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.., .., .., .., .., .. (, , ) . , . THE EFFECT OF WEAK AND LOW-FREQUENCY MAGNETIC FIELD ON RADICAL PAIR RECOMBINATION PROBABILITY Shigaev A.S., Susak I.P., Ponomarev O.A., Kubarev S.I., Kubareva I.S., Fesenko E.E. (Pushchino, Tomsk, Moscow) The dependence radical pair recombination probability on lowintensity magnetic fields, which is very well defined and nonmonotone is presented. . , () . « » , , , , .
296


.. . -- -10, 2002, .296-297

[1-6]. , , , [2]. [7] : , , , . , ( ) , , , , . , . - . [4, 6]. . , , [8 ­ 11]. , . , , [12, 13]. .
297


2. ,

, ( , , ) . , , . . . . , . , ­ , , , , (1) = i H 0, - H d - H S ( PS - PS ) - H T ( PT - PT ) .
t

H 0
H0 =
,



Q S1 S 2 -
2 q







A1q S1 + A2 H


q

S2 ( rq



( 0 ) rq ( 0 ) ) (t )
S2 ,

2 q

t

(2)

exp -

+ 2

2 q

t 2 + g1



(t )

S1 + g 2



H



Q - , (, , .), ­ , ri ­ - (-) i ­ ; S1 S2 ­ - - 1- 2- ,
298


.. . -- -10, 2002, .296-299





­ 3-


, A1q

A2

q

­ , 1- 2-

- q- , rq ( 0 ) rq ( 0 ) ­ - - q , q ,
q



q

­ -

q- , , g1 g 2 ­ g - 1- 2- , H ( t ) - - , ­ , H d ­ , H S , H T - , PS , P - T .
WS = 2 H
S

Sp (
0

PS ) dt ,

(3)

Sp ­ , PS .
1

( x)

=1= S

­ , ­ -

2 ( x) = 2 = T0 , 3 ( x) = 3 = T+ , 4 ( x) = 4 = T-

, , Gnm (t ) = n U ( t ) m , Gnm ( 0 ) = nm ,
nU ( t ) m = n ( x ) U ( t ) m ( x ) d 3 x .

U ( t ) ­ , -



299


2. ,

d U = H ( t )U ( t ) , U ( 0 ) = 1 , dt i
t U ( t ) = T exp -i H ( t ) dt , 0 T ­ . ( t ) = U ( t ) ( 0 ) U ( t )

(4)

(5)



( 0 ) = 1 1 = 1 ( x) 1 ( x) .

, .
1 (t ) 1 = 1 U (t ) 1 1 U


(t )

1 = G11 ( t

)

2

,

(6)

[14, 15]

i

d Gnm ( t ) = dt


q

H

nq

( t )Gqm

, n, q, m = 1, 2, 3, 4.

(7)

, Q , z S1+ = S1x + iS1y S1- = S1x - iS1y ,
( ( H = 01) S1z + 02) S1z +

Q

1 1 1 + S1 S2 + f1 ( t ) S1+ + f1 ( t ) S1- + f2 ( t ) S2 + 2 2 2

1 1 - + f2 ( t ) S2 - iHS P - i Hd - iHT P , S T 2 2

(8)


( 01) =

g1 ( H0 + H2 ( t ) ) + g0


q

3

2 + 2 2 A1q rq ( 0) rq ( 0) q t exp - q q t 2 , (9) 2
2 2 q +q 2 , t 2

H 2 = H 2 cos 2t ,
( 02) =

g2 ( H0 + H2 ( t ) ) + g0

q,



2 3 A2q rq ( 0) rq ( 0) q t exp -

300


.. . -- -10, 2002, .296-301

(10)
f1 ( t ) = g1 H1 exp [ -i1t ] + 2 g0
2 q q,

(



1

- i

2

)

2 A1q zq ( 0 ) rq ( 0 ) q t

exp -
f2 (t ) =

+ 2

2 q

t2 ,

(11)
g2 H1 exp [ -i1t ] + 2 g0
2 q q ,

(



1

- i

2

)

A2

q

2 zq ( 0 ) rq ( 0 ) q t

exp -

+ 2

2 q

t2 ,

t > 0,

(12) g 0 - g 2 g1 , H 0 , H 2 - , z , H1 - , z . , . H T = 0 . (8) H nm
Q xx + Q yy + Q zz - 4 iH -iH s - d 2 -
( 01) -
0

( 2)

2 Q xx + Q yy + Q zz - 4 iH -d 2 - f 2 + f1 22

f 2 - f1 22

f1 - f 22

2

0 -
2 H
nm

(1)

0

( 2)

f 2 + f1 22
( 01) +
0

f 2 + f1 22 +

= f 2 - f1 22

( 2)

2 +

Q H -i d 4 2
xx yy

Q xx - Q 4 - +
( 01) +

yy

f -f 22

1

2

f +f 22

2

1

Q -Q 4

0

( 2)

2 H Q -i d 4 2

+

301


2. ,

(13)

, , , f1 = 0 f 2 = 0 .

