparently, the earth's atmosphere does 7.8 Hz. Man may have done as low as 3 Hz, but it was not clear. Submarine communications go from perhaps as low as 30 Hz to 300 Hz, and upwards to 3 KHz. These are low radio frequencies.

Nano antennas are interesting. I'll look into them. Ditto the web site URL. Thanks.

Gamma ray antennas are the size of nucleons. Thus, xrays interact (send/receive) with the larger electron shells, while gamma rays interact (send/receive) with the smaller nucleons. Which gives a type of cross section for xrays and gamma rays, via the antenna analogue. Visible light cross sections must be larger than xrays. A very qualitative analysis, and a starting point for answering my question.

I realized my post about matching, did not cover all bases. There are 2 for any antenna type. Receiving and transmitting. Therefore, my post covered both, but for different antenna types. My bad. I should have covered both receiving and transmitting for both the quarter wave antenna, and larger antennas, for a fair comparision - talking about gain versus matching performance.

It's off topic for me to go further in any of these area. I prefer the thread to stay focused on photon 'size', via types of measured cross sections.

I have not mentioned my college education included the fact that the EM components are at right angles to the direction of travel. And their 'magnitude' has no physical size, meaning the EM components change phase inside a physical length of zero units. There is no EM width of a photon is what I was taught. Thus, I talk about measured cross sections, which can vary from the 'zero width' of the photon's EM field.

There are two other areas I have been quiet about.

First, traveling at the speed of light, any EM phase change over a distance traveled, should be zero, due to time stopping at that velocity. Yet, all the material I read states phase changes, magnitude of right angle E and M fields, occurs in the direction of travel. I've not gotten a decent explanation. Should likely be a different RG post. I do know that photons do not age over any distance travelled, due to time stopping at their velocity. With the possible exception of frequency change due to the expansion of space, from dark energy, which I have some ... doubts about. No one has gone out there to measure this effect, so it's unproven theory to me.

Second, I'm fine with the QM wave function description of the location of the photon, being spread out, to take all pathways. The notion of duality being either a particle or wave, and never both at the same time, appears to have been finally put to rest. Duality means all three can occur. It's my belief that neither particle or wave exist solely alone. That the photon is dual at all times. Regarding being spread out in space, according to the wave function, a probability measurement, I have some trouble with that physical interpretation, not that I can not visual it, or manipulate the state, but it seems to require instantenous communications between all non zero wave function locations. Which I am 'likely' fine with, due to other 'beliefs.'

These two points, as well as the zero width assertion for the EM fields and phase changing, must be consistent any cross section analysis, and is why I have added them. As eventually, they must be integrated.

@Graham You are right that classical interpretation, and it's underlying non classical basis would have to be consistent with any 'cross section analysis.' I'm now thinking to first enumerate the frequency quality of any cross section size. And once that is completed, derive quantitative equations, using every decent theory. You have mentioned several such theories. Even through they have great weaknesses in this area, their thinking method should be attempted, for completeness.

You write, "Currently, the spatially constrained EM field is a postulate with no distinguishing experimental verification", and I was surprised to realized I have never made that connection. Most all antenna near field mathematic theory makes the assumption. If we are talking about the same thing. In my last post, I clarified my understanding. I'm wondering if it matches yours.

I did have time to read your profile page, and see several papers I must now review, before responding to your infinite plane approach, rather not doing that approach. I dislike any 'infinite' approach due to the likelihood the universe does not offer that option. That is, any theory with infinite boundaries likely does not match any theory of the creation of the universe, therefore the theory can not be correct.

@Krasnoholovets There are some natural limits to your theory that appeal to me, the lack of infinite, using Planck as the rationale. I've thought along those lines, using Planck concepts to limit fields of GR and QM. At some point in the spreading of a 3D field from a central point, the 'energy' density must reach some definitive minimum value, that a lower value does not exist, the Planck unit.

I'm glad to see someone exploring this realm. With a qualitative approach, I think many a thought experiment can be done. I'd like to see how a quantitive approach would derive equations that give predictions.

I wish I had more time to read other such Planck limit theories, as it seems to have become popular among some physicists, to explore this thought area. Changing from a calculus with infinitely small divisions, to a quantized division has not fruitfully recreated GR or QM, at least at the time of my last review of the literature.

The reason for me to review the "quantitive approach," is I am not getting an level of understanding with just a "qualitive approach." I read some of your papers, scanning really, looking for a paper with lots of equations. Given the number of papers, likely I missed those with such.

Dear Peter Benjamin

Thank you very much for your nice opinions, Yes very nice views. I am reading and get much more ideas from you.

Since my last post, I have found about a dozen ways to measure for a specific application the photon cross section. That is, the articles I read could have derived a cross section equation. To see the value of having such cross sections per application, per frequency, I'm thinking I need to actually itemize what I have found, and do the cross section calculations myself. Or least list where each study 'stopped' at.

For example, the single mode fiber cable can support multiple frequencies based upon it's diameter. Not the best example, as most studies I found did not see their effort as determining a cross section value, at all. But they all had an 'extreme' in physical dimensions where their 'process' stopped being feasible. That's a type of cross section. Make the fiber too big and it becomes multi mode. Make it too small and it supports fewer frequencies.

