Under the Standard Model, an antineutron would be very short-lived inside an atom. It would quickly turn into an antiproton (much more quickly than a free antineutron; effectively instantaneously) through inverse beta decay, and the antiproton would annihilate a proton in short order. So right there, the simple stability of any atom is already experimental proof that it does not contain antinucleons.

However, the proposed process involving neutrinos (condition (2) in the question details) amounts to throwing the Standard Model out the window. Unless we know what model takes its place, it is quite impossible to answer the question, since in the absence of a predictive theory, anything goes.

Presumably, whatever this model is, it should prevent the decay of antineutrons inside an atom, in addition to leading to the violations of lepton and baryon number conservation mentioned in the question details. I sincerely doubt that a self-consistent model with these properties exists, much less one that is also consistent with the experimental verifications of the Standard Model.

In any case, not knowing what this model is, it really isn't possible to answer the question. As I said above, under the Standard Model, no stable atoms can possibly exist that contain both nucleons and antinucleons.

As to Question C in the question details, I suspect that existing experimental data from any particle accelerator (which already provide strict constraints, e.g., on lepton number conservation) would establish very strict upper limits for the cross section of the proposed process. Even if it did happen, it would be an extremely rare process.

Under the Standard Model, an antineutron would be very short-lived inside an atom. It would quickly turn into an antiproton (much more quickly than a free antineutron; effectively instantaneously) through inverse beta decay, and the antiproton would annihilate a proton in short order. So right there, the simple stability of any atom is already experimental proof that it does not contain antinucleons.

However, the proposed process involving neutrinos (condition (2) in the question details) amounts to throwing the Standard Model out the window. Unless we know what model takes its place, it is quite impossible to answer the question, since in the absence of a predictive theory, anything goes.

Presumably, whatever this model is, it should prevent the decay of antineutrons inside an atom, in addition to leading to the violations of lepton and baryon number conservation mentioned in the question details. I sincerely doubt that a self-consistent model with these properties exists, much less one that is also consistent with the experimental verifications of the Standard Model.

In any case, not knowing what this model is, it really isn't possible to answer the question. As I said above, under the Standard Model, no stable atoms can possibly exist that contain both nucleons and antinucleons.

As to Question C in the question details, I suspect that existing experimental data from any particle accelerator (which already provide strict constraints, e.g., on lepton number conservation) would establish very strict upper limits for the cross section of the proposed process. Even if it did happen, it would be an extremely rare process.

@V. T. Toth : Your arguement relies on the traditional assumption (and dogma) that a massive particle and a corresponding antiparticle would annihilate if their distance is extremely small, and that this happens to   all   kind of particles under   all   circumstances, even for the hypothetical quarks inside a nucleus, which have never been observed as free particles. Obviously, the Standard Model is in accordance with this dogma. But it seems that such annihilations can be observed in experiments "directly"  (i.e. nearly without argueing in the context of a physical model or a physical theory) basically in the case of high energy collisions of stable particles, i.e. electron-positron-collisions and proton-antiproton-collisions.

"Throwing the Standard Model out the window" is just the right way to obtain particle models and physical theories beyond the Standard Model and which can describe physical phenomenons which cannot be explained by the Standard Model, for example why the proton and electron and neutrino and corresponding antiparticles seem to be the only stable massive particles which can exist in reality.

There are attempts twords an 'elementary' particle theory beyond the Standard Model (and beyond perturbative methods of QFT) which consider hadrons as well as leptons as compound systems of fundamental objects.

One of such an (unpublished) attempt considers 'elementary' 'particles' as objects having a 'core' which is 'made out' of 6 constituents of 2 sorts of 'fundamental' building blocks of matter and radiation, called the 'low-hypotron' (el. charge +1/3) and the 'high-hypotron' (el. charge +2/3) and corresponding 'anti-low-hypotron' and 'anti-high-hypotron'.

