The Constant Linear Force Model

Summary

This model is based on the assumption that all charged elementary particles have the same quantity of Linear Force (F_l). We show how this assumption leads to an alternative interpretation of particle experiments.

Linear Force

Linear force is found by the following equation:

……………………………………………….………….………..1

F_l = linear force

m = mass (MeV)

r = radius (fermi)

Using the Classical Electron Radius and electron mass to find the Linear Force constant we have:

0.5109989MeV x 2.817941fermi = 1.4399648......………………………….…2

Radius

Using F_l and m we can calculate the radii off other particles as show in Table 1

Charge

Using the formula for finding the Classical Radius to find the radii of other particles produces the same result as shown in Table 1 only if all particles have the same charge value.

de Broglie Wavelength

Calculations show that:

Circumference divided by de Broglie wavelength = constant……………….3

Confirming that a mathematical relationship exists between particle and particle wavelength.

Energy

Energy multiplied by radius = constant………………………….……………….4

FQHE

Robert B Laughlin, Horst L StÖrmer and Daniel C Tsui¹, were awarded the 1998 Nobel Prize in Physics for their discovery of Fractionally Charged Electrons; the fractional sequence is 1/3, 2/5, 3/7, 4/9 etc.

In astrophysics the sequence found by Tsui et al, is the measurement of waves within a field for example; measuring the distance between the centres of the dust bands around comet Hale-Bop on two radii (maximum and minimum length) gives the following table:

Band		A	B	C	D
4 (outer band)	Actual	38	39	60	48
	less 1/3 =	25.3	26	40	32
3	Actual	25	27	40	32
	less 2/5 =	15	16.2	24	19.2
2	actual	16.5	16	23	19
	less 3/7 =	9.5	9.1	13	10.9
1 (inner band)	Actual	9.4	9	12	10

The cause of these dust bands is believed to be the sun’s magnetic field that I take to mean - magnetic compaction of charged (dust) particles.

We are unable to match the Tsui sequence to particle compaction and find that the magnetic compaction of single particles can be better explained using the Laughlin and Jain sequences.

H Heiselberg’s² quotes the Laughlin sequence (1/2, 1/3, 1/4, 1/5 etc) as being the most important sequence and the Jain sequence (1/2, 2/3, 3/4, 4/5 etc) as being the next most important sequence; no comment is made on the fact that, placed in order these two sequences add up to a constant value of 1.

One possible cause for the constant is that Laughlin and Jain sequences are two measurements of the same particle in different compaction states as shown in Fig. 1.

Fig.1

This compaction between two parallel force fields will be referred to as single plane compaction. It was then necessary to match the fractional sequences to the particle mass values reported by the Particle Data Group (2004 tables).

Mass

Two points immediately become obvious. The first is that if we are to give a cause for stopping compaction, then the practice of measuring wavelength at mid-point between peak and trough; has to be abandoned as it does not provide a cause. But, at the peak and trough the wave changes direction to start a new wave and this provides a cause because at both points, there must be sufficient wave force to commence the building of a new wave.

Secondly it was realised that each fraction is a fraction of the previous wave and not a fraction of the wave at which compaction started.

This lead to the construction of Table 1 as illustrated by Fig.2

TABLE 1 (Extracted from full table)
Fraction deducted	radius	theoretical mass: CLF formula	mass from PDG 2004 tables	Margin of error	PDG reference
a	b	c	d	e	f
(1)	14.089705	0.1021998			Graviton?
1/2	7.0448525	0.2043996	0.26	±48	56 CHETYRKIN 98 THEO MS scheme
1/3	4.6965684	0.3065994	0.3	±10	57 CUCCHIERI 98 LATT MS scheme
1/4	3.5224263	0.4087991	0.43	± 8	52 MALTMAN 99 THEO MS scheme
1/5	2.817941	0.5109989	0.5109989	electron
1/6	2.3482842	0.6131987	0.553	±12	55 BECIREVIC 98 LATT MS scheme
1/7	2.012815	0.7153985	0.66	±19	58 DOMINGUEZ 98 THEO MS scheme
1/13	1.0838235	1.3285972	1.3	±0.3	ASTIER 00D NOMD
1/17	0.8288062	1.7373963	1.7	±0.3	1 AUBIN 04A LATT MS scheme
1/18	0.7827614	1.8395961	1.79	±0.38	VILAIN 99 THEO MS scheme
1/23	0.6125959	2.350595	2.3	±0.4	3 NARISON 99 THEO MS scheme
1/27	0.521841	2.7593942	2.7	±0.06 4.72	3 AUBERT 04X THEO
1/28	0.5032038	2.8615939	2.9	±0.6	2 JAMIN 02 THEO MS scheme
1/30	0.4696569	3.0659935	3	±0.7	5 NARISON 95C THEO MS scheme
1/33	0.4269608	3.3725929	3.4	±0.11	5 HOANG 04 THEO
1/35	0.402563	3.5769924	3.6	±0.03 4.68	4 BAUER 04 THEO
1/37	0.3808029	3.781392	3.8	±0.2	27 EICKER 97 LATT MS scheme
1/38	0.3707817	3.8835918	3.9	±0.5	6 AUBIN 04A LATT MS scheme
1/39	0.3612745	3.9857916	3.95	±0.3	17 CHIU 02 LATT MS scheme
1/40	0.3522427	4.0879913	4.05	±0.6	19 MALTMAN 01 THEO MS scheme
1/41	0.3436514	4.1901911	4.19	±0.9	7 JAMIN 02 THEO MS scheme
1/42	0.3354692	4.2923909	4.25	±0.7	5 NARISON 95C THEO MS scheme
1/43	0.3276676	4.3945907	4.4	±0.1 ±0.4	14 BECIREVIC 03 LATT MS scheme
1/44	0.3202206	4.4967905	4.5	±0.11	6 MCNEILE 04 LATT
1/45	0.3131046	4.5989903	4.57		20 AOKI 00 LATT MS scheme
1/46	0.306298	4.70119	4.7	±2	21 GOECKELER 00 LATT MS scheme
1/51	0.2762688	5.212189	5.2	±0.9	7 JAMIN 02 THEO MS scheme
1/63	0.2236461	6.4385864	6.4	±1.1 8	NARISON 99 THEO MS scheme
1/69	0.2041986	7.0517851	7	±1.1	9 JAMIN 95 THEO MS scheme
1/72	0.1956904	7.3583844	7.4	±0.7	10 NARISON 95C THEO MS scheme
1/223	0.0631826	22.790552	22.7	±20	61 EICKER 97 LATT MS scheme
1/224	0.0629005	22.892752	22.8	±14.1	59 CHETYRKIN 97 THEO MS scheme
1/744	0.0189378	76.036639	76	±0.09	9 CORCELLA 03 THEO
1/793	0.0177676	81.044428	81	±0.09	7 BAUER 03 THEO
1/827	0.0170372	84.519221	84.5	±0.10	11 EIDEMULLER 03 THEO
1/861	0.0163644	87.994014	88	±0.05	16 KUHN 01 THEO
1/900	0.0156553	91.979805	92	±0.06	13 MAHMOOD 03 THEO
1/910	0.0154832	93.001803	93	±0.05	8 BORDES 03 THEO
1/930	0.0151502	95.045799	95	± 4	49 GOECKELER 00 LATT MS scheme
1/969	0.0145405	99.03159	99	±0.090 ±0.025	18 PINEDA 01 THEO
1/978	0.0144067	99.951388	100	±0.82	19 BARATE 00V ALEP
1/979	0.014392	100.05359	100	±14	50 AOKI 99 LATT MS scheme
1/1008	0.0139779	103.01738	103	±0.57	15 ABBIENDI 01S OPAL
1/1027	0.0137193	104.95918	105	±17	40 GAMIZ 03 THEO MS scheme
1/1037	0.013587	105.98118	106	±0.031	12 ERLER 03 THEO
1/1086	0.012974	110.98896	111	±12	55 BECIREVIC 98 LATT MS scheme
1/1115	0.0126365	113.95276	114	±12	45 MALTMAN 02 THEO MS scheme
1/1125	0.0125242	114.97476	115	±0.06	17 NARISON 01B THEO
1/1135	0.0124139	115.99675	116	±0.10	10 DEDIVITIIS 03 LATT
1/1145	0.0123054	117.01875	117	±0.070	14 PENIN 02 THEO
1/1155	0.0121989	118.04075	118	±17	41 GAMIZ 03 THEO MS scheme
1/1223	0.0115206	124.99034	125	± 2 ± 8 38	BECIREVIC 03 LATT MS scheme
1/1262	0.0111646	128.97613	129	±16	44 JAMIN 02 THEO MS scheme
1/1272	0.0110768	129.99812	130	± 9 ±16	39 CHIU 03 LATT MS scheme
1/1370	0.0102845	140.0137	140	±15	48 AOKI 00 LATT MS scheme
1/1448	0.0097305	147.98529	148	±48	56 CHETYRKIN 98 THEO MS scheme
1/1487	0.0094753	151.97108	152	±27	47 KOERNER 01 THEO MS scheme
1/1663	0.0084725	169.95824	170	-3	42 ALIKHAN 02 LATT MS scheme

Fig.2

A section of Table I illustrating how particles are compacted by the
external wave system; five particles found by experiment are shown
set in waves with wavelengths drawn to scale (amplitude is not to
scale).

