6
!"#$%&%’ )*+,-./01-* +- 2/0345, 5*. !5,1034 !678908 :40+/,4 ;’ <6433 <+,/0+/,4 5*. <9*=34>!5,1034 ?-.438 @64-,41053 5AA,-50648 +- */0349’ 39B/9.>.,-A C-.43 D<E?FG "#$%&%’( +406*9B/48 D+64 .4/+4,-*G H-9*= +- 5.. IC45*>J43. +64-,7KL <6433 8+,/0+/,4 98 5 0-CC-* A64*-C4*-* 9* C5*7>M-.7 878+4C8’ */034-*8 9* */0349 4340+,-*8 9* 5+-C8 4340+,-*8 9* 0-*./0+-,8 DM5*.8NG 5+-C8 9* 5+-C90 03/8+4,8 ?45*>F943. !-+4*153 )#$%&%’( ?-.438’ O,9+4 .-O* +64 <06,P.9*=4, 4B/51-* Q-, 4506 */034-* 9*03/.9*= 9*+4,501-*8 O9+6 533 -+64, */034-*8 /89*= */034-*>*/034-* 9*+4,501-*L D@--G ?5*7 4B/51-*8R 4506 -*4 .4A4*.8 -* 0->-,.9*5+48 -Q 533 +64 -+64, */034-*8L *+"&$,+-. ?-.438’ S88/C4 +65+ 9*+4,501-*8 O9+6 533 -+64, */034-*8 5T4,5=48 -/+ +- 8-C4 A-+4*153 +65+ -*37 .4A4*.8 +64 0--,.9*5+48 -Q +64 */034-* 9* B/481-*L UD,G , )*89.4 */0345, T-3/C4R ,-/=637 0-*8+5*+ .4*89+7 49+64, 89.4V VL*- ,48/3+5*+ Q-,04 5*. 0-*8+5*+ A-+4*153L <65A4 =/9.4. M7 W*-O34.=4 -Q 5* 5X,501T4 86-,+>,5*=4. Q-,04 5*. +64 T5,951-* 9* */0345, .4*89+7L 245, 8/,Q504 5 */034-* 98 A/334. M50W 9*+- +64 */034/8L S.. "-/3-CM A-+4*153 9Q .4539*= O9+6 A,-+-*L

01-*(+-(2/0345,(5*.( !5,1034(!678908(

  • Upload
    others

  • View
    7

  • Download
    0

Embed Size (px)

Citation preview

Page 1: 01-*(+-(2/0345,(5*.( !5,1034(!678908(

!"#$%&%'()*+,-./01-*(+-(2/0345,(5*.(

!5,1034(!678908(

:40+/,4(;'(<6433(<+,/0+/,4(5*.(

<9*=34>!5,1034(?-.438!

@64-,41053(5AA,-50648(+-(*/0349'(

(39B/9.>.,-A(C-.43(D<E?FG(

("#$%&%'(!+406*9B/48(D+64(.4/+4,-*G(

H-9*=(+-(5..(IC45*>J43.(+64-,7KL(

<6433(8+,/0+/,4(98(5(0-CC-*(A64*-C4*-*(9*(

C5*7>M-.7(878+4C8'(

( (*/034-*8(9*(*/0349(

( (4340+,-*8(9*(5+-C8(

( (4340+,-*8(9*(0-*./0+-,8(DM5*.8NG(

( (5+-C8(9*(5+-C90(03/8+4,8(

?45*>F943.(!-+4*153(

)#$%&%'(!?-.438'(O,9+4(.-O*(+64(<06,P.9*=4,(4B/51-*(Q-,(4506(*/034-*(

((((((9*03/.9*=(9*+4,501-*8(O9+6(533(-+64,(*/034-*8(/89*=(*/034-*>*/034-*(9*+4,501-*L!

