Isotopic and isotonic yields in nuclear fission

T. A. E. C.

ÇEKMECE NUCLEAR RESEARCH CENTER

ISTANBUL - TURKEY

I S O T O P I C A F D I S O T O P I C Y I I F !' UC L E A R F I S o I 0 P

iı. Talât—Er ben and Binay Güven Department o f Chemistry

ÇFAİı - 2 1962 E L D S

Çelcmece Fuclear Research Center P.R. 1, Hava A la n ı, Istan bu l - Turkey

I S O T O P I C A N D I S O T O P I C Y I I P !' U C L E A K F I S o I O P

ii. Talât—Erben and Binay Güven Department o f Chemistry

Çelcmece Fuclear Research Center

ÇFAİ : - 2 1962 E L D S

. ı .

I iOTOPIC AIT I3OT0M C YIBIDS II' HJC IEAi'i F IS S IO I ( )

ii. Talât-Erben and Ginay Güven

Chemistry Department, I uclear research Center P .K . 1, Hava A la n ı, Istan b u l

Turkey

A B S T R A C T

The curves fo r is o t o p ic and is o to n ic f i s s i o n y ie ld s are calcu la ted and shown to be the W eierstrass transforms o f the ıs o o a r ic y ie ld curve. The Well-known mass asymmetry o f the f i s s i o n i s associated with asymmetry in charge and in neutron co n ten ts. There are "fo rb id d en " zones at

44

48

and at

64

235 thermal neutron f i s s i o n o f U .

2

-I F T O D U C T I O F

Any hypothesis on charge d is tr ib u tio n in nuclear f i s s i o n defin es two q u a n titie s : (1) The most probable atomic number (not n e c e s s a r ily an in te g e r )

Zp fo r the product which has the high est y ie ld among a l l products o f a given mass chain A, and (2) the fr a c t io n a l chain y ie ld fo r a .nuclide defined as the y ie ld o f th is nuclide divided by the t o t a l y ie ld o f the chain to which th is nuclide b elo n g s. The curve ^i(Z,A) i s c a lle d the charge d isp ersio n curve. This inform ation along with the experim ental yield-m ass curve y (A ), permits one to ca lcu la te the is o t o p ic and is o to n ic f i s s i o n y ie ld curves, y(Z ) and y (F ), as fo llo w s :

(D

j y(z)

The mathematical operation defined by the foregoing formulas i s e s s e n t i a lly a f i n i t e lin e a r in t e g r a l transform ation o f the fu n ction y(A)

in to y(Z ) or y ( l ') , the kernel o f the transform being ft (Z,A ) or ^ (F ,A ), r e s p e c t iv e ly . 2 3

decent work( * ) e sta b lish e d th at the charge d isp ersio n curve i s the Gaussian:

(3)

*l/p .

rj (Z,A ) =

( * c f

with C = 0 . 9 ( ' ) . Therefore, by tr e a tin g the mass number A as a continuous v a r ia b le , one can w rite ;

U ) y

(z) =p*=

3

-and

y (î’ ) I y(A) •exp:_-(Z-Zp)2/ c j dA

The in te g r a l transformation defined by (A) and ( 5 ) , whose kernel i s the normalized Gaussian (

3

the in te g r a l forms given above are u se fu l when an a n a ly tic a l expression for y(A) i s a v a ila b le . Fongfs (^ ) s t a t i s t i c a l theory o f nuclear fis s io n provides such an expression, but i t i s too complicated. However, since y(A) is discontinuous and p r a c tic a lly n e g lig ib le below A - 80 and above A = 160, the f i n i t e summation formulas (1) and (

2

Accordingly, we have calculated the iso to p ic and iso to n ic y ie ld curves by making use o f various p o stu la tes(^ ) of charge d istrib u tio n as w ell as

3 6

Wahl*s( * ) em pirical fu nction, in the case o f the thermal neutron 235

f is s io n o f (J . Some o f the calculated curves are shown in F ig s. 1 to A.

7

The tabulated values fo r y(A) reported by Steinberg and Glendenin ( ) are used throughout.

