b-Decomposition of Polarized Neutron

V. T. Vertushkoff

Dnepropetrovsk, 49128, Ukraine

www.vertushkov.dp.ua

 

                                                                   Date of placing: 27.12.2000

 

          Process of free neutron decomposition is presented in such a way that final decomposition products emerge as a result of serial structural changes of the initial particles.

          Planck's particles  and  [1, 2] have no mass. Masses of d-, s-, b- quarks appear as positive defect of the mass Dm > 0 in the process of mutual repulsion of likely charged  and particles [2]. In this case, P1^- particle is considered as neutrino n, and particle is designated as -squark. Accordingly,  is anti-neutrino , and - is anti-squark.

Structure of quarks is the following:

	- quark (when the distance between and –squark is equal to m [2]);
	neutrino impulse,
	neutrino spin (-), determining spin of d-quark;
	-quark (under m);
	-quark (under m).
	-, -, - anti-quarks (correspondingly, under the same l values between  and - anti-squark with those existing between and - squark in d-, s-, b- quarks).
	-, -, - quarks (depending on mutual distances l between , - and - antisquarks).
	-, -, - anti-quarks.

   

          Structure of neutron n, proton p and electron-positron pair e ^-, e⁺ [2]:

          Neutron decomposition is not a spontaneous process. Free neutron is not resistant to the action of particles fluctuating in vacuum. Neutron decomposes with the participation of vacuum pairs e ^-, e⁺ and n, , which fluctuations occur inside the neutron.

1)

          Due to interaction with quarks of neutron, e ^- and e⁺ emit, accordingly, n and , generating vector bosons W^– and W⁺. W^– boson, having absorbed vacuum neutrino, turns into electron. W⁺  boson, after generation of u-quark in it, decomposes into d-anti-quark and u-quark. d-anti-quark, after amalgamation with one of neutron d-quarks, forms neutral pion. u-quark, joining to du-quarks, remained from neutron, forms proton.

          The large mass of W^– and W⁺  bosons appear as a result of the space internal reorganization of particles, remained from e ^- and e⁺ after n and  emitting by them. Boson mass appears as positive defect of the mass Dm > 0 under approach of likely charged interacting particles to each other (first of all, probably, of -squarks in W^–  boson and -anti-squarks in W⁺  boson). Neutral pion is generated by dd -quarks, which mass taken separately in free state is equal to m_d » 7,5 MeV. Mass p° is equal to m_p » 134,963 MeV. In free dd-quarks, distance between n and -squark (as well as between and -anti-squark) makes l » 7,49x10^-16 m. Simple calculation using Coulomb law [2] shows that in p° the distance l is 10 times less  – l » 8,31 x 10^-17 m. Just at this distance mass of each quark in p° is equal to m_p /2. Therefore, mass p° also emerges, evidently, as defect of the mass Dm > 0 under approaching of likely charged particles to each  other (interaction of quark masses is not taken into account).

          Let’s consider interaction of n and W^- boson in neutron decomposition. Since week interactions become apparent at the distances l < 10^-18 m, this may influence the interaction of n and W^- boson. Neutrino in electron moves along circular orbit with radius r » 6,57 x 10^-14 m [2]. Position of n, moving in the electron, can be determined accurate to the electron dimensions, i.e. Dx = 2r » 13,14 x 10^-14 m. Then, indetermination of the impulse

Hence, indetermination of energy DE in the neutrino energy E_n is equal to  . The value r¢»6,32 x 10^-14 m corresponds to the value (maximal kinetic energy of electron E_max in b-decomposition of neutron). At the distance r¢ neutrino is initially combined with -squark transferring energy and impulse to W^- boson. Values r¢ for some of radioactive nuclei are given in Table.

          After neutrino emission by electron, kinetic energy E_w of W^- boson formed is equal to

                             E_w = E_n + E_v ,

where E_n » 1,22 x 10²² MeV – average statistic value of neutrino energy, E_v – kinetic energy of vacuum electron, appeared inside neutron as a result of fluctuation of the pair e^-, e⁺; E_v is variable. Energy of vacuum neutrino E¢_n interacting with W^-  boson, is equal to

                             E¢_n  = E_n + DE ,

where E_n » 1,22 x 10²² MeV , DE = const = 0,782 MeV ( DE is the quantity of deflection from average statistic value of neutrino energy E _n ).

 

Table 1

 

          Impulses of longitudinally polarized n and W^- boson are directed towards each other. Then, energy and direction of the impulse vector of b-decomposition electrons formed under interaction of n and W^- boson are determined by correlation of the values E_v (energy of vacuum electrons) and DE (value of indetermination in the energy E¢_n of neutrino).

          Under 0 £ E_v £ DE we obtain that under E_v = 0 energy of the electron of  b-decomposition is equal to E_b=-E_v= 0,782 MeV. Under E_v = DE, E_b = DE - E_v = 0.

          Under DE £ E_v £ 2DE we obtain that under E_v = DE  E_b = E_v - DE = 0. Under E_v = 2DE  E_b = E_v - DE = DE.

          In accordance with experimental data [3], number of electrons of free neutron b-decomposition, emitted in the direction opposite to neutron spin is 20% higher than electron number emitted along spin direction. It means (see interaction of n and W^- boson in the neutron decomposition process described above), that in 40% of cases the value E_v > DE – electrons move along neutron spin direction. In 60% of cases E_v < DE , namely, electrons move in the direction opposite to neutron spin. At that, electrons turn by 180°. To preserve the angular moment, it is necessary to assume that e^- turn by 180° is accompanied by emission of photon of circular polarization. Process of neutron decomposition in this case looks like as follows:

 

2)   

The above mentioned is presented in the Figs. 1 and 2.

          Why the value DE in free neutron decomposition is equal just to 0,782 MeV? Probably, at such short distances the vacuum neutrino responds to W^- boson (by value of its energy E_w) as to its antiparticle - (with which n is absorbed by vacuum after interaction). As a result, the component of neutrino wave packet with the energy  E¢_n  = E_n + DE participates in the interaction with W^- boson. In this case value DE = 0,782 MeV is the average value of energy E_v of vacuum electrons.

          Similarly, we can record proton decomposition process:

 

1)   

 

2)  

Fig.1. b-spectra of free neutron decomposition. 1 - DE £ E_v £ 2DE, E_b = E_v- DE, electrons move along the neutron spin direction. 2 - 0 £ E_v £ DE, E_b = DE - E_v, electrons move in direction opposite to the neutron spin. 3 – total b-spectrum.

Fig. 2. Spectrum of E_v energies of vacuum electrons participating in free neutron decomposition.

 

REFERENCES

[1] V. T. Vertushkoff. Planck's units.

[2] V. T. Vertushkoff. Planck's particles P1 and P1 – possible connection with other particles.

[3] Burgi M.T., Krohn V. E., Novey T.V. et al. // Phys. Rev. 1958. V. 110, P.1214; 1960. V.120. P.1829.

E-mail: Vertushkoff@ua.fm

 

 

                                                          V. Vertushkoff,

                                                          Kommunarovskaya str. 16,

                                                          Flat 332,

                                                          city of Dniepropetrovsk,

                                                          UKRAINE, 49128.