Roeders, J.D.A.

English

Proceedings - University of Groningen

   University of GroningenCross section fluctuations in alpha particle scattering by 24Mg, 26Mg and 28SiRoeders, J.D.A.IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:1971Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Roeders, J. D. A. (1971). Cross section fluctuations in alpha particle scattering by 24Mg, 26Mg and 28Si.s.n.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 01-02-2024t 2 7.  R e v .  1 7 4  ( 1 9 6 8 )  I  1 4 0 .e r  Woude ,  Phys .  Rev ..  2 9  ( 1 9 6 2 )  4 6 2 .nbosch  and9 4 ., n B ,  P h y s  .  R e v .  L e t t .h y s . l 3  ( 1 9 5 9 )  3 2 .e conmunicat ion tou c 1 .  P h y s ..  S e l s k .r  Woude ,23  ( r9ss )  t 6 .l J u c l .  P h y s .osch and0 .r  a n d  D . A .  B r o m l e y ,and  T .  P .  I u l a r v i n ,Lzenga ,  Nuc l .  Phys .A  127  (  l  969 )  289  .3 r  I n s t i t u u t ,S U M M A R YT h e  a i m  o f  t h e  p r e s e n t  i n v e s t i g a t i o n  i s  t o  e v a l u a t e  a v e r a g e  p r o p e r -t i e s  o f  h i g h l y  e x c i t e d  c o m p o u n d  n u c l e u s  s t a t e s  f r o m  a n  a n a l y s i s  o ff l u c t u a t i o n s  o b s e r v e d  i n  n u c l e a r  r e a c t i o n  c r o s s  s e c t i o n s  a s  a  f u n c -t i o n  o f  e n e r g y .  S t u d i e d  a r e  t h e  e l a s E i c  a n d  i n e l a s t i c  s c a t , t e r i n g  o fa l p h a  p a r t i c l e s  b y  ' o u r ,  ' u u ,  a n d  2 8 r i  a t  b o m b a r d i n g  e n e r g i e sr a n g i n g  f r o m  a b o u t  i 8  t o  2 8  M e V .  F r o m  t h e  c r o s s  s e c t i o n  f l u c t u a t i o n si t  i s  p o s s i b l e  t o  d e t e r m i n e :  (  I  )  t h e  a v e r a g e  t o t a l  l e v e l  w i d t h  fo f  c o m p o u n c l  n u c l e u s  l e v e l . s  a s  a  f  u n c à o n  o f  e x c i t a t i o n  e n e r g y ;( 2 )  t h e  r e l a t i v e  c o n t r i b u t i o n  o f  d i r e c t  i n t . e r a c t i o n  p r o c e s s e s ,  y D ,a n d  c o m p o u n d  n u c l e u s  f o r m a t i o n ,  l - y D ,  t o  t h e  c r o s s  s e c t i o n ;  ( 3 )  t h ee f f e c t i v e  n u m b e r  o f  r e a c t i o n  c h a n n e l s ,  N e f f .  F r o m  t h e  v a l u e  o f  I  o n em a y  d e r i v e  t h e  l e v e l  d e n s i t y  a t  h i g h  e x c i  t a t i o n  e n e r g i e s .I n  t h e  i n t r o d u c t o r y  c h a p t e r  s o m e  a s p e c t s  o f  t h e  p r e s e n t  i n v e s t i g a t i o na r e  m e n t i o n e d .  A t , t e n t i o n  i s  d r a w n  t o  o t h e r  r e a c t . i o n  s L u d i e s  l e a d i n gt o  t h e  s a m e  c o m p o u n d  n u c l e i  2 8 S i ,  ' o r i  a n d  3 2 ,  a t  c o m p a r a b l e  e x c i t a -t i o n  e n e r g i e s .C h a p t e r  t \ r o  d e a l s  w i t h  t h e  t h e o r y  o f  c r o s s  s e c t i o n  f l u c t u a t i o n sd e v e l o p e d  b y  E r i c s o n ,  a n d  b y  B r i n k  a n d  S t e p h e n .  T h e  a s s u m p t i o n st rnde r l y i ng  t he  t . heo ry  a re  d i scussed  and  t he  re l a t i ons  connec t i ngtheo ry  w i t h  expe r imen t  a re  g i ven .  