karlov-kirichenko-kvantovaya-mekhanika-2016 (810755), страница 24
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"" AON "'" "5& !"' ! !& & ("(! ( "( ! !!! !& "! "! !5& 0J! 3 .!( 0-( & " !& ! !5*INÓðîâíè He2 1S 032 S1Óðîâíè Ne5S3,39 ìêì4S1,15 ìêì4P0,63 ìêì3P3S11 S02 # :0) , 1 ) +=,4) )1D ,? 1 B# 7 .B$ 7 : 1 3 S1 1 S0 T)= )) 4+ ) S S =+ ,) 3 S1 1 S0 1B - + ,8 ,? -,1 1 , )% '- * "'* ( '! ( ' *". !"# ! ""( ' *'. ! ' ! -!05 ! *" ' ""(5* "0& !! !41* 4 ".' * !;" ( 05 ! * (? * /> ( Po2 ."'5 '"(41 "-!# .5 '"- 0"#;& 1 ! 102 ÷ 103 %! 2 ' ! λ = 10,6 λ = 9, 6 % !* "'* '"-IOINB,- .L- / 5)()& =! *- "!"#& 0!& ('#4 .1 !"(& 22! 6 ( '"-( '.! % "'* !( ' ! 4 "! '"-22! 6 '"-( 0 -! ! !# ".( '! 2! !"#5 ! !5 & !'"-(@- 2!"#5* "(* 2' . !& * ! !( "! "4 ' !# 6!!# 4 "!!. '"-( ! ! !"# !" =!(" ! - ! 5& # "( ! - ! !*! '! & 0" !(* !6 !- * T ,( " # "+ :(!B)) ""( ( + (@9+ =U + ",T CU CB $$A/ ' &;* "& & ("(! ( ((2' % !& 0" ! "& ("(4! ( '5 !&* ! (( 2' ! '0'&; .( & !* F-!5( ' 5 !& " !2" 5 !"( 0 ! ( & !*$ !7- '" ! -! ! ! ( !&.; & ! 0*4 !"4% AOAA = G'2 '-( ( α.- !6 !""- *2"#* !" -! !5 !(! ' ! ( '41'-!"#4 "4 0J ! "! *(1* ( ! ( '-!"# !( @5" !" -! ( ' ! !! A ' !5* 6* 5 'R ≈ r0 A1/3 ,A A "- r0 = 1,3·10−13 ,"( ( '! -! &0 & 0!5 !"(!a=2me e2≈ 5,3 · 10−9 .% (& 2' ; (! ( !( 6 "58M 1 8 = 10−13 C 1 0'-M 8 " 89 0' r0 = 1, 3 8?&- ! !" -! ! ( !! ' - !6 *,- .3- Q( & / (.3-0- 7)( A :(/ &( A :(/ / (! 3 ! &! =! - !65 '54! ! "!BGCDHG< 3 ( * 5 5 1)$ ( 9 ! # 9 !.
!INImp c2 = 938,3 МэВ, mn c2 = 939,6 )%.A I < !;4 "! me c2 = 0, 511 )% "-mp = 1836,2 me , mn = 1838,7 me .A I 0G' !# &! ! !"(! mn − mp ≈ 2, 5 me < ! !5 !5 "Mμp = 2,8 μя ,μn = −1,9 μя ,μя =e2mp c= 5,0508 · 10−24 · >−1A '5! ( (5 ! ? 5 & !- !#4 5"(! ( !.;μpμn3=− .A 2< !# ( ! A " ! - " Z ! N = A − Z&! 9 ( 0'-4! " AZ 3 " "!7 " 168 o 0'-! ( ! " 1 N! N &! 3 A "!5 ( !5* ! ! - " ! Z '- " &! N = A−Z '54! ( < '!("(4! ( 11 H &!& 21 !!& 31 !5 ( !5* ! - " " A '- " ! Z '54! ( % - ! '0 '!# '! "( 32 HY !!& 31 ?& ! ( ' (! ! ! -!5 " -!5 ("(! ( - "" !! !41 ! % (' ! (! "41( !."(M-!5 Z,-!5 N3-!.-!5 (-!5 Z,-!5 N3-!.-!5 (-!5 Z,-!5 N3-!.-!5 (-!5 Z,-!5 N3-!.-!5 (7 + + )0 -5 ) -5 - +)? D0 @ , ,+? 0 1? mc2 )1)/ ' 5* "& ( !(" ! -! ( !! ' !.
