ORNL-TM-2685 by Jon Morrow

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HELP O A K RIDGE NATIONAL LABORATORY operated by

UNION CARBIDE CORPORATION NUCLEAR DIVISION for the

U.S. ATOMIC ENERGY COMMISSION

ORNL - TM - 2685 COPY NO.

DATE

- August 10, 1969

INHERENT NEUTRON SOURCE IN MSRE WITH CLEAN 233UFUEL R. C, Steffy, Jr. ABSTRACT

I I

After about three years of nuclear operation, the MSRE fuel, enriched 235U,was replaced with a 233Ufuel mixture. In this new mixture there are quantities of 232u , 233U,and 234U Each of these, along with the 232U decay chain, is a strong alpha emitter and interacts with fluorine, beryllium, and lithium to produce neutrons. This neutron source is time-dependent because of the buildup of 232Udaughters, and at the time of reaching critieality with the 233Ufuel, the neutron source in the MSRE core was about 4 x lo8 neutron/sec, primarily from the reactions 9Be(ol,n)I2C and "F(~t,n)~~Na. Alpha-n reactions with lithium will produce <3 X lo6 neutrons/sec. Spontaneous fission will produce <lo2 neutrons/sec.

Keywords: Inherent neutron source, 3U fuel, (a,n> reactions, alpha particles , particle sources, 2U decay chain, fluorine, beryllium, lithium.

nOTlCL This document contains information of a preliminary nature and was prepared primarily for internal use a t the Oak Ridge National Laboratory. It is subject to revision or correction and therefore does not represent a final report.

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Assumes any l i a b i l i t i e s w i t h respect to the use of, or for domoges resulting from the use of any informotion, opporotus, method, or process disclosed i n t h i s report.

As used i n the above, "person

octing on behalf of the Commission"

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CONTENTS Page

Introduction

...........................

......................... .......................... ..........................

4 6 7

.........................

Fuelcomposition Alphasource. Neutron Source

7Li(a,n)10B Spontaneous F i s s i o n s . 'Be(a,n) Discussion.. Appendix..

.................... and 1gF(ap)2%a. . . . . . . . . . . . . . . . . ..........................

...........................

C a l c u l a t i o n of I n h e r e n t Neutron Source i n MSRF: f o r 23% F u e l Mixture Source

................... from 'Be(a,n)l% and ''F(c~,n)~%a . . . . . . . .

Source from 7Li(a,n)'oB

................

8 8 12 12

1'7

INTRODUCTION

I n t h e KRE f u e l mixtures, a l p h a - e m i t t e r s a r e d i s p e r s e d i n l a r g e q u a n t i t i e s of f l u o r i n e , beryllium, and l i t h i u m .

All t h r e e of these e l e -

ments undergo alpha-n r e a c t i o n s t o produce neutrons.

Haubenreichâ&#x20AC;&#x2122; c a l c u -

l a t e d t h e i n h e r e n t neutron source f o r t h e i n i t i a l f u e l l o a d i n g (- 35% 23% and

65% 2â&#x20AC;&#x2122;8U),

t h e 23%

b u t t h e d i f f e r e n t c o n c e n t r a t i o n s of uranium i s o t o p e s for

f u e l loading, a l l of which a r e s t r o n g a l p h a e m i t t e r s , r e q u i r e d

t h a t a n o t h e r c a l c u l a t i o n be performed.

were performed b e f o r e t h e

23%

The c a l c u l a t i o n s r e p o r t e d h e r e i n

w a s loaded i n t o t h e r e a c t o r .

T h i s memorandum i s d i v i d e d i n t o two p a r t s .

The f i r s t p a r t p r e s e n t s

f i n a l r e s u l t s and g e n e r a l d i s c u s s i o n s ; t h e second p a r t (appendix), i n t e r m e d i a t e r e s u l t s and d e t a i l s of t h e c a l c u l a t i o n s .

FUEL COMPOSITION The s t r e n g t h of t h e i n h e r e n t neutron s o u r c e is, of course, determined by t h e composition of t h e f u e l s a l t .

Except f o r t h e change i n uranium,

t h e major c o n s t i t u e n t s of t h e f u e l s a l t were e s s e n t i a l l y unchanged by t h e

chemical processing which removed t h e 235U-rich uranium and r e p l a c e d it with

233J f u e l

load.

