Смелов В.В. Лекции по теории переноса нейтронов

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181

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(28.11)

184

. 2)

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C H,lI.POM,

HMelOIUHM

CKOpOCTb

vo.

Torna

BpOHTHOCTb

M3MeHeHHSI

CKOpOCTH

HeHTpOHa

C v'

'aa

e,iI.HHHUY

BpeMeHH

npe,llCTaBHTCH

B BH,lI.e

narerpana:

1JJ(v'_v)dvdQ=dV::

Jdo. J

dQ.v'R.'"i.s(v'R.)

v1t(v.)g(v'-v,

vol;

(28.14)

rne

v'~=lv'-vor.

,llJIH

pa60TbI

<P0PMYJIOH

1(28.14)

norperiyerca

3HaTb

<PYHKUHIO g

(v'--+v,

vo).

STy

<PYHKUHIO

6Y,ll.eM

HCKaTb

paxxax

rHnOTe3,

C<pOpMyJIHpOBaHHbIX

B § 22.

Ilpexcne scero .

sanaxy

coyziapenaa

HeHTpoHa.

,lI.BHiKymHMcSI

SI,llpOM

CBe,lleM

nO,llp06HO

H3ytIeHHOH

B § 22

3a~alIe

pacceHHHH

HeHTpoHa

HenO,llBHiKHOM

snpe, ,UJISI

sroro

,lI.OCTaTOllHO

BBeCTH

paccxorpeuae

cncrexy

KOOP,ll.HH3T, JKeCTKO

cBSl3aHHYlO

C ,lI.BH2KY-

IUHMCH

H,lI.pOM. B

3TOH

CHCTeMe·

KOOp,ll.HHaT

SI,lI.pO nOKOHTCSI, a

noroxy

13--301 185

.HMelOT~HJiy

see

pesyJlbfaThI

"§

22~""':B'

qaCTHOCTR,

OCHOBHoH

pe3YJIb!8T

sroro

naparparpa-s-

~opMYJla

(22.16)-

Mo~eT

6hITb nepenacan

BH,lle

g(V

v'R' COS(V

V'R»==

_ (1

+Mls

-!!!L

a(·

M +1 oR _ M

-1

o'R

-cos

v')

.), (28.15)

- 4nM"

v~z

2" v'R 2

" R'

R-",'

rae

VB=V-VO;

V'R=V'-VO.

CymecTBeHHO

OTMeTHTh,

qTO

aarepecyio- .

mas

aac

BeJIUqUB8

g(V/~,

vol He MO:>KeT

6hITb

DpBMO

npapasaeaa

Bhlpa2KeHHIO

(28.15). )leno B

TOM,

qTO

3TH

4>YHKUHH

HMeIOT

pasuue

HOpMHpOBKH(CM.

21),'

noroxy

MO}KHO

aamtcars

TOJIbKO

,T3Koe

paseacrso [cp..c

q>OpMyJIOH

(21.14)]:

g(v'

....

v.)ldudQf=g(vR,

v'R' cos(vR'_'f'R»fdvtiQR1· (28.16)

BhIqHCJISISI S1KOOH3H nepexona OT

nepexeaaax

v, 0 K

nepeueaasra

VB,

OR!

YCTaH3BJlHBaeM;

QTO

v"dvdQ

V"tiVtiQR.

(28.17)

paaeacra

(28.15)"- (28.17)

HaXOAHM

g(v'-v,

v.) =

:.:

g(fJ

fJ'R'

cos(vR' V'R»=

- (I

+M)I.~a

(M+

°R"_

M-l

V'R.

-COS(V

V'»).

(28•

.18)

4ttM'

'vR'JR

v'R

2 vR R' R

)laJIbHeHWaSl

nama saaasa COCTOHT B npeotipaaoaaaaa npaeoa

qaCTH

epOpMyJIbI

(28.18). Ilpescne scero

OCHOBe

epOpM'yJlhl

(22.19)

'nOJIyq3eM

,(, ,

.)"

(1 +

M)*

1 i M - 1

( , ) )

g v

-+V,

y. =

4~M

V'R

-2-

R-

-2-

- VR' V R •

ECJI.H B

apryxeare

6-epyHKU'HH

BeJl'HtiHIHbI

V'R

aalMeHHTb

paa-

aepayrsrxa

DhIpa}KeHHSlMH

COfJIaCHO

4>opMyne

"(28.4) H

CHona

BOC-

DOJIh30BaTbCH

q>opMyJIoii>

(22.19), TO

OKOHQ3TeJlbHO

oy,zteM

HMeTb

(

.)_(l\+M)1

,(V

_ V ' 2

. )

(2819)

g v

-v,

v. -

4KMl

o'R

8 2 2M (b, v.) , · .

rae

= v - v',

nOCJIe

nOltCTaHOBKH

(28.2), (28.7) H. (28..19) B (28.14)

npHx04BM K

CJIeAYlOmeMy

BbIp31KeHHIO

AJiH

(v'

v):

(28.20)

186

tlJIfl·BhllJHCJIeHHBHHTerpaJl8

(28.20)

nepeH,lleM

c.epep~qe~

CHCTeMhI

KoopAHHaT

npsMoyrOJIbHoii:

v2odvod,g~·oxd{1ovdVot.