D@--G(?5*7(4B/51-*8R(4506(-*4(.4A4*.8(-*(0->-,.9*5+48(-Q(533(+64(-+64,(*/034-*8L(

*+"&$,+-.!?-.438'(S88/C4(+65+(9*+4,501-*8(O9+6(533(-+64,(*/034-*8(5T4,5=48(-/+(

+-(8-C4(A-+4*153(+65+(-*37(.4A4*.8(+64(0--,.9*5+48(-Q(+64(*/034-*(9*(B/481-*L(

UD,G(

,(

)*89.4(*/0345,(T-3/C4R(,-/=637(

0-*8+5*+(.4*89+7(49+64,(89.4V(

VL*-(,48/3+5*+(Q-,04(5*.(0-*8+5*+(

(((((((((A-+4*153L(

<65A4(=/9.4.(M7(W*-O34.=4(

-Q(5*(5X,501T4(86-,+>,5*=4.(Q-,04(5*.(

+64(T5,951-*(9*(*/0345,(.4*89+7L(

245,(8/,Q504(5(*/034-*(98((

A/334.(M50W(9*+-(+64(*/034/8L(

S..("-/3-CM(A-+4*153(

9Q(.4539*=(O9+6(A,-+-*L(

Page 2: 01-*(+-(2/0345,(5*.( !5,1034(!678908(

@7A9053(#Y(!-+4*153(!,-M34C(Q-,(F4,C9-*8(

•! Z,9+4(.-O*(<06,P.9*=4,(4B/51-*(O9+6(/012[(#Y(A5,153(.9\4,4*153(4B/51-*L(

•! <4A5,5+4(9*+-(,5.953(5*.(5*=/35,(4B/51-*8L(

•! D?59*37G(04*+,53(J43.'(5*=/35,(4B/51-*(98(+64(49=4*T53/4(4B/51-*(Q-,(-,M9+53(

5*=/35,(C-C4*+/CL(

•! ]5.953(4B/51-*(0-*+59*8(W9*410R(A-+4*153(5*.(04*+,9Q/=53(+4,C8L(

•! <-3/1-*8(O933(=9T4(4*4,=7(34T438(9*(+64(O433L(

•! @-(M/93.(/A(O6-34(&34-+35R(5..(*/034-*8(9*+-(34T438(500-,.9*=(+-(!5/39(A,9*09A34L(

H5A8(9*(5*7(34T43(8+,/0+/,4(5,4(588-095+4.(O9+6(.980-*1*/9148(-,(^/CA8(9*(A,-A4,148'(

EB/5337(8A504.(34T438L(<C--+6(T5,951-*(*/034-*(

84A5,51-*(4*4,=7(O9+6(*/034-*(*/CM4,L(

Y980-*1*/9148(9*(

T5,951-*(*/034-*(

84A5,51-*(4*4,=7(O9+6(

*/034-*(*/CM4,L(

EL=L(*/034-*(84A5,51-*(4*4,=7(D4*4,=7(+-(,4C-T4(3458+(M-/*.(*/034-*G(58(5(Q/*01-*(-Q(6(-,(7!

H,5./5337(J33(/A(

4*4,=7(34T438(O9+6(

9*0,4589*=(6(-,(7(

Z64*(2(-,(_(0-,,48A-*.8(+-(J339*=(/A(+-(5(=5AR(+65+(

*/034/8(98(A5,10/35,37(8+5M34(O,+(*49=6M-/,8L(

ET9.4*04(Q-,(I?5=90(2/CM4,8K(

D5G(?58848R(M9*.9*=(4*4,=948(5*.(84A5,51-*(4*4,=948'(

86-O(.980-*1*/9148(5+(04,+59*(*/034-*(*/CM4,8(

O64,4(8"9%4(*/CM4,8(5,4(588-095+4.(O9+6(9*0,4584.(

M9*.9*=(,4351T4(+-(+649,(*49=6M-/,8L(

DMG(?5=90(*/CM4,8(86-O(69=64,(5M/*.5*048(

0-CA5,4.(+-(*49=6M-/,9*=(*/0349L(

D0G(]4501-*(,5+48(-*(*/0349(O9+6(C5=90(*/CM4,8(86-O(,43/0+5*04(+-(

05A+/,4(*4/+,-*8L(

D.G(F9,8+(4`09+4.(8+5+48(9*(C5=90(5,4(A5,10/35,37(69=6(D4`5CA34(35+4,GL(

D4G(E\40+8(5,4(4`5==4,5+4.(Q-,(M-+6(_(5*.(2(C5=90R(.(3#-:!8"9%4!