One of the preliminary results of this 'hypotron theory' (HT) is that --on the basis of  (1) a symmetry principle concerning the hypotron configuration of such 'cores' of elem.particles and (2) a minimum principle concerning a non-additive quantity called 'supercharge' (which is mathematically realated to el. charge by some squaring processes)-- :

(A) the quark model can be recoverd in a slightly modified manner (the notion of 'color' can be introduced in a quite different way)

(B) the concepts of charge-conjugation/anti-'particle', and the concept of boson and fermion, and leptons and baryons can be formulated in a manner that does not rely on any kind of QFT formalisms

(C)

4 stable chargeless ('forces-mediating') bosons can be identified and

1 stable chargeless fermion can be identified (neutrino)

1 charged boson can be identified having charge +1 (W+) and

1 charged boson can be identified having charge +3 and

2 stable charged fermions having charge +1 can be identified (positron and proton)

2 stable charged fermions having charge +2 and +3 resp. can be identified (corresponding to constituents of  'dark matter' ?) .

(D)

the 'valley of stable nuclei' can be predicted from a supercharge-minimum-principle, provided one admits the case that the 'core' of a nucleus is made out of protons and neutrons as well as antineutrons.

Furthermore, forming (mathematically) compound objects from these stable elem.particles several equivalence relations concerning the hypotron configurations can be recognized easily, and which allow to consider other unstable 'particles', including the neutron, as compound objects of proton and electron and neutrino and corresp. antiparticles (similar to Barut's ideas concerning stable matter, e.g. neutron=proton+electron+antineutrino).

In HT the concept of 'vacuum fluctuations' is incorporated AB INITIO, and thereby it is possible to state precisely ( and axiomatically ) what the notions of 'events' and 'histories' and 'clocks' and 'distances' on the level of hypotrons should mean, and it is possible to setup space-time as a continuous topological structure by means of fundamental axioms concerning the fundamental 'dynamical' notions and properties (i.e. 'states', 'state transitions', 'histories', 'standard clocks', etc.) of hypotron dipoles (which embody the 'vacuum fluctuations').

These axioms include mathematical approximation processes to pass from a 'lattice' to a 'continuum' and to arrive at the traditional space-time idea (SRT and GRT).

Because of the possibility of new interaction mechanisms of photons HT comes in contact with cosmological questions (redshift, expansion, (anti)neutron stars, dark matter, etc.) as well as with questions concerning the foundations of the probability credo of QM and QFT.

A booklet (up to now in German) on HT is still under construction. Some illustrations of the preliminary results of HT concerning the 'valley of stable nuclei' and an info page are presented here:

http://www.kreuzer-dsr.de/kdsr/test/KDSR-PRS-02/KIPS/START-AND-RUN.htm

http://kreuzer-dsr.de/kdsr/bulletin/KDSR_HypotronTheory_Flyer.pdf

Hi!

I am not a specialist in this area of physics, but I am familiar with a researcher, namely prof. Norma Mankoč Borštnik, who also works on a theory fundamentally different from the Standard Model.

Perhaps she can help. You will find below the two links to her websites at the University of Ljubljana.

Regards, Vid M. :_)

http://www.fmf.uni-lj.si/~mankoc/norma/

https://www.fmf.uni-lj.si/en/directory/3237/

Indeed-deuterium would be unstable, since it would have baryon number zero instead of two and thus could decay into positron and neutrino, by weak interactions, which isn't observed. Similarly for any nucleus where number of protons = number of neutrons. Not to mention the fact that beta decay would involve the emission of positrons along with the instability of the nucleus through proton-antiproton annihilation, more generally. 

@Stam Nicolis : Your arguement relies on the assumption that any massive particle and corresponding antiparticle, having extremely small distance to each other, would annihilate under ALL circumstances. Obviously, annihilation is observed in collisions with almost zero impact parameter. For any other situations of interaction between particle and antiparticle this seems to be merely a hypothesis, but not an undoubted physical fact.

