Alpha Institute for Advanced Studies

In a message dated 26/09/2012 23:23:09 GMT Daylight Time writes:

Dr. Evans…hope you (all) are well. Here is another potentially interesting LENR commercial venture named Brillouin Energy Corporation: http://brillouinenergy.com/?page=history. They have just signed a development agreement with Stanford Research Institute from where one of their scientists came.

When you mentioned in this current note the Wentzel / Kramers / Brillouin approximate solution of the Schroedinger equation, the name association clicked. This company is further claiming that they will be early to market based on an “understanding of the underlying theory,” an intriguing comment given your reference here.

Very best,

Steve Bannister
University of Utah

On 9/26/2012 6:50 AM, EMyrone wrote:

In this case the transmission coefficient of the standard theory is eq. (23) or eq. (26). This is the Gamov theory at its simplest. So computer algebra can be applied now by co authors of UFT229, Horst Eckardt and Douglas Lindstrom, to determine whether tunnelling through the Coulomb barrier is ever possible This means checking the derivation of eq. (23) and evaluating it by computer algebra. By inspection of eq. (23) tunnelling seems possible when:
a >> x

i.e.

V >> E

when x sub 1 reduces to

x sub 1 ~ 8.33 x 10 power 6 root ((Z sub 1 Z sub 2) a)

so for small a or low E, T becomes enough for low energy nuclear fusion. This theory is described in Merzbacher pp. 126 ff. and uses the well known Wentzel / Kramers / Brillouin approximate solution of the Schroedinger equation for any barrier as shown in Fig. (1). This theory already gives the gist of LENR, and can be made much more sophisticated. The fine structure constant enters into the theory, which gives a clue as to how the ECE vacuum may affect the process, i.e. how energy from spacetime may enter the calculation in the simplest way as in UFT85 for the Lamb shift.

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i.e.

V >> E

when x sub 1 reduces to

x sub 1 ~ 8.33 x 10 power 6 root ((Z sub 1 Z sub 2) a)

so for small a or low E, T becomes enough for low energy nuclear fusion. This theory is described in Merzbacher pp. 126 ff. and uses the well known Wentzel / Kramers / Brillouin approximate solution of the Schroedinger equation for any barrier as shown in Fig. (1). This theory already gives the gist of LENR, and can be made much more sophisticated. The fine structure constant enters into the theory, which gives a clue as to how the ECE vacuum may affect the process, i.e. how energy from spacetime may enter the calculation in the simplest way as in UFT85 for the Lamb shift.

a229thpapernotes1.pdf

In a message dated 26/09/2012 09:16:09 GMT Daylight Time, writes:

Doug, The problem is that the model contains only one particle and a barrier. The “target particle” is only described by the barrier but not by its mass. The radius of the nucleus grows only slightly with the nucleon number so there is no real target dependence. It would proabably better to find a combination of particle tunneling with the new ECE scattering methodology.

Horst

Sent: Wed, Sep 26, 2012 2:39 am
Subject: Re: Fwd: Transmission plots, E dependence

I believe so. I will do it tomorrow.

Would it worthwhile to solve

Nia + p→Cu a+1 + MeV

or

2 6C12 + 2 8O16 →→26Fe56

or something similar with the model.

Doug

:

Doug, your picture looks good. For the paper it would be helpful to add an axis description (letters T, a, E). Can you add this to Mathematica?

Horst

Am EMyrone

These are excellent graphics from co author Dr Douglas Lindstrom to add to those by co author Dr Horst Eckardt. It would be most important to use these graphics to find the optimal m, a, V sub 0 and E for maximum transmission in the non relativistic limit. It is important to find the condiutions under which an atomic mass can quantum tunnel optimally (T goes to one). The important finding is that relativistic velocities inhbit quantum tunnelling. It is known that atoms can quantum tunnel from the dissertation just quoted.

a228thpapernotes1.pdf

a228thpapernotes10.pdf

a228thpapernotes11.pdf

a228thpapernotes12.pdf

a228thpapernotes3.pdf

a228thpapernotes4.pdf

a228thpapernotes5.pdf

a228thpapernotes6.pdf

a228thpapernotes7.pdf

a228thpapernotes8.pdf

a228thpapernotes9.pdf

a288thpapernotes2.pdf

a228thpaper.pdf

In a message dated 26/09/2012 00:38:12 GMT Daylight Time, writes:

This is the mass dependence for the e-e tunneling. The three curves are for non-relativistic to ultra-relativistic electrons (v/c=0 to 0.99). The higher v/c, the smaller the mass required for maximizing T. The m scale is in units of electron masses.
If the included Figure cannot be seen, I can resend it as an attachment.

Horst

Am 25.09.2012 20:30, schrieb EMyrone

These are important results from Dr Horst Eckardt, they show that the slower the incoming particle the more the tunnelling – so it seems that this is strong evidence for low energy nuclear reaction. The high energies needed for relativistic effects inhibit the quantum tunelling and fusion. I used google keywords “quantum tunnelling of atoms” to find that there is a complete dissertation on the net on the subject of atomic quantum tunnelling. I suggest a plot of T against m from the standard equation for transmission, eq. (10) of note 228(12) without relativistic effects, keeping everything constant except m. Looks as if UFT228 will be a good paper.

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