&34-+%!8/06(58(&$a!M(D_ba&(2b%&;G(5*.(c$"5(D_b2b&$GL(

(NEAR STABiLity) Magic numbers: 2, 8, 20, 28, 50, 82 and 126

DQG(<9C935,(*/C4,-3-=7(9*64,4*+(9*(C5*7(*/0345,(A,-A4,148L(

Page 3: 01-*(+-(2/0345,(5*.( !5,1034(!678908(

<-3/1-*8(5,4(*-+(+--(.4A4*.4*+(-*(+64(4`50+(Q-,C(-Q(

+64(A-+4*153[(*4/+,-*(805X4,9*=(8/==48+8(+65+((

/;(d(e$(?4U(5*.(1<=>?)=@?!QCL(*(5A!B(A+&'"-5!

5"'5C:%&9!AD%5!9+(8+A1:!9%E+!5%8%-"1!1+53-A5>!

f/5*+/C(*/CM4,8(Q,-C(8-3/1-*(5,4'(

&!*/CM4,(-Q(*-.48(9*(,5.953(O5T4(Q/*01-*(4`04A+(5+(-,9=9*L!

-!-,M9+53(5*=/35,(C-C4*+/CL!

8-!A,-^401-*(-Q(-,M9+53(5*=/35,(C-C4*+/C(-*(g(5`98L(

F"1%A:!%5!9%E+&!#:!0$2-!

F9339*=(500-,.9*=(+-(!5/39'(

4506(-(T53/4(658(G-H=!8->8/M8+5+48R(0-CM9*4.(O9+6(+O-(

9*+,9*890(8A9*(.9,401-*8R(=9T9*=(5(+-+53(.4=4*4,507(-Q(G0G-H=2L(

I"4D!&34-+(&!"-5(!D"5!%&A1%&5%4!5B%&!5<J!K%AD!85<LJM!

"-/3.(.4J*4(5(+-+53(5*=/35,(C-C4*+/C(N(Q,-C(+64((

T40+-,(0-/A39*=(-Q(-,M9+53(5*=/35,(C-C4*+/C(5*.(9*+,9*890(

8A9*VLhi@(4*4,=948(64,4(5,4(-*37(.4+4,C9*4.(M7(&(5*.(-L(

2

8

40

20

70

112

2

8

20

40

58

92

112

<-3/1-*8(-Q(+64(<06,P.9*=4,(4B/51-*((

<A9*>j,M9+(F-,04(

)Q(8-C4+69*=(98(9*+,-./04.(O6906(39k8(+64(

.4=4*4,507(9*(N(9*(+64(,9=6+(O57R(05*(,4A,-./04(

+64(-M84,T4.(C5=90(*/CM4,8V(

c$(

&$(

&$(

&a(

e$(%=(

&A(

%Q(

%=lm&(

%=nm&(

&A%m&(

&A#m&(

%Qlm&(

%Qem&(

2-M43(!,9g4(%n;#'(o5*8(p4*84*(5*.(?5,95(?574,(

VLS = −U01r

∂V

∂rl.s

l.s =!2

2

[j(j + 1)− l(l + 1)− 3

4

]

S..9*=(5(+4,C(-Q(+64(Q-,C'(

Y-48(+64(^-M(89*04'(

O%8%-"1!"4'(&!A(!PO!4(3B-%&9!%&!"A(85M!#3A!

"A(8%4!E+15%(&!%5!+-+4A1(8"9&+'4!"&.!6QR!

