Atom And Particle Structure

[1157396]

Introduction

 

This paper deals with three related problems:

1) The problem of transferring two dimensional Composite Fermions (CF) theory into the three dimensional frame of the real world. Jainendra K. Jain1 found that:

 

“Comparing Composite Fermions1 theory with real life experiments also necessitates an inclusion of the effects of nonzero thickness of the electron wave function, Landau² level mixing, and disorder, which are not as well understood as the Fractional Quantum Hall Effect^3,4,5 (FQHE) and the accuracy of quantitative comparisons between theory and experiment is determined largely by the accuracy with which these effects can be incorporated into theory. At present, the quantitative agreement between theory and laboratory experiment is roughly within a factor of two, although a 10-20% agreement has been achieved in some cases¹”.

 

We show how the magnetic compression of electrons and electron shells of atoms produce compression fractions comparable to the compression fractions of Composite Fermions1 theory.

 

2) The order in which the electron periods of atoms are filled and the cause of the closing of the periods. Dmitri Mendeleev^2,3 published the first periodic table (1869) based on the order of atomic weights (in rows) and the similarity of chemical properties (in columns), an arrangement that is still in use today. With the development of modern quantum mechanical theories of electron configurations within atoms, it became apparent that each row in the periodic table corresponded to the filling of a quantum period by electrons; however the current quantum filling explanation is open to question as detailed by Eric R. Scerri⁴. Scerri emphasises that Pauli’s Noble Prize-winning work⁶ does not provide a solution to the “closing of the periods” and that the filling order has never been derived from quantum mechanics.

 

3) Scerri⁴ points out that there are more than twenty exceptions to the Madelung rule⁵ not all of which have been explained by subsequent theories. We do not propose an alternative theory, but will show the cause of exceptions to Madelung’s filling order.

 

This proposal assumes that forces of adjacent stable force fields are equal to each other at the point of contact, notwithstanding the fact that both fields may overlap and reach beyond the contact point.

 

Inner and Outer Fields

 

According to Scerri⁴ there is currently no explanation as to the cause of why shell structure ends at the observed ends or why there are only seven shells, we propose that shells are completed at the maximum compression state and that seven shells are the maximum allowed by the compression system.

 

Dividing electron shells into two halves and counting the number of electrons in each half gives the number of Inner Field electrons (IFe) and the number of Outer Field electrons (OFe) as shown in Figs.1a and 1b.

 

Fig. 1a shows that IFe for each period form plateau on which the changes in OFe numbers that determine the nature of the elements are superimposed.

 

Fig. 1a

 

Fig. 1b and Table 2 show the mathematical progressions that exist with the periods.

 

Fig. 1b

 

Table 2

 

A) Period number.

B] Number of IFe.

C) Number of OFe occurring at the end of each pair of periods and at the top of the first period of the next pair of periods .

D) Number of OFe not repeated in next period.

E) Increase in (D).

F) Root of structural compression.

 

Table 2 illustrates that the attempts to add an eighth period requires a complete rebuild of the first seven periods in order to obtain as single ‘0’ structural root (col.F).

 

Magnetic Fractions

Composite fermions theory postulates that when a two-dimensional electron system is exposed to a strong transverse (external) magnetic field, electrons minimize their interaction energy by capturing an even number of quantized vortices to create composite fermions7; (italics added). The magnetically compressed electrons are sometimes describe as an atom of electrons1 the results are given in wave related approximate fractions describe as filling orders.

 

In atomic structure an internal magnetic force compresses electrons, the filling order fractions are found by dividing the number of IFe and OFe by the total number of protons (Table 3).

 

Taking the OFe values (Table 3) for comparison with the fractional values found in CF theory shows that all atomic element fractions (coloured dots in Fig. 3)) are CF2 fractions (black dots in Fig. 3), note that all fractions found by FQHE experiments and CF theory, are approximate fractions1, but atomic element fractions are exact fractions; both are measurements of the width of compressed electron magnetic waves. CF waves are compressed by an external magnetic force, Atomic element electrons are compressed by an internal magnetic force (Fig. 2)

 

Fig. 2

 

Exceptions to Madelung’s Rule.