Thus, changes i n t h e s t r e n g t h of t h e i n h e r e n t

neutron source were b a s i c a l l y a f u n c t i o n of t h e change i n t h e a l p h a production r a t e and t h e a s s o c i a t e d a l p h a e n e r g i e s .

Table 1 l i s t s t h e

approximate weight percentages of t h e components i n t h e

233Jf u e l

ioading.

These were estimated based on t h e p r e d i c t e d c r i t i c a l uranium c o n c e n t r a t i o n

of 15.8 grams o f uranium p e r l i t e r of s a l t (- 1 l b / f t 3 ) .

It w a s assumed

t h a t a l l o f t h e uranium i n t h e f u e l w a s loaded as p a r t of t h e

235f E e l

loading, and t h a t t h e small amount p r e s e n t from o t h e r s o u r c e s was n e g l i gible.

The c o n c e n t r a t i o n s o f t h e uranium i s o t o p e s which are p r e s e n t i n

t h e 23%1 f u e l l o a d i n g are l i s t e d i n Table 2 w i t h a comparable l i s t i n g f o r the

2qf u e l

Ta.ble 1 MSRE F u e l S a l t Composition

wt; % E 1emen t

23-%

in Mixture

68.1

* Li

11.0

8.8

11.0

0.73

99.99% 7 L i

Table 2 Uranium I s o t o p i c Concentration i n YSRE Fuels

A t o m $ in a

Nuclide

23%

Mixture

Atom $ i.n b I n i t i a l Loading

0.022

91.49 7 .6 0.7

0.3 35

0.05

0.3

0.14

64.4

Data from Reference 2.

s Data

from Reference 1.

6 ALâ&#x201A;Ź"ASOURCE Each of t h e uranium i s o t o p e s i n t h e 23%-fuel a l p h a emission.

mixture decays by

These a l l have long h a l f - l i v e s and e m i t a l p h a p a r t i c l e s

a t e s s e n t i a l l y a c o n s t a n t r a t e f o r t h e l i f e t i m e of t h e MSRE.

W i t h one

exception, t h e daughters of t h e uranium i s o t o p e s a l s o have long h a l f - l i v e s f o r a l p h a emission and never reach high enough c o n c e n t r a t i o n s t o e m i t a l p h a p a r t i c l e s a t a s i g n i f i c a n t rate. 228Th,

t h e daughter of

a l p h a emission.

The v e r y important exception i s

which decays w i t h a 1.91 y e a r h a l f - l i f e by

23%,

T h i s i s fpllowed by an e n t i r e s t r i n g of a l p h a e m i t t e r s

w i t h very s h o r t h a l f - l i v e s ; s o s h o r t , i n f a c t , t h a t t h e y a r e e s s e n t i a l l y i n e q u i l i b r i u m w i t h t h e 228Th.

An a l p h a decay by 228Th is q u i c k l y f o l -

lowed by a cascade of alpha emissions u n t i l the p a r e n t has f i n a l l y decayed t o x)8Pb,

which i s s t a b l e .

Immediately a f t e r t h e

was p u r i f i e d (- June

23%

1964),

t h e only a l p h a

emissions were from t h e decaying uranium atoms, b u t as t h e c o n c e n t r a t i o n of 228Th increased, t h e a l p h a a c t i v i t y obviously i n c r e a s e d .

So t h e a l p h a

a c t i v i t y i n t h e f u e l s a l t i s composed of a time-independent c o n t r i b u t i o n from t h e decaying uranium atoms and a time-dependent c o n t r i b u t i o n from t h e decay c h a i n .

23%

The time-dependent c o n t r i b u t i o n i s c o n t r o l l e d by t h e

22&rh h a l f - l i f e of 1.91 y e a r s and reaches 755 of t h e s a t u r a t i o n v a l u e about

4 years

after t h e

23%

purification.

The e n e r g i e s a t which t h e a l p h a p a r t i c l e s are e m i t t e d a r e a l s o i m -

portant.

A l l o f t h e s i g n i f i c a n t a l p h a emissions from t h e uranium atoms

are between 4 . 1 and 5.3 23%

MeV.

