CALCULATIONS: Electron K-Capture
(see Autodynamics book for a more detailed explanation)
A proton in the vBe7 nucleus captures an Electron from the K-Shell. This
transforms the Proton to a Neutron, yielding the 3Li7 atom, the recoiling
energy being equivalent to the Electron momentum transfer to 3Li7.
Special Relativity
In order for momentum to be conserved, the absorption momentum of the electron and the recoiling momentum of the 3Li7 atom must be equal. The electron momentum as calculated by Special Relativity is 1.273494 MeV/c. For SR to maintain momentum conservation, the 3Li7 nucleus must recoil with the calculated energy of 124 eV. Yet the experiment yields 17 to 47 eV leaving 77 to 107 eV unaccounted for. Where is the missing momentum or energy? To make up for this missing momentum, SR uses the neutrino. To conserve momentum, the momentum for the recoiling 3Li7 is assumed to be equivalent to the experimental energy value of 45 eV (or a momentum of 0.4668 MeV/c). Knowing that the absorbed electron momentum is 1.2734 MeV/c, the neutrino must carry away the difference:
1.2734 MeV/c (electron) - 0.4668 MeV/c (3Li7 energy of 45 eV) =
0.8066 MeV/c for the neutrino.
Autodynamics
By analyzing the experiment in depth, AD yields a new conclusion, which forms the gateway to new ideas about the atomic nucleus composition. For Autodynamics, there is no loss in momentum: Autodynamics predicts the experimental value of 45eV for 3Li7 recoil. No neutrino or other particle is involved. In other words, there is nothing to fix because Autodynamics correctly predicts the experimental values.
This is because the Electron is absorbed by the Proton at different angles with respect to the Proton line of action. In technical terms, the recoiling nucleus is NOT "monochromatic" even though SR assumes that the recoiling nucleus is "monochromatic".
The variance of the electron absorption angle as calculated by Autodynamics neatly falls within the experimental bounds. Because Special Relativity assumes that the electron and proton are always absorbed in the same direction, it cannot explain the variance. (This was the original explanation. Now many physicists attempt give the neutrino properties to make up for this variance.)
Basic Listing
10 MBE=7.016929 ' 4Be^7 in mass units.
20 MLI=7.016004 ' 3Li^7 in mass units.
30 U=p32 'Equivalence between mass and energy in MeV.
40 EBLI=.000925*U ' Mass' energy difference between Be and Li.
50 PRINT "EBLI="EBLI "Decay energy."
60 MN=1.008655 ' Neutron mass.
70 MP=1.007277 ' Proton mass.
80 ME=.00005489 ' Electron mass.
90 EE=ME*U ' Electron rest mass.
100 EBE=MBE*U ' Be rest mass energy in MeV.
110 ELI=MLI*U ' Li rest mass energy in MeV.
120 EN=MN*U ' Neutron rest mass energy in MeV.
130 EP=MP*U ' Proton rest mass energy in MeV.
140 BETAE#=SQR(1-(EE/EBLI))^2) : PRINT "Betae="BETAE#" "Electron velocity in AD"
150 BETAER#=SQR(1-(/(1+(EBLI/EE))^2)) ' Electron velocity in SR.
160 PRINT "Betaer="BETAER# "Electron velocity in SR."
170 PRINT
180 PER#=(EE*BETAER#)/(BETAER#^2))) : PRINT "Per="PER# "Electron momentum in MeV/c
in SR."
190 BETALIR#=PER#/ELI : PRINT "BetaLi="BETALIR# "Beta Li for SR."
200 RELIR#=(ELI*(BETALIR#^2))/2 : PRINT "RELiR="RELIR# "Li recoiling energy in SR"
210 RLIR#=RELIR#*1000000! : PRINT "RLiR=" "Li recoiling energy in eV in SR *******"
220 PRINT
230 PE#=EE*BETAE# : PRINT "pe="PE# "Electron momentum in MeV/c in AD."
240 'There is momentum conservation between the electron and proton, with them going
242 'away back-to-back, and, for the moment, at 90 degrees with respect
244 'to the neutron line of motion. We also suppose that the neutron
246 'momentum is equal to the proton momentum.