Particle jets

In a paper on particle jet experiments J M Campbell, M A Cullen and E W N Glover³ reported on the difficulties of extracting useful information. By measuring the width of the jets shown in figure 3 of their report and comparing the result with CLF radii predictions we show how the particle jets match CLF predictions. Six of the jet particles have already been discovered and reported by the PDG while two appear to be new discoveries

TABLE 2
fraction of remainder	CLF 2r	particle jet width	PDG mass	PDG ref.
a	b	c	d	e

1/10	2.817941013	2.75
1/11	2.561764557
1/12	2.348284177
1/13	2.167646933		2.1676469	13
1/14	2.012815009
1/15	1.878627342
1/16	1.761213133
1/17	1.65761236		1.6576124	17
1/18	1.565522785	1.6	1.5655228	18
1/19	1.483126849
1/20	1.408970506
1/21	1.341876673
1/22	1.280882278
1/23	1.225191745	1.21	1.2251917	23
1/24	1.174142089
1/25	1.127176405
1/26	1.083823466	1.07
1/27	1.043681856		1.0436819	27
1/28	1.006407504		1.0064075	28
1/29	0.971703797
1/30	0.939313671
1/31	0.90901323
1/32	0.880606566
1/33	0.853921519		0.8539215	33
1/34	0.82880618
1/35	0.805126004	0.81	0.805126	35
1/36	0.782761392
1/37	0.761605679		0.7616057	37
1/38	0.741563424	0.75	0.7415634	38
1/39	0.722548978		0.722549	39
1/40	0.704485253		0.7044853	40
1/41	0.687302686		0.6873027	41
1/42	0.670938336		0.6709383	42
1/43	0.655335119		0.6553351	43
1/44	0.640441139	0.64	0.6404411	44
1/45	0.626209114		0.6262091	45
1/46	0.612595872		0.6125959	46
1/47	0.599561918
1/48	0.587071044
1/49	0.575090003
1/50	0.563588203
1/51	0.552537453	0.55	0.5525375	51

A graph of Table 2 is shown in Fig. 3 (below).

Structural constants

Einstein showed that:

.................................................5
c²

The CLF model formula shows that:

……………………………. 6
r

Then:

………………………………7
c² r

c² and F_l are constants therefore:

Constant…………..……………..8

Because the linear force is the same for all elementary charged particles and because speed alters the position of the field force centre, the density forward of the force centre increases with speed; causing an increase in the apparent mass of the particle, when, in fact; the total matter content of the particle remains unchanged. Energy increases with increasing speed because of the increase in density forward of the field force centre, and is at it maximum on the shortest radial,.

Circular waves

Using the Laughlin sequence to visualize the internal wave structure we show how wave rotation creates the prism effect that leads to the ring pattern observed in experiments.

Returning to atomic structure, the wave pattern shows how the wave structure contains the nuclear particles and why nuclear particles undergo a reduction in volume. Particles compacted between the rings are subject to compression in one plane only and do not undergo a change in volume because they can expand in the non-compaction (concentric) plane, but, Particles compacted in the nucleus are subject to compaction in all planes and consequently are forced to undergo a reduction in volume.

The circumference shows a possible cause for de Broglie waves (dotted line) in that there is a variation in wave force on the particle/field surface.

Electron binding energies⁵

The average value for each sub-shell for elements 1 to 92⁵ is used to construct table 3. Limiting the fractions to those with single digit denominators, reveals the Jain sequence; indicating that the internal wave structure is the probable cause of the Jain sequence. These fractions occur on the transverse radial of electrons as shown in Fig. 1.

The space between groups of sub-shells can be seen clearly in a graph of average values. It does not agree with current grouping in the two outermost shells. The current grouping is, of course; present in individual atoms, but disappears in the table of averages.

(Table 3 [produces the fractions used to construct the circular wave diagram).

Table 3
Shell	Average value	Middle shell value	Fraction Of Higher value
1s	35923.376	35923.376

2s	6607.7259
2p(1/2)	6415.4193	6415.4193	1/6
2p(3/2)	5660.2928

3s	1710.7432
3p(1/2)	1547.9213
3p(3/2)	1363.292	1363.292	1/5
3d(3/2)	1302.9508
3d(5/2)	1257.5032

4s	481.01455
4p(1/2)	396.22807
4p(3/2)	338.29123	338.29123	1/4
4d(3/2)	275.32955
4d(5/2)	258.94318

4f(5/2)	112.325
4f(7/2)	104.26765	104.26765	1/3
5s	110.00811

5p(1/2)	78.442105
5p(3/2)	63.705405
5d(3/2)	52.784615	52.784615	1/2
5d(5/2)	50.830769
6s	37.86
6p(1/2)	21.325

By extending the EBE energy investigation to cover each sub-shell we find that the following fractions are (Heiselberg) n1 sequence fractions:

2p(1/2) and 2p(3/2)
1s 1s

Shells 3,4,5, and sub-shell 2s divided by 1s produce fractions in the sequence:

1 1 1 1 1 1 etc

2 3 4 5 6 7

Laughlin sequence fractions are shown in bold type, the complete sequence will be referred to as the 'modified Laughlin sequence'. The complete table is shown in appendix A.

The modified Laughlin sequence agrees with the wave structure shown in fig. 2 and the tables shown in fig.1 explain the appearance of the n1 sequence in the following manner:

Within an atom, electrons are compacted in the transverse plane (modified Laughlin sequence), allowing the longitudinal plane to spread on the atomic field concentric. When the atomic field concentric sphere is no longer large enough to allow for transverse plane electron compaction, the electrons are forced to compact on the longitudinal plane (Heiselberg n1 sequence). When there is insufficient space for both transverse and longitudinal compaction; the electron is forced to compact in all planes (spherical compaction). The particle is now small enough to allow for further compaction in the transverse plane. When there is insufficient space for plane or spherical compaction, further (spherical) compaction is only possible by the creation of composite particles.

Summary

We have shown that compaction of a single elementary particle is responsible for the creation of all observed charged elementary particles. The fractional sequence:

1 1 1 1 1 1 etc

2 3 4 5 6 7

used to determine compaction changes is similar to that found in the compaction of particles within an atomic field, as shown by an examination of the Electron Binding Force values. There is however one obvious difference, collision experiment particle compaction occurs in steps that are fractions of the remainder (remaining radius) while atomic compaction occurs in fractions that are fractions of the whole (1s); this occurs because atomic compaction is compaction within a field; collision compaction is compaction within a vortex.

References

¹ http://nobelprize.org/nobel_prizes/physics/laureates/1998/press.html

² arXiv:cond-mat/0510688 v2 20 Dec 2005

³arXiv:hep-ph/9809429v2 17 Nov 1998

⁴ ‘The structure of Spiral Galaxies' by Berlini and Linn.

⁵ The Elements, John Emsley, OUP, Third edition, 2000

Appendix A


			Laughlin			n1
			fractions			sequence

		2s/1s	2s/1s		2p(1/2)/1s	2p(1/2)/1s
Element		True	sequence		True	sequence
No.	EBE	fraction	fraction	error	fraction	fraction	error
	(1s)	a	b	(a-b)	a	b	(a-b)