The a l p h a s from t h e lower members o f t h e

decay c h a i n are emitted w i t h e n e r g i e s between 5.2 and 8.77

MeV.

S i n c e t h e neutron y i e l d i n c r e a s e s s h a r p l y w i t h i n c i d e n t s l p h a energy, t h e higher-energy a l p h a s i n t h e 23%

decay c h a i n add weight t o t h e importance

of t h e c h a i n . Tabulated information p e r t a i n i n g t o t h e p r o p e r t i e s of t h e decay of t h e uranium i s o t o p e s and t h e 23%

decay-chain a r e given i n t h e appendix

i n a d d i t i o n t o tables of t h e numbers o f alphas/sec e m i t t e d by t h e v a r i o u s isotopes.

7 NEXJTIION SOURCE

C a l c u l a t i o n of t h e neutron source i s necessary p r i m a r i l y t o i n s u r e t h a t , even when s u b c r i t i c a l , t h e r e a r e enough neutrons a v a i l a b l e t o meet d e t e c t i o n c r i t e r i a and guard a g a i n s t a s t a r t u p a c c i d e n t . 3

From t h i s

s t a n d p o i n t , t h e g r a p h i t e r e g i o n i n t h e c o r e i s t h e r e g i o n of concern, f o r only i n t h i s region of t h e MSRE is c r i t i c a l i t y f e a s i b l e .

The c a l c u -

l a t i o n s p r e s e n t e d h e r e i n are f o r 25 f t 3 of s a l t , t h e approximate voiurne of s a l t i n t h e e f f e c t i v e core, whereas t h e t o t a l volume of s a l t i s about

75 f t 3 . So m u l t i p l i c a t i o n of t h e source s t r e n g t h i n t h e c o r e by

-3

will

g i v e t h e approximate source i n a f u e l d r a i n t a n k when it c o n t a i n s t h e e n t i r e f u e l loading. 7 L i ( a , n) 'OB Haubenreich'

found l i t h i u m t o be a n i n s i g n i f i c a n t neutron producer

when compared t o b e r y l l i u m and f l u o r i n e i n t h e

23%

f u e l mixture.

A cai-

c u l a t i o n ( s e e appendix) of t h e neutron y i e l d from t h e most e n e r g e t i c a l p h a (8.77 MeV) i n t h e

23%

f u e l showed t h a t l i t h i u m produced l e s s tLlan

one neutron f o r every 110 produced by b e r y l l i u m and f l u o r i n e .

Alphas

s t a r t i n g a t lower e n e r g i e s produce p r o p o r t i o n a t e l y fewer neutrons from l i t h i u m because of t h e r a p i d decrease with d e c r e a s i n g a l p h a energy i n t h e c r o s s s e c t i o n o f l i t h i u m f o r (a,n) r e a c t i o n s . * 7Li(a,n)10B

4.3 Mev.)

(Threshold energy f o r

The t o t a l neutron source from a l l ( a , n ) r e -

a c t i o n s w i t h l i t h i u m i s <3 x lo6 n/sec. Spontaneous F i s s i o n s

All of t h e uranium i s o t o p e s which a r e p r e s e n t i n t h e

23%

f u e l loading

undergo spontaneous f i s s i o n , w i t h h a l f - l i v e s f o r t h i s process ranging frotx

y r for

'3%

to 3 x

yr for

23%.

The t o t a l r a t e of spon-

taneous f i s s i o n s i n t h e MSRF: i s simply t h e sum of t h e products of t h e inventory of each i s o t o p e and i t s spontaneous f i s s i o n t i m e c o n s t a n t . Less t h a n 100 n/sec w i l l be produced i n t h e MSRE c o r e by spontaneous fission.

'Be(a, n) 13C and "F(a, n) 22Na High neutron production r a t e s r e s u l t from a l p h a r e a c t i o n s w i t h b e r y l l i u m and f l u o r i n e .

