ANOMALOUSLY LARGE PEAKS OBSERVED IN THE 48Ti(a,y0)52Cr REACTION The 48Ti(a,y ) 52Cr excitation function showed large peaks at

In document Alpha capture to the giant dipole and quadrupole resonances (Page 125-129)

sfl"c aa l

4.5 ANOMALOUSLY LARGE PEAKS OBSERVED IN THE 48Ti(a,y0)52Cr REACTION The 48Ti(a,y ) 52Cr excitation function showed large peaks at

0

8.25, 8.375, 9.75 and 10.00 MeV alpha-particle bombarding energy with relative cross sections o/<o> = 2 . 8 where <o> is the average cross

section obtained by smoothing the data. The widths of the peaks at E^ = 8.25 and 8.375 MeV determined by measurements made in 25 keV steps were 75 ± 15 keV, which is ^ 15 coherence widths. However, as similar peaks were not observed at the same energies in the (a,y ) reaction, it

1

was tentatively assumed that the peaks were probably due to fluctuations. In order to show that such peaks are consistent with fluctuation theory, the number of peaks with a relative cross section greater than

a/<a> = 2.8 in the energy range of the data was calculated. Although equation 4.4 can be used to estimate the probability for large peaks, it

73.

was shown by Branford and Newton (Br 74) to be inaccurate unless <T>/<D> 'v oo. They used synthetic excitation functions to show empirically that the number of peaks above a given relative height, o / < o > in an energy interval Ej to E2 is

H = 1.2 PN (E2 - E O / r , 4.15

where is the integral of x2 for 2N degrees of freedom between the

limits of integration 2N o / < o > to °° and r is the coherence width.

Using the result that the effective value of N for 48Ti (a,y)52Cr excitation

function is 5, the above expression gave H = 1.5 ± 0.75. The number

of peaks predicted by artificial excitation functions is therefore in reasonable agreement with the actual number observed, providing further support to the conclusion that the peaks are most probably due to

Ericson fluctuations.

4.6 SUMMARY

From the results of the fluctuation analysis it can be concluded t h a t :

(i) The fine structure observed in the 56Fe(a,y)60Ni and

48T i(a,y)52Cr reactions is due to Ericson fluctuations.

(ii) The coherences widths, T deduced from the values of R ,(0)

are r(48Ti) = 3.3 ± 1.2 keV and r(60Ni) = 4.5 ± 1.5 keV.

(iii) The fine structure observed in the 38A r(a,y)42Ca and

40Ar ( a,y)44Ca reactions is probably due mainly to

excitation of individual isolated resonances with widths % 40 keV.

(iv) The anomalously large peaks observed in the 48Ti(a,yQ) 52Cr

reaction are probably due to Ericson fluctuations, supporting conclusion (i).

74.

CHAPTER 5

HAUSER-FESHBACH CALCULATIONS OF (y,a0) CROSS SECTIONS

5.1 INTRODUCTION

Hauser-Feshbach calculations have very successfully predicted the average cross sections and angular distributions of both particles and gamma-rays following particle-induced compound nucleus reactions

(Vo 68). Similar calculations of photon-induced reactions have met with

mixed success although the evaporation spectra of neutrons, protons and alpha particles have provided convincing evidence that the photo- nuclear reaction proceeds predominantly through the compound nucleus in

a statistical manner (Ha 70). Exceptions are the (y,pQ) and (y,nQ) channels

where the measured yield can be orders of magnitude larger than predicted

by the statistical model. There is evidence to show that this is also the

case for the (y,otQ) reaction on heavy nuclei. For example Meneghetti

and Vitale (Me 65) were unable to fit the high energy tail of the alpha particle spectra obtained by bremsstrahlung irradiation of Bi and In, whereas good fits were obtained to the spectra from irradiated Cu and

Ag. They concluded that this was due to a direct (y,aQ) reaction similar

to the (y,pQ) reaction. Kellar and McConnell (Ke 72) measured (y,a)

excitation functions for a range of nuclei between Ti and Ag and compared the results to Hauser-Feshbach calculations with disappointing results. This was attributed to the large uncertainties in level density parameters rather than a failure of the statistical model, Hauser-Feshbach calculations were also used to successfully explain the rapid fall in the cross section

which occurs in the 89Y(p,yQ)90Zr excitation function (Ma 69) following

the opening of the neutron channel. However at higher energies the

7 5.

by t h e s t a t i s t i c a l model due t o t h e n o n - s t a t i s t i c a l n a t u r e o f t h e (p,Y0 )

r e a c t i o n a t GDR e n e r g i e s .