250 PNP#+SQR(PE#^2+PE#^2) : PRINT "pnp="PNP# "New vector proton momentum."
260 BETALI#=PNP#/(ELI-EP) : PRINT "BetaLi="BETALI# "Li velocity."
270 RECENER#=(ELI&(BETALI#^2))/2 : PRINT "RecLi="RECENER# "Li recoiling energy in AD
in MeV."
280 RLIA#=RECENERGY#*1000000! : PRINT "RLiA="RLIA# "Li recoiling energy in eV in
AD. *******
290 PRINT
300 ' If the PROTON_ELECTRON line is 0 degree and the proton
310 ' is going in the same direction as the neutron, the proton
320 ' momentum needs to be only a half of the new vector
330 ' momentum to have the same Li recoil energy..
340 BETAP#=PNP#/EP : PRINT "Betap="BETAP# "Proton velocity."
350 BETAN#=PE#/EN : PRINT "Betan="BETAN# "Neutron velocity."
360 EMN#=((EN*BETAN#^2)/2)*100000! : PRINT "KEn="EMN# " Neutron velocity en eV ---"
370 BETAN2#=(PNP#/2)/EN : PRINT "Betan2="BETAN2# "Neutron 2 velocity."
380 EMN2#=((EN*BETAN2#^2)/2)*1000000! : PRINT "KEn2="EMN2# "Neutron 2 KE in eV ---"
390 ' The experimental results in the paper: J. S. Allen,
400 ' Phys. Rev., 61, 692(1942), are between 41 and 47 eV
410 ' (40-45 eV in the abstract). A neutrino with an
420 ' equivalent energy to 58 eV is accepted although
430 ' the difference is larger and equal to 124-45=79 eV.
440 ' In the paper: P. B. Smith and J. S. Allen, 81, 381
450 ' (1951) the maximum value is 56.6 eV and they reject
460 ' the neutrino hypothesis: " The experiment would also
470 ' have provided convincing corroboration of the neutrino
480 ' hypothesis if monochromatic recoils had been observed.
490 ' The coincidence measurement described above proves
500 ' that, although very nearly monolayer surfaces were
500 ' produced, the recoil energy spectra observed were
510 ' in sharp disagreement with the prediction of the
520 ' neutrino hypothesis".
530 ' This conclusion is irreversible because, as is accepted,
540 ' the electron always has the same energy.
550 ' This experimental lack of monoenergetic recoils, explained
560 ' by AD, could be used to calculate the neutron velocity,
570 ' or if this is known, to calculate the angle between
580 ' proton-electron line of motion and neutron line of
590 ' motion.
Program Output
EBLI= .861175 Decay energy
Betae= .913698 Electron velocity in AD.
Betaer= .928066 Electron velocity in SR.
Per= 1.273494 Electron momentum in MeV/c in SR.
BetaLi= 1.949653 E-4 Beta Li for SR.
RELIR= 1.241436 E-4 Li recoiling energy in SR.
RLIR= 124.143625 Li recoiling energy in eV in SR. *******
pe= .466877 Electron momentum in MeV/c in AD.
pnp= .660264 New vector proton momentum in MeV/c.
BetaLi= 1.180282 E-4 Li velocity.
RecLi= 4.549686 E-5 Li recoiling energy in MeV in AD.
RLIA= 45.496861 Li recoiling energy in eV in AD *******
Betap= 7.040759 E-4 Proton velocity.
Betan= 4.971767 E-4 Neutron velocity.
KEn= 116.060371 Neutron KE in eV. ---
Betan2= 3.515570 E-4 Neutron 2 velocity.
p= .466877 Test neutron momentum = electron momentum.