A New Experiment With RaE

Ricardo L. Carezani

Abstract

The classic discrepancy between a calorimetric measurement of the total decay energy of RaE(210/83 Bi) and the kinetic energy calculated to be available by special relativity from the element's beta decay velocity spectrum led to Pauli's postulate of the neutrino. A new experiment is proposed in which a calorimetric measurement can be used to judge the validity of the kinetic energy formula of special relativity, independent of the existence of neutrinos.

Key words: Special Relativity, Autodynamics, neutrino, RaE, beta decay.

In the experiment of Ellis and Wooster(1), a pellet of radium E was placed inside a calorimeter, and the total energy emitted by it during beta decay was measured. The value of the energy deposited per atom was expected to be 1.16 MeV; instead, an average of 0.36 MeV per atom was obtained.

This apparent violation of the law of conservation of energy led Pauli to postulate the existence of a new particle, later named the neutrino by Fermi. The neutrino is responsible for carrying away the difference in energy between the calorimeter's measurement and the 1.16 MeV predicted from the end point of the kinetic energy spectrum as calculated by special relativity from the measured velocity spectrum.

More than 60 years after being postulated by Pauli, the neutrino problem is illustrated by the following comments:

       "After more than thirty years of experiment, the nature of the Neutrino is still an extremely elusive subject.... Not much progress has indeed been made since that time.... we are still dealing with the same problem."(2)
       "The question is now in the hands of the experimenters. Of theories we have plenty- so many that no matter how reality turns out, one will accommodate it. But within the next year, we will know enough to rule out a very large part of speculation ....assuming they really exist".(3)

In referring to the solar neutrino problem, another author wrote:

       "Meanwhile, the GALLEX results provide an unambiguous proof that p-p reactions (among others) power the Sun and that the solar neutrino problem is as slippery as ever".(4)

Whatever the problem is, we expend million of dollars searching for new neutrino qualities, properties, etc., and to confirm neutrino existence(3), even though Buechner and Van de Graaff(5) proved that the neutrino doesn't exist, at least in the case of energy loss by electrons traversing absorbers.

Regarding energy conservation, three observations are relevant:

1. Taking into account the "missing mass" between 83BI210 and 84Po210, the total energy is equal to 1.16 MeV and it is equal to the energy given in the tables(7) as the energy of beta decay.
2. If from this total energy of 1.16 MeV we subtract the electron rest mass, the residual energy available as electron kinetic energy is only .649272 MeV. Energy conservation according to E = mo c^2.
3. If the special relativity kinetic energy is equal to 1.16 MeV and the electron rest mass energy is equal to 0.510999 MeV, the total energy is equal to 1.67 MeV which is bigger than the total energy available by mass difference between Bi and Po. No energy conservation according to E = mo c^2.

The fact that energy is apparently not conserved may lead to any of the following conclusions:

1. There is a new particle, the neutrino, which carries away the energy difference.
2. The formulation of special relativity is not correct for the beta decay reaction, with autotransformation of mass into energy, and the maximum kinetic energy available is indeed 0.649272 MeV per atom.
3. The formulation of special relativity is correct for the free flight of the electron when the energy is taken from the external medium but is not sufficient to characterize the behavior of the system at the moment of creation by decay process.

It is the purpose of this new experiment to obtain data that will indicate which of these conclusions is correct. If (1) is correct, the experiment becomes one more confirming test of special relativity, and the best signature for neutrino existence. The possibility described by (2) is exemplified by the formalism called autodynamics.(8,9,10) The case described by (3) is a natural extension of Eddington's objection to the application of special relativity in atomic systems and of the many possible alternatives to Dirac's equation for the motion of electrons.(11,12).

The experimental setup is shown in Fig. 1. The difference between this setup and the classic one consists in placing the RaE source outside of the calorimeter (an electronic device to measure electron quantity and temperature), so that beta decay electrons reach it only after passing through a standard momentum filter. If the number of particles is counted(13,14) and their mean velocity during the flight is selected by the position of the slots in the filter's vanes, the total kinetic energy that can be delivered to the calorimeter can be calculated from special relativity and autodynamics (8,9,10). The temperature can also be calculated and compared with the experimental results.

To perform a clear experiment, it will be also necessary to measure the electron's time of flight, to disambiguate the equal energy at the same velocity in both theories, from the moment that we cannot use the maximum electron spectrum velocity because at this point the electron quantity is zero.

All the special relativity calculations are known and it is also known that 1.16 MeV is taken as the electron KE in RaE ß-decay, and this is not the case, as will be demonstrated later.