C1(8!5A1(&9!C(14+S"&.!%5!AD+!(BB(5%A+!5%9&T!

)*(*/0349R(9+(5,9848(Q,-C(+64(:L<L(+4,C(9*(+64(*/034-*>*/034-*(

9*+4,501-*(S2Y(0-CA34`(+6,44>M-.7(Q-,048L(

Page 4: 01-*(+-(2/0345,(5*.( !5,1034(!678908(

<9*=34>2/034-*(:4T438(

<A9*>-,M9+(Q-,04(J`48(533(+64(C5=90(*/CM4,8(

844*(5,-/*.(8+5M939+7VLhi@(.-*q+(65T4(+-(=-(

Q5,(9*(4`-10(*/0349(M4Q-,4(+6484(0-335A84(5*.(

*4O(-*48(Q-,CL(

2-104(=4*4,53(53+4,*51-*(-Q(A5,9148(M4+O44*(

864338VO9+6(+64(-..(69=6>N(%&A13.+1!-,M9+53L(

I<A/.8(-Q(A/=R(.986(-Q(A9=K(

H4+8(7-/(8-C4O64,4(+-(,4C4CM4,9*=(+64(-,.4,L(

53+6-/=6(+698(98*q+(4`A40+4.(-Q(7-/NN(

2/0345,(<A9*8(5*.(!5,9148(

S*=/35,(C-C4*+/C(-Q(+64(O6-34(*/034/8(98(+64(T40+-,(8/C(-Q(+64(5*=/35,(

C-C4*+/CR(NR(-Q(4506(*/034-*L(

S(Q/33(^>-,M9+R(6-O4T4,R(O933(0-*+,9M/+4(*-+69*='(E506(N(658(0GNH=2(C>8/M8+5+48L(

)Q(Q/33(4506(8/M8+5+4(0-*+59*9*=(-*4(*/034-*L(

@64*(*<U8%<N!H!0N$=2!H!0N$G2SH!0$NH=2!H!0$N2<;!

<-(05*(-*37(65T4(5(pb$(8+5+4L!!5,9+7(-Q(-*4(*/034-*(9*(5(N!-,M9+(98(0$2->(

!5,9+7(-Q(0GNH=2!*/034-*8(98(V0$2-W0GNH=2!b(A-891T4N(

<-(4`A40+(.-/M37(C5=90(*/0349(+-(65T4(=,-/*.>8+5+4(8A9*>A5,9148(-Q($rL(

S*.(89C935,37(Q-,(*/0349(0-CA-84.(-Q(Q/33(N!-,M9+8L(

IX"8B-+5Y!Z[\"!07<G;M!6<G[2!;H!91(3&.!5A"A+M!G;[F#!07<[GM!6<=G]2!;H!91(3&.!5A"A+!

!!!!!!!!!!!!!!!!!!!=G\!07<]M!6<]2!D"5!C3--!=B?@G!!-+E+-!"&.!;H!91(3&.!5A"A+>!!!!!!!!!!!!!!!!!!

S..9*=(-*4(*/034-*(=9T48(+64(O6-34(*/034/8(+64(8A9*>A5,9+7(-Q(+64(-,M9+53(9+(=-48(9*+-L(

IX"8B-+5Y!Z^\"!07<G;M!6<G^2!(..!&+3A1(&!%&!GB?@G!!5(!91(3&.!5A"A+!D"5!?@G_M!!

!!!!!!!!!!!!!!!!!!G;^`%!07<[?M!6<=G]2!(..!B1(A(&!%&!=D^@G!!5(!91(3&.!5A"A+!D"5!^@G_M!!

!!!!!!!!!!!!!!!!!!!=?\!07<]M!6<?2!(..!&+3A1(&!%&!=B=@G!!-+E+-!"&.!=@G_!91(3&.!5A"A+>!!!!!!!!!!!!!!!!!!

