Глава V. Статистический подход в теории ядерных реакций. § 12

реклама
!"#$#%&'%()#)*+)*,-+.*/%012312%$%)-14**%52-4673%4-#.8*/'
9%:;'%!*01)-<#%+1+)#$61=1%524#'
!!!!!"! #$%&''! ()$&*+,! &$-./'0! '1$$#2(! )3-! #'4-! 5-)-67! 3! .%#%&+,! *$%8,%)'1%
4&'1$*(#9!2#-#'2#'6$2.'$!1$#%)+:!"%;4$&3+,7!<#%!%4'2-*'$!4&'!*'5.',!<*$&='(,
*->$#-?@$0! 6-2#'/+! 2#-#'2#'6$2.%=%! 1$,-*'51-! &$-./''7! 4&'! <#%1! 1%=A#
&-221-#&'3-#92(! .-.! A4&A=%$! '! *$A4&A=%$! &-22$(*'$7! #-.! '! &$-./''! 2
4$&$&-24&$)$>$*'$1! *A.>%*%3:! "%;3#%&+,7! <#%! %4'2-*'$! 4&%/$22%37! 3! .%#%&+,
4&%'2,%)'#!3%58AB)$*'$!3+2%.%>$B-@',!2%2#%(*'0!()&-;%2#-#.-:!"!<#%1!2>A6-$
&-221-#&'3-?#2(! =>A8%.%*$A4&A='$! &$-./''7! *%! <*$&='(! *->$#-?@$0! 6-2#'/+
1%B$#! 8+#9! 2.%>9! A=%)*%! 8%>9C%0:! ! "! *-2#%(@$0! =>-3$! 8%>$$! 4%)&%8*%
%2#-*%3'12(!*-!%4'2-*''!2#-#'2#'6$2.%=%!1$,-*'51-!&$-./'':
!!!!!D2*%3%0!)>(!#$%&$#'6$2.%=%!%4'2-*'(!2#-#'2#'6$2.%=%!1$,-*'51-!1%B$#!8+#9
$)'*-(! #$%&'(! E$C8-,-7! '! )>(! -14>'#A)+! <#',! 4&%/$22%3! '24%>95A$#2(
&$5%*-*2*-(! -14>'#A)-:! F%2.%>9.A! 3! %8>-2#'! 4&%(3>$*'(! ! 2#-#'2#'6$2.%=%
1$,-*'51-! &$5%*-*2%3! 1*%=%! '! %*'! 1%=A#! 2'>9*%! 4$&$.&+3-#92(7! *$%8,%)'1%
'24%>95%3-#9!2%%#3$#2#3A?@'$!4&%/$)A&+! A2&$)*$*'(:!"!&$5A>9#-#$!4%>A6-?#2(
)%3%>9*%! =&%1%5).'$! 3+&-B$*'(7! .%#%&+$! #&A)*%! *$4%2&$)2#3$**%! 4&'1$*(#9
)>(! -*->'5-! <.24$&'1$*#->9*+,! )-**+,:! F%<#%1A! %8+6*%! )>(! %4'2-*'(
2#-#'2#'6$2.%=%!1$,-*'51-!'24%>95A$#2(!#$%&'(!G-A5$&-;E$C8-,-!2!*$.%#%&+1'
1%)'H'.-/'(1':
!!!!!D82A)'1! ,-&-.#$&'2#'.'! 2#-#'2#'6$2.%=%! 1$,-*'51-! &$-./'':! I>(! *$=%
,-&-.#$&*%! 8%>9C%$! 3&$1(! 4&$8+3-*'(! 2'2#$1+J! *->$#-?@'0! *A.>%*! K! ()&%;
1'C$*9!3!.%14-A*)!2%2#%(*''J
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ∆" ≈ LN −LM !
O-3'2'1%2#9! 2$6$*'0! %#! <*$&=''! %6$*9! 2>-8-(:! P=>%3+$! &-24&$)$>$*'(
'5%#&%4*+7!>'8%!'1$$#2(!*$.%#%&-(!-*'5%#&%4'(7!%)*-.%7!2%,&-*($#2(!2'11$#&'(
%#*%2'#$>9*%! QN%:! ! R%>'6$2#3%! 2#$4$*$0! 23%8%)+! ()&-;1'C$*'7! 3%3>$6$**+,! 3
4&%/$22!&$-./''7!3$>'.%:
!!!!!F$&3-(! 3$&2'(! 2#-#'2#'6$2.%0! #$%&''! ()$&*+,! &$-./'0! 8+>-! )-*-! S:T$#$! *%2*%3$!='4%#$5+!U:T%&-:!V1$$#2(!)3$!&-5>'6*+,!2'#A-/''7!3!.%#%&+,!4&%(3>($#2(
2#-#'2#'6$2.'0! 1$,-*'51:! "! 4$&3%1! 2>A6-$! 3! .%14-A*);2'2#$1$! ! %8&-5A?#2(
A5.'$!&$5%*-*2*+$!2%2#%(*'(7!#-.!6#%J
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!WXS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!YZ:L[
U%! 4&'! <#%1! <.24$&'1$*#->9*%$! &-5&$C$*'$! ∆# ! *$! )%2#-#%6*%! ,%&%C$$! '
3+4%>*($#2(!A2>%3'$J
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ∆# XXWXS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!YZ:\[
]-.'1! %8&-5%17! 3! '*#$&3->$! ∆# ! %.-5+3-$#2(! 1*%=%! 2%2#%(*'0! 2'2#$1+:! "%
3#%&%1!2>A6-$7!&$5%*-*2+!2'>9*%!4$&$.&+3-?#2(!!'