For t h e a l p h a p a r t i c l e s emitted from t h e uranium

i s o t o p e s ( e n e r g i e s between 4 . 1 and 5.3 MeV) t h e n e u t r o n production r a t e s The neutron

from t h e b e r y l l i u m and f l u o r i n e a r e approximately e q u a l , y i e l d of f l u o r i n e '

i n c r e a s e s more r a p i d l y w i t h i n c r e a s i n g a l p h a energy

t h a n does t h e y i e l d of b e r y l l i u m (see Fig. l ) ; 6 , 7 therefore, f o r the higher-energy a l p h a p a r t i c l e s produced by t h e

23%

decay chain, most of

t h e neutrons r e s u l t from ( a , n ) r e a c t i o n s w i t h f l u o r i n e . F i g u r e 2 shows t h e t o t a l c a l c u l a t e d neutron s o u r c e f o r t h e MSRE c o r e r e g i o n and t h e i n d i v i d u a l production r a t e s f o r t h e most s i g n i f i c a n t a l p h a -

emitters. with

The

23%

decay c h a i n obviously dominates t h e n e u t r o n production

"'90b e i n g t h e a l p h a e m i t t e r ( a l p h a energy of 8.77

MeV)

which causes

t h e most p r o l i f i c neutron production.

DISCUSSION

When t h e 233,mixture w a s p l a c e d i n t h e E R E : f u e l salt, the reactor a l r e a d y had about t h r e e y e a r s of o p e r a t i n g h i s t o r y .

The long runs a t high

power i n s u r e d t h a t a l a r g e photoneutron source would be p r e s e n t f o r some time a f t e r shutdown of t h e r e a c t o r .

However, i f s u f f i c i e n t time were a l -

lowed t o e l a p s e , t h i s source would weaken.

More important as a r e l i a b l e

neutron source i n t h e MSRE i s t h e i n h e r e n t neutron production from ( a , n ) reactions w i t h the salt constituents.

The (a,n) source i s e s s e n t i a l l y

independent of power h i s t o r y ana SLctualiy i n c r e a s e s a s y m p t o l i c a l l y t o a l i m i t i n g value.

A t t h e time t h e MSEiE achieved c r i t i c a l i t y w l t r ,

the fissile material (the

23%

mixture w a s t h e e q u i v a l e n t of

o l d ) , a t h e i n h e r e n t neutroll source ir. t h e c o r e r e g i o n was

23%

4 years

k x loa n/sec,

about a f a c t o r of 1000 Over the i n h e r e n t s m r c e which was c a l c u l a t e d f o r t h e 235U f u e l mixture.

The accuracy of t h e s e c a l c u l a t i o n s i s dependent on t h e accuracy t o which t h e f u e l i s o t o p i c composition and t h e v a r i o u s y i e l d data are known.

The f u e l composition is thought t o b e known t o w e l l w i t h i n k

and i s

9 ORNL-DWG

69- 40029A

I o3

2I IO2 a

-I

0 -

-J

I E W Q

L1: I-

40â&#x20AC;&#x2122; 3-

1 oc 0.5

E, ALPHA ENERGY ( M e V )

Fig. 1. Neutron Yield from Thick Beryllium and Fluorine Targets as a Function of Incident Alpha-Particle Energy.

O R N L - D W G 6 9 - 10030A

io9

a 0 0

W ( I

In 5 W

I I-

z W

108

0 v)

2 W

z +z a

TOTAL URANIUM

( O C T 1968 - M S R E C R I T I C A L I

o7 0

TIME

2 3 A F T E R PURIFICATION

W I T H 233U) 4 5 OF T H E 2 3 3 ~F U E L ( y e a r s )

Fig. 2. Total Inherent Neutron Source and the Neutron Source Resulting from Individual Alpha Emitters in the 3U-Fueled-MSRE Core.

The a r e a of t h i s c a l c u l a t i o n

probably n o t a n a p p r e c i a b l e s o u r c e of e r r o r .

which c o n t a i n s t h e most p o s s i b i l i t y of e r r o r i s t h e y i e l d data f o r t h e r e a c t i o n , igF(ar, n) *'%a.

Due t o i n s u f f i c i e n t data, we had t o e x t r a p o l a t e

t h e known y i e l d d a t a ( s e e F i g . 1), which only went t o a l p h a e n e r g i e s of

5.3 MeV, t o g e t t h e y i e l d from t h e h i g h e r - e n e r g i e d a l p h a s from t h e

23%

We made t h e assumption t h a t t h e y i e l d c o n t i n u e d i n c r e a s i n g

decay c h a i n .

w i t h t h e same f u n c t i o n a l r e l a t i o n s h i p t o t h e h i g h e r e n e r g i e s .

