永江・永宮『原子核物理学』p34(裳華房) | |||
∵エネルギー準位の間隔Δ⋍2ℓ+1 | |||
(調和振動子) | (1/2)ℓh^2W | j⋍ℓ+1/2 | |
(ウッズ・サクソン型+スピン軌道) | -(1/)(ℓ+1)h^2W | j⋍ℓ-1/2 | |
エネルギー準位の間隔は、(1/2)(2ℓ+1)h^2Wとなる. | ∴Δ⋍2ℓ+1 | ||
実際には、j⋍ℓ+1/2のエネルギー準位の方が | |||
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) | |||
調和振動のエネルギ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 | ||||||||
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 |
図7.10 | モーズレィ・ダイアグラム(特性X線)p178 | |||||
72 | Hf | ( | 1923 | ) | ヘヴェシー | D.コスター |
75 | Re | ( | 1925 | ) | イダ | ワルター・ノダック |
87 | Fr | ( | 1939 | ) | マルグ゙リット・ペレー | |
91 | Pa | ( | 1917 | ) | オットー・ハーン | リーゼ・マイトナー |
… | ||||||
図4.2 | 赤外吸収の直線関係p89 | |||||
( | 1901 | ) | H.ルーベン | F.クールバウム |
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 (クラインゴルドン方程式) | |||||
∴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 |