7	409.9	0.090998	1/11	0.000089
8	543.1	0.076597	1/13	-0.000326
9	696.7			0.000000
10	870.2	0.055734	1/18	0.000179	0.447423	4/9	0.002978
11	1070.8	0.059301	1/17	0.000478	0.478740	1/2	-0.021260
12	1303	0.067997	1/15	0.001330	0.559819	5/9	0.004264
13	1559	0.075561	1/13	-0.001362	0.618846	5/8	-0.006154
14	1839	0.081403	1/12	-0.001930	0.666667	2/3	0.000000
15	2145.5	0.088091	1/11	-0.002818	0.719577	5/7	0.005291
16	2472	0.093406	1/11	0.002497	0.708532	5/7	-0.005754
17	2822	0.095677	1/10	-0.004323	0.748148	3/4	-0.001852
18	3205.9	0.101781	1/9	-0.009330	0.768005	3/4	0.018005
19	3608.4	0.104922	1/9	-0.006189	0.785261	7/9	0.007484
20	4038.5	0.108555	1/9	-0.002556	0.797673	4/5	-0.002327
21	4492	0.110864	1/9	-0.000247	0.810442	4/5	0.010442
22	4966	0.112948	1/9	0.001837	0.820467	5/6	-0.012866
23	5465	0.114675	1/9	0.003564	0.829424	5/6	-0.003909
24	5989	0.116213	1/9	0.005102	0.838793	5/6	0.005460
25	6539	0.117617	1/9	0.006506	0.845014	5/6	0.011680
26	7112	0.118757	1/8	-0.006243	0.852356	6/7	-0.004787
27	7709	0.120003	1/8	-0.004997	0.857421	6/7	0.000278
28	8333	0.121037	1/8	-0.003963	0.862582	6/7	0.005439
29	8979	0.122141	1/8	-0.002859	0.868332	7/8	-0.006668
30	9659	0.123843	1/8	-0.001157	0.873516	7/8	-0.001484
31	10367	0.125301	1/8	0.000301	0.880062	7/8	0.005062
32	11103	0.127407	1/8	0.002407	0.882299	7/8	0.007299
33	11867	0.128676	1/8	0.003676	0.890046	8/9	0.001157
34	12658	0.130510	1/8	0.005510	0.892433	8/9	0.003545
35	13474	0.132255	1/8	0.007255	0.895623	8/9	0.006734
36	14326	0.134092	1/7	-0.008765	0.901041	8/9	0.012152
37	15200	0.135855	1/7	-0.007002	0.902663	8/9	0.013775
38	16105	0.137597	1/7	-0.005260	0.905686	8/9	0.016797
39	17038	0.139277	1/7	-0.003580	0.908555	8/9	0.019666
40	17993	0.140721	1/7	-0.002136	0.911137	8/9	0.022249
41	18986	0.142105	1/7	-0.000752	0.913640	8/9	0.024751
42	20000	0.143300	1/7	0.000443	0.925331	8/9	0.036443
43	21044	0.144602	1/7	0.001745	0.917844	8/9	0.028955
44	22117	0.145770	1/7	0.002913	0.920285	8/9	0.031396
45	23220	0.146942	1/7	0.004085	0.922040	8/9	0.033151
46	24350	0.148008	1/7	0.005151	0.923973	8/9	0.035084
47	25514	0.149173	1/7	0.006316	0.925906	8/9	0.037018
48	26711	0.150425	1/7	0.007568	0.927576	8/9	0.038687
49	27940	0.151682	1/7	0.008825	0.929212	8/9	0.040323
50	29200	0.152911	1/7	0.010054	0.930795	8/9	0.041906
51	30491	0.153914	1/6	-0.012752	0.933305	8/9	0.044416
52	31814	0.155246	1/6	-0.011421	0.933792	8/9	0.044903
53	33169	0.156411	1/6	-0.010256	0.935235	8/9	0.046346
54	34561	0.157779	1/6	-0.008888	0.936549	8/9	0.047660
55	35985	0.158788	1/6	-0.007878	0.937872	8/9	0.048983
56	37441	0.159958	1/6	-0.006708	0.939055	8/9	0.050166
57	38925	0.160976	1/6	-0.005690	0.940153	8/9	0.051264
58	40443	0.161907	1/6	-0.004760	0.941356	8/9	0.052467
59	41991	0.162773	1/6	-0.003894	0.942209	8/9	0.053320
60	43569	0.163557	1/6	-0.003110	0.943306	8/9	0.054417
61	45184	0.164394	1/6	-0.002272	0.944130	8/9	0.055241
62	46834	0.165200	1/6	-0.001466	0.945069	8/9	0.056180
63	48519	0.165956	1/6	-0.000711	0.945976	8/9	0.057087
64	50239	0.166723	1/6	0.000056	0.946753	8/9	0.057864
65	51996	0.167474	1/6	0.000808	0.947634	8/9	0.058745
66	53789	0.168176	1/6	0.001509	0.948596	8/9	0.059707
67	55618	0.168902	1/6	0.002235	0.949329	8/9	0.060440
68	57486	0.169624	1/6	0.002957	0.950056	8/9	0.061168
69	59390	0.170332	1/6	0.003665	0.950672	8/9	0.061783
70	61332	0.170971	1/6	0.004304	0.951554	8/9	0.062666
71	63314	0.171684	1/6	0.005017	0.952070	8/9	0.063181
72	65351	0.172469	1/6	0.005802	0.952799	8/9	0.063910
73	67416	0.173282	1/6	0.006616	0.953261	8/9	0.064373
74	69525	0.174038	1/6	0.007371	0.954050	8/9	0.065161
75	71676	0.174773	1/6	0.008106	0.954658	8/9	0.065769
76	73871	0.175793	1/6	0.009126	0.953719	8/9	0.064831
77	76111	0.176308	1/6	0.009642	0.955660	8/9	0.066771
78	78395	0.177052	1/6	0.010385	0.956268	8/9	0.067379
79	80725	0.177801	1/6	0.011135	0.956873	8/9	0.067984
80	83102	0.178564	1/6	0.011897	0.957544	8/9	0.068655
81	85530	0.179434	1/6	0.012767	0.957712	8/9	0.068823
82	88005	0.180228	1/6	0.013562	0.958325	8/9	0.069437
83	90526	0.181031	1/6	0.014364	0.958689	8/9	0.069800
84	93105	0.181934	1/5	-0.018066	0.958970	8/9	0.070082
85	95730	0.182733	1/5	-0.017267	0.959527	8/9	0.070638
86	98404	0.183417	1/5	-0.016583	0.960552	8/9	0.071663
87	101137	0.184295	1/5	-0.015705	0.960728	8/9	0.071839
88	103922	0.185110	1/5	-0.014890	0.960857	8/9	0.071968
89	106755	0.185846	1/5	-0.014154	0.961845	8/9	0.072956
90	109651	0.186701	1/5	-0.013299	0.961948	8/9	0.073059
91	112601	0.187432	1/5	-0.012568	0.962521	8/9	0.073632
92	115606	0.188200	1/5	-0.011800	0.964471	8/9	0.075582


			Laughlin			n1
			fractions			sequence

		2s/1s	2s/1s		2p(1/2)/1s	2p(1/2)/1s
Element		True	sequence		True	sequence
No.	EBE	fraction	fraction	error	fraction	fraction	error
	(1s)	a	b	(a-b)	a	b	(a-b)