While it

i s r e a s o n a b l e t o e x p e c t t h e neutron p r o d u c t i o n r a t e t o i n c r e a s e w i t h a l p h a energy, it i s n o t known whether t h e y i e l d w i l l i n c r e a s e a c c o r d i n g t o t h e same power f u n c t i o n which could b e used t o d e s c r i b e i t s b e h a v i o r f o r lower energied alphas.

Yield data f o r b e r y l l i u m (which i s known from experiment

f o r a l p h a s t o % Mev and i s e x t r a p o l a t e d t o

8 Mev by t h e e x p e r i m e n t e r s ) 6

i s a l s o shown i n F i g . 1 and does indeed i n c r e a s e as a power f u n c t i o n w i t h i n c r e a s i n g a l p h a energy.

S i n c e t h e data f o r b e r y l l i u m i n c r e a s e s uniformly

t o h i g h e r a l p h a e n e r g i e s , one would t e n d t o e x p e c t t h e assumption about f l u o r i n e t o b e good, b u t even i f t h e assumption were n o t good and t h e y i e l d d a t a f o r t h e 8.77-Mev a l p h a were lower by a f a c t o r of 2 t h a n t h e

e x t r a p o l a t e d curve, t h e c a l c u l a t e d t o t a l n e u t r o n s o u r c e would be i n e r r o r

by only of

25$.

k 25% t o

We f e e l t h a t it i s fair to assign a probable error band

t h e s e c a l c u l a t i o n s w i t h t h e e x p e c t a t i o n t h a t t h e e r r o r i s much

smaller b u t w i t h t h e r e a l i z a t i o n t h a t more e x p e r i m e n t a l d a t a on high-energy alpha i n t e r a c t i o n s with f l u o r i n e is necessary before stronger confidence i n t h e c a l c u l a t e d n e u t r o n y i e l d i s warranted.

1.2

APPENDIX C a l c u l a t i o n of I n h e r e n t Neutron Source i n E R E f o r 23%

Source from 'Be(a,, n) 1%

F u e l S a l t Mixture

and 19F(a,n) 22Na

For b o t h r e a c t i o n s 'Be(a, n) I;%

and 19F(a, n ) 22Na,

t h e g e n e r a l equation

used t o determine t h e neutron source w a s

where Aa, = Alpha a c t i v i t y ( a / s e c ) i n E R E : c o r e ( 2 5 f t 3 of s a l t )

N = Neutron source (n/sec) Nmax

= Maximum number of neutrons produced i f t a r g e t were

( N/Nmax)=

composed completely of neutron-producing n u c l e i ('Be o r I9F as t h e c a s e may b e ) . %ax i s given i n u n i t s of neutrons p e r m i l l i o n a l p h a s . F r a c t i o n a l y i e l d of neutrons produced i n f u e l mixture t o number t h a t would be produced i n pure t a r g e t material.

Each of t h e t h r e e terms enclosed i n p a r e n t h e s e s i n t n i s equa%ion i s found independently.

Each term i s d i s c u s s e d i n t h e f o l l o w i n g paragraphs.

For. t h e l i f e of t h e MSRE, each of t h e irraniun; i s o t o p e s p r e s e n t i n

t h e f u e l w i l l b e a n e a r - c o n s t a n t a l p h a source due t o i t s long h a l f - i i f e ( s e e Table 3 ) .

Each of t h e i s o t o p e s , except

which a l s c has a long decay h a l f - l i f e .

23%,

decays t o a n u c i i a e

The secona, ana subsequent n u c l i d e s

i n each of t h e s e decay c h a i n s a r e Thus e l i m i n a t e d as s i g n i f i c a n t a l p h a sources. Whiie 232U produces a c o n s t a n t supply of a l p h a s , F t also produces t h e same number of 22&rh atoms.

Thorium-228 has a i.91 y e a r h a l f - l i f e

and s t a r t s a c h a i n of s h o r t h a l f - l i v e d elements ( s e e Table 4 ) .