Ilpa

.9TOM

KOOpAHHaTHl.ie

OCR OX H OY paCnOnO>KHM B ItJlOCKOCTH

BeKTOpOB

H V

HalFpaBHB

OCb X

HanpaBJIeHHIO

BeKTOpa·

Puc. 28. Pacnoaozceaae

KOOPAHHaT-

BhtX

oceii

H or no

OTHoweHHIO

BeKTopy

~.yI--v

(pac,

28).

Harerpan

(28.20) MO>KHO

Tenepb

npencraaars

BHAe

npo-

H3BeAeHHJI

Tpex

HHTerpaJIOB

II,

1)1(

)3/2

• CO

[(

I ]

= 4K

.tlIT

vexp

- y+

vir

••

. dv

••

-00

1,=

exp

[-y(V'z-O.Z)I-

]

-00

XIS

C,I-;V'

I +

-Cv.

)dV

1 [ ( ,

VI_V'1

l)l_

==TexP

-y

v % - 2t 2M

:IT

(OliO'

+2~)ll=+exp

(-y

~YV'T

xex

{ -

[11

~yVlr

(VI;tV

+2~)-

V:~YVIT

v'z]'}.

Bupasceaae ,llJISI /3 6bIJIO noayseao C ynerox

npaBHJI

AeAcTBHSI

C.6~4JYHIKnHeH

(22.18) H (22.19). Ilepesmoxcas

noayseeaue

BbIpalKe-

13* 187

(29.3)

lIHB

aaxenaa,

qTO

V'x=(V2~'V'2S2)/2~,

OKOHQaTeJIbHO

HMeeM

+1)2 1:

W (V'

-4V)

---,0

. - X

4 (7tM)3/2

IV -

[

(IV

V'I

Xexp

"('I:

V - 4't

T M

1+'1:

Iv-v'l

,(28.21)

rAe'~

..1

+il1

(1 - 1:

) .

B TOM

QaCTHOM.CJIyqae,

xorna

~8(VR)-~O=const,

ssrpaaceaae

(28.21)

HeCKOJIbKO

ynpouiaerca

(1'=0,:

'(-A=I)

Ilocae

nonpoonoro

MaTeMaTHqeCKOrO

onHcaHHSI

rrponeccos

B3a-

HMO,ll.eHCTBHSI

HeHTpoHa

BemeCTBOM

06JIaCTH

TepMaJIH3aUHH

MbI

MO)Ke.,.

H B rpyrme

6bICTPbIX

HeHTpoHoB,

H B

TenJIOBOH

rpynne

nOJIb-

aO·BaTbCSI O.nHO·H H TOH 2Ke epOpMOH

ypaBHeHHH

(21.7) H (25.5),

ecna

06JIaCTH

TepMaJIli3aUHH

<popMaJIhHO

nOJIO)KHTb

(v)

(v)/v;

(v)

(v)/v;

(v)

(v)/v;

(v') g (v, o',

00')

W (v'

~·v).

.1.

29.

3~ME'IA"HEO

ABYX

3TAnAX

PEWEHHSI

YPA,BHEHHSI

nEPEHOCA

llOJI02KHM,

QTO

Hac

anrepecyer

perueaae

sanaua

CTaUHOHapHOM

pacnpeneaeaaa

'HeA:TpoBOB

Bepa3-MHO}KaIOIUeA

cpene,

HMeHiHO

3TO-

cnyxaio

<popMaJIbHO

~BOJlHTCH

.pe,aJIH3aUHH

onnoro

HTepaUHOHHoro

nrara

cxexe

(21.13).

0603HalIHM

yCJIOBHylO

rpanauayro

CKO-

POCTh

Me2KJlY

rpynnoa

6bICTPbIX

rpynnoH

TenJIOBbIX

HeHTpoHoB.