A graph of atomic compression fractions (Table 3 Fig. 3) shows why Atomic radii decrease from left to right and top to bottom, in the standard Table of Elements. Ignoring compression (Table 1 Fig.4) illustrates how the division of electron shells into inner and outer shells determines the nature of the elements.

 

The nuclear pair (Alkali and Alkaline Earths) and the six outer elements (Other Metals, Metalloids, Non-Metals, Halogens and Noble Gases) are closest together in compression terms indicating the presence of inner and outer compression forces. Like the inner pair (Alkali and Alkaline Earths) the last two elements (Halogens and Noble Gases) have the same nature in all periods indicating the absolute dominance of the inner and outer forces over an equal number of elements in each period.

 

The inner four elements of the end group of six elements (Other Metals, Metalloids, and Non-Metals) undergo changes of nature as the number of periods increases. This is attributable to the fact that the nuclear force increases with each increase in proton numbers, but the external force remains constant altering the balance in favour of the internal force.

 

Fig.4 demonstrates that both Lanthanides and Actinides belong to the same (Rare Earth) group. Transitional Metals and Rare Earths are the central pair of groups; the nuclear force exerts its greater influence over the Transitional Metals while the external force exerts its greater influence over the Rare Earths.

 

Exceptions to Madelung’s rule are shown in blue boxes (Fig. 4) ten are in a lower compression state than the nearest main line; ten are in a higher compression state than the nearest main line. This difference (higher and lower states) is the cause of the difficulties encountered in the creation of a single ‘filling order’ rule.

 

Fig. 3

 

Fig. 4

 

A graph of the rows of Table 3 (Fig. 5) illustrates that the increase in nuclear force (Strong Force) in comparison to the constant external force (Gravity) results in increasing compression of the atomic structure.

 

Fig. 5 can be adjusted to include atomic radii; for example Fig. 6 shows the radii of period 4 (excluding 36Kr due to unknown Atomic Radius), which demonstrates how the radii are determined in three separate groups Alkaline and Alkali Earths, Transitional Metals and the end group (Other Metals, Metalloids, Non-Metals, Halogens and Noble Gases); this explains the cause of the difficulties encountered when attempting to construct a formula that embraces all Atomic Radii

 

Fig. 5

 

Fig. 6

 

Arranging Electron Binding Energies in numerical groups (Table 5) then taking the av-erage value of each numerical group reveals the large scale fractional wave structure of atoms; the fractions are simplified for comparison with CF fractions to reveal that the fractions are all short axis fractions as is to be expected in the case of a radial compres-sion force. Note that there are only six waves for seven periods, the proposed cause be-ing that Period 7 is made of radioactive elements that lack the stability needed to create a static wave.

 

Table 4

 

Table 5

 

Summary

Dividing atomic electron shell structure into inner and outer fields allows an explanation for the cause of the exceptions to Madelung’s rule and the cause of the nature of elements; this division also shows why an eighth period is not possible using the observed seven periods as a base for the proposed eighth. Creating fractions out of the relationship between individual electrons and all the protons of the nucleus provides a mathematical connection to the work of Composite Fermions theorists. Replacing the approximate fractions of CF theory with the actual fractions deduced from atomic structure of the elements would reveal the exact vortex and spin width fractions for atomic structure in the manner shown by Table 4.

 

This hypothesis avoids the approximations and averages of current theory^3,5.

 

References

¹Composite Fermions, Jain J.K., Cambridge University Press, ISBN 978 0 521 86232 5 (Table 7.1,p204)

Ref. 1 (col. A) is the CF1 fractions extracted from a table of Lowest Landau Levels where the fractions are described as indicating the presence of a ‘gap’.

