Virtual neutrons in orbital capture and in neutron synthesis

by Lino Daddi

Abstract

1. The orbital capture

The orbital capture is a radioactivity (of beta type) of many atoms whose nuclei are characterized by excess of protons compared to stability. So that  an electron may be captured, it must last for some time close to the nucleus. This closeness is expected from the uncertainty principle, for which the orbital electrons of atoms have a small (but significant) probability of being temporarily on the nucleus (while maintaining the energy that lies to orbital). Of course the orbital electrons of the nearest, i.e.  K and L orbitals, are most interested in the process. The presence of a K or L electron on the nucleus does not alter the size of the atom, which remains that of the outer orbital of left electrons.
When an electron is captured by the nucleus, it lowers by one unit the atomic number Z (a nucleus proton becomes a neutron). Then the energy defect of about 0.78 MeV between the sum of the masses of proton and electron and the mass of the neutron is provided at the expense of released energy by rearrangement of the nucleus (and not by the single capturing proton ). In order to this may be, the isobar of atomic number (Z-1) must be of suitably low mass. The orbital capture is not possible in the case of fully ionized atoms (as happens, for example, in certain astrophysical situations), in the absence of orbital electrons to be captured.
The casual approach of an orbital electron to the nucleus is an event that the uncertainty principle allows for all atoms, even for those who do not have excess protons. But so that  the electron is captured the requirement of sufficiency of the mass-energy, which occurs more easily for the nuclei that have a high value of the ratio Z / A, must be satisfied.
We intend to analyse the phases of the process that brings an orbital electron to be captured, by separating that is question of the strong force with respect to the weak interaction. Although the beta decay theory was originally set (starting from Fermi) ignoring underlying quarks, we will find appropriate to take into account the quark composition of the nucleons in the nucleus.
In the following we will distinguish  two zones of the orbital: the peripheral orbital (where the electron is usually) and the central orbital (area of the nucleus, where the electron can be only occasionally).
The presence of a particular electron on the nucleus should have very short duration, waiting to return in the orbital  itself. However statistically there is always a certain number of electrons in contact with its nucleus. If  f  is the probability of finding an electron on the nucleus and N is the total number of nuclei of the nuclear species under consideration, f N is the total number of electrons that each moment can be found on the nuclei.
Then with  q  We denote the probability for each of the N f electrons that are on the nucleus, to be in touch, in time unit, with one of the protons. We suppose, for simplicity, that the contact with the proton involves to the certainty of orbital capture from the nucleus, then, in the absence of alternative disintegrations, N decreases of dN in the time dt:

dN  = – f q  N dt
(1)

So the product fq  is the decay constant λ for capture. As λ is typical of a given nucleus and f of the atom, q should depend on both so that, multiplied by f, has precisely the λ value. Only when f = 0, i.e. when the atom is fully ionized, will be also λ = 0 (and then the q  value is indeterminable). Among the nuclei showing typical orbital capture We can remember 40K  and 136La , which are very different examples of instability, since the 40 potassium is almost stable (half-life of billions of years) and 136 lanthanum is decidedly unstable (half-life of 9.5 min). For the latter radioisotope the value of λ is about 1,2.10ˆ-3 sˆ-1, from which one can deduce that  the f and q  factors should not be too small.

2. Virtual neutrons and virtual quark down in orbital capture

The uncertainty principle in conjugated variables “time and energy” permits, although the sum of mass-energy of the nuclear proton and orbital electron is not enough, their temporary synthesis into a virtual neutron (which is not yet a neutron, but in some verses, it could already have some feature). The virtual neutron can be thought of as a completely imaginary particle, or rather  as a very compact (pe) couple. The life of the virtual neutron is obtained using the relationship:

Δ t = h / Δ E
(2)

where ΔE is given by the difference in mass between neutron and proton/ electron pair.
We can evaluate whether the available energy is sufficient by consulting the tables of nuclear masses. The nucleus  however will be informed of sufficient energy in his attempts, promoted by the strong force, to absorb the virtual neutron as if it were real. If the available energy from the nucleons rearrangement is sufficient, the orbital capture is accomplished, the neutron virtual becomes real and a neutrino is emitted.
Otherwise, the electron returns to its peripheral orbital (as do the other electrons, which, although arrived on the nucleus, have not formed virtual neutrons); this can happen, especially, because the nucleus has no excess of protons, being stable or radioactive beta minus. But the ” virtual neutron reversibility” should be ensured , in the sense that during Dt must not be anything that results in the impossibility for electron of returning to the itself  orbital.
One might think that for one of the  N f  electrons that are on the nucleus, the weak force begins to act, when the electron comes into contact with the  quark up of one of the protons. So a very compact (quark up, e) couple is formed, which behaves like a virtual quark down. But then the virtual neutron can be thought of as a neutron which has one of two quarks down in virtual state. So it would seem more logical to use the difference between the mass of  (quark up, e) couple and the mass of the quark down for ΔE in (2), namely to assess the life of the virtual neutron. But it is possible that significant contributions to ΔE, and consequently to Δt, can come from the coulomb interaction.