Since t h e

f u e l mixture w a s about f o u r y e a r s o l d when loaded i n t o t h e r e a c t o r , w e may assume t h a t 228Th and i t s decay c h a i n are i n e q u i l i b r i u m ( i . e . 9 t h e a c t i v i t y (alphas/sec) from 22&rh and each member of i t s decay c h a i n w i l l be t h e

same).

Table Alpha Source i n %RE:

Isotope

Core from Uranium I s o t o p e s

a Energy (MeV)

Emission Percentage

Source (a/sec)

232tr

5.31 5.26 5.13

68 31 0.3

1.29 x io12 0.59 x lo1* 0.06 x io12

a33J

1.62 x 10’

4.82 4.78 4.73

83 15 2

3.01 x 1 O I 2 0.54 x 10’’ 0.07 x 1Ol2

4.76 4.70 4.60

1.45 x lo1’

0.45 x 10’’ 0.06 x io1’

234v

“#U

236v

Decay Half Life (Yr)

2.48 x io5

7.13

10’

2.39 x 107

4.39 4.57 4.18

4.50 4.45

73 27

5.30 x lo6 0.63 x lo6 0.25 x

lo6

9.80 x lo6 3.61 x lo6

11 Table

Inforrnntion Relateci t o Members of' 'v IJ Chain

i h c 1i de

Decay Mode

22"Th

Decay Half- L i f e

1.91 y r

Alpha Energy (MeV)

Erniss ion I'e r c en t a g e

5.42

5.20

71 28 0.6

5.68

5.33

3.64 day

5.44

4.6

5.19

0.1;

52 s e c

6.25

'l"po

0.16 s e c

6.77

?12pn

R-

10.64 h

none

21231

0-(66.35) a( 33.7%)

60.5 m i r ? 60.5 min

riorie

6.09

6.05

8.77

100

k : '

L L

Rti

Activity

Oi'

1-00

each o f t h e uranium n u c l i d e s i s simply t h e product X3,

where X is t h e decay c o n s t a n t ana I3 i s t h e number of atoms of t h e part i c u l s r isotope.

A c t i v i t y of 228Th (and o t h e r members o f decay chain)

ii:ny be c a l c u l a t e d using t h e r e l a t i o n

where ( A ( Y ) ~ = 228Th a c t i v i t y ( a / s e c ) = 23%

decay c o n s t a n t

h2 = 22&rh decay c o n s t a n t

N1 = Number of

‘lJ%

atoms

N2 = Number of 228Th atoms

R e s u l t s of t h i s c a l c u l a t i o n a r e shown i n Tables

3 and 5 and completes

t h e c a l c u l a t i o n of t h e a l p h a a c t i v i t y . Runnalls and Boucher6 g i v e t h e neutron y i e l d f o r a l p h a s i n c i d e n t upon a b e r y l l i u m t a r g e t as a f u n c t i o n of a l p h a energy, E ( i n Mev), Nmax = 0.152 E3*65 neutrons p e r m i l l i o n a l p h a s .

(3)

T h i s r e l a t i o n i s expected t o b e good over t h e range of a l p h a e n e r g i e s

encountered i n t h e %RE

fuel.

Apparently l i t t l e work has been performed on t h e n e u t r o n s o u r c e from (a,n) reactions with f l u o r i n e .

The only neutron y i e l d d a t a we could lo-

c a t e was i n an a r t i c l e by S e g r e and Wiegand.’ g i v e n f o r a l p h a e n e r g i e s up t o 5.3 MeV. i n c r e a s i n g as a power f u n c t i o n of energy.

The y i e l d d a t a w a s only

Up t o t h i s energy, t h e y i e l d w a s

Assuming t h a t t h i s h e l d t r u e

up t o 8.77 Mev (as w a s t h e a p p a r e n t c a s e w i t h b e r y l l i u m ) , t h e data was extrapolated.

The a n a l y t i c e x p r e s s i o n f o r t h e n e u t r o n p r o d u c t i o n of

f l u o r i n e as a f u n c t i o n of a l p h a energy was found t o b e

Nmax

= 1.02 x lo‘* E6*83 neutrons p e r m i l l i o n a l p h a s .