The q u a l i t a t i v e ar gume nt p r e s e n t e d i n s e c t i o n s 3 . 1 . 4 . 1 / 2 and

t h e a n a l y s i s o f t h e f i n e s t r u c t u r e i n t e r m s o f E r i c s o n f l u c t u a t i o n s s u g g e s t t h a t t h e ( a, Y0 ) r e a c t i o n s c o n s i d e r e d h e r e , p r o c e e d p r e d o m i n a n t l y t h r o u g h t h e compound n u c l e u s i n a s t a t i s t i c a l manner . H a u s e r - F e s h b a c h c a l c u l a t i o n s may t h u s be a b l e t o p r e d i c t t h e a v e r a g e c r o s s s e c t i o n s and r e p r o d u c e t h e s h ap e o f t h e e x c i t a t i o n f u n c t i o n s . T h e r e f o r e , c a l c u l a t i o n s were p e r f o r m e d t o e s t i m a t e t h e c r o s s s e c t i o n s f o r t h e (Y,a 0 ) r e a c t i o n on

30S i , 32S, 4 0 >4 2 >4 4 Ca, 52Cr and 60Ni a s d e s c r i b e d i n t h e f o l l o w i n g s e c t i o n s .

5 .2 THE HAUSER-FESHBACH FORMULA APPLIED TO (Y,<*0) CROSS SECTIONS

The d e r i v a t i o n o f t h e H a u s e r - F e s h b a c h e x p r e s s i o n f o r t h e r e a c t i o n

c r o s s s e c t i o n , i s o u t l i n e d i n Appendix A where i t i s shown t h a t

ttX2 CC1 ( 2 i + l ) (21 + 1) Jtt I (2J+1)

I Ts* I

i

sa

S ' v

l

5. 1 S"£" S"£"

The i , I , and J a r e t h e s p i n s o f t h e p r o j e c t i l e t a r g e t and compound n u l e u s

s t a t e r e s p e c t i v e l y . The T^ a r e t r a n s m i s s i o n c o e f f i c i e n t s which were c a l ­

c u l a t e d a s d e s c r i b e d i n s e c t i o n 5 . 4 and t h e summation o v e r l " i s t a k e n ove r

a l l p o s s i b l e d e c a y c h a n n e l s . For t h e p a r t i c u l a r c a s e o f t h e ( y , a 0) r e a c t i o n t h e above e x p r e s s i o n can be s i m p l i f i e d c o n s i d e r a b l y . T h i s i s b e c a u s e t h e a b s o r p t i o n o f e l e c t r i c d i p o l e r a d i a t i o n a c c o u n t s f o r a p p r o x i m a t e l y 90% o f t h e t o t a l a b s o r p t i o n c r o s s s e c t i o n i n t h e r e g i o n o f t h e GDR. T h e r e f o r e , f o r e v e n - e v e n t a r g e t n u c l e i t h e ( y , a 0) r e a c t i o n p r o c e e d s a l m o s t e n t i r e l y t h r o u g h 1 s t a t e s of

t h e compound n u c l e u s and h e n c e e q u a t i o n 5 . 1 can be w r i t t e n ,

T T

o ( y , a ) = ( 2 J + l ) i r * 2 y , 5 . 2

l t £

76.

This allows the expression to be separated into the independent processes of formation and decay, giving

°<Y' V =

5-3

where g c n is, to a good approximation, the total photonuclear absorption cross section. Thus the (y,aQ) cross sections can be estimated using experimental values of cr and calculated values of the transmission coefficients.

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