3. Hydrogen and deuterium miniatoms

It’s should try to understand to what extent the considerations made about the orbital capture can be applied to atoms of hydrogen and deuterium. For the hydrogen atom the capture of its electron would lead to the transformation of the proton in a neutron; for the deuterium atom the capture has two neutrons as a result. In the first case the mass-energy shows a deficit of 0.78 MeV while in obtaining two neutrons from the deuteron the deficit is of  3.01 MeV. But, in both the atoms the energy level in the ground state is just of the order of tens of eV, so  they can not receive energy from the nucleus rearrangement , the inverse beta reaction in hydrogen and deuterium is prohibited by the law of conservation of energy. In other words in hydrogen and deuterium can not occur capture radioactivity.
However, in order to justify certain LENR reactions observed in metals or alloys that have absorbed hydrogen or deuterium, in the past the assumption was made that proton or deuteron can associate very closely the atomic electron. There being no other electrons in atoms of hydrogen / deuterium, the presence of the electron on the nucleus   minimizes the size  of the system-atom.
Said system-atom of hydrogen / deuterium intend to refer to its atoms (in nascent state ), and not to the free proton / deuteron in a plasma or to  hydrogen / deuterium molecules. When it is not ionized, hydrogen in nature is almost always in the molecular state; the membership of a molecule (hydrogen / deuterium or different) alters the probability distribution of the  presence of the electron, with the likely decline to be on the nucleus.
In particular, the probability that the electron  of hydrogen atom is in contact with the proton is very low. It sometimes refers to the 10ˆ-14. From the point of view of probability is an intermediate situation between that of 136La and the 40K, as referred in the case of orbital capture. Nevertheless  CONTE [1], with a calculation in the General Relativity, has found a 1000 times greater value. So every 10ˆ11 atoms of atomic hydrogen, one would be very compressed.
From now on we will call “hydrogen miniatom” and denote with (pe) any proton/electron system much more compact of the normal hydrogen atom. Similarly will call “deuterium miniatom”, indicating with (de), a neutron / proton / electron system decidedly more compact of  the normal  deuterium atom.
For the formation of miniatoms may be sufficient, therefore, that the single electron of hydrogen / deuterium atom is occasionally found himself on the proton / deuteron, just as in orbital capture the  K / L electrons are asked to be on the nucleus.

A way to maintain the largest number of atoms into the nascent state is  they are loaded on metals which promote the dissociation of hydrogen molecules, for example, nickel, tungsten, titanium, zirconium (as happens in many LENR reactions). In such cases, the large number of atoms loaded into the lattice can offset the low probability and produces a observable number of processes. On absorption of hydrogen (and its isotopes) in metal lattices  a major review was due to  SHLAPBACH [2].
In the past, processes have been hypothesized of miniatoms production alternative to that based on the uncertainty principle, so far shown. For the most part they were based on the possible existence of quantized states different from those calculated with the ordinary quantum mechanics [3-5]. But very significant and important is the theory of WIDOM [6], which suggests  the formation of electrons “heavy” with a consequent decrease of atomic radius.
However formed, these compact systems would behave as neutral particles and could pass through thick materials without electrical actions from charged particles encountered in their path, and in particular from nuclei of atoms of the metal or present in its crystal structure.

4. Absorption of miniatoms as virtual neutrons

Hhydrogen miniatoms and deuterium miniatoms can be so compact that the electron, as in orbital capture, can come to be close to one of the quark up of the proton, thus beginning to feel the effects of  the weak force. This would promote the following reactions, both endoenergetic:

p + e = n + υν          (Q = – 0.78 MeV)
(3)

d + e = n + n +  υν          (Q = – 3.01 MeV)
(4)

The Q energies are not initially available, so the neutron of the first reaction  and one neutron of  second reaction could occur only in a virtual  state (nv), as follows:

p + e = (pe) = nv
(3′)

and

d + e = (de) = n + nv
(4′)

In the recent past several Authors [7-11], and in particular MILEY [10] have proposed the virtual neutron, variously justified, as a transitional phase for the production of nuclear transmutations at low energy.
The:

nv = n + υν
(5)

would the final reaction of virtual neutrons that appear in (3 ‘) and (4’).
The missing mass-energy in order to  virtual neutrons become real according to (5) can not be obtained, as in  orbital capture, by a rearrangement of (hydrogen or deuterium) nucleus. However it may be abundant energy available in the virtual neutron capture, as if it were a slow neutron by a nucleus absorber N (Z, A) with which the miniatom is able to come into contact. Indeed it is well known the ease with which the nuclei absorb slow neutrons.

