From the orbital capture to some types of L.E.N.R. reactions

Prof. Lino Daddi
Retired. Earlier Professor at Naval Academy. Leghorn

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In this article the process is discussed by which an orbital  electron happens to be on the nucleus and is captured by a quark up of a proton of the nucleus itself, which for what becomes a quark down.
It is assumed that the involvement of virtual particles allows the nucleus to determine whether, having enough energy available, the process, in which they are part the weak interaction and the strong interaction, can be completed.
A parallel process can be considered for certain types of observed reactions LENR, starting from the reduction of the hydrogen atom to the condition of “miniatom”.

From the orbital capture to some types of L.E.N.R. reactions

The reaction of nuclear capture of one of two K-shell electrons by the nucleus NuZ,A can be written:

NuZ,A + e- = NuZ-1,A + ν.       (1)

Denoting by MZ,A and MZ-1,A the masses of the initial and final nuclei, it will
E = [MZ,A – MZ-1,A] c^2   the available energy from the process. The energy of the emitted neutrino is:

εν = E + mec^2 – εk,    (1′)

being εk the electron energy on the K orbital (which may often be overlooked in these assessments). If the energy E is insufficient, the capture (1) does not happen, so the nucleus does not undergo the beta decay of type K capture. This, however, is not directly observable, but:

1 – measuring the recoil momentum received from the nucleus, or
2 – observing X-rays following the rearrangement of the electronic layers.

It should be noted that the K electron should not be on the nucleus because it was attracted by the Coulomb force. This force is actually the one that “keeps” the electron in the orbital K. If this were to bring the electron to the nucleus it do make a work, and the electron  would arrive with much more energy. But the energy remains that εk of the orbital K, because the electron moves to the nucleus by fluctuation of its distance from it, according to the probability admitted by quantum mechanics, according to the Uncertainty Principle (U.P.).

In ref [1] it is assumed that the probability of capture is the product of the probability f of an electron  K be in the nucleus for the probability q that an electron, having attained the nucleus, is captured by the nucleus itself. The fact that there are very strong differences in the half-lives of the various nuclei that decay by orbital capture  can be considered as an indication that q is very dependent on the nucleus structure.

Among the typical nuclei that show orbital capture we can remember  40K and  136La, which are very different examples of instability, as the 40K almost stable (half-life of billions of years) and 136La very unstable (half-life of 9.5 min). So the picture is more complex than could result from a simple positional fluctuation.

Recall that, according to U.P., two particles in contact, which by their nature should fuse but can not do so for lack of energy, may temporarily act as a virtual particle. The permanence in the life of the virtual particle is given by:

Δ t = ħ / ΔE    (2)

where ΔE is the energy deficit.
Thus, if the energy is insufficient, the system of two particles in the left hand side of (1) can be considered as the virtual nucleus Nu Z-1,A.
Table 1 shows, from first to third line, the presumed evolution of the three phases.
In the  phase 2 the (1) can be seen as a reaction

p + e-  =  n + ν    (3)

of one of the Z protons of the nucleus. Until  the mass difference is acquired between neutron and proton in the nucleus ,  the neutron can not be formed, and the system (p,e) of Fig.1 can be considered as “virtual” neutron. This can become real after the exchange of W bosons, made possible by having received the necessary energy ΔE. In the final phase of table 1 the electron is interacting with a quark up of a proton in the nucleus, converting it into a quark down. The Fig. 2 illustrates the situation at the level of quarks before the exchange of W. But now we’re talking about a different system: no more (p,e) subject to the Coulomb force, but (quark up,e) subject to the weak force.

Phases 2 and 3 of Table 1 can be viewed as one phase consisting of two processes.
In order to  the K capture occurs, it is necessary that the rearrangement of nucleons (promoted by the strong interaction) makes available the necessary energy.

This is the chronological succession :

I)  The K electron goes on the nucleus, but it is unknown whether the capture is energetically possible;
II) To explore the possibility of capture, the electron form a virtual neutron with a proton;
III) You may think that  the nucleus to rearrange itself by replacing the proton with the virtual neutron as if this was real. So the nucleus NuZ, A would become the nucleus NuZ-1, A and the energy E would be made available by the rearrangement;
IV) If this is sufficient, the exchange of W bosons (not yet in the case of Fig.1 and Fig.2) takes place, and a neutrino is emitted (Fig.3).
But of course the final transformation is on Stage 3 of the Tab. 1, as illustrated in Fig.2.