Consider for example (according to an old idea of Barut) the neutron as a bound system of proton+electron+antineutrino, i.e. antineutron=antiproton+positron+neutrino. In such a model a nucleus which contains antineutrons instead of neutrons would embody a system of charged objects, i.e. protons and antiprotons AND positrons and chargeless neutrinos. Then it could be argued (not in the standard model) that the presence of the positrons (and neutrinos) might influence the interaction between protons and antiprotons in such a (unknown) way that they do NOT annihilate in this case. The stabilty of deuterium could then be interpreted as an indication that particles and antiparticles do not necessarily annihilate in all cases of interaction.

It's not, just,  a question of ``small'' distances; it's a question of allowed transformations. If one starts with a proton-antineutron system, that has, therefore, baryon number zero, then there is a finite probability for the transformation to positron and electron antineutrino-that, in fact, should take about the lifetime of the neutron, i.e. of the order of 10 minutes. This isn't observed-the deuteron lasts for much longer than 10 minutes. Therefore the neutral baryon is a neutron, not an antineutron. 

That a neutron can transform into proton, electron and electron antineutrino doesn't mean its a bound state of them-that statement can be given content. 

The transformation rate of the reaction proton + antiproton -> 2 photons is not infinite simply because it's an allowed interaction. It can be slowed down, simply by having too few antiprotons and by how much can be calculated. All this is well known. 

@Stam Nicolis : These arguements sound reasonable provided that one believes in the probability credo of QFT for scattering processes and in QFT beeing the ultimate vehicle twords a 'final theory' of matter. However, it is a very vivid question of whether or not there is something beyond QFT, in particular beyond the probability credo. Maybe baryon number B and B=0 is not the only way to characterize a system with repsect to stability, decay, allowed transformations, and so on. And maybe other future particle models and theories will allow for much more detailed statements.

In HT (mentioned above, an informal preliminary paper is still under construction) there is a (non-additive) quantity which I called 'supercharge'. It turns out that a minimum principle for the supercharge of sextets of fractional charged objects ( +1/3 | -1/3 | +2/3 | -2/3 ) can be formulated which allows to identify among the sextets having integral charge all of those (massive and masslss) elem. particles which are known up to now to be stable. And this is done without any kind of QFT formalism.

Furthermore, in HT the neutron is considered as the compound system of 3x6=18 fractional charged objects which are interpreted as (proton)(electron)(antineutrino). In HT the supercharge of (proton)(neutron)=132 and supercharge of (proton)(ANTIneutron)=24. Considering supercharge as an indicator for stability or lifetime or halflife leads in the case of the deuteron to the conjecture that deuteron=(proton)(ANTIneutron), and similarly and more generally that nucleus=(protons)(ANTIneutrons)(neutrons) plus some bosonic "glue".

It is absolutely clear to me that this hypothesis of antineutrons inside a nucleus is not compatible with the quark model or standard model.  My question was wether or not the existence of antineutrons inside a nucleus can be verifyed by an experiment directly, i.e. without making use of arguements which rely basically on the quark model or QFT and on underlying assumptions and credos of such models and theories.

It isn't excluded that baryon number might be violated-it's just not violated so often that deuterium is unstable, that's all. In beta decay, as in any other process, the final products of the transformations aren't in the nucleus; if they were, the angular momentum of the nucleus would have been different and so on. All these statements can be checked and have been checked. And the consequences I've mentioned are experimental-the half life of deuterium can be measured and so on.

One can observe the breakup reaction pi D -> pi p n. If the D contains an antineutron, this says that the pi nucleon reaction violates baryon number, which is problematic since the pi nucleon reaction is responsible for the long range part of the force that holds nuclei together......

@Charles Benesh : This observation is not a contradiction to the assumption D=(proton)(antineutron) if one considers a special reaction between neutrons and neutrinos to be allowed.