3Ta

BeJIHqHHa,

OqeB~,lI.HO,

,lI.OJI2KHa

y,ll.OBJIeTBopHTb

aexoropoti paaysraofi

creneasto

TOqHOCTH)

cJIeJlYlOmeMY·

npaauany:

~s(v')g(v,

v',

00')==0

npa

v>v

H v'

•

(29.1)

Cooraercrayromee

.naurea

aanase

ypaaneaae

nepeaoca

MO}KHO

aanacars

aane

0\7cp +

~cp

= Sdo' S

dQ'~s

(v') g (v, o',

00')

(r,

o',

0')

+ Jdv' J

dQ'~s(v')g(v,v',

OO')cp(r, o',

O')+q(r,

o, 0). (29.2)

ECJIH

Vrp,

TO B·

CHJIy

paseacraa

(29.1)

nepsua

H'HTerpaJI

ypaaue-

H8H

(29.2)

paaea

HyJIIO.

eTO

oanasaer,

lITO

nOTOK

HeHTpOHOB

6bICTpOH

rpynnsr

«He

lIYBCTByeT>~

pacnpeneneaas

TeUJIOBbIX

HeHTpOHOB.

,llaHHoe

oricroarenscrso

n03BOJIHeT

pa36HTb

peureaae

aanasn

JlBa

srana.

nepsou

srane

06JIaCTH

V>Vrp

HmeTCB

peureaae

ypaBHeHHH

0\7cp+~cp=

I do'

JdQ'~s(v')g(v,

o', OO')cp(r, o',

O')+q(r,

v, 0).

f88

(29.4)

npOCTeHm~M

npH6JIH>KeHliOM'

-cnoco6e

pemeaas

STOrO

'ypaBHeHHSI

cnyxae

TjlJKeJIOro

3aMeJlJIHTeJIjI

paCCKa3aHO·

:B. § .24. C 60nee

ooma-

60JIee

TOqHbIMH

MeTOJlaMH

'pemeHHH

ypaaneaaa

.(29.3) MOJKHO

n03HaKOMHTbCjI,

aanpauep,

B'KHHre

r. H. Mapsyxa [3].

CJIeJlYIOUI.HH

sran

peurenas

sanaxa

OTHoeHTCH

06JIaCTH

O<v<

<vrp. B

3TOM

cay-rae

BTOPOH

lfHTerpaJi

B (29.2)

6YJle'T

Y2Ke

H3BecTHoH

Q>yHKUHeH,

TaK

tITO

pens

nOHJleT

0 peureaaa

ypaBHeHHH

BHJla

0\7f(r,

O)+a(v)fP(r,

0)=

- Sdv'

JdQ'a

(v'-+v)

cp(r, o',

O')+s(r,

0),

rAe

1 . 1

a (v)= - [w

(e) +W

(v)];' a.

(v'

-+ v) ==

(v'

---.v).

v . v

(29J5)

§ 30. nPM&nM)f(EHHYA METOA

PEWEHHSI

YPAB~EHHSI

nEPEHOCA

O&nACTH TEPMAtlH3AL\HM

Cpasy

JKe

orOBOpHMCjI,

tITO

onHCbIBaeMhIH

)laHHOM

naparpaqie

'MeTOJl

otinanaer

lIaBeCTHoH

06IUHOCTblO',

'nOCKOJIbKY

BCe

OTHOCjlIUHeCH

HeMy

MaTeMaTH~ecKHe

onepauna

caasaau

npe,lJ.nOJIOJKeHHeM

KOHKpeTHOMMexaHHaMe

BaaHMo,neHCTBHjI

HeHTpOHa

BemeCTBoM.

STOT

MeTO,lJ. nposepen

KaK

paxxax

ra30BOH

MOJleJiH

aaMe,nJIHTeJIjI,

TaK

6aae

Mo,UeJIeH,

ytIHTbIBalOIUHX

MOJIeKyJIHpHbIe

KpHCTaJIJlH-

·tIeCKHe

CBHaH

[50]. . .

OCHOBy

MeTOJla

nOJI02KeH

MeTOJl

c$epHtIeCKHX

rapxoaax,

nozr-

p06HO

pasoopaaasm

B § 12 H

npHJIOJKeHHH

,UJIjI

npocrorsr

orpana-

tIHMCH

aayseaaesr

nJIOCKOH

aanaxa.

InOCJIe

npHMeHeHHH

ypaBHeHHIO

(29.4)

onacanaoa

B § 12

npouenypsr

npaxonax

CJIe,nyIOIUeH

CHCTe-

ypaBHeHHH:

(

k + l

o,k+t + k

iJfk-t)+'

( )

'2k +1-az-

2k+T

a.fPk

z, o =

- Sak (e, v')

cp,k

(z,

v')

do'

(a, o),

k·

0, 1, 2, ... , (30.1)

rJte

(z, a)= Sf (a, a,

.-1

...

)Pk(

...

;

Sk(Z,

v)=

s(z,

...

)Pk(

...

...;

-1

ak (e, v') = Ja

(v'

-v)

e,(1'.)dQ

=2'11:

(v'

-+v) Pk(....

....; (30.2)

-1

1-'.

cos

(v,

Vi).