Pyrinikes Antidraseis 7ou. Blackboard

7/25/2019 Pyrinikes Antidraseis 7ou. Blackboard

1/46

. - 2010

1

:

. .

2010


2/46

. - 2010

2

1.1.

( )

( ).

.

: ) (

), ) , )

.

. ) ,

)

) .

.

)

.

: )

, ddE

d 2.

d/dE. )

,

.

Pin Pout.

. , ,

.

: )

) ,


3/46

. - 2010

3

, ,

.

, )

, linc

.

.

1.2

.

, . .

, ,

( ) ().

.

()

- (

L.S). To .

. .

( ).

.

, ( ).

.

,

, . :

+ + (1.1)

C, :

+ C + (1.2)

( )


4/46

. - 2010

4

.

(, )

. .

, ,

, .

.

. ,

, .

1.1 . .

,

. , , .

, ,

1, 1.1.

1 .


5/46

. - 2010

5

TPP MM = )( (!.3)

:

PTp

p

MM

M

+= (1.4)

, CMV ,

.

. :

LABTMPM

PMPP

TMPMPM

CMTPCM EMVMME ++ ==+= 2

212

21 )( (1.5)

LABE . cmE

(

) :

CMcmLAB EEE += (1.6)

:

2

21

cmLABTMPM

TMcm EE == + (1.7)

:

TMPMTMPM

+= (1.8)

, cm , P .

r, )(rV ,

:

)(rVEE cm= (1.9)

( ) b ,

,

( 1.2) .

:

bLcm

= prL = (1.10)

h .

b

. :

kbL ==h

l (1.11)


6/46

. - 2010

6

( fmMeVc .327,197=h ). l

, , h , :

2

2

hh

cmEcm == (1.12)

.

1.2 .

1.3

.

.

inN 1.3.

dx, ndx,

n .

1.3 . .

:


7/46


8/46

. - 2010

8

d

d

, .

1.4 .

.

-. :

)(nSxS

NxnNin = (1.19)

S . (S

inN

)

.

-, 1.2.

:

R2= (10)

2fm

2= 10

-28m

2= 10

-24cm

2

barn. H

barns/steradian (b/sr).

b. b Coulomb

. ( )

. ,

, , .


9/46

. - 2010

9

b,

:

2

0

2 A

Ab

A bbdb == (1.19)

,

l. l,

b = l/ b =

(l+1)/. :

2

)12(22

2])1[(

kk

+=+ lll (1.20)

(1.19) :

2

20

2)1()12( +=+= A

k

A

kA ll

l (1.21)

l :

AAA kbkb = 1l (1.22)

1.4

.

( ).

dx .

dxEn )( n ( )

)(E . To )(E ,

. :

dxEInxdI )()( = (1.23)

:

xeoIxANeoI

xEneoIxI === /)()()( (1.24)

x=0 =Io, = /)(E , x

. :

== eIeIxI oxAN

o

/)()( (1.25)


10/46

. - 2010

10

=x / (

gr/cm2).

2

:

)(1

=

n

(1.26)

:

/)(

xoeIxI

= (1.27)

()

, ,

. :

)()()()( EEEE rinel ++= (1.28)

, .

Coulomb .

()

, .

, (1.24) (1.25).

.

. .

2x xxddNNxxxx++ddxx..

:: ==

oN

oNoN

dN

oN

xdN

xdNx

0

1

0

0


11/46

. - 2010

11

2.

2.1 :

.

.

Coulomb

.

.

. ,

8.7 MeV 60

, 2.1.

. , 4

4, .

=28.

.

= 20, 28, 50, 82, 126

.

2. 1 . 4.


12/46

. - 2010

12

-

.

.

. Coulomb ( )

()

=. (

) , .

() , , .

-

.

(,) ( 2) ,

= ,

.

Coulomb,

.

2. 2 , .

.


13/46

. - 2010

13

. - >206.

(,) Segre

,

.

2. 3.

2.3 . .

- , ,

2.4. ,

(2.4). , ,

, , (2.4). -

- -

. - - ,

, .


14/46

. - 2010

14

Coulomb

.

.

,

( )

. .

2.4 =135 =102.

2. 2

,

MeV Coulomb

( ).

Coulomb

,

. 6-8 MeV

. ,

( 2.5).

- .

.

Coulomb


15/46

. - 2010

15

2.5 . 1.

. 2. .

3. .

.

. , (n,).

1/.

2.6.

,

(n,). 1

.

-.

,

14

(n,p)14

C, 14

C.

,

( ).


16/46

. - 2010

16

2. 6 (=69). 1/

.

15

,

. .

