∵ｴﾈﾙｷﾞｰ準位の間隔Δ⋍2ℓ+1

永江･永宮『原子核物理学』p34(裳華房)
∵ｴﾈﾙｷﾞｰ準位の間隔Δ⋍2ℓ+1
(調和振動子)		(1/2)ℓh^2W	j⋍ℓ+１/2
(ｳｯｽﾞ･ｻｸｿﾝ型+ｽﾋﾟﾝ軌道)		-(1/)(ℓ+1)h^2W	j⋍ℓ-１/2
ｴﾈﾙｷﾞｰ準位の間隔は､(1/2)(2ℓ+1)h^2Wとなる.			∴Δ⋍2ℓ+1
実際には､j⋍ℓ+１/2のｴﾈﾙｷﾞｰ準位の方が
j⋍ℓ-１/2の準位より低くなっているので､
W＜0でなければならない(原子と逆符号)
調和振動のｴﾈﾙｷﾞｰ縮退が解けて分離し､
2,8,20,28,50,82,126(原子核魔法数)となる.

∴v⋍Δγs⋍k＾2・γ(s-2) abc予想

∴v⋍Δγs⋍k＾2・γ(s-2)         abc				予想
γ(s)⋍(s-1)!		Δγs		⋍α	ｘ	β
1				⋍k＾2	ｘ	⋍γ(s-2)		⋍k＾2/(s-3)	⋍k^2/n
1	・	0	⋍	0	ｘ
2	・	1	⋍	1	ｘ	1
6	・	4	⋍	4	ｘ	1			⋍4/1
24	・	18	⋍	9	ｘ	2	⋍	4.5	⋍9/2
120	・	96	⋍	16	ｘ	6	⋍	5.333333	⋍16/3
720	・	600	⋍	25	ｘ	24	⋍	6.25	⋍25/4
5040	・	4320	⋍	36	ｘ	120	⋍	7.2	⋍36/5
40320	・	35280	⋍	49	ｘ	720	⋍	8.166667	⋍49/6
362880	・	322560	⋍	64	ｘ	5040	⋍	9.142857	⋍64/7
3628800	・	3265920	⋍	81	ｘ	40320	⋍	10.125	⋍81/8
39916800	・	36288000	⋍	100	ｘ	362880	⋍	11.11111	⋍100/9
479001500	・	439084700	⋍	121	ｘ	3628800	⋍	12.1	⋍121/10
5748019199	・	5269017699	⋍	144	ｘ	39916800	⋍	13.09091	⋍144/11
80951270382	・	7.5203E+10	⋍	169	ｘ	4.79E+08	⋍	14.08333	⋍169/12
1.2205E+12	・	1.1395E+12	⋍	196	ｘ	6.23E+09	⋍	15.07692	⋍196/13

あくまでも線形

図7.10	ﾓｰｽﾞﾚｨ･ﾀﾞｲｱｸﾞﾗﾑ(特性X線)p178
72	Hf	(	1923	)	ﾍｳﾞｪｼｰ	D.ｺｽﾀｰ
75	Re	(	1925	)	ｲﾀﾞ	ﾜﾙﾀｰ･ﾉﾀﾞｯｸ
87	Fr	(	1939	)	ﾏﾙｸﾞﾞﾘｯﾄ･ﾍﾟﾚｰ
91	Pa	(	1917	)	ｵｯﾄｰ･ﾊｰﾝ	ﾘｰｾﾞ･ﾏｲﾄﾅｰ
	…
図4.2	赤外吸収の直線関係p89
		(	1901	)	H.ﾙｰﾍﾞﾝ	F.ｸｰﾙﾊﾞｳﾑ

零点⋍11(√2k+1-s/11)

k	文献値	文/11	(	s	)	+s/11	⋍√2k+1
1	14.13472	1.284974545454550	(	5	)	0.4545454545454550	1.739520
2	21.02203	1.911093636363640	(	4	)	0.3636363636363640	2.274730
3	25.01085	2.273713636363640	(	4	)	0.3636363636363640	2.637350
4
5	30.42487	2.765897272727270	(	8	)	0.7272727272727270	3.493170
6	32.93506	2.994096363636360	(	7	)	0.6363636363636360	3.630460
7	37.58617	3.416924545454550	(	5	)	0.4545454545454550	3.871470
8	40.91871	3.719882727272730	(	3	)	0.2727272727272730	3.992610
9	43.32707	3.938824545454550	(	5	)	0.4545454545454550	4.393370
10
11	48.00515	4.364104545454550	(	5	)	0.4545454545454550	4.818650
12	49.77383	4.524893636363640	(	4	)	0.3636363636363640	4.888530
13	52.97	4.815454545454550	(	5	)	0.4545454545454550	5.270000
14	56.446	5.131454545454550	(	5	)	0.4545454545454550	5.586000
15	59.347	5.395181818181820	(	2	)	0.1818181818181820	5.577000
16	60.831	5.530090909090910	(	1	)	0.0909090909090909	5.621000
17
18	65.112	5.919272727272730	(	3	)	0.2727272727272730	6.192000
19
20	75.8	6.890909090909090	(	#	)	0.9090909090909090	7.800000

①(□-m^2)φ=0 (ｸﾗｲﾝｺﾞﾙﾄﾞﾝ方程式)

①(□-m^2)φ=0 (ｸﾗｲﾝｺﾞﾙﾄﾞﾝ方程式)
∴Hφ⋍-⒤aφ/aｔ
時間部分f(t)⋍e^i√ℓ･t⋍e^i√2k+1･t
微分して　i√ℓ･f(t)⋍i√2k+1･f(t)
∴⓪⋍√ℓ･f(t)⋍√2k+1･f(t)				文/11
k	文献値	文/11	(s/11)	+(s/11)	√2k+1
1	14.13472	1.284975	0.454545	1.73952	1.732051
2	21.02203	1.911094	0.363636	2.27473	2.236068
3	25.01085	2.273714	0.363636	2.63735	2.645751
4				0	3
5	30.42487	2.765897	0.727273	3.49317	3.316625
6	32.93506	2.994096	0.636364	3.63046	3.605551
7	37.58617	3.416925	0.454545	3.87147	3.872983
8	40.91871	3.719883	0.272727	3.99261	4.123106
9	43.32707	3.938825	0.454545	4.39337	4.358899
10				0	4.582576
11	48.00515	4.364105	0.454545	4.81865	4.795832
12	49.77383	4.524894	0.363636	4.88853	5
13	52.97	4.815455	0.454545	5.27	5.196152
14	56.446	5.131455	0.454545	5.586	5.385165
15	59.347	5.395182	0.181818	5.577	5.567764
16	60.831	5.530091	0.090909	5.621	5.744563
17				0	5.91608
18	65.112	5.919273	0.272727	6.192	6.082763
29				0	7.681146
30	75.8	6.890909	0.909091	7.8	7.81025