The autodynamics kinetic energy and mass equations are: (8,9,10)

 (1)

 (2)

In RaE beta decay the total energy is equal to 1.16 MeV ( mv + KE) by mass difference between Bi and Po, and consequently the maximum KE available is only .649272 MeV (the difference between total energy (1.16 MeV) and electron rest mass energy 0.510 MeV).

This maximum KE available per atom is taken by the emitted electron or/and the proton interacting with the nucleus. In AD the total energy in RaE decay (1.16 MeV) is equivalent to the particle rest mass that should decay, that is, in this case, equal to mo c^2 in equation (1). We can calculate all the values with equation (1), but, for practical calculations, it is better to introduce equation (2) in equation (1), and working out the equation we find:

When the neutron inside the Bi (RaE) atom decays, the total energy available is distributed between the proton and the electron, given the known electron spectrum.

It is important to point out that taking the sum of all KE in autodynamics columm KE, in Table I, and dividing it by the number of given values, the energy average is:

0.354105 MeV

equal to the experimental value found. This energy is generated as follows:

Taking into account the electron quantity in Table 1 (column Ne) and the corresponding energy, we find an average of:

Ae = .203699 MeV

The proton carries the energy difference and through momentum conservation it transfers its momentum to Po atom, adding a very little energy to the material. This energy is only:

Apo = .001415 MeV.

A small quantity of electrons (column Ni) lose their energy inside the matter(15) adding the energy difference to give the .3553 MeV found experimentally.

Ai = .150210 MeV

The temperature calculation is very simple. A theoretical calculation demonstrates that a pellet of 125 mm3 yield 3 10^10 electrons per second which could be sent to the calorimeter through the standard magnetic filter. The experimental period of time is 10 minutes, and the calculation is done with a calorimeter of Lead of 1 gram. F is the coefficient of electron reduction at the corresponding energy. T is the temperature in degrees centigrade. The calculated results are the following:

Special Relativity Autodynamics

 

Special Relativity     Autodynamics KE (MeV) T (oC) F KE (MeV) T (oC) .4 3.9191 1.0 .218181 2.1377 .7 2.8551 .4163 .381818 1.5573 1.0 .4134 .0422 .545454 .2255

6. CONCLUSION

The experiment is inexpensive and easy to perform (in the sense that it requires only conventional equipment), compared with the millions of dollars we expend in many experiments looking for neutrino properties and neutrino existence.

If the results confirm the energy expected by autodynamics, the implication with respect to special relativity is enormous. Autodynamics' application to decay phenomena in general, and to particle annihilation in particular, opens a new conceptual pathway to energy conservation without ad hoc hypotheses.

 

SPECIAL RELATIVITY			AUTODYNAMICS
Beta	KE (MeV)	Ne	Beta	KE (MeV)	KE+erm (MeV)	Ni
particle velocity in c units		number of electrons in the spectrum			Kinetic energy plus electron rest mass	number of electrons losing energy inside the matter
.548331	.1	79.	.428575	.054545	.565273	.005
.695425	.2	82.7	.566596	.109090	.619818	.008
.776625	.3	78.9	.653012	.163636	.674364	.01
.827957	.4	68.7	.713481	.218181	.728909	.02
.862939	.5	56.	.758312	.272727	.783455	.03
.888015	.6	42.3	.792816	.327272	.838000	.04
.906672	.7	28.6	.820103	.381818	.892546	.06
.920962	.8	17.7	.842139	.436363	.947091	2.0
.932165	.9	8.17	.860237	.490909	1.001636	2.8
.941121	1.0	2.9	.875311	.545454	1.056182	3.0
.948399	1.1	0.33	.888015	.6	1.110727	.9
.95213	1.16	0	.897859	.649272	1.160000

REFERENCES

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3. Jeremy Bernstein, Since Digest (Aug. 1986) pp. 6.
4. Laurence Kraus, Nature 357, 437 (11 June 1992).
5. W. W. Buechner and R. J. Van de Graaff, Phys. Rev. 70, 174(1946).
6. The RaE decay is not the only case known. It is well known the U235 decay. From mass diference(16), the available energy is around 200 MeV, but the calorimetric measurement gave 163(18) and 177(19) MeV.
7. Handbook of Chemistry and Physics, 1991-1992
8. D.R. Walz, H.P. Noyes and R.L. Carezani, Phys. Rev. A29,2110(1884).
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10. Ibid. 6, 384(1993).
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12. Ibid.,42, 278(1946).
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14. H. P. Noyes suggested the electronic counter (private communication).
15. It is well known that the Po case, because of its short half-life (138.38 d), entails a tremendous energy output of ~ 140 W per gram of metal: in consequence, there is considerable self-heating of Po and its compounds.
16. E.A. Plassmann and L.M. Lange, Phys. Rev. 96, 1593(1954).
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