S S L ) I T S AID D I o C 0 S 3 1 0 i:

The curves thus obtained lead to the follow ing observations:

(1) Both y(Z) and y(F) are "double-humped" as i s the o r ig in a l y(A) curve, sig n ify in g that the asymmetry o f f is s io n with respect to mass i s

4

-(2) The y(Z) and y(l ) curves must s a t is fy some s t r i c t conservation conditions, and therefore, provide u sefu l te sts for the charge d istribu tion postulate used to rela te to A. These conditions ares

(a) The sum o f the abscissa of any two points of equal ordinates situated on two complementary branches of the curves, must equal 92 for the y(Z) and 14.1.5 (see statement 9 below) for the y(F) curve, in the

235

case of the thermal neutron fis s io n o f IT . (The lig h t side o f the lig h t peak is complementary to the heavy side o f the heavy peak, and the heavy side of the lig h t peak i s complementary to the lig h t side of the heavy peak.)

(b) The area under the y(Z) curve, as w ell as that under the y ( i ) curve, must equal the area under the o rig in a l y(A) curve. This i s a requirement of the conservation of the number of fragments.

(

3

(see Table 1 ) .

( i) The peak widths of y(Z) and y(T) d iffe r only s lig h t ly , whereas the trough width for y(î') i s more than twice that for y(Z) (refer again to Table I ) .

(5) There are "forbidden" zones on the isotopic and isoton ic yield curves at 44^ Z '? 4o and at 6 4 q l < 7C, respectively, where the formation probabilities are extremely lowj the maximum to t a l yields amount to less

3 than 0.5% in these zones. I t i s interesting to note that Wahl et a l . ( ) conclude in d ire c tly that 4 2 ' Z<T5ö i s a forbidden range, however, they do not specify such a range for neutron contents.

5

-Table I . Some ch aracteristic parameters of the isoto p ic and isoto n ic yield curves, calculated by using Wahl's empirical Z function. I’ote that the

P

parameters for y(Z) and y (lT) are additive with respect to those of y (A ).

+ Curve

Average Z , V t or A number

Sum Peak width at Trough width

lig h t group Hoavy group haIf-height at half-depth

y ( z ) 38.15 53.95 92.10 7 .2 8 .5

y(N) 56.69 84.78 14.1.47 8.3 19.5

Sum 94.84 138.73 233.57 15.5 28 .0

-H-y(A) 95 139 234 15 28

+ Weighted average (probably except fo r A ) , ++ Values taken from reference 7 .

(6) The much larger extension of the forbidden zone for neutron i s to be correlated both with the wider variation range o f the number o f neutrons and with the property stated in (

4

From Table I , the o v era ll widths at half-h eigh t are found to be ( 2 ) ( 7 .2 ) + (G.5) = 22.9 and ( 2 ) (8 .3 ) + (1 9.5) = 3 6 .1 for y(Z) and y (F ), respectively, and

6

-their ratio (

36

22

9

lig h t group peak Trough Heavy group peak

8 .3 19.5 8 .3

and not in th is way:

(1.58) (7.2) = 11.3 (1.5-3)(S.5)=13.4. (1 .5 S )(7 .2 ) = 11.3

sig n ifie s that the neutron number distribu tion of the fis s io n fragments of the lig h t and heavy groups is r e l a tiv ely narrower than the corresponding proton d istrib u tion and, as a r e s u lt, the P-forbidden zone is much larger than what would normally be expected by comparison with the Z-forbidden zone. This i s an interesting property of the fis s io n process which, as far as we know, has not been pointed out before.

(7) I’o one o f the charge d istribu tion postulates introduces any isotopic or isoto n ic y ield anomalies at Z=50 or at F=82. Pappas1( )

discontinuous Z^ produces a pronounced structure on the y(Z) curve, but the maxima do not occur at s h e ll closures.

(8) D iscontinuities in Z produce discon tin u ities on the y(Z) curve P

alone; the y(F) curve i s always smooth, implying that the proton closed g

s h e ll contribution ( i f any( )) to the fine structure should be larger than the neutron closed s h e ll contribution. This conclusion i s in agreement with the fa c t that T7ahl, s(^>) empirical Z line t^nds to approach and re: min close to the 50-proton s h e ll edge, but there i s no pronounced tendency for i t to remain close to the 82 (or 50) neutron s h e ll edge.