Another example is a sheet with a grid of tiny holes, to let light through, allows much more light through than the sum of the hole cross section areas. Light behaves strangely for this example. Very strange. What are the 'cross section' relationships between photon wavelength and hole size and material thickness?

The stopping power of shielding material thickness relates to the radiation frequency. Is there a way to calculate a cross section?

I have many ideas now. I just had to get the right perspective to write a properly worded problem statement, so to have a solid approach to problem solution direction, that was doable.

So, will 'value' be found in itemizing? A literature search with summary table I think is the first approach, to even begin understanding what value may become apparent, as one or more patterns emerge in the data analysis.

Thanks to the many leads provided in this thread, which I based my literature search on. Each lead will have at least one set of entries in my data collection.

I had thought my question just too narrow minded, a fool's errand, as everyone knows a photon has no width. But a cross section is not a width, but application specific parameter for design predictability. By cross correlating between application, I will look for a pattern, a mathematical relationship.

Expectations are 1 year to collect the data, it will be web based storage, and another year to analysis for mathematical relationships between applications. That's an estimated schedule. Then, I might answer my question, of what is the cross section of a photon hitting a particular atom, or electron shell, or set of, in a surface. Another way to say this, is what is the cross section area of the surface the photon impacts, say 90% of the time. How many atoms wide is that cross section? Of course its surface material dependent, and incident angle, and dependent on the frequency degree of transparency of the material.

This 1998 article has a 'width' or diameter of a photon, which now has confirmation since 2010 through 2013. I have some catch up reading to do, as do many reading this thread.

Title: Confirmation of Helical Travel of Light through Microwave Waveguide Analyses

http://omsriram.com/Helical%20Travel%20of%20Light.pdf

Abstract

The essence of this theory is that photons are small particles of ponderable mass that travel in set helical trajectories. For any photon, the diameter of its helix may be calculated by dividing its wavelength by (equation removed) ...

201X confirmation studies abound and here are two.

http://iopscience.iop.org/1367-2630/13/5/053017/pdf/1367-2630_13_5_053017.pdf

http://www.colgate.edu/portaldata/imagegallerywww/98c178dc-7e5b-4a04-b0a1-a73abf7f13d5/ImageGallery/imaging-spatial-helical-mode.pdf

http://en.wikipedia.org/wiki/Orbital_angular_momentum_of_light

Happy reading.

An electromagnetic wave packet with the same energy hf and angular momentum h/(2*pi) as a photon must have a certain radius r=0,338*lambda. The length of the wave packet is unknown, i would take the coherence length. http://vixra.org/pdf/1408.0139v1.pdf

This post will be asked as a separate question later this month. I add it here, only to expand this thread from it's current answer level, to include another type of photon cross section, that has a very complex answer, thus a new thread is needed to focus on the complexities. The last two paragraphs contain the point pertaining to the photon cross section questions. The next paragraphs are background, and assume you have knowledge of the QM double slit experiment, in likely more detail than taught in college physics.

The double slit photon experiment has much published on it. I recall reading equations predicting the behavior based upon slit separation and slit width. I will try to find the information again, for the new thread.

The current Copenhagen interpretation of QM is the singularly emitted photon, electron, particle, molecule, aggregate aimed at the double slits and detected on the other side will form a detection pattern similar/identical to that of macroscopic waves. Everything I have read states:

A 'localized' particle is aimed at the slits and the path the particle travels is all possible paths, to the slits, through the slits, and then to the detectors, where self interference has occurred, of a wave nature (non localized particle).

At some point the 'localized' particle 'seems' to have turned into a wave. [Though recent 2018 experiments have detected both types of behaviors simultaneously - the concurrent measurements done show both particle and wave behavior.]

Of course, the QM duality terms of 'particle' and 'wave' are ill defined, as both are suppose exist at the same time.

Thus, the slit experiment with it's emitted 'localized' particle, that goes through BOTH SLITS, somehow turned into a wave before reaching the slits ... yet, I read nothing about this affect. Instead, I read about the particle going through both slits, meaning the particle energy decided to double itself, or half itself (could it then still be a 'particle?'), to go through both slits. I have doubts about my interpretation of the particle travel from the emitter to the slits.

Copenhagen interpretation states where one can not measure, do not worry, just calculate what you can. Thus, Copenhagen interpretation is not ever going to address how a generated particle, localized, can go through both slits, or when the particle turns into a wave, other that it is so detected, thus must now be a wave, in order to exhibit wave behavior. This leaves the questions of why the Copenhagen interpretation states the particle goes through both slits, as no measurements are done, so the theory should be silent on this point. Sorry, I got verbose, but felt the ambiguity in Copenhagen leads directly to the cross section issue, stated below.

The point is the particle cross section can be measured, by increasing the distance between the slits, until the detected wave behavior stops (the particles are fired one at a time, not millions at a time). If the slits are wide enough, I read the wave behavior stops, and one gets two separate slits, with two detected humps of particles, not a wave interference pattern.

Seems this slit width is another type of cross section. A measurement that might enhance the Copenhagen interpretation, or at least ask serious questions of it. Tracking this cross section of all sorts of particles would interest me. At a minimum, adding this "double slit cross section" to the collection for each type of particle, is of interest in defining the particle 'size.'

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