Some  re levan t  quan t i t i es  as  au to -c o r r e l a t i o n  a n d  c r o s s  c o r r e l a t i o n  f u n c t i o n s ,  d i s t r i b u t i o n  f u n c t i o n sa n d  e f f e c t i v e  n u m b e r  o f  r e a c t i o n  c h a n n e l s  a r e  d i s c u s s e d .The  me thods  t o  ob ta in  t he  t r ue  f l uc tua t i on  pa rame te rs  f r om expe r imen -t a l  e x c i t a t i o n  f u n c t i o n s  a r e  t r e a t e d  i n  c h a p t e r  t h r e e .  T h e  f i n i t el eng th  o f  t he  ene rgy  i n te r va l  ove r  wh i ch  measu remen ts  can  be  madei n  p r a c t i c e ,  t h e  e x p e r i m e n t a l  e n e r g y  r e s o l u c i o n ,  a n d  t h e  d i s t a n c eb e t w e e n  t h e  e x p e r i m e n t a l  p o i n t s  o f  a n  e x c i t a t i o n  f u n c t i o n  l e a d  t oa p p a r e n t  v a l u e s  o f  t h e  f l u c t u a t i o n  p a r a m e t e r s  r v h i c h  d i f f e r  c o n s i d e -r a b l y  f r o m  t h e  t r u e  o n e s .  T h e  c o r r e c t i o n s  w h i c h  a r e  n e c e s s a r y  t oo b t a i n  t h e  t r u e  v a l u e s  a r e  d i s c u s s e d  i n  d e t a i l .  l l a n y  o f  t h e  c o r r e c -128t i on  f o rmu las  g i ven  i n  t h i s  chap te r  a re  ob ta ined  by  s tudy ing  eache f f e c t  i n  p a r t i c u l a r  b y  m e a n s  o f  c o m p u t e r  g e n e r a t e d  e x c i t a t i o nfunc t  i ons  .I n  c h a p t e r  t h r e e  a l s o  a  m e t h o d  i s  g i v e n  t o  p e r f o r m  a  f l u c t u a t i o na n a l y s i s  w h e n  e f f e c t s  o f  n o n - s t a t i s t i c a l  o r i g i n  a r e  p r e s e n t  i n  t h ee x c i t a t i o n  f u n c t i o n s .  F o r  t h a t  p u r p o s e  a  n e w  " r e d u c e d "  e x c i t a t i o nf u n c t i o n  i s  c o n s t r u c t e d  b y  d i v i d i n g  e v e r y  e x p e r i m e n t a l  p o i n t  o f  t h eo r i g i n a l  e x c i t a t i o n  f u n c t i o n  b y  t h e  a v e r a g e  v a l u e  o f  n e i g h b o u r i n gp o i n t s .  B y  c h o o s i n g  a n  a p p r o p r i a t e  v a l u e  o f  t h e  a v e r a g i n g  i n t e r v a lr e d u c e d  e x c i t a L i o n  f u n c t i o n s  a r e  o b t a i n e d  w h i c h  y i e l d  u n d i s t o r : t e da u t o c o r r e l a t i o n  a n d  d i s t r i b u t i o n  f u n c t i o n s ,  l e a d i n g  t o  u n a m b i g u o u s* 1 - ^ " ^ 1 -  i - ^ ^ - - a q g  v a l u e s  o f  f  a n d  y , . , , .  l L  c a n  b e  s h o w n ,  h o r v e v e r ,  i nL r a v u Ë l t  r r r L v ! r E L L  v q ! u g D  v !  uw h i c h  w a y  t h e  p a r a m e t e r s  o b t a i n e d  f r o m  t h e  a n a l y s i s  c f  r e d u c e de x c i t a t i o n  f u n c t i o n s  h a v e  t o  b e  c o r r e c t e d  i n  o r d e r  t o  f i n d  t h e  t r u ev a l u e s .  T h e  c o r r e c t i o n  f a c t o r s  a r e  d e r i v e d  a n a l y t i c a l l y  a n d  t e s t e db y  t h e  s y n t h e t i c  e x c i t a t i o n  f u n c t i o n s .I n  c h a p t e r  f o u r  w e  d e s c r i b e  t h e  e x p e r i m e n t a l  s e t  u p .  