"! =! !' !-" !"#55 % " 6 4 "! ( <"( -!"! *! ( 0" ! ( ' ( 2R ∼ 6 · 10−13 ("(! ( "#!"(! ! Ee ≈ pc) *p∼h2R,Ee ∼ pc ∼hc2R∼A K "-INK∼2 · 3,14 · 6, 6 · 10−16 ( · ) · 3 · 1010 (/)6 · 10−13 ∼ 200 )%.?!! ! β . ( " 05 !# "!5 .( ! ( / 5!* 0"4" # !"# ".! ( A )% <! "!.!( "# ( .!-1( !"#5 5 05" !0;% AOKI , !5" &!5 3 - !65 & 0"'& ! !"# "!- &!"#5 % ! % >&.'0 ' , , "" "# !&( !! ' ! &! /6 4 " (<"( -! - !6 "(! ! ( ! ( 0" ! (2R ∼ 6 · 10−13 *p∼h2R,En ∼ Ep ∼p22Mp∼h28Mp R2∼ 6 )%.=! "- !! !! "#5 '-( (' ".
($" K ?"5 41 "5 ( " 1 ! 5.;4! 05-5 " "5 % '"#!! "& 05" !." -! ( '& ! 0"! "41 5& !MA !& ! ("(41 ( ! -! (5 "5 & !4! !((* r ∼ 10−13 eI 51 ("(41 ( ! -! 5& " '&.!! !"# 0"#; - " * "eK '(( ' !# (5* " !(1( ! -! ' 5.-! " * " "5 !(( "40& p : p p : n n : n0 ""5 (5 '& ! !- 5e (5 "5 6!"#5 ' (! ! !& .",- .3- Q( & / (IN.3-6- :!/ ! / (- 4( M&K*))($$ (8! !2 !!05 '"!# ( !"#5 "5 '!!!# .! "- ! '5 1 ( ('# & & E = mc2 ' !# "41 5 (' ( 1 A " ! - " Z !MEсвяз = [Zmp + (A − Z)mn − mя (A, Z)]c2 ,A mя (A, Z) 3 ( %"-Δ = Eсвяз c2A '5! ( ) f = Δ/A 3 1))(% - ! -! ( (' &! ( &!( !"(! Eсвяз (21 D) ≈ 2,25 )% ( (' α.- !65 ( "(.
Eсвяз (42 HY) ≈ 28,11 )%7 A A ' !"# !"( ' !#"#& (' ( -! " ε = Eсвяз /A !! - " " ' A A 0"#; '-( ε 4! ( 1- " " A ∼ 50 ÷ 60 ! ( "! Pn : s^ % - ! ! "("' 5626 pY ( (' !! "-5 εmax ≈ 8,7 )%/" "( 238εmax ≈ 7,5 )%/"92 ?! ( A A ' ";# ( ' !#ε(A) % & !!"# ! ! ( ' ! !"# ! A ! Z @" ! 4! ( !"#5 "#5 "( ! * ."#& ' ! ε(A, Z) !-41 0 !&-5 ! '5.5 - (9! 2! -! "#( ( (' ! !"# " (! (! ( ( '-! "- 51( (5* " C " 05 5&" '& !" 5 ! ! A " 1 !.A(A + 1)" 05('& ! -! !6"#( ( 1 ! 05" 052, (" & ! 51( (5* " ("(! ( !!2! -! 0J ( !! 6"# - " "M V ∼ AC " 05 51 ! ! !." ! " 05" 05 . ε, ÌýÂ/íóêëîí!- 5 "#0"'!# ( #; !6. 9,0"#4 4 1) < "- 8,5 51( 55; 8,0 !5 " '-!" 7,5 #; 0J !5! #; !(( 7,0 - !6 '"-5 6,52!5 & 5 .A4! "5 ! "# 0".50100150 200 250( !!"0 "" 6 <" 2 /) , 1!*- ( .