It seems difficult to separate the effects of the strong and weak interaction. The hypothesis of the virtual particles, as an interim step, may reduce this difficulty.

This is, of course, a process which affects not only the nucleus, but involves the whole atom. The orbital capture, however, seems more likely event than the capture of an electron met by chance. When atoms are fully ionized (as in supernovae) the capture can not occur.

In the few cases (such as, for example, 64Cu and 74As) in which a nucleus can decay in three ways:  beta minus, beta plus and orbital capture, its disintegration constant λ is unique. It is in fact equal to λ = λ1 + λ2 + λ3, λ1 being the constant of β- decay, λ2 the constant of β+ decay and λ3 that of the orbital capture.

But a temporary presence of a K electron on the nucleus is considered to be possible for the nuclei of all atoms. Ultimately all nuclei have the possibility of capture an orbital electron to convert a proton into a neutron, but only those able to obtain energy from the restructuring (as defined in the point III of the chronological order) have this type of beta decay.

Even the electron of the hydrogen atom can be found in the nucleus, that is, on the only proton. This event has a low probability of occurring but this, according to CONTE [3], could be greater than you think. However it is suitable the atom be in unbound state. The atomic state (or nascent) hydrogen is rare in nature but can be achieved under specific conditions, for example when hydrogen is absorbed by metals that favor molecular dissociation. Nickel is one of them, but so are zirconium, titanium and tungsten.
The capture of the electron could be achieved as indicated by Fig.3;  but that was designed meaning that p was one of the protons in the nucleus NuZ,A which undergoes K capture. But the presence of electron on the proton greatly reduces the atomic dimension, up to nuclear dimensions, so the atom becomes a “miniatom” (p, e). It is understood that the miniatom is still an atom, consisting of separate proton and  electron  interacting via the Coulomb force. It would be inappropriate to consider it now as virtual neutron. By itself, the miniatom has not the energy to become real neutron (the rearrangement of the three quarks is not sufficient). Since, however, the nucleus consists of a proton, the steps 1) and 2) in Table 1 coincide. It is essentially a neutral particle, able to approach a nucleus without suffering the Coulomb repulsion. If it encounters a nucleus NuZ,A may react with it, but its short life limits the likelihood of such reaction.

The nucleus NuZ,A could capture the entire miniatom in two different ways, A) and B).

A) as virtual neutron, pending  the energy made available by rearrangement of NuZ,A+1 . This would be equivalent to the capture (n, γ) of a thermic neutron with the excess energy derived from the rearrangement of the nucleus NuZ,A+1.

B) with separate proton and electron capture. The steps of this mode are presented in Table 2.
The nucleus NuZ,A could confine himself (according to line 2) to capture the proton of the miniatom (p, e); that is generally an exothermic reaction. But (line 3-a) it can absorb the electron of the miniatom. Also this process would be equivalent to the capture (n, γ) of a thermic neutron

Finally, it should also consider the possibility that NuZ+1,A+1 is beta radioactive for K capture.

With the hypothesis of miniatoms and virtual neutrons some of the reactions LENR, such as those mentioned, for example, in a review of STORMS [4] could be justified. To keep in mind an article of MILEY [5] on the possibilities offered by virtual neutrons.

The formation of a hydrogen miniatom  may also occur in other way, different from the U.P.,giving access all the same to A) and B) modes as well as to phases 2 or 3 of Tab.2. Below are a number of the proposals.
According to STREMMENOS [6] do not hydrogen atoms, but protons are spread in the defects of crystal structures, in particular Ni. Thanks to the positive charge they capture electrons to form unstable miniatoms  and would soon be absorbed by nuclei of Ni. Their size (<10^-14 m) allows a corresponding approach, to make up the predominant nuclear forces of cohesion.

The miniatom of MILLS [7] is called hydrino, and is expected by the Grand Unified Theory of Quantum Mechanics (CQM) developed by the author himself, who still denies a role of hydrino in cold fusion and LENR processes. The heat produced in its reactor would be due to hydrinos  formation. The technique to produce hydrinos involves the use of a catalyst (potassium or strontium ions) and monoatomic hydrogen.

