⑤1/2± | 2πi・M(4.5+y+I(I+1)+n+σ) | ||||||||||
シュワルツが求めた式シキ(多面体方程式) | |||||||||||
x=[s^k-1/s^k+1]^2 | |||||||||||
y=[s^k-1/s^k+1]とおき、y[s^k+1]=[s^k-1] | |||||||||||
LNy+LN[s^k+1]=LN[s^k-1] | |||||||||||
∴LN[s^k+1]=-LNy+LN[s^k-1] | |||||||||||
①k=2のとき、-LNy≌ay、s^2-1=(s+1)(s-1) | |||||||||||
t(t+2)=4I(I+1)≌bI(I+1) | |||||||||||
∴LN[s^k+1]=-LNy+LN[s^k-1]=ay+bI(I+1) | |||||||||||
②ゲルマン・大久保の質量公式 | |||||||||||
M=a+by+c[I(I+1)-y^2/4] | 周期 | ||||||||||
y | I(I+1) | σ補正 | = | M | ~ | ⋆2π | 文献値 | n+σ | ①部 | ||
1 | +0.75 | +0.5 | = | 2.25 | ~ | 14.13717 | 14.13472 | / | 4.5 | ≒ | 4.5 |
2 | +0.75 | +0.625 | = | 3.38 | ~ | 21.20575 | 21.02203 | / | ≒ | 6.75 | |
3 | +0.75 | = | 3.75 | ~ | 23.56194 | 25.01085 | / | △7 | ≒ | 7.5 | |
4 | +0.75 | = | 4.75 | ~ | 29.84513 | 30.42487 | / | ≒ | 9.5 | ||
32.93506 | / | 10.5 | |||||||||
5 | +0.75 | = | 5.75 | ~ | 36.12832 | 37.58617 | / | △(2+0.5) | ≒ | 11.5 | |
~ | 40.91871 | / | 13 | ||||||||
6 | +0.75 | = | 6.75 | ~ | 42.4115 | 43.32707 | / | △2 | ≒ | 13.5 | |
~ | / | 15 | |||||||||
7 | +0.75 | = | 7.75 | ~ | 48.69469 | 49.77383 | / | △2 | ≒ | 15.5 | |
~ | / | 17 | |||||||||
8 | +0.75 | = | 8.75 | ~ | 54.97787 | 52.97 | / | △2 | ≒ | 17.5 | |
~ | / | 19 | |||||||||
9 | +0.75 | = | 9.75 | ~ | 61.26106 | 56.446 | / | △2 | ≒ | 19.5 | |
~ | 59.347 | / | 21 | ||||||||
10 | +0.75 | = | 10.8 | ~ | 67.54424 |