7	409.9	0.090998	1/11	0.000089
8	543.1	0.076597	1/13	-0.000326
9	696.7			0.000000
10	870.2	0.055734	1/18	0.000179	0.447423	4/9	0.002978
11	1070.8	0.059301	1/17	0.000478	0.478740	1/2	-0.021260
12	1303	0.067997	1/15	0.001330	0.559819	5/9	0.004264
13	1559	0.075561	1/13	-0.001362	0.618846	5/8	-0.006154
14	1839	0.081403	1/12	-0.001930	0.666667	2/3	0.000000
15	2145.5	0.088091	1/11	-0.002818	0.719577	5/7	0.005291
16	2472	0.093406	1/11	0.002497	0.708532	5/7	-0.005754
17	2822	0.095677	1/10	-0.004323	0.748148	3/4	-0.001852
18	3205.9	0.101781	1/9	-0.009330	0.768005	3/4	0.018005
19	3608.4	0.104922	1/9	-0.006189	0.785261	7/9	0.007484
20	4038.5	0.108555	1/9	-0.002556	0.797673	4/5	-0.002327
21	4492	0.110864	1/9	-0.000247	0.810442	4/5	0.010442
22	4966	0.112948	1/9	0.001837	0.820467	5/6	-0.012866
23	5465	0.114675	1/9	0.003564	0.829424	5/6	-0.003909
24	5989	0.116213	1/9	0.005102	0.838793	5/6	0.005460
25	6539	0.117617	1/9	0.006506	0.845014	5/6	0.011680
26	7112	0.118757	1/8	-0.006243	0.852356	6/7	-0.004787
27	7709	0.120003	1/8	-0.004997	0.857421	6/7	0.000278
28	8333	0.121037	1/8	-0.003963	0.862582	6/7	0.005439
29	8979	0.122141	1/8	-0.002859	0.868332	7/8	-0.006668
30	9659	0.123843	1/8	-0.001157	0.873516	7/8	-0.001484
31	10367	0.125301	1/8	0.000301	0.880062	7/8	0.005062
32	11103	0.127407	1/8	0.002407	0.882299	7/8	0.007299
33	11867	0.128676	1/8	0.003676	0.890046	8/9	0.001157
34	12658	0.130510	1/8	0.005510	0.892433	8/9	0.003545
35	13474	0.132255	1/8	0.007255	0.895623	8/9	0.006734
36	14326	0.134092	1/7	-0.008765	0.901041	8/9	0.012152
37	15200	0.135855	1/7	-0.007002	0.902663	8/9	0.013775
38	16105	0.137597	1/7	-0.005260	0.905686	8/9	0.016797
39	17038	0.139277	1/7	-0.003580	0.908555	8/9	0.019666
40	17993	0.140721	1/7	-0.002136	0.911137	8/9	0.022249
41	18986	0.142105	1/7	-0.000752	0.913640	8/9	0.024751
42	20000	0.143300	1/7	0.000443	0.925331	8/9	0.036443
43	21044	0.144602	1/7	0.001745	0.917844	8/9	0.028955
44	22117	0.145770	1/7	0.002913	0.920285	8/9	0.031396
45	23220	0.146942	1/7	0.004085	0.922040	8/9	0.033151
46	24350	0.148008	1/7	0.005151	0.923973	8/9	0.035084
47	25514	0.149173	1/7	0.006316	0.925906	8/9	0.037018
48	26711	0.150425	1/7	0.007568	0.927576	8/9	0.038687
49	27940	0.151682	1/7	0.008825	0.929212	8/9	0.040323
50	29200	0.152911	1/7	0.010054	0.930795	8/9	0.041906
51	30491	0.153914	1/6	-0.012752	0.933305	8/9	0.044416
52	31814	0.155246	1/6	-0.011421	0.933792	8/9	0.044903
53	33169	0.156411	1/6	-0.010256	0.935235	8/9	0.046346
54	34561	0.157779	1/6	-0.008888	0.936549	8/9	0.047660
55	35985	0.158788	1/6	-0.007878	0.937872	8/9	0.048983
56	37441	0.159958	1/6	-0.006708	0.939055	8/9	0.050166
57	38925	0.160976	1/6	-0.005690	0.940153	8/9	0.051264
58	40443	0.161907	1/6	-0.004760	0.941356	8/9	0.052467
59	41991	0.162773	1/6	-0.003894	0.942209	8/9	0.053320
60	43569	0.163557	1/6	-0.003110	0.943306	8/9	0.054417
61	45184	0.164394	1/6	-0.002272	0.944130	8/9	0.055241
62	46834	0.165200	1/6	-0.001466	0.945069	8/9	0.056180
63	48519	0.165956	1/6	-0.000711	0.945976	8/9	0.057087
64	50239	0.166723	1/6	0.000056	0.946753	8/9	0.057864
65	51996	0.167474	1/6	0.000808	0.947634	8/9	0.058745
66	53789	0.168176	1/6	0.001509	0.948596	8/9	0.059707
67	55618	0.168902	1/6	0.002235	0.949329	8/9	0.060440
68	57486	0.169624	1/6	0.002957	0.950056	8/9	0.061168
69	59390	0.170332	1/6	0.003665	0.950672	8/9	0.061783
70	61332	0.170971	1/6	0.004304	0.951554	8/9	0.062666
71	63314	0.171684	1/6	0.005017	0.952070	8/9	0.063181
72	65351	0.172469	1/6	0.005802	0.952799	8/9	0.063910
73	67416	0.173282	1/6	0.006616	0.953261	8/9	0.064373
74	69525	0.174038	1/6	0.007371	0.954050	8/9	0.065161
75	71676	0.174773	1/6	0.008106	0.954658	8/9	0.065769
76	73871	0.175793	1/6	0.009126	0.953719	8/9	0.064831
77	76111	0.176308	1/6	0.009642	0.955660	8/9	0.066771
78	78395	0.177052	1/6	0.010385	0.956268	8/9	0.067379
79	80725	0.177801	1/6	0.011135	0.956873	8/9	0.067984
80	83102	0.178564	1/6	0.011897	0.957544	8/9	0.068655
81	85530	0.179434	1/6	0.012767	0.957712	8/9	0.068823
82	88005	0.180228	1/6	0.013562	0.958325	8/9	0.069437
83	90526	0.181031	1/6	0.014364	0.958689	8/9	0.069800
84	93105	0.181934	1/5	-0.018066	0.958970	8/9	0.070082
85	95730	0.182733	1/5	-0.017267	0.959527	8/9	0.070638
86	98404	0.183417	1/5	-0.016583	0.960552	8/9	0.071663
87	101137	0.184295	1/5	-0.015705	0.960728	8/9	0.071839
88	103922	0.185110	1/5	-0.014890	0.960857	8/9	0.071968
89	106755	0.185846	1/5	-0.014154	0.961845	8/9	0.072956
90	109651	0.186701	1/5	-0.013299	0.961948	8/9	0.073059
91	112601	0.187432	1/5	-0.012568	0.962521	8/9	0.073632
92	115606	0.188200	1/5	-0.011800	0.964471	8/9	0.075582


			n1			Laughlin
			sequence			fractions

		2p(3/2)/1s	2p(3/2)/1s		3s/1s	3s/1s
Element		True	sequence		True	sequence
No.	EBE	fraction	fraction	error	fraction	fraction	error
	(1s)	a	b	(a-b)	a	b	(a-b)

10	870.2	0.445361	4/9	0.000916
11	1070.8	0.480315	1/2	-0.019685
12	1303	0.555305	5/9	-0.000251
13	1559	0.615450	5/8	-0.009550
14	1839	0.662659	2/3	-0.004008
15	2145.5	0.714286	5/7	0.000000
16	2472	0.703768	5/7	-0.010518
17	2822	0.740741	3/4	-0.009259
18	3205.9	0.761263	3/4	0.011263	0.009139	1/109
19	3608.4	0.778130	7/9	0.000352	0.009644	1/104	0.000029
20	4038.5	0.789690	4/5	-0.010310	0.010969	1/91	-0.000020
21	4492	0.800602	4/5	0.000602	0.011376	1/88	0.000012
22	4966	0.809057	4/5	0.009057	0.011820	1/85	0.000056
23	5465	0.817137	4/5	0.017137	0.012132	1/82	-0.000063
24	5989	0.824856	5/6	-0.008477	0.012373	1/81	0.000027
25	6539	0.830451	5/6	-0.002882	0.012586	1/79	-0.000072
26	7112	0.836846	5/6	0.003513	0.012837	1/78	0.000017
27	7709	0.841098	5/6	0.007765	0.013102	1/76	-0.000056
28	8333	0.845429	5/6	0.012096	0.013297	1/75	-0.000037
29	8979	0.850278	6/7	-0.006865	0.013643	1/73	-0.000056
30	9659	0.854205	6/7	-0.002938	0.014474	1/69	-0.000019
31	10367	0.859430	6/7	0.002287	0.015385	1/65	0.000001
32	11103	0.860314	6/7	0.003171	0.016221	1/62	0.000092
33	11867	0.866798	7/8	-0.008202	0.017250	1/58	0.000008
34	12658	0.867978	7/8	-0.007022	0.018139	1/55	-0.000043
35	13474	0.869809	7/8	-0.005191	0.019074	1/52	-0.000157
36	14326	0.873712	7/8	-0.001288	0.020438	1/49	0.000030
37	15200	0.873608	7/8	-0.001392	0.021493	1/47	0.000217
38	16105	0.875451	7/8	0.000451	0.022273	1/45	0.000050
39	17038	0.876528	7/8	0.001528	0.023007	1/43	-0.000248
40	17993	0.877962	7/8	0.002962	0.023915	1/42	0.000105
41	18986	0.878799	7/8	0.003799	0.024576	1/41	0.000186
42	20000	0.879274	7/8	0.004274	0.025315	1/40	0.000315
43	21044	0.879724	7/8	0.004724	0.025851	1/39	0.000210
44	22117	0.880273	7/8	0.005273	0.026500	1/38	0.000184
45	23220	0.880422	7/8	0.005422	0.027050	1/37	0.000023
46	24350	0.880411	7/8	0.005411	0.027581	1/36	-0.000197
47	25514	0.880452	7/8	0.005452	0.028181	1/35	-0.000391
48	26711	0.880538	7/8	0.005538	0.028902	1/35	0.000331
49	27940	0.880132	7/8	0.005132	0.029606	1/34	0.000195
50	29200	0.879955	7/8	0.004955	0.030298	1/33	-0.000005
51	30491	0.880460	7/8	0.005460	0.031026	1/32	-0.000224
52	31814	0.878923	7/8	0.003923	0.031621	1/32	0.000371
53	33169	0.878373	7/8	0.003373	0.032319	1/31	0.000061
54	34561	0.877682	7/8	0.002682	0.033237	1/30	-0.000096
55	35985	0.877144	7/8	0.002144	0.033653	1/30	0.000320
56	37441	0.876106	7/8	0.001106	0.034534	1/29	0.000052
57	38925	0.875040	7/8	0.000040	0.034990	1/29	0.000508
58	40443	0.874007	7/8	-0.000993	0.035507	1/28	-0.000208
59	41991	0.872568	7/8	-0.002432	0.035984	1/28	0.000270
60	43569	0.871176	7/8	-0.003824	0.036150	1/28	0.000435
61	45184	0.869548	7/8	-0.005452			0.000000
62	46834	0.868037	7/8	-0.006963	0.036790	1/27	-0.000248
63	48519	0.866493	6/7	0.009350	0.037099	1/27	0.000062
64	50239	0.864733	6/7	0.007590	0.037441	1/27	0.000404
65	51996	0.862885	6/7	0.005742	0.037849	1/26	-0.000612
66	53789	0.861154	6/7	0.004011	0.038056	1/26	-0.000405
67	55618	0.859165	6/7	0.002023	0.038261	1/26	-0.000201
68	57486	0.857143	6/7	0.000000	0.038375	1/26	-0.000087
69	59390	0.854883	6/7	-0.002260	0.038845	3/77	-0.000116
70	61332	0.852947	6/7	-0.004196	0.039099	2/51	-0.000117
71	63314	0.850414	6/7	-0.006729	0.039344	2/51	0.000128
72	65351	0.848283	6/7	-0.008860	0.039800	1/25	-0.000200
73	67416	0.845831	5/6	0.012498	0.040169	1/25	0.000169
74	69525	0.843554	5/6	0.010220	0.040561	3/74	0.000020
75	71676	0.840983	5/6	0.007650	0.040906	2/49	0.000090
76	73871	0.837132	5/6	0.003799	0.041275	4/97	0.000038
77	76111	0.835755	5/6	0.002422	0.041702	1/24	0.000036
78	78395	0.833141	5/6	-0.000192	0.042043	1/24	0.000377
79	80725	0.830419	5/6	-0.002915	0.042428		0.042428
80	83102	0.827819	5/6	-0.005515	0.042863	1/23	-0.000615
81	85530	0.824787	5/6	-0.008547	0.043306	1/23	-0.000172
82	88005	0.823088	5/6	-0.010245	0.043759	1/23	0.000281
83	90526	0.818831	5/6	-0.014502	0.044175	1/23	0.000697
84	93105	0.815514	4/5	0.015514	0.044563		0.044563
85	95730	0.812554	4/5	0.012554	0.045096	1/22	-0.000359
86	98404	0.809962	4/5	0.009962	0.045547	1/22	0.000092
87	101137	0.806427	4/5	0.006427	0.045997	1/22	0.000542
88	103922	0.802828	4/5	0.002828	0.046400		0.046400
89	106755	0.799950	4/5	-0.000050	0.046855	1/21	-0.000764
90	109651	0.796209	4/5	-0.003791	0.047259	1/21	-0.000360
91	112601	0.792845	4/5	-0.007155	0.047664	1/21	0.000045
92	115606	0.788987	4/5	-0.011013	0.047991	1/21	0.000372