Consider the following arguements:

ASSUMPTION 1 :

neutron = (proton)(electron)(A-nue)

A-neutron = (A-proton)(A-electron)(nue)

where "(...)(...)(...)" means "beeing a bound state of ... ... ..."

and "nue" means neutrino and "A-" means "anti"

ASSUMPTION 2 :

For neutrons and neutrinos

A-neutron + nue -> neutron + A-nue

is (randomly) possible inside the nucleus

and

B+L is conserved in this case

ASSUMPTION 3 :

deuteron   D = (proton)(A-neutron)

ASSUMPTION 4 :

Neutrinos are always present when particle reactions happen on earth, because neutrino radiation of the sun is always and everywhere present on earth (surface as well as deep below surface).

CONCLUSION :

Because of assumption 4 in the reaction of a deuteron D with a pion pi the neutrino nue must be included. Because of assumptions 1,2,3 the reaction then is:

D + pi + nue   =   (proton)(A-neutron) + pi + nue

->

(proton)(A-neutron)(pi)(nue)  ->   (proton)(neutron)(pi)(A-nue)

->

proton + neutron + pi + A-nue

i.e. the outcome is the observed result  pi + proton  + neutron  plus  the additional antineutrino A-nue.

The antineutrinio might react at once with another solar neutrino, forming the very neutral bound object (nue)(A-nue) which might be not detectable by contemporary detectors. 

Assumption 1 is false-the neutron is not a bound state of a proton, an electron and an antineutrino; it can transform into  a superposition of such particles. 

Assumption 3 leads to deuterium being unstable, as has been noted already.

That neutrinos are always present doesn't mean they always interact-there's a finite probability for them to do so. So the reaction in Assumption 4 has a finite probability, depending, of course, on all other conservation laws and it appears to violate baryon number, at least. All this is covered in standard reviews on nuclear and particle physics, so there's no need for guessing. 

@Stam Nicolis:   Assumption 1 would seem to be false provided one believes in the contemporary quark model as the ultimate model for hadrons.

Assumption 1 goes back to some ideas of Barut.

Considering even the hypothetical quarks AND leptons to have some "constituents" one can set up new particle models which allow to consider a neutron as a bound object of constituents in such a way that Baruts's idea is realized in such a particle model AND which include some of the typical aspects of the quark model.

The "hypotron theory" (HT) (mentioned in one of my answers) is such a particle model. In HT there is a simple mechanism which allows for an identification of those (massive) particles which are STABLE, and yields a result which can be interpreted as neutrino, positron, proton, and two particles having el.charge Q=2 and Q=3. In HT there are "constituents" which I called "hypotrons" and which are charged objects, el. charge +-1/3, +-2/3, 6 hypotrons for each particle. In HT the hypotron configuration of proton and electron and neutrino yields neutron=(proton)(electron)(antineutrino) and the reaction A-neutron + neutrino -> neutron + A-neutrino. Wether or not this HT makes sense for physical reality depends also on the answer (independant form some model) to the question of what happens inside a nucleus in the case of decay, i.e. in the case where a neutron is ejected. What about the neutron before it was ejected? Antineutron-neutron conversion INSIDE the nucleus because of (random) reactions with solar neutrinos?

Answers independent of particle models are very welcome. Argueing in the contex of the contemporary quark model and standard model tells us something about the cababilites of these models but not about some hidden facts of reality which are in question.

@Stam Nicolis :   In HT there is a quantity I called "supercharge" which is related to el. charge by some squaring processes, i.e. a nonlinear relationship. In HT supercharge is used to identify STABLE particles among all of those hypotron sextetts having integral charge. Supercharge can also be used to identify STABLE nuclei or at least to determine the "valley of stable" nuclei by minimizing supercharge over the number of neutrons and antineutrons of a (hypotheical) nucleus with a fixed number of protons.

