Financial Consulting Group 0 © 2010 ООО "Группа Финансового Консультирования", компания, зарегистрированная в соответствии

Financial Consulting

Group1© 2010 ООО "Группа Финансового Консультирования", компания, зарегистрированная в соответствии с законодательством Российской Федерации. Все права защищены. Напечатано в России.

Gravitational radiation of the relativistic theory of gravitation

1. Gravitational radiation as a radiation of the same level as electromagnetic

1.1. The essence of the problem of the generalization of relativistic equations on the quantum level was thus outlined :

4 2G c

0,10

;)//)(//(

40

42222

2

GK

crercmmcLLmcr

rK

KTgRgR 2

1

GK 8( ОТО )0и

(*)

:such generalization must match the numerical values of the gravity constants in the quantum and classical regions .



1.2. The stationary states of an elementary source in the proper gravitational field

"The gravitational field within the region of localization of an elementary particle having a mass m0 is characterized by the values of the gravity constant K and of the constant that lead to the stationary states of the particle in its proper gravitational field, and the particle stationary states as such are the sources of the gravitational field with the Newtonian gravity constant G".



f

rf e K e K

l l

rfn

2

2 102

02

2

er r r

l f e K Kl l

rf en

1 12 1

12 2

2 202

22

er r r

l f K K el l

re fn

1 12 1

12 2

202 2

22

1

2 4

1 11 02

2

r re

r rn

(6)

(7)

(8)

(9)

(10) f rn 0 (11)

1.3. stationary states of electrons in proper gravitational field:

01 f



000

12

0

2 drrfnr

(12)

(13)

g

x xg

xK

02 0

R g R T g 1

2

after the substitution

f r Y

iEtEl lm , exp

into them and specific computations in the central-symmetry field metric with the interval defined by the expression

dS c e dt r d d e dr2 2 2 2 2 2 2 2 sin (16)

(15)

(14)

Equations (6)—{8) follow from equations (14)—( 15)



With l = 0 the approximate solution has the form :

E E enn

0

11

where 60,1;65,1 511,01 E МeV, E 2 0 638 , МeV, … E 0 681, МeV,

The presented numerical estimates for the electron show that within the range of its localization, with K~ 1031N m2 kg-2 and ~ 1029m-2

, there exists the spectrum of stationary states in the prоper gravitational field.

The numerical value of K is, certainly, universal for any elementary source. Existence of such numerical value denotes a phenomenon having a deep physical sense: introduction into density of the Lagrange function of a constant member independent on a state of the field. This means that the time-space has an inherent curving which is connected with neither the matter nor the gravitational waves.



2. Registration of electron gravitational radiation lines

Transition over stationary states of electron in proper gravitational field

E

Ei

Ek

E1

Basic stationary state

Eikfigure eV

E=171 keV

E12137 keV



Regular rotational bands in the nucleus of 171Er. Lower rotational energy levels of nuclei are apart from the main one by scores and hundreds of keV.

A scheme of K-, L- and M-levels of energy of the atom, and the main lines of K- and L- series; n, l, j are the principal, the orbital and the inner quantum numbers of energy levels к, L1, L2 etc. The energies of photons of the main lines reach units and scores of keV.

A contribution into widening of spectral lines may be given by a resonance of the energy spectra of electrons (in proper gravitational field) with the energy spectra of multicharged ions and the spectrum of rotational energy levels of nuclei .



Electron energy spectra: 1 – after passing the grid, 2 – after passing the Al foil 13 μm thick; 3 – spectrum calculation according to ELIZA program based on the database [D.E. Cullen et al., Report IAEA-NDS-158, September, 1994] for each spectrum 1. The spectrum is normalized by the standard.

0

5

10

15

20

25

0,04 0,05 0,06 0,07 0,08 0,09 0,1 0,11 0,12 0,13 0,14 0,15 0,16 0,17 0,18 0,19 0,2 0,21 0,22 0,23 0,24

E, MeV

1

2

3

МeV

electron

E

N e ,



Difference of spectral density for theoretical and experimental spectra of electrons passed through Ti, Ta and Al foils.

-0,3

-0,2

-0,1

0

0,1

0,2

0,3

0,4

0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2 0,22

E, MeV

Ti

Ta

Al

МeV

electron

E

N e ,



3. Micropinch plasma electron gravitational radiation in pulse high-current discharges

A part of vacuum sparkle spectrum and a corresponding part of solar flare spectrum



Experimental (a) and calculated (b) parts of a micropinch spectrum normalized for line Lyβ intensity in the area of the basic state ionization threshold of He-like ions.

The firm line in variant (b) corresponds to density of 0.1 g/cm3 , the dotted line – to 0.01 g/cm3; it was assumed that Te = 0.35 keV



The additional mechanism of spectral lines widening of the characteristic electromagnetic radiation of multiple-charge ions (in the conditions of plasma compression by radiated gravitational field) is the only and unequivocal way of quenching electrons excited states at the radiating energy levels of ions and exciting these levels by gravitational radiation at resonance frequencies . Such increase in probability of ion transitions in other states results in additional spectral lines widening of the characteristic radiation.

The reason for quick degradation of micropinches in various pulse high-currency discharges with multiple-charge ions is also clear. There is only partial thermolization of accelerated plasma with the power of gravitational radiation

not sufficient for maintaining steady states.

Measured Fe He-δ line at 8.488 keV (broken curve) compared to calculation (smooth curve) , M.G. Haines et al., PRL, 96, 075003 (2006).



Conclusion

• a) Stationary states in the proper gravitational field (their existence arises from combination of principles of quantum mechanics and relativistic gravitation theory) result in hidden mass phenomena and spectra resonance of stationary states of electromagnetic and gravitational interactions, while transitions over stationary states give the spectrum of gravitational radiation as radiation of the same level with electromagnetic emission.

• b) A resonance between energy levels of stationary states of electromagnetic and gravitational interaction combined with cascade transitions over the stationary states of electron in the proper gravitational field is a mechanism to transfer the gravitational radiation spectrum into long wavelength region in multiple-charge ion plasma that contributes to spectral line broadening of the plasma’s electromagnetic radiation.

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Financial Consulting Group 0 © 2010 ООО "Группа Финансового Консультирования", компания, зарегистрированная в соответствии