			Laughlin			Laughlin
			fractions			fractions

		3p(1/2)/1s	3p(1/2)/1s		3p(3/2)/1s	3p(3/2)/1s
Element		True	sequence		True	sequence
No.	EBE	fraction	fraction	error	fraction	fraction	error
	(1s)	a	b	(a-b)	a	b	(a-b)

18	3205.9	0.004960	1/202	0.000009	0.004897	1/204	-0.000005
19	3608.4	0.005071	1/197	-0.000005	0.005071	1/197	-0.000005
20	4038.5	0.006289	1/159	0.000000	0.006289	1/159	0.000000
21	4492	0.006300	1/159	0.000011	0.006300	1/159	0.000011
22	4966	0.006565	1/152	-0.000014	0.006565	1/152	-0.000014
23	5465	0.006807	1/147	0.000004	0.006807	1/147	0.000004
24	5989	0.007046	1/142	0.000004	0.007046	1/142	0.000004
25	6539	0.007218	1/139	0.000024	0.007218	1/139	0.000024
26	7112	0.007410	1/135	0.000003	0.007410	1/135	0.000003
27	7709	0.007640	1/131	0.000007	0.007640	1/131	0.000007
28	8333	0.008160	1/123	0.000030	0.007944	1/126	0.000008
29	8979	0.008609	1/116	-0.000012	0.008364	1/120	0.000031
30	9659	0.009463	1/108	0.000203	0.009173	1/109	-0.000002
31	10367	0.009984	1/100	-0.000016	0.009646	1/104	0.000031
32	11103	0.011249	1/89	0.000013	0.010880	1/92	0.000010
33	11867	0.012320	1/81	-0.000026	0.011899	1/84	-0.000006
34	12658	0.013154	1/76	-0.000004	0.012696	1/79	0.000037
35	13474	0.014027	1/71	-0.000057	0.013507	1/74	-0.000006
36	14326	0.015510	1/64	-0.000115	0.014966	1/67	0.000040
37	15200	0.016362	1/61	-0.000032	0.015730	1/64	0.000105
38	16105	0.017405	1/57	-0.000139	0.016765	1/60	0.000098
39	17038	0.018230	1/55	0.000048	0.017537	1/57	-0.000007
40	17993	0.019091	1/52	-0.000140	0.018329	1/55	0.000148
41	18986	0.019809	1/50	-0.000191	0.018993	1/53	0.000125
42	20000	0.020580	1/49	0.000172	0.019700	1/51	0.000092
43	21044	0.021270	1/47	-0.000007	0.019849	1/50	-0.000151
44	22117	0.021870	1/46	0.000131	0.020866	1/48	0.000033
45	23220	0.022450	1/45	0.000228	0.021382	1/47	0.000106
46	24350	0.022994	1/43	-0.000262	0.021860	1/46	0.000121
47	25514	0.023665	1/42	-0.000144	0.022458	1/46	0.000719
48	26711	0.024432	1/41	0.000042	0.023152	1/43	-0.000104
49	27940	0.025168	1/40	0.000168	0.023812	1/42	0.000002
50	29200	0.025908	1/39	0.000267	0.024473	1/41	0.000082
51	30491	0.026654	1/38	0.000338	0.025135	1/40	0.000135
52	31814	0.027372	1/37	0.000345	0.025775	1/39	0.000134
53	33169	0.028068	1/36	0.000291	0.026380	1/38	0.000064
54	34561	0.028995	1/35	0.000424	0.027216	1/37	0.000189
55	35985	0.029762	1/34	0.000351	0.027873	1/36	0.000095
56	37441	0.030368	1/33	0.000065	0.028391	1/35	-0.000180
57	38925	0.031060	1/32	-0.000190	0.028979	1/35	0.000407
58	40443	0.031501	1/32	0.000251	0.029350	1/34	-0.000062
59	41991	0.031840	1/31	-0.000418	0.029578	1/34	0.000166
60	43569	0.032202	1/31	-0.000056	0.029769	1/34	0.000357
61	45184	0.032565	1/30	-0.000769	0.030033	1/33	-0.000270
62	46834	0.032903	1/30	-0.000430	0.030316	1/33	0.000013
63	48519	0.033265	1/30	-0.000068	0.030524	1/33	0.000221
64	50239	0.033599	1/30	0.000266	0.030733	1/33	0.000430
65	51996	0.034003	1/29	-0.000480	0.030983	1/32	-0.000267
66	53789	0.034245	1/29	-0.000238	0.031159	1/32	-0.000091
67	55618	0.034575	1/29	0.000092	0.031303	1/32	0.000053
68	57486	0.034895	1/29	0.000413	0.031521	1/32	0.000271
69	59390	0.035191	1/28	-0.000523	0.031739	1/32	0.000489
70	61332	0.035430	1/28	-0.000284	0.031794	1/31	-0.000464
71	63314	0.035758	1/28	0.000044	0.031968	1/31	-0.000290
72	65351	0.036189	1/28	0.000475	0.032241	1/31	-0.000017
73	67416	0.036623	1/27	-0.000414	0.032544	1/31	0.000286
74	69525	0.037037	1/27	0.000000	0.032808	1/30	-0.000525
75	71676	0.037418	1/27	0.000381	0.033024	1/30	-0.000310
76	73871	0.037796	1/26	-0.000666	0.033261	1/30	-0.000073
77	76111	0.038220	1/26	-0.000241	0.033517	1/30	0.000184
78	78395	0.038612	1/26	0.000151	0.033739	1/30	0.000406
79	80725	0.038997	1/26	0.000535	0.033980	1/29	-0.000503
80	83102	0.039458	1/25	-0.000542	0.034259	1/29	-0.000224
81	85530	0.039939	1/25	-0.000061	0.034573	1/29	0.000090
82	88005	0.040384	1/25	0.000384	0.034839	1/29	0.000356
83	90526	0.040828	1/25	0.000828	0.035095	1/28	-0.000619
84	93105	0.041394	1/24	-0.000273	0.035465	1/28	-0.000249
85	95730	0.041868	1/24	0.000201	0.035788	1/28	0.000074
86	98404	0.042265	1/24	0.000598	0.035954	1/28	0.000240
87	101137	0.042784	1/23	-0.000695	0.036218	1/28	0.000504
88	103922	0.043205	1/23	-0.000273	0.036489	1/27	-0.000548
89	106755	0.043614	1/23	0.000136	0.036617	1/27	-0.000420
90	109651	0.044049	1/23	0.000571	0.036899	1/27	-0.000138
91	112601	0.044413	1/23	0.000935	0.037069	1/27	0.000032
92	115606	0.044825	1/22	-0.000630	0.037221	1/27	0.000184


