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Coupling effects in the elastic scattering of $^{6}$He on $^{12}$C

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(1)Coupling effects in the elastic scattering of 6He on. 12. C. V. Lapoux, N. Alamanos, F. Auger, V. Fekou-Youmbi, A. Gillibert, F. Marie, S. Ottini-Hustache, J.-L. Sida, D.T. Khoa, Y. Blumenfeld, et al.. To cite this version: V. Lapoux, N. Alamanos, F. Auger, V. Fekou-Youmbi, A. Gillibert, et al.. Coupling effects in the elastic scattering of 6 He on 12 C. Physical Review C, American Physical Society, 2002, 66, pp.034608. �10.1103/PhysRevC.66.034608�. �in2p3-00011989�. HAL Id: in2p3-00011989 http://hal.in2p3.fr/in2p3-00011989 Submitted on 21 Dec 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(143) /" Q   " ! . , !  2   /"!"  !    !   ,    ; Q  N   . 

(144) .   . . ¼. 4.   = +. .

(145)   ¼. ¼. <44>. %" 3   <4?> ! " )!   ! /" " / !      "   ,  , ;. N <, ,    , , > . <45>. /"   " 6!+     ! . !    , " (      + , G9 4  .    %"  2   Q    ""  !    " !    (    ! !"   "   /  ! , D 6! "   . . !  "  ! !  "" + ! ; "  !  , ,  ! ( "    "    "      "   3  , !,  (     %" !  Q   "  ! ( "  ,   ( " !    ." Q  N

(146)  =   "  2   <

(147)     > "  !   !  /  ; N . = Q  N  <- :. I> =

(148)  = . /"   !       /  !  "  , ( !   "  ! !   / . " !  ( " Q   "  !        (      " "  (     7548

(149)  "   2 ( "  ( .   , " (!    ! +   /,     !!  6!+ , " $00 !   %" / "     , ( " !     /"  ""  , (     " !  !    "  "  T ! ( Q   D " ! (  ,  )!  !"     "     2 !  / "/    !!        ! , . " $00  "  (    75: CI8 D  /  " / " ( "  ,  )!  "  6! !   " $00    " (!  75? 5: B58 '  "   4I.

(150) ( !!!   /" + !  ! !"      !  (!   Q  N

(151)  =   /"   +   !      " (! 6! ! , "  2   7@ 5: B:8 D " / /  " " "  < +>   ,  ( Q  "+ "    " 

(152)  <> N 

(153)  / <>   <> N  / <> /".       / <> N  74 =  8 . . . . . <4:>. 

(154)   ? !"  ! ( ( " !  $00 "   !  , 7@8  "    , ( "  !   !       " "  + (!     "  ! ( "  !    /"!"    "  3  2   4 ( ( "  ,  )!  75? 5: CI B58 %"    ( "    !   6! (  "  ! !"   "  %"  ( " "   !  2   !     " !!! !" , !    " +  ( "    " (!  " .   , &"    1( 75:8 ( "  =- , %" $00  <

(155)     > / 3  + +  (

(156)  <>  <>  1 N IB ( !   "    " !!! ! . !2 !"  ! !   (  1( 7B58  / "+    !  /"  ,   ! !   "( / ! !   " $00  (  = - ,  (  /"!" /   ).  "   3  "  D   , / +  " "   ! ( ( "  = - $00 '"  !  '$:4  -$:I +       = - /"" " (      /" " !!  , <EF>  /" " "  <(!I>    /   ! DDD

(157)  -$:I " +    ( =-  /  /  "   , ( "  ! !  (       , " -$:I  ! 

(158)  " 3   !   /"    < N ?>     ,   !"  7B:8 % ("   "  +, ( "   "  !    / "+   N ?     ) " "

(159)  . 6   ( "   ( " $00   ( " .  ,    "   3

(160) +, (!,   /" "  <  4?> / !" /"    2.  (    .     $00 /"

(161)  N IC   N 4:: (   .  ,   + ,  N 4@   N 44: (   N ?I: ( %" / 4A.

(162) "+   " ! " 6! !  ( "  , $00   ! ,    !!  , " 3 .  ,     4? ! "  /" " / ! !  ! !    /" . /" " $00 <" "  "   !+ !+ ,> ."   2  "    /"  $00 "  3 /   /"   ,  !     N5?   N 44: (   N?I: ( +, !   "      ". ! (  =  -  ! !   :J: H !   %"    ( " ! !  /" "    ,   !  " " < > $00 .   "    = - (        . ! ( " " 3    " "   " .  /"!" "   !"+ ,      2 !  ( " (     %"  < >    !    " $00      44  !  " "    2   2 (       /" "   , ,

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

(164)  !   + " $   , ( 4CAB  ",     ! !,   !   " ! , " !   -  3. (      "  ( "   !  %" -  $!2 -   4J.