S o m e  c h a r a c t e -r i s t i c s  o f  t h e  P h i l i p s  A V F  c y c l o t r r n ,  t h e  a c c e l e r a t o r  w h i c h  p r o -v i d e d  t h e  a l p h a  p a r t i c l e  b e a m ,  a r e  g i v e n .  l ' h e  m e t h o d  u s e d  t o  d e t e r -m i n e  t h e  e n e r g y  o f  t h e  p a r t i c l e  b e a m  i s  o u t l i n e d .  T h e  s c a t t e r i n gc h a m b e r ,  p r o v i d e d  w i t h  f o u r  s u r f a c e  b a r r i e r  d e t e c t o r s ,  a n d  t h ee l e c t r o n i c  e q u i p m e n t  u s e d  i n  o u r  e x p e r i m e n t s  i s  d e s c r i b e d .T h e  a c t u a l  a n a l y s i s  o f  e x p e r i m e n t a l  d a t a  i s  g i v e n  i n  c h a p t e r  f i v e .T h e  c o h e r e n c e  w i d t h  f  i s  o b t a i n e d  w i t h  t h e  a u t o c o r r e l a t i o n  m e t h o d ,a n d  a l s o  f r o m  t h e  n u m b e r  o f  m a x i m a  p r e s e n t  i n  e x c i t a t i o n  f u n c t i o n s .T t r e  a m o u n t  o f  d i r e c t  i n t e r a c t i o n  y O  i s  o b t a i n e d  f r o m  t h e  d i s t r i b u -t i o n  o f  t h e  c r o s s  s e c t i o n s .  T h e  v a l u e  o f  t h e  a u t o c o r r e l a t i o nfunc t i on  a t  ze ro  a rgumen t  and  Lhe  va lue  o f  yn  y i e l d  t he  expe r imen -t a l  v a l u e  o f  t h e  n u m b e r  o f  r e a c t i o n  c h a n n e l s .  T h i s  q u a n t i t y  i s  a l s oc a l c u l a t e d  t h e o r e t i c a l l y  w i t h  t h e  H a u s e r - F e s h b a c h  f o r n a l i s m .  I ns e c t i o n  5 . 5  a  m e t h o d  i s  o u t l i n e d  t o  d e t e c t  i n  e x c i t a t i o n  f u n c t i o n ss t r u c t u r e s  o f  l a r g e r  w i d t h  t h a n  t h o s e  d u e  t o  p u r e l y  c o m p o u n d  n u c l e a rp r o c e s  rc r o s s  (Chap te rT  - , -  - .  1 . ,f  v : ; ! J i, i R\ 1e x c i t a ra  L  - . . . - , ,- , . 1 =  -  !  y  ,- . . '  . ; 'r .  !  ! L l  = ti s  c a l .  in , l c  1e - i l ld t i u  L  d L,1!  i : " s  iÍ -  :  - .I !  ! ;  imecnan iine ia*"  t' . :' - 6  t5 "2i tvlet f  A  ) ' ;her :e  i - in Y n n ê e (H  r  v  v v  v  sr  t : c  g t t l -: :  o r ê É  r ^i n  t heIn  t hep r e  s  e n ci o r  t h e, i , -  ^ l - ^ -r ! r  L r t d !a r e  f o us tudy ing  eache x c i t a t i o nf  l uc  l ua f  i  onp r e s e n t  i n  t h eJ "  e x c i t a t i o n-  |  - ^ . i  - r  , - F  r l ' ' ,A I  P O I T I L  O I  L I I Cne ighbou r  i ngd Ë r r ! Ë  r r r L c L  v d fC  u n d i s t o r : t e dto  unamb iguoush  n r . r p r r p r  i  no f  r e d u c e do  f i n d  t h e  t r u eI  l r r  n n À  Í - r : q t a á-  - JS o m e  c i r a r a c  t e --  , , L i  ^ L!  w L l r L r t  P ! uu s e d  t o  d e t e r -e  s c a t t e r i n gs ,  a n d  t h er i b e d .c h a p t e r  f i v e .1  ^ r i , . -  * ^ 1 L ^ lI C l L  I U I I  I I I S  L I I . \ J I I ,t i o n  f u n c t i o n s .t h e  d i s t r i b u -r e  l a t  i o nthe exper imen-. . ^ . ^ ! . : F . -  : ^  ^ 1 ^u a n t r t y  I S  a I S or m a l i s m .  I nt i o n  f u n c t i o n scompound nuc lear129p r o c e s s e s ;  t h e  m e t h o d  i s  b a s e d  o n  s o m e  s t a t i s t i c a l  p r o p e r t i e s  o fc r o s s  c o r r e l a t i ó n  c o e f f i c i e n c s .C h a p c e r  s  i : <  c o n t a i n s  t h e  d i s c u s s i o n  o f  r e s u l - t s  .  