			Laughlin			Laughlin
			fractions			fractions

		3d(3/2)/1s	3d(3/2)/1s		3d(5/2)/1s	3d(5/2)/1s
Element		True	sequence		True	sequence
No.	EBE	fraction	fraction	error	fraction	fraction	error
	(1s)	a	b	(a-b)	a	b	(a-b)

30	9659	0.001056	1/947	0.000000	0.001046	1/956	0.000000
31	10367	0.001804	1/554	-0.000001	0.001804	1/554	-0.000001
32	11103	0.002684	1/373	0.000003	0.002630	1/380	-0.000002
33	11867	0.003514	1/285	0.000005	0.003514	1/285	0.000005
34	12658	0.004385	1/228	-0.000001	0.004313	1/232	0.000003
35	13474	0.005195	1/192	-0.000013	0.005121	1/195	-0.000007
36	14326	0.006631	1/150	-0.000035	0.006548	1/153	0.000012
37	15200	0.007434	1/135	0.000027	0.007368	1/136	0.000015
38	16105	0.008445	1/118	-0.000030	0.008333	1/120	-0.000001
39	17038	0.009256	1/108	-0.000003	0.009144	1/109	-0.000030
40	17993	0.010065	1/100	0.000065	0.009937	1/101	0.000036
41	18986	0.010797	1/93	0.000045	0.010655	1/94	0.000017
42	20000	0.011555	1/87	0.000061	0.011395	1/88	0.000031
43	21044	0.012241	1/82	0.000046	0.012065	1/83	0.000017
44	22117	0.012850	1/78	0.000029	0.012660	1/79	0.000002
45	23220	0.013432	1/74	-0.000081	0.013230	1/76	0.000072
46	24350	0.013984	1/72	0.000095	0.013766	1/73	0.000067
47	25514	0.014659	1/68	-0.000047	0.014423	1/69	-0.000069
48	26711	0.015421	1/65	0.000036	0.015170	1/66	0.000018
49	27940	0.016156	1/62	0.000027	0.015888	1/63	0.000015
50	29200	0.016890	1/59	-0.000059	0.016606	1/60	-0.000061
51	30491	0.017628	1/57	0.000084	0.017323	1/58	0.000082
52	31814	0.018338	1/55	0.000156	0.018011	1/56	0.000154
53	33169	0.019024	1/53	0.000156	0.018692	1/53	-0.000176
54	34561	0.019936	1/50	-0.000064	0.019571	1/51	-0.000037
55	35985	0.020578	1/49	0.000170	0.020192	1/50	0.000192
56	37441	0.021252	1/47	-0.000024	0.020846	1/48	0.000013
57	38925	0.021914	1/46	0.000175	0.021477	1/47	0.000201
58	40443	0.022313	1/45	0.000091	0.021853	1/46	0.000114
59	41991	0.020202	1/48	-0.000631	0.022119	1/45	-0.000103
60	43569	0.023028	1/43	-0.000228	0.022502	1/44	-0.000225
61	45184	0.023283	1/43	0.000027	0.022729	1/44	0.000002
62	46834	0.023720	1/42	-0.000090	0.023133	1/43	-0.000123
63	48519	0.023879	1/42	0.000070	0.023238	1/43	-0.000017
64	50239	0.024322	1/41	-0.000069	0.023679	1/42	-0.000131
65	51996	0.024558	1/41	0.000167	0.023869	1/42	0.000060
66	53789	0.024782	1/40	-0.000218	0.024020	1/42	0.000210
67	55618	0.025028	1/40	0.000028	0.024291	1/41	-0.000100
68	57486	0.025276	1/40	0.000276	0.024510	1/41	0.000120
69	59390	0.025509	1/39	-0.000132	0.024718	1/40	-0.000282
70	61332	0.025696	1/39	0.000055	0.024914	1/40	-0.000086
71	63314	0.025887	1/39	0.000246	0.025097	1/40	0.000097
72	65351	0.026258	1/38	-0.000058	0.025432	1/39	-0.000209
73	67416	0.026596	1/38	0.000280	0.025736	1/39	0.000095
74	69525	0.028033	1/36	0.000255	0.026019	1/38	-0.000296
75	71676	0.027192	1/37	0.000165	0.026271	1/38	-0.000045
76	73871	0.027494	1/36	-0.000284	0.026533	1/38	0.000217
77	76111	0.027802	1/36	0.000024	0.026803	1/37	-0.000224
78	78395	0.028089	1/36	0.000311	0.027068	1/37	0.000041
79	80725	0.028380	1/35	-0.000191	0.027327	1/37	0.000300
80	83102	0.028700	1/35	0.000128	0.027617	1/36	-0.000161
81	85530	0.029054	1/34	-0.000358	0.027932	1/36	0.000154
82	88005	0.029385	1/34	-0.000027	0.028226	1/35	-0.000346
83	90526	0.029693	1/34	0.000281	0.028500	1/35	-0.000071
84	93105	0.030052	1/33	-0.000251	0.028817	1/35	0.000245
85	95730	0.030388	1/33	0.000085	0.029113	1/34	-0.000299
86	98404	0.030710	1/33	0.000407	0.029389	1/34	-0.000023
87	101137	0.031007	1/32	-0.000243	0.029663	1/34	0.000251
88	103922	0.031254	1/32	0.000004	0.029878	1/33	-0.000425
89	106755	0.031568	1/32	0.000318	0.030153	1/33	-0.000150
90	109651	0.031837	1/31	-0.000421	0.030387	1/33	0.000084
91	112601	0.032069	1/31	-0.000189	0.030568	1/33	0.000265
92	115606	0.032247	1/31	-0.000011	0.030725	1/33	0.000422


			Laughlin			Laughlin
			fractions			fractions

		4s/1s	4s/1s		4p(1/2)/1s	4p(1/2)/1s
Element		True	sequence		True	sequence
No.	EBE	fraction	fraction	error	fraction	fraction	error
	(1s)	a	b	(a-b)	a	b	(a-b)