(165) -"   <-$--> "  "+  !!(  "/  "/ "  ( "  )!     . !  6! "  ! !   6   75?8 $ ( "  ! !  (    !    6    +  "  ,  !   , 3 "  ( "  ,   ( "   2   ( " /"         "  !  %" ( ( " $00 (  = - / "   ! ( " ( =- &.  

(166) '

(167)     (  ! "   .   .   " . # # $ ) ). *#  . 

(168)

(169) . +,+ &-.# . 0+ (     , 7CI8 ( ( "  =- , " !  ,  !. "  (   $00   .   " (     D 1( 7CI8 " (    / ! !  /" " '$:4   !  %"     ,    /" " (      !  " -$:I  !  / !    "  ! =-    4IB H !  7BC8 5I H !  7BB8 :B H !  7BI8  B: H !  7BA8 %"   , (    " (   ! !   ! !  !  75C8 ; " !"  , (    !. ( <> !  7BJ8  (  ( " 3  2 ( "    "   ,     "   "    %"    ( "   ,  .  " /,  5C: ( ."  ,  2    "  9      2 ( "  (      !! , !   "/   4: %"  2 (!  "  ( "  ,   !  (  %  D

(170)  " /  , ( @@  " 3  2 (!  ?BI  9 6  ( "  .  ""   %"    @@   "(   , ( "  ,   ( 4BIK:4J  ( /"!"   ( ,! "+ !  (  /" "   (! (  ?JB   6    ?I (

(171)  / " ! ( =- "  2 (! "  !"  /" "  ,   ( " ""   %" !   " (! " (   G 5I   6!  / ,  "  ,   !   ,  /   <G 4@.

(172)  5? >. ', 3   N ?JB   N ?I  4BIK:4J  < %  >  "  !" "  !    ( " .  ,     +  ?@?K?@A

(173)  @@  " 3 !" " +   +  ( "   ( "  ,  D  !     !  +  / !"  D +  "" 0 +   "   /" "  /  (!, %"    2 "   ( " !" ( "  ( "  ,     " + "  3 " /" " 3    +  %"  +     ! ( "   "/   4C D !   " "   2 !  ( "  (      Æ!   ! " ! !       <+ :?Æ !> /"!" !.  " (!+   G+ (  "  <        >  ( ,  .  " !" "       /  !  @@  4BI   "/   4:  "   2 !    + " " (!+ !    /"!"  +,  +  "  !        / "/  1( 7B@8 %"   " "   2 !  /"!"  ! "    " /"        +  !!       !   ! %"(   "    "  2    /"!"  ! " (       ,     CB (  "/  "   (     , , &"   7CI8 ( "  =-  D 1( 7CI8     " "     "  "  " ( " $00 D    , /   ( " $00 " (!  3   ! D  .   " (    ! !  /" -$:I . !"  3 " +  ( "     ,     /"  !    ,  "    /"!" "  " ( " (         +  ,  (! /  !     ( "  < > N  <?>5        9  5JB (  " +   " 3  " ! !    !    " $00 ( " (  (  %"  !   ( "  ,      3   +   . ( :4J   " +  )  <   > %" +  ( " 6   ( " $00      / ,     "  ,  !  3   +  ( ?@B %"  /   /" " " ( " .  ,   ( "   ( 4BI 54?  :4J  .  ) " " (

(174)          .   /" "    4B

(175) "      " ( " $00 5?.

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

(177)

(178)  .  ! "  /. . "+   ("    , ( "  !  = -    " .   ,   " " "  "     (  =- !

(179) "  / !" ( "  3  "       /" "   !    (  /" "   , ,  "  , ( " : ,   * </"!" "+ "     ( 5BC (>  ! /" "    4J . 4@ !+ ,   ( " $00   ( "  ,    +  "   DD %"   /" "       " ! /"   " ,  3  "     " 3   + , " (      .  , D( /   " " ( "  !        5?  54 ( " / ! / 3 " "     <  = 1Q  > "+  "   "  " (!  B (   ! /" "  =- . 54.

(180) = -   < " "! "         5?  54 >   !  " "  = -     !+  " (! <C  I (> /"!"  !  ,.   "    ( "    ,     " : ( " $00   ! " (      ,  , C? O  !     5? %" ! / "     /" "   " *  ,  ! "    , , " "   " !  D  ,  !  6!  !  " $00  " " , 

(181) " !    (!+ 6!     