27Al(p,)

28Si.

( ).

1. (n,)


17/46

. - 2010

17

2. 3

,

.

, .

. .

.

2.7

206

Pb .

(

).

Coulomb

3 ( ).

.

2.7. (p,xn) 206

Pb .

3 ,

.


18/46


19/46

. - 2010

19

2.4

. , ,

. .

.

.

.

.

,

2.8.

. ,

( )

.

32S(n,p)

32P

7Li(p,n)

7Be

. 32

,

, ..

in vivo

.

, 7Li(p,n)

7Be,

.

9Be

9Be(d,n)

10B. (stripping)

( )

.

2.9

12C(p,pn)

11C.


20/46


21/46

. - 2010

21

2. 10 2/.

.

, 2.11, 1

MeV.

.

.

, 0,025 eV

.

. .

( 2.1)

1 MeV/ 190 MeV

. 170 MeV .

.

(80% 20% ).


22/46

. - 2010

22

2.11 . ) ) .

( 2.2)

-.

.

, ,

.

.

.

(

).

,

92


23/46

. - 2010

23

2.6 .

.

50 MeV

.

.

, (> 150 MeV)

, .

, ,

.

70 MeV 38

Cl.

. , ,

(8Li) .

, 500 MeV (),

, .

. 2.11

. 1 GeV

. .

.

.

.

.

, 12

C

16

O . Coulomb

Rytherford. Coulomb.

.


24/46


25/46

. - 2010

25

2.12


26/46

. - 2010

26

3.

3.1

. Coulomb - - .

Coulomb .

,

,

. , ,

.

,

, .

.

2.2.

,

.

,

.

MeV,

.

3.2

,

.

,

:

112211 mmm +=

211

222

211 mmm +=


27/46

. - 2010

27

3.1 , .

:

( )21A1A

+=

. ,

,

.

.

, ( )

:

( )21A

12A

2

EE EE+

++ ==

.

(dE/dx).

, ( ).

(

)

,

.

1-2 MeV. :

( )kTE

2kT

E econst)E(N

=

.

.

. 10 MeV


28/46

. - 2010

28

10 s,

100 s.

.

3.3

,

.

- .

. 14

(n,)15

10.8 MeV, (n,)D 2.3 MeV .

( 2.2)

.

, 10

(n,)7Li,

11

7Li.

, 1 mbarn 103-10

4barn Cd

(2550 barn Cd) (46000 barn).

1-10 barns.

1/, Breit-

Wigner.

:

( ) 4/22 +

. Breit-Wigner,


29/46

. - 2010

29

.

, -=/2.

R2, R .

D ( D== 2ph ).

:

( )2R+= D R>>D 2D=

,

:

24 D=

22D . :

( )4

22

22

+

= D

/

, :

( )4

22

o

2+

= D

Breit-Wigner

.

(>>)

2

. :

h~

: 2D ( )

2

mh

1

1/ (n,)

.


30/46

. - 2010

30

3.4

, .

,

. , .

,

,

( ).

3.5 ,

,

2/ ( ) ( 2.5).

,

.

, ,

. .

Coulomb,

.

200 MeV.


31/46


32/46

. - 2010

32

4.

4.1 Fermi

, .

6

Fermi.

( ) Pauli.

, Pauli,

( Fermi).

.

.

, Fermi,

.

,

.

,

, 4.1

c Coulomb:

Re

C ZZE2

)1(5

3=

Ec.

,

. .. ,

. ,

.

, .

,

Pauli.

6 , , (..

). ,

, Fermi-Dirac.


33/46

. - 2010

33

4.1 .

, ,

,

. ,

Fermi, EF, EF,n EF,p.

:

2md8

2h2nnE = ......3,2,1n= (4.1)

m d .

d3 :

)nnn(E 2322

212

md8

2h3n2n1n

++= (4.2)

: ......3,2,1n1=

......3,2,1n2=

......3,2,1n3=

, .

(n1, n2, n3) = (1,1,1)

, :

(2,1,1) (1,2,1) (1,1,2)

. :

(1,2,6), (1,6,2), (2,6,1) (2,1,6) (6,1,2) (6,2,1) (3,4,4) (4,3,4) (4,4,3)


34/46

. - 2010

34

.

EF EF

F. (n1, n2, n3)

:

2h

2dFmE823

22

21 nnn ++ (4.3)

:

2h

2dFmE82R = (4.4)

(4.3) :

223

22

21 Rnnn ++ ((44..55))

n1, n2, n3 , R

. (n1, n2, n3)

. ,

, .