DUFOUR [8] instead has developed the hydrex, that would be formed in solids permeated of hydrogen under the effect of intense electromagnetic fields. It would be accounted by the weak nuclear force and its half-life would be a few days. A recent evolution of the virtual neutron concept was named “hypole”.

HEFFNER [9] calls “deflated state of Hydrogen” the miniatom. He proposed that there would be “briefly but frequently”. It could  promote fusion process between two hydrogen nuclei, but also processes LENR between hydrogen and nuclei belonging to the solid. In the second case the interaction is weak, and it is rather infrequent, since the nucleus is unstable and its life is too short. But the rearrangement of the nucleus could give additional time the overall process.

WIDOM and LARSEN [10] presented a LENR theory  based on the capture of an “heavy” electron  by a proton. A neutron is generated of ultra low momentum “(ULM) and a neutrino. The ULM neutron is absorbed by a nucleus, resulting in a beta emitter.

Some of the cases here reported enable a  miniatom life much longer than that assessed with U.P. Consequently, the frequency of LENR reactions may be greater and be compatible with a heat played more abundant. In particular could justify, at least in part, the exothermal reactions observed in Ni-H systems by PIANTELLI [11] and, recently, by FOCARDI and ROSSI [12] with  theirs “Energy Catalizer”.

Even with deuterium, which can undergo the reaction

d + e = n + n + ν    (4)

one may consider the formation of miniatom (d, e) and subsequent conversion into a neutron (first virtual, then real) of the proton in initial deuteron. The production of a temporary dineutron corresponds to an hypothesis formulated by RUSSELL [13] several years ago.


[1] –  L. DADDI – J.N.P. (Nuclear Experiments Blog) – March 2010
[2] –  L.DADDI – Infinite Energy 47, 22 (2003) ; Proc.Workshop TESMI (Lecce 2002) page 1
[3] – E.CONTE – Proc.Workshop TESMI (Lecce 2002) page 50
[4] –  E.STORMS – Library LEN-CANR Org (2003)
[5]  – G.H.MILEY et al. – Proc. ICCF10 (2003)
[6] –  E.STREMMENOS – J.N.P. (Nuclear Experiments Blog) – January 2011
[7] –  R. L.MILLS – Infinite Energy 17 ,21 (1998) ; Fus.Technol. 28 , 1697 (1995)
[8] –  J.DUFOUR – Fus.Technol. 24, 205 (2003) ; J.N.P. (Nuclear Experiments Blog) – April 2010
[9] –  H.HEFFNER – J.N.P. (Nuclear Experiments Blog)- March 2010
[10] – A.WIDOM and L.LARSEN – Eur.Phys.J.C.DOI 10/1140/epje/S2006-02479-8
[11] – F.PIANTELLI et al. – Nuovo Cimento  107A,163 (1994)
[12] – S.FOCARDI and  A.ROSSI – J.N.P. (Nuclear Experiments Blog) – February 2010
[13] – J.L.RUSSEL-JR – Ann.Nucl.Energy – 18 /2-75 (1991)

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131 comments to From the orbital capture to some types of L.E.N.R. reactions

  • Andrea Rossi

    Dear Malcom,
    There are no problems.
    Warm Regards,

  • Malcolm

    Dear Dr. Andrea Rossi,

    Can you see any problems in getting the required documentation to export the 1MW plant from the US to Greece?

  • Andrea Rossi

    Dear H. Hansson:
    We are making agreements with strong partners: I suppose we will be able to sustain the demand. In contrary case we will license. I am used to face problems when they are real.
    Honestly, in this moment I am focused on my first 1 MW plant.
    Thank you very much for your comment,
    Warm Regards,

  • H. Hansson

    Dear Rossi,

    If there are serious bottlenecks in the production.. do you think that it is a risk that countries start to issue compulsory licenses? Like have been done for some types of medicines?? … your eCat will probably be life saving in situations like Desalination of seawater.

  • Gherardo

    Just in case, this could be an interesting innovative way to go from heat to electricity for your e-cat.

  • Andrea Rossi

    Dear Robert Mockan:
    Our attorneys are working on this issue.
    Warm Regards,

  • Robert Mockan

    Dear Dr. Rossi,

    Do you anticipate any problem with obtaining product liability insurance for E-Cat sales in the USA?