36	14326	0.001920	1/521	0.000000	1/1016	1/1016
37	15200	0.002007	1/498	-0.000001	0.001072	1/993	0.000065
38	16105	0.002415	1/414	0.000000	0.001341	1/746	0.000001
39	17038	0.002571	1/389	0.000000	0.001432	1/698	-0.000001
40	17993	0.002812	1/356	0.000003	0.001584	1/631	-0.000001
41	18986	0.002971	1/337	0.000003	0.001717	1/582	-0.000001
42	20000	0.003160	1/316	-0.000005	0.001880	1/532	0.000000
43	21044	0.003303	1/303	0.000002	0.002010	1/497	-0.000002
44	22117	0.003391	1/295	0.000001	0.002102	1/476	0.000002
45	23220	0.003506	1/285	-0.000003	0.002175	1/460	0.000001
46	24350	0.003577	1/280	0.000006	0.002287	1/437	-0.000001
47	25514	0.003802	1/263	0.000000	0.002497	1/401	0.000003
48	26711	0.004111	1/243	-0.000005	0.002392	1/418	0.000000
49	27940	0.004399	1/227	-0.000007	0.002631	1/380	-0.000001
50	29200	0.004695	1/213	0.000000	0.002863	1/349	-0.000002
51	30491	0.005024	1/199	-0.000001	0.003135	1/319	0.000001
52	31814	0.005325	1/188	0.000006	0.003247	1/308	0.000000
53	33169	0.005608	1/178	-0.000010	0.003708	1/270	0.000005
54	34561	0.006169	1/162	-0.000004	0.004245	1/236	0.000007
55	35985	0.006455	1/155	0.000004	0.004791	1/209	0.000006
56	37441	0.006771	1/147	-0.000032	0.005128	1/195	0.000000
57	38925	0.007057	1/142	0.000015	0.005287	1/189	-0.000004
58	40443	0.007195	1/139	0.000001	0.005521	1/181	-0.000004
59	41991	0.007252	1/138	0.000005	0.005627	1/177	-0.000022
60	43569	0.007326	1/136	-0.000027	0.005584	1/179	-0.000002
61	45184			0.000000	0.005356	1/187	0.000008
62	46834	0.007413	1/135	0.000006	0.005671	1/176	-0.000011
63	48519	0.007420	1/135	0.000012	0.005853	1/171	0.000005
64	50239	0.007536	1/133	0.000017	0.005693	1/176	0.000011
65	51996	0.007616	1/131	-0.000018	0.006200	1/161	-0.000011
66	53789	0.007700	1/130	0.000008	0.006200	1/161	-0.000011
67	55618	0.007774	1/129	0.000023	0.006176	1/162	0.000003
68	57486	0.007825	1/128	0.000012	0.006370	1/157	0.000001
69	59390	0.007929	1/126	-0.000008	0.006498	1/154	0.000004
70	61332	0.007834	1/127	-0.000040	0.006338	1/158	0.000009
71	63314	0.008005	1/125	0.000005	0.006514	1/154	0.000020
72	65351	0.008232	1/121	-0.000032	0.006705	1/149	-0.000006
73	67416	0.008357	1/120	0.000024	0.006874	1/145	-0.000023
74	69525	0.008545	1/117	-0.000002	0.007054	1/142	0.000011
75	71676	0.008725	1/115	0.000030	0.007237	1/138	-0.000010
76	73871	0.008910	1/112	-0.000018	0.007433	1/135	0.000026
77	76111	0.009080	1/110	-0.000011	0.007592	1/132	0.000016
78	78395	0.009253	1/108	-0.000006	0.007770	1/129	0.000018
79	80725	0.009441	1/106	0.000007	0.007962	1/126	0.000025
80	83102	0.009653	1/104	0.000038	0.008185	1/122	-0.000012
81	85530	0.009894	1/101	-0.000007	0.008424	1/119	0.000021
82	88005	0.010134	1/99	0.000033	0.008657	1/116	0.000037
83	90526	0.010373	1/96	-0.000044	0.008895	1/112	-0.000034
84	93105	0.010687	1/94	0.000049	0.009140	1/109	-0.000034
85	95730	0.010885	1/92	0.000015	0.009255	1/108	-0.000004
86	98404	0.011148	1/90	0.000037	0.009441	1/106	0.000007
87	101137	0.011400	1/88	0.000037	0.009690	1/103	-0.000019
88	103922	0.011624	1/86	-0.000004	0.010181	1/98	-0.000023
89	106755	0.011887	1/84	-0.000018	0.010117	1/99	0.000016
90	109651	0.012129	1/82	-0.000066	0.010652	1/94	0.000014
91	112601	0.012318	1/81	-0.000028	0.010870	1/92	0.000001
92	115606	0.012447	1/80	-0.000053	0.010994	1/91	0.000005


			Laughlin			Laughlin
			fractions			fractions

		4p(3/2/1s	4p(3/2)/1s		4d(3/2)/1s	4d(3/2)/1s
Element		True	sequence		True	sequence
No.	EBE	fraction	fraction	error	fraction	fraction	error
	(1s)	a	b	(a-b)	a	b	(a-b)

36	14326	1/1016	1/1016
37	15200	0.001007	1/993	0.000000
38	16105	0.001248	1/801	0.000000
39	17038	0.001356	1/738	0.000001
40	17993	0.001506	1/664	0.000000
41	18986	0.001622	1/616	-0.000001
42	20000	0.001775	1/563	-0.000001
43	21044	0.001896	1/527	-0.000002
44	22117	0.001953	1/512	0.000000
45	23220	0.002037	1/491	0.000000
46	24350	0.002090	1/478	-0.000002
47	25514	0.002285	1/438	0.000002
48	26711	0.002392	1/418	0.000000	1/2283	1/2283
49	27940	0.002631	1/380	-0.000001	1/1579	1/1579
50	29200	0.002863	1/349	-0.000002	1/1173	1/1173
51	30491	0.003135	1/319	0.000001	0.001092	1/916	0.000000
52	31814	0.003247	1/308	0.000000	0.001317	1/759	0.000000
53	33169	0.003708	1/270	0.000005	0.001507	1/663	-0.000001
54	34561	0.004210	1/238	0.000008	0.002011	1/497	-0.000001
55	35985	0.004482	1/223	-0.000002	0.002218	1/451	0.000000
56	37441	0.004770	1/210	0.000008	0.002473	1/404	-0.000002
57	38925	0.005035	1/199	0.000010	0.002705	1/370	0.000002
58	40443	0.005106	1/196	0.000004	0.002695	1/371	0.000000
59	41991	0.005182	1/193	0.000001	0.002741	1/365	0.000001
60	43569	0.005155	1/194	0.000000	0.002766	1/362	0.000003
61	45184	0.005356	1/187	0.000008	0.002656	1/377	0.000003
62	46834	0.005282	1/189	-0.000009	0.002754	1/363	0.000000
63	48519	0.005297	1/189	0.000006	0.002741	1/365	0.000001
64	50239	0.005394	1/185	-0.000011			0.000000
65	51996	0.005464	1/183	-0.000001	0.002894	1/346	0.000004
66	53789	0.005451	1/183	-0.000014	0.002856	1/350	-0.000002
67	55618	0.005541	1/180	-0.000014	0.002877	1/348	0.000003
68	57486	0.005570	1/180	0.000014	0.002915	1/343	0.000000
69	59390	0.005600	1/179	0.000014	0.002955	1/338	-0.000004
70	61332	0.005539	1/181	0.000014	0.003117	1/321	0.000002
71	63314	0.005673	1/176	-0.000009	0.003255	1/307	-0.000002
72	65351	0.005825	1/172	0.000012	0.003366	1/297	-0.000001
73	67416	0.005947	1/168	-0.000006	0.003529	1/283	-0.000005
74	69525	0.006093	1/164	-0.000005	0.003681	1/272	0.000004
75	71676	0.006234	1/160	-0.000016	0.003821	1/262	0.000005
76	73871	0.006372	1/157	0.000002	0.003968	1/252	-0.000001
77	76111	0.006514	1/154	0.000021	0.004098	1/244	0.000000
78	78395	0.006625	1/151	0.000003	0.004230	1/236	-0.000007
79	80725	0.004375	1/229	0.000009	0.004151	1/241	0.000002
80	83102	0.006938	1/144	-0.000006	0.004551	1/220	0.000006
81	85530	0.007126	1/140	-0.000017	0.004743	1/211	0.000004
82	88005	0.007210	1/139	0.000016	0.004935	1/203	0.000009
83	90526	0.007498	1/133	-0.000020	0.005126	1/195	-0.000003
84	93105	0.007572	1/132	-0.000004	0.005370	1/186	-0.000006
85	95730	0.007730	1/129	-0.000022	0.005568	1/180	0.000012
86	98404	0.007805	1/128	-0.000008	0.005762	1/174	0.000015
87	101137	0.008009	1/125	0.000009	0.005962	1/168	0.000010
88	103922	0.008458	1/118	-0.000016	0.006120	1/163	-0.000015
89	106755	0.008337	1/120	0.000004	0.006323	1/158	-0.000006
90	109651	0.008813	1/114	0.000041	0.006494	1/154	0.000001
91	112601	0.008943	1/112	0.000015	0.006599	1/152	0.000020
92	115606	0.009022	1/111	0.000013	0.006732	1/149	0.000021


			Laughlin			Laughlin
			fractions			fractions

		4d(5/2)/1s	4d(5/2)/1s		4f(5/2)/1s	4f(5/2)/1s
		True	sequence		True	sequence
		fraction	fraction	error	fraction	fraction	error
		a	b	(a-b)	a	b	(a-b)