First results see the second picture in   http://www.kreuzer-dsr.de/kdsr/KDSR_results.htm and http://www.kreuzer-dsr.de/kdsr/bulletin/KDSR_ValleyOfStableNuclei-3.txt .

For   proton  |  (proton)(neutron)  |  (proton)(antineutron)    on obtains:

supercharge   =   24  |  132  |  24

i.e. supercharge of (proton)(antineutron) = supercharge of (proton) !!!

and

supercharge of (proton)(neutron)   >   supercharge of (proton) !!!

In HT this "explains" why deuterium is stable provided deuterium is considered as (proton)(antineutron) instead of (proton)(neutron).

And this is one of serveral reasons why I think it makes sense to continue my work on HT.

I could point out that the well-studied process I quoted was a strong interaction process, and that there were no neutrinos involved,  or that deep inelastic neutrino scattering off nuclei reveals that nuclei are composed of 3A valence quarks, not 3Z valence quarks and 3N valence anti-quarks, or that the neutrino processes in assumption 2 have never been observed, but I suspect that these observations would not convince you.

Instead let me remind you of what a new theory needs to do to be taken seriously(at least by me, but probably others as well).

If you can't do #2 or #3, then at best your model is a rearrangement of the standard model, and so not really different. If you can't do #1, then I'm sorry to say that your idea is in conflict with existing data, and therefore simply wrong. 

@Charles Benesh : Thanks for your general remarks concerning particle models, particle theories, and physical theories which are by no means new to me. 

As far as I know the quark model and standard model do not explain why neutrino and electron and proton seem to be the only stable particles in the particle zoo,  and the quark model and the standard model give no hints to the presumed objects "dark matter" and "dark energy". Furthermore the quark model and standard model and all of QFT make no statement why (3+1)-spacetime should be the "correct" one even for interaction processes on a subatomic scale. To my point of view this is reason enough to search for models and theories which go behind quark model, standard model, QFT, and especially the probability credo of QFT. However, even this takes more time (at lest for me) than just 7 days or a couple of months or years.

As far as neutrinos are concerned I think that it is really difficult (or even impossilble ?) to guarantee that in experiments nothing has been overlooked. Is there any experiment in which "free A-neutron + nue -> free neutron + A-nue" has been tested systematically? Is it possible to shield scattering regions in accelerators from solar neutrino radiation? Is it possible to test experimentally (without making use of arguments of a particle model) that a neutron, which is ejected by a nucleus, even before this ejection existed inside the nucleus as a neutron too?

I think this question is still open.

Nevertheless, I will not stop my work on HT.

The electron is stable, because there doesn't exist a lighter, electrically charged lepton-so the reason is electric charge conservation, a consequence of the unbroken gauge invariance of electromagnetism.  The proton is stable because it's the lightest baryon. The point is that the Standard Model can describe baryons, is consistent with baryon number conservation, therefore the lightest baryon is stable. Extensions of the Standard Model can and have been written, that describe baryon number violation and there are bounds that can be deduced. 

The neutrinos are stable, because there don't exist any lighter particles they can decay to-they can only exhibit flavor oscillations. All these features are described by the symmetries of the Standard Model. 

There have been many models that attempt to describe quark and lepton substructure-that's, for the moment, excluded at accessible energies. However Barut's model, in particular, doesn't have anything to do with considering the neutron as a bound state of its decay products-that's, simply, incorrect. 

Dark matter is not described by the Standard Model at all; however whatever model does describe it and its interactions with ordinary matter must be consistent with the Standard Model. So there's no point in introducing features that are known to be incompatible with the Standard Model, in the energy range where it's known to be valid.

Dark energy doesn't have anything to do with the non-gravitational interactions. For the moment it's perfectly well described by the cosmological constant, whose presence is inevitable, due to the symmetries of general relativity, but whose numerical value isn't fixed by classical physics and that's well known. What fixes its value relative to the normalized value of Newton's constant can only be quantum effects, that are not, yet, known.