+ - ," !# "# ( ! 9! 2! -! ( ε(A) ! '-! -! !- 55 ! '!# ( 6 "( ( % " !. 64MA→ A1+A2A N(240) → (120) + (120) .?" A A ε240 ≈ 7,5 )%/" ε120 ≈ 8,5 )%/" <.! ! "( " 5"(!# ( (ΔE = Eкон − Eнач = 2 · 120ε120 − 240ε240 == 240(ε120 − ε240 ) ≈ 240 МэВ . A O,"( ( '! -! *- * 6(* !- &5* 05- !"(! "- ∼ (1 − 100) %/акт ! "- : ( #;4' A A ! -! "( "* ( !- 556 !' "( !("5* ( 3 6 "($' -! . ! %.3 #;2A(A + 1)U ∼ −|U1 | U1 3 ( & 5 ' !.2! "- !(( " < ! ( (' " 05 6"# - " " A 05 ! ∼ A2 ) =! !.-! !"# && ' ! ?' '-! -!" ! 22! '& !!# !"# 0"#; - "* " ?!6( ' # "- !& -! ! ! "-! '& !41* ! 0'41* ""? ! ""5 "(! ( ";# "! !( "! ! " ! !# !"# ! 0' ."" PH4 " - "! ! -54! (IN/& ' 5* ! ! # "!& (" # ! .'5( "#( "# !& ( !" # "(( 1 ! 3 !- & !7 - 1 1 )4 +)B - = ,8 )4, )0-) -5)B ) 1D51 4 ) = = 1 4 ))1 +)41=I)1),- .3- Q( & / (IN.3-9- 1&$+& *"(/6 "! !# ( 1 ! <0( 2! 5 4 & " ! ( Mя ≈ Am m 3 " ? & !5 " "! !# ( 1 !4 !# ρя ! ! ' !# Mя ≈ ρя πR3 (3(' - " " 2"& A A R ≈ r0 A1/3 9 0'*ρя ≈Am(4/3)π R3≈3m4π r03≈ 1,7 · 1014 / 3 .A AB'( 5 '"-5* ( '" -! ( (' 2.6( - " " '( ( "( 0"#; ! ( "!!"#! ( "- & 2"&Eсвяз = aV A − aS A2/3 − aCZ2A1/3− aT(A − 2Z)2A+ aPδAν.A AA%*(1 ! 2" 226!5 5aV = 15,75 )%,aS = 17,8 )%,aT = 23,7 )%,aC = 0,71 )%,aP = 34 )%.A AI i<'!"# ! ν " " ' ! ! 0 6 ! '- !" 1/3 < ν < 1 ! ! (226! δ ! '- ' ! ! -! ! - " Z N = A − Z M⎧−1 -!5* N Z,⎪⎪⎨0 -!5* A = Z + N,⎪⎪⎩+1 -!5* N Z.A AI 0?!; A AA ! ' ) (P p ~[^ YW _i]Yn AOK<( 5 " "5* 2" A AAA < "# 0J ( " A A 6" - " ".