T h e  e x p e r i m e n t a ll ' - v : r i u .= "  ,  r r h i ch  raneec i  f  r on  31  t o  |  16  keV  f  o r  t he  compound  nuc leus; 5 . .  _ " a ^ .  _  3 2 ^- S t .  t r o r n  5 - {  : : r  q ' i  i . - e \ i  i r r :  - - S i  a n d  i r o u i : l  t ' - ' c 9  k e \ '  f o r  " - S  a Lexc i t aE io r i  ene rg ies  be tween  abou t  23  and  33  l ' 1e \ . '  a re  compared  w i t hl he r , r : r * .  I ' : ' , e  r a t , he r :  : ; n i a l .  i  i nc rease  o f  t he  expe r imen ta l  i - r , ' a1ues- - r j - : t i  ene rgy  can  De  e ; ' : p -a ine r l  r a the r  i ve i l  when  the  l eve l  dens i t r l 'i s  c a L c u l a t e r i  a : c r - r r d i n : :  t i . ;  i h e  b a c k  s h i f c e d  ! e r m i  g a s  m c c l e r ,  a . n d  anuc lea i  r r io in€ l i i i  u i '  i l+ : " - l ; ;  is  i i : i i :od ' . :cer l  ,  ' . , -h ;  ch is  enet :g) ,  c icpendentanc  r ; r ngcs  f r : cn  50 I  i r  : , j l Í r  r i g i c  b . : . ; ' -  - . 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SI r  i s  - t ou i r . , j  c i r a ;  ; - ; r  t i : :  r ne rg ) /  r eg i - c r i  s i - u i i ec  r i t a  C i rec t  i n te rac t  j  onm e c h a n i s m  g o v e r n s  t i i e  e L - a s t i c  a l p l l a  i a ï t i . c t : e  s c a L c e r : i n g  a n d  t h ei n e l a s i i i :  s c a t l e r i r - r :  i o  l l i e  l o i ^ ' e s t  t ? x c i t e d  2 ' a n d  O *  s i a t e s , l f: i  l r .  - ' 4  +-  l i g ,  - -  l - t s  . r nC  - ' l i t.  0n l , ' u  L i i e  sc ; ; t r - e :  í . ng  f  o  che  J  i eve l  a t5 .22  r l l ev  an , l  L f i e  4 *  r eve I  a t  o .00  P le ' , r  r - n  2oo ,n .  anc  t o  t he  3 *  l eve Ia r -  6 , 2 1  M e V  a n < l  t i r e  4 u  l e v e l  a t  4 . 6 1 l l e V  i n  t u o i  a r e  e x c e p t i o n s :h e r e  t h e  s c , a r - t e r i n g  p r o c e e C s  a l - m o : :  e n r : - r e 1 . , '  b v  c o m p o u n d  n u c l e a rp r o c e s s e s .T h e  e x p e r i r n e n t a l  v a l u e s  c f  t h e  e f f e c c i v e  n u m b e r  o f  ï e a c t i o n  c h a n n e l sa g r e e  w e i i  i . r i t h  t h e c : : e i i c a i  c a i : u i a : i o n s  o f  i i ^ . " ,  g i v i n g  c o n i i c j e n c ei n  t h e  c o r l s i s t e n c y  o f  s h e  a n a r y s e s .I n  t h e  l a s i  s e c l i o n  o f  t h i s  c t r a p c e r  r r e  p r e s e n t  e v i d e n c e  f  o r  t h ep r e s e n c e  o f  i n r e r m e d i a t e  s E r u c t u r e s  i n  t h e  e x c i t a t i o n  f u n c t i o n s) 1 ,  , af  c r  t he  - - l ' Í 9+6 i ,  and  - "S i+c r  r eacc ions ,  us ing  t he  me thod  ou t l i nec li n  c h a p t e r  f i v e .  T h e s e  s t r u c t u r e s  h a v e  a  w i d t h  o f  a b o u t  4 O O  k e V  a n daye  f ound  i n  t t r e  bombard ing  ene rgy  reg ion  be tween  20  and  23  MeV.

Cross section fluctuations in alpha particle scattering by 24Mg, 26Mg and 28Si

https://pure.rug.nl/ws/files/14655268/Roeders_1971.PDF

Cross section fluctuations in alpha particle scattering by 24Mg, 26Mg and 28Si

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