 

²http://arxiv.org/PS_cache/cond-mat/pdf/0510/0510688v2.pdf

Ref.2 is the n1 sequence of Table 11 extracted from a paper by H Heiselberg where the ractions are again referred to as ‘gaps’.

 

³Composite Fermions, Jain J.K., Cambridge University Press, ISBN 978 0 521 86232 5 (Table 6.2,p182)

In ref.³ the fractions are said to represent quasi-particles and quasi-particle holes. The same fractional sequence occurs as 2CF+ fractions in Table 7.1 (see ref.1)

 

⁴Composite Fermions, Jain J.K., Cambridge University Press, ISBN 978 0 521 86232 5 (Table 11.1,p313)

In ref.4 the fractions refer to particles with ‘spin states’.

 

⁵A Suggested periodic table up to Z < 172 based on Dirac-Fock calculations on atoms and ions. Pekka Pyykkӧ. DOI: 10. 1039/c0p01575j

 

 

Appendix A

The balanced field hypothesis used to interpret electron shells in the main article is extended to particle structure by adapting what is known about gravitational field structure which is that the inner structure of a G field increases at a 1:1 ratio, the outer structure decreases according to the inverse square law. Using a vertical mass scale and a horizontal radius scale then by dividing the particle mass along the radius so that the force acting on the inner and outer fields are equal to each other demonstrates that:

 

 

as shown in Table 1 and Fig. 1. Where a comparison is made between RαQMC2 and r=0.5G/2

 

Table 1

 

Fig. 1 shows the concept in graphical form; the total radial force acting on the radius of each particle (measured at each unit of radius) is 1669 units.

As both RαQMC² and r = (½G)/m are theoretical predictions there is a need to justify the balanced field hypothesis using a different measurement; this is done using the ‘adjusted radius (inverse MeV)’ of the most common baryons.

 

Fig. 1

 

No solution was found when restricting the baryon content to three elementary particles (quarks) as in current practice, but on the basis that each baryon must contain whatever is required to construct all the particles in the final decay state, the next attempt was made using the number of elementary particles in the most common final decay states. This did not produce a result with a constant, but the results were closer to producing a constant than the first attempt using only the quark numbers. Further mathematical experiment revealed that:

 

 

m = mass

r = adjusted radius (inverse MeV)

n = number of elementary particles in final decay state

as shown in Table 2.

Replacing the constant (plus force compression) with G/2 (plus force compression) shows that the radius is far larger than expected (the expected being about 10-15), this can be explained by proposing that the two additional particles required to find the G/2 constant are gravitons implying that the gravitons compressed by the baryons, have a short radius (Table 5 of main article) about 100 000 times larger than the observed baryon radius.

 

Table 2

 

Table 3

 

This hypothesis allows an alternative explanation of gravitational action. Newton and Einstein calculate the G force at a point between two bodies replacing the point measurement with a radial G measurement (i.e. the sum of the force measured at regular intervals) shows the true G force acting on the mass; what is needed is a standard interval that can be applied at all levels (micro, macro etc.).

 

Fig. 2 uses an electron and a u quark scaled using data from Table 1 to illustrate this concept as shown in Table 1 and Fig. 1 the sum of the force acting on r1 is equal to the sum of the force acting on r2.

 

Fig. 2

 

Both FQHE and atoms compress electrons radially creating electrons with different short axis radii, as a result the electron ‘surface’ force on both the short and long axis varies between electrons causing the field to overlap until the fields reach a point of equality (Fig. 3); it is proposed that this overlap action is the cause of vortex creation in both FQHE and atomic structure. In FQHE the magnetic compression force is variable allowing the creation of different plateaus (2CF, 4CF etc.), but in atoms the balance between positive (protons) and negative (electrons) is constant hence there is only one atomic plateau equivalent to the 2CF plateau of FQHE as shown in Fig. 2 in the main article.