  • Andrea Rossi

    Dear Mr Charlie Zimmermann:
    Leonardo Corp. and Partners will develope their structures in due time. We are much more solid that can be imagined, and there is no reason, so far, for us to disclose our structures. We want to work in peace, without hordes of curiuos persons around. And spies.
    Our site is not yet ready for the sales because our sales will start in November.
    As for the domestic applications, 10 years is for sure a longer time than necessary.
    Thank you for your kind attention,
    Warm Regards,

  • Charlie Zimmerman

    Dear Mr. Rossi,

    Thank you for your attention and reply to my previous note. Some friends of mine (skeptics) were questioning my decision to put off an upgrade of my home heating/hot water system until more information came out about when residential grade E-Cats would be available. The upgrade I had planned would pay for itself in about 10 years, but I feel like I am likely to get an ECat in my home long before that. They brought up that they didn’t think that Leonardo Corp was a ‘real’ company. They even called the phone number from the web site as ‘evidence’. I think that their ‘evidence’ is just an indication of the youth of Leonardo Corp.

    I understand your reluctance to deal with skeptics, but for some of us, these are real world decisions.

    Your response concerning LTI and their licensing efforts is very comforting in this regard. If Leonardo Corp. cannot grow fast enough, it seems as though licensing the technology will surely make the technology’s penetration into all markets much faster. I think this confirms my decision. Do you agree?

    Again, congratulations on an amazing achievement.

    Charlie Zimmerman

  • Andrea Rossi

    Dear Mr Arun:
    Please contact us in November when we will start our commercial operation.
    Warm regards,

  • Arun

    Dear Andrea Rossi,

    My heartfelt congratulations on your game changing invention. Hopefully before November you will have the last laugh against the critics. The real world is more interested in the commercially usable results than the science behind the invention.

    I am very interested in using the E-Cat for process heat applications in India in 2012. It is not clear whether to contact Leonardo Corporation, Leonardo Technologies or Defkalion for applications of E-Cat in India. I would appreciate your response in this regard.

    Thanks and Regards,


  • Andrea Rossi

    Dear John Hartley:
    Bob Gentile is a great man, comes from a family of heroes (his father fought with Patton and got decorations). I am honoured to work with him. We will do a great job for the USA.
    Warm regards,

  • John Hartley

    Mr. Rossi,

    I am writing so that when you are in charge of the world and putting non-believers up against the wall to be shot, you will remember that I supported you! I admit I was skeptical until I learned a former secretary of fossil energy for the DOE was on board(Robert Gentile). I hope that in the new world order such an admission is not a hanging offense.

    Best of luck,
    John Hartley

  • Andrea Rossi

    Dear Mr Charlie Zimmerman:
    1- I am absolutely not interested to the skepticism, since we are manufacturing the reactors which in october will start their operation in the market
    2- there is no reason why I have to disclose where we manufacture our reactors. Our Customers will receive the reactors in their factories, they are not interested about the manufacturing sites. Our NON-Customers have no reason to know anything at all about this issue.
    3- The reactors are manufactured by Leonardo Corporation, while LTI (Leonardo Technology Inc.) is the company with the exclusive commercial license of Leonardo Corp. in the Americas and Caribeans.
    For any info about LTI, please coontact them directly:
    Warm regards,

  • Charlie Zimmerman

    Dear Mr Rossi,

    Congratulations on your momentous achievement. Future generations will owe you the highest debt of gratitude.

    I am most disheartened when talking with friends about your device to still find such a high degree of skepticism. Some of it is based around the confusion over some of your United States businesses. Specifically, some people seem to be confused about Leonardo Corporation and where the production of the power plant is happening. It would be great if you could shed some light on these issues to help in these conversations. Having a little back story information could help me in silencing these doubters.

    Is your US Company Leonardo Corporation or Leonardo Technologies Inc?
    Is the production at a Leonardo Corporation owned factory or is it outsourced to another production facility?
    What is and what relationship do they have with Leonardo Corporation and yourself?
    Is this a different Leonardo Technologies Inc. from the one in the September 2004 report on your TE device from the US Army Corps of Engineers?

    Warmest regards and best of luck in the future.