In LENR reactions that could be a nucleus of the lattice which has absorbed hydrogen or deuterium, or a different nucleus in it (or even a nucleus of a detector placed in the immediate vicinity).
For hydrogen would take place the process:

N (Z, A) + (pe) = N (Z, A) + nv = N (Z, A +1) + ν
(6)

So it could have happened in the transmutation  of 133Cs in the of 134Cs (observed by VYSOTSKII [12]) and of 56Fe in 57Fe (observed by OHMORI [13]). For iron we have the situation that three adjacent isotopes are stable. But more often the capture of a neutron generates a β-radioactive isotope: NOTOYA [14], for example, refers transmutations from 23Na to 24Na, detected by measuring the gamma radiation emitted by the produced nucleus.
In the case of deuterium we can think of the possibility that both the neutron (4′) are absorbed by a nucleus N (Z, A), with the reaction:

N (Z, A) + (de)  =  N (Z, A) + n + nv  =  N (Z, A +2) +  ν
(6′)

According to which, OHMORI [15] observed transmutations from 39K to 41K.
But it could be absorbed only the virtual neutron, while the other remains free:

N (Z, A) + (de) = N (Z, A) + n + nv = N (Z, A +1) + n + ν
(6”)

that would explain, at least partially, the transmutation of 6Li to 7Li observed by COUPLAND [16] and the transmutation from 53Cr to 54Cr viewed by MIZUNO [17]. Simultaneously the neutron n would be free, so that the deuterized solid will operate as a source of neutrons. The (6) and (6′) may include the capture of virtual neutrons by the deuterium. Tritium is found frequently in research, although often attributed to D + D fusions.
Very interesting, for the possibility of remedy the waste of nuclear fission reactors, are the reactions with radioactive isotopes. For example WYSOTSKII [18] has obtained the accelerated decay of 137Cs, from half-life of about 30 years to less than a year.
Many of these processes require that the total life of the chain miniatom-virtual neutron is not too short. However, if the proximity of the electron to quark up remains at the end of Δt, should be able to begin an additional Δt life to virtual neutron. That, however, should be determined, through (2), by the difference between the mass of the  couple (quark up, e) and the mass of the quark down (with the possible contribution to ΔE of the colulomb force).

5. Alternatives for miniatoms

The processes involving virtual neutron can explain that part of LENR reactions that led to final products in accordance with reactions (6), (6 ‘) and (6”) (which are equivalent to absorption of neutrons).   But to justify other also observed reaction, the fact can given that, come in the immediate vicinity of the target nucleus, the miniatom of  hydrogen / deuterium could give rise to a different event from the virtual neutron capture. The proton / deuteron of miniatom, closer at nucleus without suffering the coulombic repulsion, could be captured by that nucleus (fusion after tunnel effect).
This type of reaction has been considered by several Authors as a possible producer of energy, being generally exoenergetic. If the target nucleus was N (Z, A), the nucleus thus formed is N (Z +1, A +1) if a proton is captured, and N (Z +1, A +2) if a deuteron is captured. They are generally stable, but after the capture , they may be  in excited state.
The simplest case is the capture of the proton:

p + N (Z, A) = N (Z +1, A +1)
(7)

probably observed by BUSH [19] with 41K (getting 42Ca), and by NOTOYA [20] with 39K, obtaining 40Ca.
Immediately after the capture of the proton, the electron of the miniatom can be captured by the new nucleus. This last is almost always an endoenergetic capture, but it can happen by using the residual excitation energy of the above reaction (7) [21]. Of course, this final nucleus is the same as if it had been absorbed a virtual neutron, according to (6”) or a real neutron.
If the interaction is that of deuteron, the reaction results:

d + N (Z, A) = N (Z +1, A +2)
(7′)

verified by VYSOTSKII [22] for 55Mn, obtaining 57Fe (10ˆ10 nuclei/second).
Immediately after the deuteron  capture, the electron of the miniatom can be captured by the nucleus. The electron capture, which transforms a proton of the nucleus of in a neutron, is endoenergetic, but even this has a chance of being achieved by utilizing the residual excitation energy of the reaction before. The overall reaction is equal, of course, to a double neutron absorption. Ultimately it would have the same result as with the (6′). I particularly remember the product nuclei seen by OHMORI [15], We already reported in par. 4 as a support of (6′) itself.
Many LENR reactions experimentally observed are reported in an article by MILEY [10] and in a review of STORMS [23]; they could find justification in the hypotheses above referred.
For other LENR reactions involving a variety of end products should be thinking about more complex processes, such as fission, (perhaps initiated by miniatoms or virtual neutrons). In particular, with a gold cathode in electrolysis, OHMORI [13] observed that the 197Au becomes 198Au or 199Au; after beta decay, they may undergo fission with production of 56Fe and 57Fe. The production of iron isotopes in the cathode of gold was confirmed by experiments made by YAMADA [24] and of MILEY [10,25], which supports the possibility of fission reactions.

6. Conclusions

The cold nuclear reactions (LENR) referred in paragraphs 3 and 4 are a large number of clues on behalf of the hypothesis given in this work. A more direct test of the function performed by the virtual neutrons could be the measurement of the gamma radiation accompanying the neutron capture. When a virtual neutron is absorbed, the  emitted gamma rays will have a total energy lower than in the slow real neutron capture.
The reproducibility of LENR can be problematic in some cases for the difficulty of maintaining a constant number of atoms to the nascent state. On the other hand, the contribution to ΔE of coulomb force close to nucleus, although difficult to quantify, may be important, leading to a variable  life of virtual neutrons.

by Lino Daddi

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