Equations (3) and (4) a n a l y t i c a l l y d e f i n e t h e e x p r e s s i o n s t o b e used f o r t h e Nmax term i n Equation (1)

) i n t h e general equation converts t h e neutron y i e l d max from t h e y i e l d i n a pure medium t o y i e l d from a m i x t u r e . An e x p r e s s i o n , The term (N/N

which a g r e e s w e l l w i t h observed d a t a , = f o r c a l c u l a t i n g t h i s term i s

(--->N N

n S

P P

max

where n

i s t h e number d e n s i t y of a n u c l i d e and Si i s t h e " r e l a t i v e atomic

s t o p p i n g power".

S u b s c r i p t "p" refers t o t h e p a r t i c u l a r n u c l i d e f o r which

t h e c a l c u l a t i o n i s being performed.

Number v a l u e s f o r "S" were o b t a i n e d

from a n a r t i c l e by Livingstone and Betheg where d a t a i s g i v e n f o r a v a r i e t y Table 9 g i v e s v a l u e s

o f elements as a f u n c t i o n of i n c i d e n t a l p h a energy.

f o r "S" f o r MSRE f u e l s a l t , o b t a i n e d by i n t e r p o l a t i o n o f t h e LivingstoneBethe data. Table 9 Relatiye Atomic Stopping Powers, Si

0.55

0.63

0.55 0.63

0.63

1.1

1.2

2.8

3.1

3-2

4.0

2.9 4.5

4.8

5 -0

Shown i n Table 10 are t h e c a l c u l a t e d v a l u e s f o r t h e f r a c t i o n a l y i e l d f o r b e r y l l i u m and f l u o r i n e as a f u n c t i o n of i n c i d e n t a l p h a energy.

I n brief,

t o c a l c u l a t e t h e neutron source from a p a r t i c u l a r a l p h a e m i t t e r , Equation (1) i s used.

Alpha a c t i v i t y ( A a ) may be o b t a i n e d from Table 3 o r

l a t e d u s i n g Equation ( 2 ) .

Using Equations (3) and

l a t e d f o r b o t h b e r y l l i u m and f l u o r i n e .

(4),

5 o r calcu-

Nmax may be c a l c u -

The a p p r o p r i a t e ( N / h a x )

may be

found i n Table 10. Multiplying these q u a n t i t i e s , one g e t s t h e s o u r c e from b e r y l l i u m and f l u o r i n e .

a p a r t i c u l a r alpha.

Addition o f these two g i v e s t h e t o t a l s o u r c e from

Table 10

F r a c t i o n a l Yie1.d Data f o r Be and F

4 079 0.695

0.078 0.688

0.074

5 079

0.692

0.647

Source from 7 ~ ( ai,n) 'OB Haubenreich' found t h a t f o r lower energy a l p h a s (<5 MeV) l i t h i u m w a s n o t a s i g n i f i c a n t neutron producer i n t h e E R E .

To be s u r e t h a t it d i d

n o t become s i g n i f i c a n t a t h i g h e r a l p h a energies, t h e neutron s o u r c e from t h e 8.77-Mev a l p h a s w a s c a l c u l a t e d . Neutron y i e l d from l i t h i u m may be c a l c u l a t e d u s i n g t h e r e l a t i o n " N'=

Aa J E o

Np a(E) ( - d x / a ) dE.

4.3

Where

N = Neutron Y i e l d (n/sec)

Aa = a l p h a a c t i v i t y ( a l p h a s / s e c of energy E) Eo = Energy of i n c i d e n t a l p h a (Mev)

N = Number d e n s i t y of l i t h i u m P o(E) = Cross s e c t i o n f o r (a,n) r e a c t i o n

4.3

= Threshold energy f o r 7 L i ( a , n ) l 0 B r e a c t i o n .

The term (-dx/dE) was o b t a i n e d from an a r t i c l e by HarrisL1 i n which he p l o t s (-dx/dE) as a f u n c t i o n of a l p h a energy for a number of elements. For t h e MSRE f u e l mixture t h i s was found by t h e r e l a t i o n

where wi corresponds t o t h e weight f r a c t i o n of component i and (-dx/dE)i is t h e v a l u e t a k e n from Harris for t h e i

are gm*cm'2*Mev'1.

component.

