①ρ⋍1/2 ω⋍1/18 φ⋍1/9 J/ψ⋍4/9 ∴c⋍2/9

①	ρ⋍1/2	ω⋍1/18	φ⋍1/9	J/ψ⋍	4/9	∴c⋍2/9
	原『素粒子』章末問題11.3p176
②	数列Sｎ；零点⋍(1/2)±⒤√s/2					α=0.5	β=0.75
③			α=0.5	β=0.75		γ=0.25	ﾀｸｼｰﾒｰﾀ
n	s	√s/2	⋆＾2	Δ	①+γ	②		文献値
1	8	1.4142136	2			α=0.5	β=0.75	14.13472
2	18	2.1213203	4.5	2.5		2.5	α+2β	21.02203
3	25	2.5	6.25	1.75		1.75	α+β	25.01085
4	36	3	9	2.75	-0.25	2.5	α+2β	30.42487
5	44	3.3166248	11	2	-0.25	1.75	α+β	32.93506
6	56	3.7416574	14	3	-0.5	2.5	α+2β	37.58617
7	65	4.0311289	16.25	2.25	-0.5	1.75	α+β	40.91871
8	78	4.4158804	19.5	3.25	-0.75	2.5	α+2β	43.32707
9	88	4.6904158	22	2.5	-0.75	1.75	α+β	48.00515
10	102	5.0497525	25.5	3.5	-1	2.5	α+2β	49.77383
11	113	5.3150729	28.25	2.75	-1	1.75	α+β	52.97
12	128	5.6568542	32	3.75	-1.25	2.5	α+2β	56.446
13	140	5.9160798	35	3	-1.25	1.75	α+β	59.347
14	156	6.244998	39	4	-１.5	2.5	α+2β	60.831
15	169	6.5	42.25	3.25	-１.5	1.75	α+β	65.112
				4	-１.75	2.5	α+2β
				3.25	-１.75	1.75	α+β

③3点ﾒｰｻﾞｰα=0.5 β=0.75

3点ﾒｰｻﾞｰ		α=0.5	β=0.75
s	√s/2	⋆＾2	Δ	①+γ	②	HMO	文献値
8	1.4142136	2			α=0.5	β=0.75	14.13472
18	2.1213203	4.5	2.5		2.5	α+2β	21.02203
25	2.5	6.25	1.75		1.75	α+β	25.01085
36	3	9	2.75	-0.25	2.75	α+2β	30.42487
44	3.3166248	11	2	-0.25	2	α+β	32.93506
56	3.7416574	14	3	-0.5	2.5	α+2β	37.58617
65	4.0311289	16.25	2.25	-0.5	1.75	α+β	40.91871
78	4.4158804	19.5	3.25	-0.75	2.75	α+2β	43.32707
88	4.6904158	22	2.5	-0.75	2	α+β	48.00515
102	5.0497525	25.5	3.5	-1	2.5	α+2β	49.77383
113	5.3150729	28.25	2.75	-1	1.75	α+β	52.97
128	5.6568542	32	3.75	-1.25	2.75	α+2β	56.446
140	5.9160798	35	3	-1.25	2	α+β	59.347
156	6.244998	39	4	-１.5	2.5	α+2β	60.831
169	6.5	42.25	3.25	-１.5	1.75	α+β	65.112
			4.25	-１.75	2.75	α+2β
			3.5	-１.75	2	α+β