V ∼ A ! " ! 0J4 4 (M EV = aV AI @"( "-4 * ! ! "5 !5 *(! ( * ! " 5!54! & ! !"# - ! * ". ( "0 4! ( ( < "# "1# *.! S = 4πRя2 ∼ A2/3 ( (' ( #;! ( ES = aS A2/3 K < "# ( ! !5 "!"# '(5- !65 '4! " "5 !!"( (1 #.;4 (' ( C " -!!# -! !5 . "5 0J ! "! !!- ( ( ( !"(" 05 Eкул =3 (Ze)25RIN /! 4 "! 6 " " *Z2" 4 ('M EC = aC 226! aC 0! ( 'A "( "-; " ( !"#5 5(A − 2Z)2(N − Z)2= aT!! .AA!"# 04 5;4 !&- !# ( 5 - "! Z &! N = A − Z ! ( Z = N = A/2 ,"( !*( " ET "# Z = N ! !! !41( 0 (' −ET ) "# %"- ET '5! ( 1< * ! " (!# ' "41* 0.& 7"5 ("(4! ( 2 <! !( "(4! ( !- ( !! ! .6 <" 7 " ! ( -!5 5* " ! !( "5 '(!# !- .( " # 3 * ' C " 4! ( "5 * ! ! '&! !"# 5&& !- & # % '"#!! ( !5 ! (#; - "- " !"# !δ < " " 2" A AA EP = aP ν '5! (A1 / '-! -! 0"#;& !&- !#4 0".4! -!.-!5 ( "( * δ = +1) #;& 3 -!.-!5"( * δ = −1) 7"- !& 0 0 "" 1 !.
( ! 0J( " ! 5 ?. 0 "" "- 62- "." '.& !( (* 1 !"( -' ! 5 3 (1 ! 7"."5 5 0"4! 6"5 ! ("(4!.( 0' ! !# ( !- "# "( * 0!! 6 <" /! ! ! !"( 0'( 5 ! 4 (' ! #.;4 !0"# ! ( %"- ET = aT$* #4# 2@< 2 - " " ( (' ( ' ! ! - ." ! 7 A I ' 2 ' ! (' Eсвяз! Z "( '0 A = 127 ' 2 1 !! 0" !&- ( ! 0"41 0"#;& & ('7& '( ( 0" !0"# '0 /- ( &-"- -!5* '-& A 9 ( ( "4 'A AA *dEсвязdZ= −ac2ZA1/3+ 2aT2(A − 2Z)A= 0,INN,- .3- Q( & / (.3-P- ;%(: / (! "!Z=A2 + (ac /2aT )A2/3≈A2 + 0,015A2/3.A AK9 0' "* (* - " ! &! 5 5 " 01 - " " % !("5* (* A 1) - " &! ! 1 ! 5;!# - "! 7 0" !&- ( 1 A = 237" " " A AK *!# ( Z = 92 ! ! ( 23792 U ) & '& !! !-41& !0"# '0 Z == Zm =! !-! "-4 -!5* A "( !5* 2"%&6' A AA "- δ = 07 "# " !6( "- -!5* '-& "- " " A % ! "- ! "'5!# ( -!.-!58,48,42Z ' ' " ."0 0' '! (!"#5 !; &! ! ! 5 .!!# ( 0" !&- ( ! - " ! 0"' "- A AK =!! 60"#;& (! !#4 ! ! ."1( " ( "! " '! < !- - 6 5 !5* - !4! "!5 '!5 '5.4! β .6 ," ! -! 5* 5* "(* .! ! 05" 05 ! '"-& '5* α.
β . γ .6& %!& ' * '" # !"(! 0& ! ".! β .- !6 ? β .6 5"(4! β − . β + . K .'*! <5& ' * !-! 4 "! !& 3 . 4 '! "& 6 !! '*! "!0"&;& ( K .0"- ! '54! 0!5β . 70*5 " β − . ("(! ( !A A 541 ! !0 -!05 '"#!! 6 0'5" #( 0"#;& & (' !! ! #;& & ."#'( " (' ! A A !# Eсвяз (A, Z) < Eсвяз (A, Z + 1) − me c2 .A A"- 0* " β + . !! ! -!M (A, Z) > M (A, Z − 1) + me ,−EñâÿçEñâÿç$, +F !M (A, Z) > M (A, Z + 1) + me ,INOA A "# '! "! 4! 5 5!05 "!# *! !" !"# !.;( &! ! ( * β .6 ! . '4 A I ,"( 0"#;& "( ! ! ! ' A K % '"#!! β .