 

Fig. 3

 

Gluons and Colour Charge

It is proposed that a similar action is responsible for the creation of gluons within atomic nuclei Fig. 4 shows the overlap between u and d quarks for a proton. As no two particles occupy the same orbit (or orbital position) it follows that each quark of a pair of quarks occupies a different orbit and therefore are subject to slightly different compression values; this causes a fractional radial difference which is currently referred to as a difference in ‘colour’. The quantity of force in each elementary particle is a constant as shown in Table 1 of the main article; this causes the observed colour of composite baryons white.

 

The overlap between quarks creates vortices (Composite Fermions theory) that are referred to in particle physics as ‘gluons’. CF fractions are approximate, in reality there is a small difference in overlap fractions that creates a small difference between gluons; as a result there are 4gluons and four anti-gluons.

 

It is also proposed that each individual quark is a charge 1 particle the charge being reduced by the overlap as shown in Fig. 4.

 

Fig.4

 

Table 5 of the main article showed that:

Short axis (A) + vortex fraction © = filled state (F)……………1

Long axis (B) – vortex fraction © = spin width (D)……….……2

(Cols. are shown in brackets.)

 

Compressing the particles shown in fig. 3 illustrates the cause of equations 1 and 2. The parti-cles are shown using dashed black lines. Field force lines are shown in black on the horizontal axis and in magenta on the vertical axis. Then overlap that creates the vortex is shown on the horizontal axis and transferred to the vertical axis. This shows that the vortex orbit lies between the particle surface and the spin width (green line; equation 2).

 

The outer magenta line is scaled to match the spread of the linear force by using the maxi-mum force on the horizontal and vertical scale. This has been reduced to obtain the (inner magenta) force line that passes through the centre of the vortex on the short axis; it can then be seen that the ‘filled state’ (equation 1) includes the whole of the vortex in both particles the cause being that both particles have contributed to the creation of the vortex.

 

The ‘spin width’ is measured on the long axis and as is to be expected, does not include the vortex (green line 2).

 

Fig. 5

 

Summary

This appendix shows in brief outline, how using the balanced field approach explains in classical terms a link between Hall fractions, Composite Fermions theory and the fractional charge assumed by Quantum theorist (fractional charge has not been found by experiment6). The article also indicates for the first time that proof of the existence of the graviton is to be found in baryon structure.

 

References (Appendix A)

¹ R.B. Laughlin (1983). "Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations". Physical Review Letters 50: 1395.

² D.C. Tsui, H.L. Stormer, A.C. Gossard (1982). "Two-Dimensional Magnetotransport in the Extreme Quantum Limit". Physical Review Letters 48: 1559. doi:10.1103/PhysRevLett.48.1559.

H.L. Stormer (1999). "Nobel Lecture: The fractional quantum Hall effect". Reviews of Modern Physics 71: 875. doi:10.1103/RevModPhys.71.875

³ P. Söding (2010). "On the discovery of the gluon". European Physical Journal H 35 (1): 3–28.

⁴ Feynman, Richard (1985). QED: The Strange Theory of Light and Matter. Princeton University Press. p. 136. ISBN 0-691-08388-6

5 Composite Fermions, Jainendra K. Jain. Cambridge University Press, 2007. ISBN-978-0-521-86232-5

⁶ http://www.slac.stanford.edu/exp/mps/FCS/FCS_rslt.htm

 

 

Due to their length Tables 1 and 4 are not submitted, the following example describes their construction.

 

Electron shell numbers for 89Ac are: 2 8 18 32 18 9 2

This gives Inner field numbers 2 8 18 16

And Outer Field numbers 16 18 9 2

Ife and OFe numbers are divided by 89 (Z) to obtain the compression fractions that are simplified to obtain the approximate fractions needed for comparison with fractions obtained by Fractional Quantum Hall Experiments.

 

PS(17 Mar 2011) The available data is not sufficient to test the equation for zero charged particles so the following is my prediction for the mass of the elementary zero charge particle:

mass = (wavelength divided by 2) divided by c^2.

m = eV

wavelength in metres