    Charlie Zimmerman

  • Andrea Rossi

    Dear Dr. Wladimir Guglinski:
    Good idea.
    Warm Regards,

  • Wladimir Guglinski


    Dear Dr. Andrea Rossi

    I am adept at swimming (I swim about 7km per week).

    But now is the beginning of winter in Brazil, and the pool water becomes too cold for swimming.

    Some clubs have swimming pools heated electrically, but very few, because the electric heating is very expensive.

    A good advertisement for the E-Cat would be to sell it to clubs (for heating swimming pools and steam sauna).
    With a cheap heating, all the clubs could have a heater for cold fusion, and the news would spread worldwide.

    I could even do demonstrations to clubs in my city

    Tell us your opinion

  • raul heining

    I think there it is a question of electroweak interactions (using weak force) and not fusion
    in a classic way of nucleous overcoming the electrostactic force to come in the range of strong
    force. Using nano particles increases reaction surface and power. I think that is one of the ideas
    behind Rossi’s concept, which I find one of the brilliant part of his creation together with Focardi,
    but he will be in a better position to explain that.

  • Gilbert Schmidt

    My last comment would more aptly describe a table.
    To be more explicit, What is most valuable is the temperature on one axis, the pressure on the other axis, and the minimum sustainable reaction rate ploted.

    If possible, this comment should be inserted at the end of my other one.

  • Gilbert Schmidt

    This is a rather simplistic explanation. I would like to get comments or thoughts on it.

    For fusion reactions to occur , the atoms have to hit each other at both a correct angle and a high enough speed.
    Since even at lower temperatures, some atoms have higher velocities and some lower , it is the average speed that makes the temperature.
    When the temperature is increased to a cirtain level, there are many more atoms that have enough speed so that they will react when then hit an atom at the correct angle.
    when the pressure is increased by packing in more atoms , the number of reactions increase due to the higher volume of impacts, increasing number of direct impacts at the correct angle.

    The question is which is more effective, the higher temperature or the higher pressure.
    We should be able to make a graph with temperature on one axis, and presure on the other axis, and plot reation rates.

    If this has been done, it is probably kept secret at the moment.
    The question is – has a graph been made of this ?
    If a graph has been made , is there a time in the future when we might see it ?

  • Andrea Rossi

    Dear Mr Tom Walkinshaw:
    In november we will start our commercial operation everywhere possible, with thermal energy production. We are not yet ready for e.power, it will take some more time.
    Warm regards,

  • Tom Walkinshaw

    Dear Mr Rossi,

    Great work with you amazing device, two questions, will the device be available globally in November (i.e. Scotland) and will the first models produce electricity (i.e. convert the heat).

    Apoligizes if these question have been already asked.

    Many Thanks


  • Wladimir Guglinski

    Dr. Pietro Cambi
    The confirmation of Rossi’s technology by an university was important one year ago, so that to show to investors that Rossi’s technology really works. That’s why the confirmation by the Bologna University was crucial.
    As the E-Cat is already going on the market, it means that it’s working. So there is no need any confirmation by any university.

    There is in general a belief that something can work only when it is confirmed by an university. The scientific community used along the 20th Century such belief in order to fool the people, by convincing them that many experiments which defy the prevailing theories cannot be taking seriously in consideration because they had no confirmation by universities.
    But the own universities refused to repeat the experiments.
    By this way they have created a vicious circle:
    – all the peer review journals refuse to publish the paper describing the experiment, because it violates some principles of current theories.
    – all the universities refuse to repeat the experiment, because it was not published in any peer review journal
    – so the experiment cannot be taken seriously, because it was not published in any peer review journal, it was not replicated by any university, and so its results were not confirmed.

    Tesla’s inventions in the field of free energy are an example.

    It seems such conspiracy of the academics against the scientific method will end in 2012.