(n1, n2, n3) 4.3;

R; n1, n2,

n3 1/8 . :

23

2h

2dFmE8

6

3

3

4

8

1 )(R = (4.6)

.

. Pauli d3 :

23

2h

2dn,FEnm8

3)(N = (4.7)

:

ArR3

4d 3o3

43o

3 =

= (4.8)

ro , ro= 1,2 fm.

, Fermi, EF,n,

:

32

AN3

2

A4N9

2ornm2

2

n,F ).()(E == h (4.9)


35/46

. - 2010

35

:

32

AZ3

2

A4Z9

2orpm2

2

p,F ).()(E == h (4.10)

EF, PF,n,p :

m2

2F

P

FE = (4.11)

= = /2 :

EF= 32 MeV

8 MeV ,

4.2 :

Vo= EF+ EB= 40 MeV

:

)(Em2

2F

p

53

Fp0

p3d

Fp0

p3Ed=

= (4.12)

20 MeV.

4.2 Fermi. , Vo, .

:

==+=+= + )()()ZpNp(m10

3EZENN,Z(E

32

A

35

Z35

N32

49

2or

2

1032

Z2nZN

h


36/46


37/46

. - 2010

37

ER,

:

iMimim

R EE += (4.17)

.

7.

* :

LMimM

i*

E)(EE +=+

(4.18)

L i .

.

Fermi.

Bethe Weisskopf.

, .

EF *

:

TTE 2

FE4N2* = (4.19)

. - :

TaTE

2*

= (4.20) :

)())((aFEA

4

2

p,FEZ

n,FEZA

4

2 =+= (4.21)

F .

:

2*aTE = (4.22)

:

a

*ET= (4.23)

:

7 115In

235, 238U.


38/46


39/46

. - 2010

39

4.4. .

.

4.2

.

: 20, 28, 50, 82 126. 2 ( ) 8 (

16) l=

0 l= 1.

,

.

.

Schrodinger

,

V(r) r .

:

0)rR(Mr2

)1()r(VE

2

2

2M2

2dr

)rR(2d =

++

hll

h

(4.28)


40/46

. - 2010

40

lh , R ,

.

:

2

2

r2

)1()r(VV hll ++=

(4.29)

nl

V.

n

l(n-1). To l

(-1)l. s, p, d, f. O (2l+1)

l .

V(r) Coulomb

, . Coulomb

.

.

22rm2

1U)r(V += (4.30)

m .

,

:

+= h)n(E21

n ((44..3311))

:

+++= h)nnn(E23

3213n2n1n (4.32)

= n1 + n2 + n3 ( 0) .

. ,

n l.

:

= 2n l 2 (4.33)

l = 2

l= 0 n = 2 ( s) l= 2 n = 3 ( d) .

, .. ,

(+1) (+2)

n, l, m


41/46

. - 2010

41

Pauli.

, :

2, 8, 20, 40, 70, 112

,

Woods-Saxon.

, :

[ ]a

)Rr(o

exp1

V)r(V

+= ((44..3344))

Fermi.

,

4.5 -.

( 4.6).

,

J .

r r2

4.5. fm3 .


42/46

. - 2010

42

4.6 - . Woods-Saxon.

l.s .

.

:

MeVA40 31

h (4.35)

1949 Mayer Haxel, Jensen

Suess. ,

- .

, . Vso

. :

Vso(r) = Vls( r).l.s (4.36)

l s

h. l s s=1/2

( 6) :

21J = l (4.37)

:

32

)21()

21(

A)12(10EE

+ += l

ll (4.38)

J


43/46

. - 2010

43

l.

4.6.

. 4.7

, Woods-Saxon.

-. J, RJ +1

, Pauli, mj J

+J. ,

4.7,

2, 8, 20, 28, 50, 82, 126.

4.7. Woods-Saxon

ls.

.

Pb20882 ,

, (

)


44/46

. - 2010

44

. Pb20882

Pb20882 .

J = 0.

J. .

:

)

.

.

) .

, J =

0. J . (.

) J = 0.

J (

).

, . 17

1d5/2, J=5/2 (-1)l= (-1)

2= + .

, .

(. p-p n-n)

Jl, ml.

0+.

)

-

. - ( )

(

0) ( ).

,

. L ,

, 2.7927 -1.9155 .

L -

:

J = L + S


45/46

. - 2010

45

: J = L 1/2

S :

= gsS

gs= -3.826 + 5.586 .

=== 18pm2eN T.eV10.1525.3h

124 gauss.ergs10.05.5

:

= gLL

gL= 0 .

H J ( S L )

J.

Z.

J Z

. S L

J S L J .

4.8.

4.8 .


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