U n i t s on (-dx/dE)

Table 11 g i v e s t h e v a l u e s of (-dx/dE)

for t h e components

of t h e MSRE f u e l mixture.

Table 11 f o r MRF, F u e l Components

(-dx/dE)

I-dxldE) x lo3

-~ ~~_

( g m -cm-2 SMev'lr

I n c i d e n t Alpha Energy (Mev) Element

Be F

8.8 68.4

0.73

1.1

1.4 1.5 1.8 3.1 5.5

1.9 1.9

4.4

1.3 1.4 1.5 2.8 5 *o

3.9 7.3

1.4

1.6

1.9

2.5

1.2

1.3 2.5

2.4

Lithium's microscopic cross s e c t i o n f o r (a,n) r e a c t i o n 4 reaches a maximum of

250 mb f o r 7.1-Mev alphas, and drops e x p o n e n t i a l l y w i t h de-

c r e a s i n g energy.

Between 7.5 and 8.8 Mev t h e c r o s s s e c t i o n i s c o n s t a n t

150 mb.

By approximating t h e c r o s s s e c t i o n by s t r a i g h t l i n e s and c a r r y i n g o u t t h e i n t e g r a t i o n , t h e neutron source from w i t h l i t h i u m is found t o be U . l x lo6 n/sec,

g i b l e when compared w i t h t h e

8.77-Mev a l p h a r e a c t i o n s T h i s is s e e n t o be n e g l i -

lo8 n/sec from f l u o r i n e and b e r y l l i u m .

The lower energy a l p h a s w i l l produce p r o p o r t i o n a t e l y less due t o t h e e x p o n e n t i a l decay of t h e cross s e c t i o n a t lower e n e r g i e s .

REFERENCES

P. N. Haubenreich, I n h e r e n t Neutron Source i n Clean MSRE F u e l S a l t , USAEC Report ORNL-TM-611, Oak Ridge N a t i o n a l Laboratory, August 27,

1963* 2.

Oak Ridge National Laboratory, MSRP Semiann. P r o g r . Rept. Aug. 31, 1967, USAEC Report ORNL-4191, p. 50.

J . R. Engel, P. N. Haubenreich, and B. E. P r i n c e , E R E Neutron Source Requirements, USAEC Report ORNL-TM-935, Oak Ridge N a t i o n a l Laboratory, September 11, 1964.

J . H. Gibbons and R . L. Macklin, Charged P a r t i c l e Cross S e c t i o n s ,

Phys. Rev.,

114, p. 571, 1959.

E. Segre and C . Wiegand, Thick-Target E x c i t a t i o n Functions f o r Alpha P a r t i c l e s , USAEC Report LA-136,Los Alamos S c i e n t i f i c Laboratory, September 1944 ( a l s o i s s u e d as USAEC Report MDE-185).

0. J. C . Runnals and R. R . Boucher, Neutron Y i e l d s from A c t i n i d e Beryllium Alloys, Can. J . Phys 34:949 (1956).

J. H. Gabbons and R . L. Macklin, T o t a l Cross S e c t i o n f o r 'Be(a,n), The P h y s i c a l Review, 137, No. 6B. Bl5OB - B1509, 22 March 1965.

J . M. Chandler, p e r s o n a l communication t o P. N. Haubenreich, Oak Ridge N a t i o n a l Laboratory, October 1967.

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10.

W. N. Hess, Nuetrons from (a,n) Sources, Annals of Phys.,

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(1959) 11.

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ORNL-TM-2685 Internal Distribution

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8. 9. 10.

11. 12.

13. 14. 1.5. 16. 17. 18. 19.

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J. D. L. A. J. D. C. R.

28.

W. R. Grimes

29.

A. R. P. P. J. A. T. P. R. T.

20. 21.

22. 23.

24. 25.

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33. 34 35. 36. 37. 38. 39. 40.

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53. 54 55. 56. 57 58 59 60. 61. 62. 63-65. 66. 67 68. 69. 70 71.

72-80. 81. 82. 83 84. 85. 86. 87. 88. 89 90

H. L. J. A. R. E. A.

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I n t e r n a l D i s t r i b u t i o n (continued)

91-92. 93-94 94-97 98

100.

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