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! % >> $ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!YZ:^[
!!!!!_-221%#&'1! =*01)-<>% +1+)#$61=1% 524#% ?'@14#! '! *6)-=4#"A6>B% C14D>">
@-)-'!I>(!2$6$*'(!&$-./''!2!4$&$,%)%1!2'2#$1+!'5!2%2#%(*'(! α !3!2%2#%(*'$! β
'1$$1J
π
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! σ αβ =
` δ αβ − &αβ ` \ !!!!!!!!!!!!!!!!!!!!!!!!!YZ:a[
\
'α
F&$)4%>%B'17!6#%!32$!4&%/$22+!3$)A#!.!%8&-5%3-*'?!2%2#-3*%=%!()&-:!]%=)-!)>(
2$6$*'(!%8&-5%3-*'(!2%2#-3*%=%!()&-!4%>A6'1J
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! σ α Y() [ =
∑ σ αβ
β ≠α
=
π
∑
'α\ β ≠α
` &αβ ` \ !!!!!!!!!!!YZ:Z[
F&'1$*'1!23%02#3%!A*'#-&*%2#'!b;1-#&'/+J
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ∑ ` &αβ ` \ = L !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!YZ:M[
β
V5!H%&1A>+!YZ:M[!*-,%)'1
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
∑
β ≠α
∑
β ≠α
J
` &αβ ` \ = L− ` &αα ` \ = *α !!!!!!!!!!!!!!!!!!!!!!!!!YZ:c[
F%!%4&$)$>$*'?7!3$>'6'*-! *α !*-5+3-$#2(!0416*8#-D1+)AB:!F%)2#-3>((!YZ:c[
3!YZ:Z[7!8A)$1!'1$#9J
π
*α !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!YZ:d[
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! σ α Y() [ =
'α\
F&'1$1!='4%#$5A!U:T%&-!%!#%17!6#%!$-415)61+)A%4#+0#2#%.1D0#>62E+*+)-D7%6<#$*+*)%1)%+01+1F#%--%1F4#<1$#6*5%'%e&=A1$*#%1!3!4%>95A!<#%0!='4%#$5+!1%B$#
8+#9!#%!%82#%(#$>92#3%7!6#%!.%14-A*);2'2#$1-!2A@$2#3A$#!)%2#-#%6*%$!3&$1(!Y4%
2&-3*$*'?!2%!3&$1$*$1!$$!%8&-5%3-*'([!!'!f5-8+3-$#!g!%!24%2%8$!23%$=%!2%5)-*'(:
h%=>-2*%! ='4%#$5$! U:T%&-! 2$6$*'$! &$-./''! 2! %8&-5%3-*'$1! .%14-A*);2'2#$1+
1%B*%! 4&$)2#-3'#9! 3! H-.#%&'5%3-**%0! H%&1$7! #:$:! 3! 3')$! 4&%'53$)$*'(! 2$6$*'(
%8&-5%3-*'(!.%14-A*);()&-!*-!3$&%(#*%2#9!$=%!&-24-)-J
π
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! σ αβ = σ α Y() [ +β =
*α +β !!!!!!!!!!!!!!!!!!!!!!YZ:Q[
'α\
O)$29! +β ;! 3$&%(#*%2#9! &-24-)-! .%14-A*);2'2#$1+! 3! .-*->$! β :! V24%>95A$1
4&'*/'4! )$#->9*%=%! &-3*%3$2'(7!2%=>-2*%! .%#%&%1A! <>$1$*#! b;1-#&'/+! 4&(1%=%
4&%/$22-!&-3$*!2%%#3$#2#3A?@$1A!<>$1$*#A!b;1-#&'/+!)>(!%8&-#*%=%!4&%/$22-J
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! &αβ = & βα !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!YZ:LN[
h!A6$#%1!H%&1A>!YZ:Q[;!YZ:LN[!4%>A6-$1J
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! *α +β = *β +α !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!YZ:LL[
D#2?)-! 2>$)A$#7! 6#%! %#*%C$*'$! ! ! ! ! *α i +α ! *$! 5-3'2'#! %#! .-*->-! &$-./'':
D8%5*-6'1!<#%!%#*%C$*'$! λ−L :!TA)$1!'1$#9J
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! +α = *α λ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!YZ:L\[
F&%2A11'&A$1!4&-3A?!'!>$3A?!6-2#'!<#%=%!2%%#*%C$*'(!4%!32$1!.-*->-1J
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ∑ +α = λ ∑ *α !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!YZ:L^[
α
α
R%14-A*);2'2#$1-!&-24-)-$#2(!4%!%)*%1A!'5!.-*->%37!#-.!6#%J
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ∑ +α = L !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!YZ:La[
α
]-.'1!%8&-5%17!)>(!1*%B'#$>(! λ !4%>A6-$1J
L
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! λ =
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!YZ:LZ[
∑ *α
α
h!A6$#%1!YZ:LL[7!YZ:L\[!'!YZ:LZ[!%.%*6-#$>9*%!8A)$1!'1$#9J
π *α * β
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! σ αβ =
⋅
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!YZ:LM[
'α\ ∑ *,
,
E%&1A>-!YZ:LM[!'!4&$)2#-3>($#!2%8%0!H%&1A>A!S:T$#$!)>(!'*#$=&->9*%=%!2$6$*'(
&$-./''! 7! ')A@$0! 6$&$5! 2#-)'?! %8&-5%3-*'(! .%14-A*);2'2#$1+:! "+6'2>$*'$
2$6$*'0! 2%=>-2*%! H%&1A>$! YZ:LM[! 23%)'#2(! .! &-26$#A! 4&%*'/-$1%2#$0! 3%! 32$,
.-*->-,:
Скачать