18
K. Hashimoto
e
± α i
T −
[ f T]
f
1 ± α i
T −
[ f T ]
f
+
1
2
α
2
i
T −
[ f T ]
f
2
,
(2.10)
e
−
α i
f
1 −
α i
f
.
(2.11)
We substitute Eqs. (2.9), (2.10), and (2.11) into Eq. (2.4) to obtain the following
final form:
Y (T ) =C 1
1 −
1 − e
−α T
αT
+C 2
⎧
⎨
⎩
e
− α
T −
[ f T ]
f
+ e
−
α
f e
α
T −
[ f T ]
f
− 1 − e
−
α
f /
T α p
1 − e
−
α
f
⎫
⎬
⎭
,
+C 3
1 + 2 [ f T ] −
[ f T ]
f T
([ f T ] + 1) − f T
+ C 4 T
(2.12)
where
C 1 = ¯
ν
2
λ d Y 7
λ f +
m 2 − m
2
1
(−ρ)
m 1 ν (ν − 1) Λ
,
(2.13)
C 2 =
¯
ν
2
λ d m 1 (−ρ)
ν (ν − 1) Λ
Y 7 ,
(2.14)
C 3 =
λ d m 1 Λ
(−ρ)
−
¯
ν
2
λ d m 1 (−ρ)
ν (ν − 1) Λ
6
i = 1
Y i ,
(2.15)
C 4 = ¯
ν
2
λ d
6
i = 1
Y i α i
2
λ f +
m 2 − m
2
1
(−ρ)
m 1 ν (ν − 1) Λ
,
(2.16)
α = α 7 .
(2.17)
In this Feynman-α analysis, Eq. (2.12) is fitted to the Y data to obtain the promptneutron decay constant α and the four coefficients (C 1 , C 2 , C 3 , C 4 ).
2.1.2.2 Rossi-α Formula
In the same manner as a derivation of the practical Feynman-α formula, the Rossi-α
formula proposed by Rana and Degweker [6] can be reduced. Their formula can be
written as follows: