Abstract

By means of high resolution optical spectroscopy, we can determine nuclear quadrupole moments of radioactive or stable nuclides with even atomic number in the heavy elements region. We discuss and summarize the main conditions applicable to the method.

© 1967 Optical Society of America

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Equations (49)

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H 0 = ( h 2 / 8 π 2 m ) k = 1 Z Δ k 2 - k = 1 Z Z e 2 / r k + k > j = 1 Z e 2 / r k j .
Δ k = i / k + j / y k + k / z k ;
G = ( 2 A ) - 1 ( i = 1 Z P i ) 2
N = ( 2 A ) - 1 i = 1 Z P i 2 ,             M = A - 1 i > j Z j = 1 Z P i P j ,
E ( A ) = E 0 + Δ N E ( A ) + Δ S E ( A ) .
Δ N E ( A ) = - m / ( m + A ) E 0 - E 0 / ( 1836 A ) .
δ N E 21 = E 0 δ A 21 / ( 1836 A 1 A 2 ) ,
δ A 21 = A 2 - A 1 .
Δ S E ( A ) = ( 2 m R y / A ) Σ n Σ n k ( n , n ) ,
K ( n , n ) = u k * ( n ) u j * ( n ) Δ j Δ k u j ( n ) u k ( n ) d τ j d τ k ,
l = l ± 1 ,             m 1 = m 1 ou m 1 = m 1 ± 1 , m s = m s .
δ S E 21 = - 2 m R y ( δ A 21 / A 2 A 1 ) Σ n Σ n K ( n , n ) .
Δ V E ( n s ) = [ N / 4 σ Γ 2 ( 2 σ ) ] a + ( 1 + σ ) K ( X 0 ) a + ( 1 - σ ) K ( X 0 ) X 0 2 σ
δ V E 21 ( n s ) = δ Δ V E ( n s ) = [ N / 2 Γ 2 ( 2 σ ) ] [ a δ K ( X 0 ) ] / [ a + ( 1 - σ ) × K ( X 0 ) ] 2 X 0 2 σ
δ V E 21 ( n s ) = [ N / 2 Γ ( 2 σ ) ] a + ( 1 + σ ) K ( a ) a + ( 1 - σ ) K ( a ) ( 2 Z / a H ) 2 σ R 1 2 σ - 1 δ R 21 ,
K ( a ) = - ( 2 a / 5 ) ( 1 + 0 , 106 a 2 ) ,
R 2 = ( 5 3 ) 0 ρ ( r ) r 2 d τ = ( 5 3 ) r 2 ;
B = [ N / 2 Γ 2 ( 2 σ ) ] a + ( 1 + σ ) K ( a ) a + ( 1 - σ ) K ( a ) ( 2 Z / a H ) 2 σ
C 21 = R 1 2 σ - 1 δ R 21 ,
δ V E 21 ( n s ) = B C 21 .
Δ V E ( n p ) = [ ( 1 - σ ) / ( 1 + σ ) ] Δ V E ( n s ) .
δ V E 21 = β B C 21 ,
δ E 21 = δ N E 21 + δ S E 21 + δ V E 21 .
δ σ 21 = δ N σ 21 + δ S σ 21 + δ V σ 21 ,
δ N σ 21 = ( δ N E 21 ) b - ( δ N E 21 ) a ,
δ N σ 21 = σ δ A 21 / ( 1836 A 1 A 2 ) ,
δ S σ 21 = ( 2 R y δ A 21 ) / ( 1836 A 1 A 2 ) [ Σ a Σ K ( n , n ) - Σ b Σ K ( n , n ) ] .
δ V σ 21 = C 21 [ ( β B ) b - ( β B ) a ] .
DIR = δ σ 21 / δ σ 32 = [ δ N σ 21 + δ S σ 21 + δ V σ 21 ] / [ δ N σ 32 + δ S σ 32 + δ V σ 32 ] .
DIR = ( δ N σ 21 + δ S σ 21 ) / ( δ N σ 32 + δ S σ 32 ) = ( A 3 δ A 21 ) / ( A 1 δ A 32 ) ,
DIR = δ V σ 21 / δ V σ 32 = C 21 / C 32 = ( R 1 2 σ - 1 δ R 21 ) / ( R 2 2 σ - 1 δ R 32 ) ,
δ S σ j i = k m j i ,
k = ( 2 R y / 1836 ) [ Σ Σ a K ( n , n ) - Σ Σ b K ( n , n ) ] ; m j i = δ A j i / ( A j A i ) .
δ σ j i = k m j i + δ V σ j i .
δ σ 21 = k m 21 + δ V σ 21 , δ σ 32 = k m 32 + δ V σ 32 , δ σ 43 = k m 43 + δ V σ 43 .
m 32 δ σ 21 - m 21 δ σ 32 = m 32 δ V σ 21 - m 21 δ V σ 32 , m 43 δ σ 32 - m 32 δ σ 43 = m 43 δ V σ 32 - m 32 δ V σ 43 .
I = [ δ σ 21 - ( A 3 / A 1 ) δ σ 32 ] / [ ( A 2 / A 4 ) δ σ 32 - δ σ 43 ] = [ δ V σ 21 - ( A 3 / A 1 ) δ V σ 32 ] / [ ( A 2 / A 4 ) δ V σ 32 - δ V σ 43 ] .
I = [ C 21 - ( A 3 / A 1 ) C 32 ] / [ ( A 2 / A 4 ) C 32 - C 43 ] .
r 2 = ρ ( r ) r 2 d τ ,
r 2 = 3 R 2 / 5 ,
R = p A 1 3 + ( 5 π 2 a s 2 / 6 p ) A - 1 3 - ( 7 π 4 a s 4 / 24 p 3 ) A - 1 × ,
R = 1 , 123 A 1 3 + 2 , 352 A - 1 3 - 2 , 070 A - 1 +
R = p A 1 3 { [ 1 + 5 π 2 ( a s 2 / 6 p 2 ) A - 2 3 - ] + 1 2 α 2 [ 1 - 13 π 2 ( a s 2 / 6 p 2 ) A - 2 3 + ] + } .
Q 0 = r 3 ( 3 cos 2 θ - 1 )
Q 0 = ( 6 5 ) α Z p 2 A 2 3 [ 1 + π 2 ( a s 2 / 3 p 2 ) A - 2 3 - ] × 10 - 24 cm . 2
R A 1 3 p [ 1 + 25 Q P 0 2 A - 4 3 / ( 72 Z 2 p 4 ) ] .
δ V σ 21 δ N σ 21 + δ S σ 21 ,
DIR = δ R 21 / μ δ R 31 = ( R 2 - R 1 ) ( R 3 - R 1 ) ,
DIR = 2 ( A 2 1 3 - A 1 1 3 ) + 25 / ( 36 Z 2 p 4 ) [ Q 02 2 / A 2 - Q 01 2 / A 1 ] 2 ( A 3 1 3 - A 1 1 3 ) + 25 / ( 36 Z 2 p 4 ) [ Q 03 2 / A 3 - Q 01 2 / A 1 ] ,

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