7

-(9) As Coryell ( ) s ta te s , there i s ambiguity about whether the fis s io n fragments of a pair are meant to complement each other before or a fter

prompt neutron b o i l - o f f . Low, this ambiguity seems to be removed. In fa c t , we found that a difference of 2.5 in the t o t a l mass of the complementary fragments causes the y(Z) and y(l ) curves to s h ift in opposite directions

4a

in such a way that, in accordance with Glendenin e t a l .( ) and not with 4b

Pappas( ' ) , the masses of a pair must be considered as complementing mutually after and not before prompt neutron b o i l - o f f ; otherwise, the proton-and neutron conservation conditions are both clea rly v io la te d .

(10) The iso to p ic yield curve drawn by taking into consideration exclusively the known nuclides, neglecting the calculated yields for a l l those nuclides that are not indicated on the Chart of iu c lid e s (~ ^ ), is irregular and indicates that new isotopes of Sr, Y, Zr, Lb, Te, and La are s t i l l to bo id en tified as primary products of the thermal neutron fis s io n of U235

A C ı\ i 0 y L C D G L V T s

The authors wish to thank Professor E. P. Wigner of Princeton

University for an encouraging discussion in the early stage of th is work. It is a pleasure to acknowledge many valuable discussions with Professor S. Akpinar and Professor F. Domaniç.

8

-k E F E ft E î C E o

c1) This work was performed under the auspices o f the Turkish Atomic Energy Commission.

c2 ) I . F. C ro a ll, J . Inorg. Fuel. Chem. 16, 353 (1 9 6 1 ).

(J) A. C. Wahl, ft. L. Ferguson, D. ft. Fethaway, D. E. Troutner, and ft. Wolfsberg, Phys. Rev. 126, 1112 (1 9 6 2 ).

(^) (a) I . E. Glendenin, C. D. C ory ell, and ft. ft. Edwards, Radioehemi c a l Studies ; The F ission Products. Edited by C oryell and Sugarman, ftcGraw-Hill book Co. I n c ., lew York, 1951, p. 469. (d) A.C. Pappas, Proceedings o f the Internatio n a l Conference of the pe ac e fu l Use s_ o f Atomic Energy, Geneva, 1955, V o l. 7 , p. 19. (c) T. J. ..ennett and H. G. Thode, Phys. Rev. İCJ3., 323 (1 9 5 6 ).

(^) P. Fong, Phys. i.ev. 102, 1 3 U (1 9 5 6 ).

(^) A. C. Wahl, J . Inorg. f u e l. Chem. 6, 263 (195B).

7

( ) E. P. Steinberg and L. E. Glendenin, Proceedings, of thei Internat i o n a l Conference on t he Peace f u l Uses of A.to,.dc Energy, Geneva, 1955,

V o l. 7 , p. 3 .

(^) H. Farrar and ft. H. Tomlinson, Can. J. Phys.

40

(^) C. D. C oryell, ft. ftaplan, and ft. D. Fink, Can. J . Chem. 3 9 , 6ft6 (1 9 6 1 ). (■*■9) Chart o f Fuclides, prepared by the In stitu te o f Radio chemistry,

Fuclear Research Center, ftarlsruhe, Germany. (lite r a tu r e revised to July 1961.)

9 -FIG. 1 FIG. 2 FIG. 3 FIG. 4 FIG. 5 F I G Ü E E C A P T I O U S

. Fission yields o f is o to p ic fragments from U ^ ^ (n ^ ,F ), calculated by using the postulate o f equal charge displacement (continuous lin e ), and Wahl’ s em pirical function (broken li n e ) .

. Fission yields o f is o to n ic fragments from U ( n ^ F ) , calculated by using the postulate o f equal charge displacement (continuous lin e ), and Wahl's em pirical Z function (oroken li n e ) .

Fission yields o f is o to p ic fragments from U^^(n^.in, by using Pappas

1

(broken lin e) discontinuous Zp fu n ction s.

F), calculated Thode ! s

, Fission yields o f is o to n ic fragments from u^^(n^, ,F ), calculated by using Pappas

1

(broken lin e) discontinuous Z^ fu n ction s.

. A comparative p lot o f the f u l l th e o re tica l is o to p ic yield curve (continuous lin e ) and the curve calculated by talln g in to account exclu sively the known nuclides (broken lin e ), in dicatin g that new isotopes o f Sr, Y, Zr, lb , Te, and La are s t i l l to be id e n t ifie d .

Ol M

oı S Ol

Ol I