Page 5: 01-*(+-(2/0345,(5*.( !5,1034(!678908(

]489./53()*+4,501-*8(5*.(!59,9*=(

a&.+B+&.+&A$B"1'4-+!8(.+-Y!4506(*/034-*(C-T9*=(9*(-,M9+8(065,50+4,984.(M7(D&N-G(

*-+(9*s/4*04.(M7(+64(C-1-*(-Q(5*7(-+64,VL5(0,/.4(5AA,-`9C51-*L!

E`A40+(8/06(5(C5^-,(A5,+(-Q(+698(+-(M4(,489./53(9*+4,501-*(+-(M4(5X,501T4(5*.(86-,+(

,5*=4.[(8-(5X,501-*(98(C5`9C9g4.(9Q(*/034-*8(5,4(03-84(+-(4506(-+64,L(

!5/39(A,4T4*+8(+698'( h/+(533-O8(+698'(

@O-(-,M9+8R(85C4(8! @O-(-,M9+8R(t8!

%>+>!A(A"-!*<;M!b<;!

<6-,+>,5*=4.(A5,+(-Q(+64(,489./53(9*+4,501-*(Q5T-/,(+64(Q-,C51-*(-Q(A59,8(-Q(*/034-*8L(

<-(533(4T4*>4T4*(*/0349(O933(65T4(=,-/*.(8+5+4(O9+6($rL(@]iEN(

<-(+64*(533(-..(*/0349(O933(65T4(=,-/*.(8+5+4(O9+6(8A9*>A5,9+7(98(-k4*(.4+4,C9*4.(M7(&N-!-Q(

+64(-..(*/034-*L(?S2u("S<E<(O64,4(jvR(M/+(<j?E@)?E<(Z]j2HN(

D/8/5337(Q-,(T4,7(=--.(,458-*8V.4Q-,C4.(*/0349R(-+64,(A5,+8(-Q(,489./53(9*+4,501-*(4+0GL(

@64,4(98(5(,489./53(9*+4,501-*R(8-(Q5,(*-+(500-/*+4.(Q-,R(+65+(50+8(M4+O44*(

*/034-*8(5*.(9*+,-./048(805X4,9*=(5*.(0-,,4351-*8L(

<9C935,(+-(8/A4,0-*./01T9+7(

D4340+,-*(A59,8G(5*.(8/A4,s/9.9+7(

DA59,8(-Q(o4(5+-C8GL(

E`09+4.(<+5+48(9*(2/0349(

<-C4(*/0345,(4`09+4.(8+5+48(05*(M4(/*.4,8+--.(9*(+4,C8(-Q(A,-C-1*=(*/034-*8(9*+-((

69=64,>379*=(89*=34>A5,1034(-,M9+8'(

2/0345,(34T438(Sd%;(

<9*=34>A5,1034(34T438(_m2da(

j+64,(*/0345,(4`09+4.(8+5+48(05**-+(M4(89CA37(/*.4,8+--.(9*(+4,C8(-Q(A,-C-1*=(*/034-*8R(

5*.(,4B/9,4(-+64,(9.458L(F-,(4`5CA34R(8/,Q504(T9M,51-*8(-Q(5(39B/9.(.,-A(-,(,-+51-*8(-Q(5(

.4Q-,C4.(*/034/8VLLM/+(+698(98(*-O(+64(8+/\(-Q(!ou<#$#&&N(

Page 6: 01-*(+-(2/0345,(5*.( !5,1034(!678908(

v47().458(V(:40+/,4(<)w(

!"#$%&'()*+,%&-./0&%12(

•! Y980-*1*/9148(9*(*/0345,(A,-A4,148(58(4T9.4*04(Q-,(86433(8+,/0+/,4L(

•! ?45*>J43.(A-+4*1538L(

•! ?5=90(*/CM4,8(5*.(8A9*>-,M9+(Q-,04L(

•! ]489./53(9*+4,501-*8(5*.(A59,9*=L(

•! <A9*>A5,9148(-Q(*/0345,(=,-/*.(8+5+48L(

•! <9CA34(9.458(5M-/+(4`09+4.(8+5+48L(