  • Thanks, Mr Rossi for your kind and fast Answer.
    As for the way our association, ASPO, and we as people, look at your and Focardi’s work and the approach we have, generally speaking, with the e-catalyzer (that is with every issue we have happened to deal with)I can only link here the comment of the President of Aspo International, that happens ( i didn’t know until today, everything is moving fast, now) to be next door with the group working on the e-catalyzer at the University of Upsala.
    I think it is an example of an honest approach form an accademic and scientific point of view.
    As I underlined in the precedent message, also the social and sistemic point of view will be a key issue in a correct exploitation of the full potential of your e-cat for the benefit of the large part of human beeings that has no access to energy, whatever the cost. I think next step could be a village-scale VERY low-cost system developed as a Social Business, in the sense promoted so efficiently by Muhammad Yunus. The most badly needed energy is that the poorer half part of humanity DOESN’T have.
    Whatever your next decisions could be, thanks again and Good work and good luck!

    Pietro Cambi

  • Andrea Rossi

    Dear Dr Pietro Cambi:
    We will not make any other validation test after the ones we already did. From November our products will be on the market. As for the R&D we already made an agreement with other Universities.
    Warm regards,

  • Dear Ing. Rossi: what are the (pre)conditions for entering the group of people that are doing a sort of “beta testing” of the E-cat, providing a STRICT Not disclosure agreement, where and if needed?
    I can ensure that some accademics here in italy are really interested in a indipendent evaluation and some has the correct “pedigree” not only as for the field of application but for the human and social point of view.
    One of these could be, Prof. U. Bardi of the University of Florence, Who has been deeply involved either on the topic of oil depletion (is the founder of aspo italia) and all the other main issues concerning the energy emergency in our little earth. Our association ha proved in the course of the years not to be easily muted or silenced by the main stream majors.
    Besides that we are not afraid to put at test new ideas as proved, with the story of the “cinquino elettrico” ( you can check on internet about that, and of kitegen.
    You could check as well by yourself about Aspo and Ugo Bardi.

    Could we arrange something about having one of the prototipe and put it at work, as well as the others, at the University of Florence, department of chimics, under the responsibility of Prof. bardi?
    Good, work, anyway,

    Pietro Cambi

  • Joseph Fine

    Wladimir Guglinski,

    There are so many readers now that it is difficult to read and remember all their responses. As of now, the number of E-Cats in operation is (at least) 330.
    Dr. Rossi recently announced, here, that all 330 E-Cats for the 1 Megawatt plant (also called the E-Tiger or ‘Hyperion’ ) have been assembled and are operating. If skeptics have continued doubts, they do not have to buy the product.

    Joseph Fine

  • Andrea Rossi

    Dear Dr Wladimir Guglinski:
    I agree.
    Warm regards,

  • Andrea Rossi

    Dear Stefan:
    Thank you,
    Warm regards,

  • Stefan

    >but to that kind of critics that say our technology doesn’t work without haveng any idea how it works.

    You are free intrepreneur, you put all your money (in fact your life), you owe critics no explanations. Money is the most objective criterion. Once it prevails, do you think those critics will apologize, never, they just will change their nicknames. 1 chance out of 100 that humanity will be grateful and recognize the risk you took; I expect the diluted down to nothing authorship is the most probable gratitude you may get at the end unless you will be able to build up a sufficient fortune to buy the mainstream. I sincerely wish you success, you definitely deserve it.

  • Wladimir Guglinski

    Dear Mr. Herald Patterson

    There are already 97 E-Cat working worldwide. But such fact is not spraid by the media, and the most academic physicists claim that Rossi’s technology does not work.

    Other many cold fusion reactors are working since many years ago. Look at the Jean-Naudin website. However, in spite of they work, they are not recognized by the academic physicists, and the media do not take them in consideration. There is a conspiracy against cold fusion.
    Those other cold fusion reactors are not so efficient like the E-Cat. But they really work. However, only their work is not enough to eliminate the resistance of the academics against cold fusion.

    Dr. Rossi decided to make a 1MW plant supplying a factory because he knows that even a lot of E-Cats, each one working alone (in several different places of the world), cannot win the conspiracy of the academic world against cold fusion reality.
    The 1MW plant is a new strategy. And when a factory starts to work in Greece it will be impossible to neglect the fact, because saving energy will decrease the cost of products. Other factories will be interested in such technology.

    This is a novelty to you and many people. But there are many cold fusion researchers that are tired with the tongue-displaced-air of the skpetics that claim cold fusion to be impossible.
    That’s why we dont want to hear theirs claims anymore. We dont care anymore on what they claim. Their tongue-displaced-air will be silenced when the 1MW plant start to work in Greece.

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