③ﾍﾞﾝｾﾞﾝ環ｴﾈﾙｷﾞｰ準位

③	ﾍﾞﾝｾﾞﾝ環ｴﾈﾙｷﾞｰ準位
n	s	√s/2	⋆＾2	Δ	①	②	HMO	文献値
1	8	1.4142136	2					14.13472
2	18	2.1213203	4.5	2.5		2.5	α+2β	21.02203
3	25	2.5	6.25	1.75		1.75	α+β	25.01085
4	36	3	9	2.75		2.75	α-β	30.42487
5	44	3.3166248	11	2		2	α-2β	32.93506
6	56	3.7416574	14	3	-0.5	2.5		37.58617
7	65	4.0311289	16.3	2.25	-0.5	1.75		40.91871
8	78	4.4158804	19.5	3.25	-0.5	2.75		43.32707
9	88	4.6904158	22	2.5	-0.5	2		48.00515
10	102	5.0497525	25.5	3.5	-1	2.5		49.77383
11	113	5.3150729	28.3	2.75	-1	1.75		52.97
12	128	5.6568542	32	3.75	-1	2.75		56.446
13	140	5.9160798	35	3	-1	2		59.347
14	156	6.244998	39	4	-１.5	2.5		60.831
15	169	6.5	42.3	3.25	-１.5	1.75		65.112
				4.25	-１.5	2.75
				3.5	-１.5	2

Sn=∓0.875+n^2/4 +7.5n+1.125

∓0.875	+	n^2/4	+	7.5n	+1.125		数列Sｎ；零点⋍(1/2)±⒤√s/2
∓0.875	+	n^2/4	+	7.5n	⋍	s	Δa	Δb	Δc	√s/2	文献値
-0.875		0.25	+	7.5	⋍	8				1.414214	14.1347
0.875		1	+	15	⋍	18	10			2.12132	21.022
-0.875		2.25	+	22.5	⋍	25	7	-3		2.5	25.0109
0.875		4	+	30	⋍	36	11	4	7	3	30.4249
-0.875		6.25	+	37.5	⋍	44	8	-3	-7	3.316625	32.9351
0.875		9	+	45	⋍	56	12	4	7	3.741657	37.5862
-0.875		12.25	+	52.5	⋍	65	9	-3	-7	4.031129	40.9187
0.875		16	+	60	⋍	78	13	4	7	4.41588	43.3271
-0.875		20.25	+	67.5	⋍	88	10	-3	-7	4.690416	48.0052
0.875		25	+	75	⋍	102	14	4	7	5.049752	49.7738
-0.875		30.25	+	82.5	⋍	113	11	-3	-7	5.315073	52.97
0.875		36	+	90	⋍	128	15	4	7	5.656854	56.446
-0.875		42.25	+	97.5	⋍	140	12	-3	-7	5.91608	59.347
0.875		49	+	105	⋍	156	16	4	7	6.244998	60.831
-0.875		56.25	+	112.5	⋍	169	13	-3	-7	6.5	65.112
0.875		64	+	120	⋍	186	17	4	7	6.819091	75.8
-0.875		72.25	+	127.5	⋍	200	14	-3	-7	7.071068	75.8
0.875		81	+	135	⋍	218	18	4	7	7.382412	75.8
-0.875		90.25	+	142.5	⋍	233	15	-3	-7	7.632169	75.8

②数列Sｎ；零点⋍(1/2)±⒤√s/2

⓪	ﾙｼﾞｬﾝﾄﾞﾙ[θ]⋍α(α+1)⋍ℓ(ℓ+1)			s(1-s)⋍-ℓ(ℓ+1)　∵s≅ℓ+1
①	ﾒｰﾄﾘｯｸgμν⋍ημν+γμν
②	数列Sｎ；零点⋍(1/2)±⒤√s/2
n	s	√s/2	文献値
1	8	1.4142136	14.13472
2	18	2.1213203	21.02203
3	25	2.5	25.01085
4	36	3	30.42487
5	44	3.3166248	32.93506
6	56	3.7416574	37.58617
7	65	4.0311289	40.91871
8	78	4.4158804	43.32707
9	88	4.6904158	48.00515
10	102	5.0497525	49.77383
11	113	5.3150729	52.97
12	128	5.6568542	56.446
13	140	5.9160798	59.347
14	156	6.244998	60.831
15	169	6.5	65.112
16	229	7.566373	75.8