48	26711	1/2496	1/2496
49	27940	1/1653	1/1653
50	29200	1/1222	1/1222
51	30491	0.001053	1/950	0.000000
52	31814	0.001270	1/787	-0.000001
53	33169	0.001507	1/663	-0.000001
54	34561	0.001953	1/512	0.000000
55	35985	0.002154	1/464	-0.000001
56	37441	0.002401	1/416	-0.000003
57	38925	0.002633	1/380	0.000002
58	40443			0.000000	0.000002	1/404430
59	41991	0.002741	1/365	0.000001	0.000048	1/20995
60	43569	0.002766	1/362	0.000003	0.000034	1/29046
61	45184	0.002656	1/377	0.000003
62	46834	0.002754	1/363	0.000000	0.000111	1/9007
63	48519	0.002632	1/380	0.000000
64	50239	0.002838	1/352	-0.000002	0.000171	1/5842
65	51996	0.002894	1/345	-0.000004	0.000148	1/6753
66	53789	0.002856	1/350	-0.000002	0.000149	1/6724
67	55618	0.002877	1/348	0.000003	0.000155	1/6467
68	57486	0.002915	1/343	0.000000
69	59390	0.002955	1/338	-0.000004
70	61332	0.002974	1/336	-0.000002	0.000041	24532.8
71	63314	0.003100	1/322	-0.000005	0.000141	7113.932584
72	65351	0.003236	1/309	0.000000	0.000243	4110.125786
73	67416	0.003358	1/298	0.000003	0.000349	2868.765957
74	69525	0.003502	1/286	0.000006	0.000483	2069.196429
75	71676	0.003634	1/275	-0.000002	0.000599	1670.769231
76	73871	0.003770	1/265	-0.000003	0.000723	1383.35206
77	76111	0.003893	1/257	0.000002	0.000838	1192.962382
78	78395	0.004013	1/249	-0.000003	0.000950	1052.281879
79	80725	0.004151	1/241	0.000002	1/962	1/962	0.000000
80	83102	0.004318	1/232	0.000007	1/799	1/799	0.000000
81	85530	0.004501	1/222	-0.000003	1/700	1/700	0.000000
82	88005	0.004684	1/214	0.000011	1/621	1/621	0.000000
83	90526	0.004862	1/206	0.000007	1/558	1/558	0.000001
84	93105	0.005080	1/197	0.000004	1/506	1/506	0.000000
85	95730	0.005296	1/189	0.000005	1/456	1/456	0.000001
86	98404	0.005498	1/182	0.000003	2/827	1/414	0.000003
87	101137	0.005705	1/175	-0.000009	2/755	1/377	-0.000003
88	103922	0.005802	1/172	-0.000012	2/695	1/348	0.000004
89	106755	0.005986	1/167	-0.000002	2/669	1/335	0.000003
90	109651	0.006158	1/162	-0.000015	1/320	1/320	-0.000002
91	112601	0.006288	1/159	-0.000002	2/607	1/304	0.000005
92	115606	0.006368	1/157	-0.000001	1/298	1/298	0.000002


			Laughlin			Laughlin
			fractions			fractions

		4f(7/2)/1s	4f(7/2)/1s		5s/1s	5s/1s
		True	sequence		True	sequence
		fraction	fraction	error	fraction	fraction	error
		a	b	(a-b)	a	b	(a-b)

54	34561				0.000674	1/1483
55	35985				0.000631	1/1585
56	37441				0.000809	1/1236
57	38925				0.000881	1135
58	40443	0.000002	1/404430		0.000935	1/1070
59	41991	0.000048	1/20995		0.000891	1/1123
60	43569	0.000034	1/29046		0.000861	1/1162
61	45184
62	46834	0.000111	1/9007		0.000799	1/1252
63	48519				0.000660	1/1516
64	50239	0.000171	1/5842		0.000717	1/1395
65	51996	0.000046	1/21665		0.000877	1/1140
66	53789	0.000080	1/12509		0.000928	1/1078
67	55618	0.000093	1/10696		0.000886	1/1128
68	57486	0.000082	1/12231		0.000880	/11136
69	59390	0.000077	1/12911		0.000921	1/1086
70	61332	0.000021	1/47178		0.000848	1/1179
71	63314	0.000118	1/8442		0.000905	1/1105
72	65351	0.000217	1/4602		0.000982	1/1018
73	67416	0.000320	1/3121		1/967	1/967
74	69525	0.000452	1/2214		1/920	1/920
75	71676	0.000565	1/1770		1/864	1/864
76	73871	0.000686	1/1457		1/879	1/879
77	76111	0.000799	1/1252		1/799	1/799
78	78395	0.000908	1/1101		1/771	1/771
79	80725	1/962	1/962	0.000000	1/753	0.001328	0.000000
80	83102	1/832	1/832	0.000000	1/654	0.001529	-0.000001
81	85530	1/726	1/726	0.000000	1/629	0.001590	0.000000
82	88005	1/643	1/643	0.000000	1/599	0.001669	0.000001
83	90526	1/577	1/577	0.000001	1/568	0.001761	-0.000001
84	93105	1/506	1/506	0.000000	1/526	0.001901	0.000000
85	95730	1/456	1/456	0.000001	1/491	0.002037	0.000000
86	98404	2/827	1/414	0.000003	1/460	0.002174	0.000001
87	101137	2/755	1/377	-0.000003	1/432	0.002315	-0.000001
88	103922	2/695	1/348	0.000004	1/409	0.002445	-0.000001
89	106755	2/669	1/335	0.000003	2/785	0.002545	0.000003
90	109651	1/329	1/329	-0.000002	1/378	0.002646	-0.000001
91	112601	1/313	1/313	0.000002	1/363	0.002755	-0.000002
92	115606	3/919	1/306	-0.000003	1/360	0.002778	-0.000001


			Laughlin			Laughlin
			fractions			fractions

		5p(1/2)/1s	5p(1/2)/1s		5p(3/2)/1s	5p(3/2)/1s
		True	sequence		True	sequence
		fraction	fraction	error	fraction	fraction
		a	b	(a-b)	a	b

54	34561	0.000388			0.000350	1/2856
55	35985	0.000395			0.000336	1/2974
56	37441	0.000454			0.000395	1/2530
57	38925	0.000496			0.000432	1/2317
58	40443	0.000490			0.000420	1/2379
59	41991	0.000531			0.000531	1/1883
60	43569	0.000484			0.000484	1/2065
61	45184					#VALUE!
62	46834	0.000455			0.000455	1/2199
63	48519	0.000453			0.000453	1/2205
64	50239	0.000398	1/2512		0.000398	1/2512
65	51996	0.000552	1/1812		0.000435	1/2301
66	53789	0.000489	1/2045		0.000489	1/2045
67	55618	0.000554	1/1806		0.000433	1/2308
68	57486	0.000546	1/1831		0.000430	1/2327
69	59390	0.000535	1/1868		0.000421	1/2376
70	61332	0.000494	1/2024		0.000393	1/2545
71	63314	0.000531	1/1884		0.000422	1/2371
72	65351	0.000581	1/1720		0.000458	1/2186
73	67416	0.000626	1/1598		0.000485	1/2062
74	69525	0.000652	1/1535		0.000529	1/1889
75	71676	0.000636	1/1572		0.000483	1/2072
76	73871	0.000785	1/1274		0.000602	1/1660
77	76111	0.000838	1/1193		0.000631	1/1586
78	78395	0.000833	1/1201		0.000659	1516
79	80725	0.000709	1/1411
80	83102	0.001000	1/1000		0.000776	0.000776
81	85530	0.001106	1/904	0.000000	0.000859	0.000859
82	88005	0.001209	1/827	0.000000	0.000947	0.000947
83	90526	0.001315	1/761	0.000000	0.001023	1/978
84	93105	0.001418	1/705	-0.000001	0.001117	1/895
85	95730	0.001546	1/647	0.000000	0.001201	1/832
86	98404	0.001667	1/600	0.000000	0.001291	1/775
87	101137	0.001800	1/556	0.000001	0.001384	1/722
88	103922	0.001925	1/520	0.000001	0.001472	1/679
89	106755	0.002014	1/497	0.000002	0.001564	1/639
90	109651	0.002088	1/479	0.000001	0.001660	1/602
91	112601	0.002060	1/485	-0.000001	0.002060	1/485
92	115606	0.002223	1/450	0.000001	0.001661	1/602

			Laughlin		Laughlin
			fractions		fractions

		5d(3/2)/1s	5d(3/2)/1s	5d(5/2)/1s	5d(5/2)/1s
		True	sequence	True	sequence
		fraction	fraction	fraction	fraction
		a	b	a	b

80	83102	0.000116	1/8656	0.000094	1/10654
81	85530	0.000172	1/5818	0.000146	1/6842
82	88005	0.000235	1/4251	0.000206	1/4862
83	90526	0.000297	1/3365	0.000263	1/3804
84	93105	0.000333	1/3003	0.000333	1/3003
85	95730	0.000418	1/2393	0.000418	1/2393
86	98404	0.000488	1/2050	0.000488	1/2050
87	101137	0.000573	1/1744	0.000573	1/1744
88	103922	0.000654	1/1528	0.000654	1/1528
89	106755	0.000749	1/1334	0.000749	1/1334
90	109651	0.000844	1/1185	0.000779	1/1284
91	112601	0.000835	1/1198	0.000835	1/1198
92	115606	0.000889	1/1125	0.000815	1/1227


			Laughlin		Laughlin
			fractions		fractions

81	85530	6s/1s	6s/1s	6p(1/2)/1s	6p(1/2)/1s
82	88005	True	sequence	True	sequence
83	90526	fraction	fraction	fraction	fraction
84	93105	a	b	a	b
85	95730
86	98404	0.000264	1/3785
87	101137	0.000336	1/2975	0.000148	1/6742
88	103922	0.000423	1/2362	0.000183	1/5470
89	106755			0.000000
90	109651	0.000378	1/2649	0.000223	1/4476
91	112601			0.000000
92	115606	0.000380	1/2633	0.000232	1/4314