H nm , (7) ­ , d i G1m = H11G1m + H12G2 m , dt d (14) i G2 m = H 21G1m + H 22G2 m , dt d i G3m = H 33G3m + H 34G4 m , dt d (15) i G4 m = H 43G3m + H 44G4 m . dt (14) , G11 ( 0 ) = 1 , G21 ( 0 ) = 0 Q xx = Q yy = 0 ( ),

SS ( t ) = G11 ( t

)

2

= g -g g -g H cos 1 2 H0t - 1 2 2 sin 2t + ( t ) = g0 2 g0 1 2 exp g1 - g2 g -g H H0 t + i ( t ) - i 1 2 2 sin 2t + K. C. , i g0 2 g0

1 = exp[ -HS t - Hd t ] 1+ 2 1 = exp[ -HS t - Hd t ] 1+ 2

(16)
302


.. . -- -10, 2002, .296-303


(t ) =


q



3

(

A1q - A2

q

) r ( 0) r ( 0)
q q


2 q

1 - exp - +
2 q 2 q

2 q

+ 2

2 q

t 2 .

, . exp [ ±iz sin ] = J 0 ( z ) + 2 J 2 k ( z ) cos 2k ± 2i J 2 k +1 ( z ) sin ( 2k + 1) ,
1 0

J k ( z ) - , (16)
1 exp [ - H S t - H d t ] 1 + cos ( h0 2t + ) J 0 ( h2 ) + 2 2 +2sin ( h0 2t + ) J 2 k +1 ( h2 ) sin 2t , i



SS

(t )

=


k =1



J

2k

( h2 )

cos 2k 2t +

g1 - g 2 H 2 g - g2 H 0 , . h0 = 1 g0 2 g0 2 , = ( ) ,
h2 =
WS = 2 H
S


0

dt

SS

(t )

=
S

=

H 1 HS 1 + J0 ( h2 ) 2 HS + Hd 2
S

((

HS + Hd ) cos - h02 sin h + ( HS + Hd
2 0 2 2 2

)

2

)

+

J ( h )
2k 2 k =1





H

((

HS + Hd ) cos - ( h0 + 2k ) 2 sin

(

HS + Hd ) +
2

(

+ -


k =0



J

2 k +1

(

H h2 )
d

HS + Hd ) cos - ( h0 - 2k ) 2 sin ) + 2 2 h0 + 2k ) ( HS + Hd ) + ( h0 - 2k ) 22 S ( ( H S + H d ) cos - ( h0 - 2k - 1) 2 sin ) - 2 2 ( H S + H d ) + ( h0 - 2k - 1) 22
2 2

)

+

H

S

((

H

S

((

HS + H

(

cos - ( h0 + 2k + 1) 2 sin ) . 2 2 2 H S + H d ) + ( h0 + 2k + 1) 2

)

(17)

. (17) h0 p =±2k . , ,
303


2. ,

. . 1 . ). . (t ) , H2 . . 1 2.

)

= 0.

b)

= 4.

) h0 = 4.

b)

h0 = 5

.

. 1. . 2. () - . .

). H0. H0 ­ . H0 , . . J0(h2) J2(h2), J4(h2) - , H0 . , J0(h2) h2, , H0 , . H0 : ( 10-5 ) . J0(h2) . H0=0 H0 0 . 3, 5.

304


.. . -- -10, 2002, .296-305

)

h2 = 0.

b)

h2 = 10

.

)

b)

. 3. .

. 4. (), (b).

). . . H0 H2. , H0 «» [16]. eH 0 4mkg 0 , , M k = (18) k = 1, 2, ... . = Mkc g1 - g 2 ). . H2 ­ . H2 H2 . 2 (. 4.).

a)

h0 = 0.3

b)

h0 = 4

.

. 5. () (b) .

H2=0 , , H0=0. H0 0, (. 5b). H2 , .. , H2 .
305


2. ,

H2 , . 5. . , -, . , : , , . . . -, , , . , , , . , . , , . , , . .
( 02-03-32434).

. 1. .., .., .., .., .. ..:., 2002, 157 . 2. Binhi V. N., Savin A. V. // Phys. Rev. E., 2002, V. 65, P. 051912­1­10. 3. .., .., .., . . . 1991.
306


.. . -- -10, 2002, .296-307

4. ..//, 1999. . 169, 8. . 889 ­ 908. 5. ..// . 1973. . 10, 1. . 183 ­ 186. 6. .., .., ..// . . . 1978. . 6 -23. 7. .., ...// . . . 1978. . 199 -208. 8. .. , . .. . . . 1980. . 7. 9. .., .., .. . . . 1978. 296 . 10. Frankevich E.L., Kubarev S.I. Triplet State ODMR Spectroscopy. N.Y, J. Wiley & Sons. 1982. P. 137. 11. Steiner U.E., Urlich T.// Chem. Rev. 1989. V. 89. P. 51. 12. . ., . ., . ., . . // , 2000, . 19, 3. . 105 ­ 112. 13. .. .//. 1988. . 33, 1. . 97 ­ 100. 14. .., .., ..// , 1995. . 14, 8. . 110 -124. 15. .., .., ..// , 1997. . 16, 6. . 121 -131. 16. . ., . ., . ., . ., . . ., . ., . . //. 1996. . 41, 4. . 815 ­ 825.

307