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

(183) "  2       " =-    " "  6!   ! ! .    , !       2 ( "   U " $00     !! , ! " /"       ( " ! !  ."  !      ( ( " =-   = - ,  "   , " $00 / "/  6! "  !     ,  " (!     CB ( %"   /" " "!   + , + -  1! -"     D " /,   ,   +   " , " ( " $00 /"!" "  (  "  +  (  6!   ! !  (  , )!  0 ! ! !  (     " 5:Æ ! <  4J  4@>  6  (    6  , ( "    , /       + " ! !  "  / 4B  55Æ !    ! !        +   !  ( " (  ( 6  !  !    D "  (   ,   !!  "+   6       ( 5B  4?? H !     6       ,! ,  , " !    3 "     ( " $00  /   (   %"! ! !   ( " $00 , -  1! -"     /"  !!! ! ( "   !   " !     " !      ,  !  %" /    ( " ! !   + +   ! ( "     " 6!      !!    !  (  " ! ( "  !  "" "  , ( ! !"   /  , + " ! /   " "    " ( (! ( " !   /  " !   /    " !"   !   " !  . #01 )$/ . . "  $ D # %" ( +    /" "    ,    $

(184)   ( " ( !  %"  ! ( " 0G !/  "  ( "    ( , ! /      ( " " <$%&> /  ,. 5:.

(185)  

(186) ! G , -   ! ! - ! (  . 89: +#   

(187)                 .       .      * # ; # 2,3 "   9 < =# $# 1. 

(188) # 2,3 9

(189) >  9# 8: +#  ; # ,# = 425

(190) " 9?"@ < 

(191) # = 652 @? 9?""# 8

(192) : ;# )# !   =# A  B  # ,# 7 > ? 9?"C# 8>: D# E  F# D  D# 1 .  * # ; # 37+ C 9??# 8@: $# %# G - =# %#  # %# H- A# $# =  A# (   A# 1# %  ; # 6# 434 ?? 9??

(193) # 8I: +#  # ! # F  1# 1(  F# 1 (  !#  ; # ,# =. 6,8 I9 9??# 8C: )# # .-   ; # 6-# , 9, 

(194) 9

(195) 9??C# 8": # # F -   * # ; # 249 >@ 9??C 8?: %# ,.   ; # ,# = 349 9"  9#. 89 : 6# 0    ; # ,# = 729 " 9???# 899: #  (  # ; # 6-# ' 38 9@ 9???# 89: # ,    ; # ,# = 34, C  9# 89

(196) : ,# %# ' - =# %#  %# # B  # # F -  $# %# G - B  # , , >@ 9?"?# 89>: =# %#  +# A# (  $# %# G - A# 1# %   A# $# =  ; # ,# =. +++ ?? 9??> < 1# *# B - # 6  =# %#  A# 1# %  +# A# (   H# # )- ; # 6-# ' 32 9>"

(197)  9??C# 89@: B# *  # %# H- # 1# A   B# ) ; # 6# +79

(198) C

(199)  9# 89I: =# 1# ;  %# 6# ; A# '  1# '# ;  6# =# 0  ; # 6-# ' 32 9C 9??C < 1# '# ; %# 6# ; 6# =# 0   A# '  

(200) # ' 27 9> 9  9# 89C: A# 1# /F A# #  - ; # 6-# ' 39 9">I 9??"# 89": A# #  -  A# 1# /F * # ; 242 >9" 9??C# 89?: !# H  # ; # 3

(201) @C 9?@" !       "# $ % & '(()#. 5C.

(202) 8 : D# 1   ; # 6- ' +3 9I9 9?"C# 89: $# B# =  )# 6# 1 ; # 6# 6,3 9>

(203) 9??C# 8: F#  D# 1 .   6# )# ,-  ; # 6-# ' 38 9>

(204)  9???# 8

(205) : # # F )# 6# 1  0# - E. ; # ,# = +3, 9> 9??@# 8>: )# 6# 1  0# )# ,- ; # 6# 33 9"

(206) 9?C?# 8@: A# 1# /F   ; # ,# = +9, >@ 9??I# 8I: A# A# F   ; # 6-# ,# 28 I

(207) 9 9??# 8C: # # F )# 6# 1  0# - E. ; # 6-# ' 32 ?@> 9??C# 8": ,# =   *+$  692 9?"? @ ?/@ # 8?: # A    ;  ' +BBB % 9 9??9 @?># 8

(208) : A# ,# =   * -  )*+,. . >> J -# 9??

(209) #. 8

(210) 9: $# $ '(    )*+, 8,56 9??"# 8

(211) : # # F ; # 6-# ' 2+

(212) > C  9# 8

(213)

(214) : =# 1 ; # 6# 65 9 9?C@< =# 1  1# # $ .  ; # ,# ,4% "? 9?C?# 8

(215) >: *# ( !#   )# H# =  * # ; # +8, I? 9?"

(216) # 8

(217) @: )# 6# 1  *  6  E  K-# ; # E  9?"

(218) # 8

(219) I: $# B# =  F# 0# $ % ; # 6-# ' 33 9

(220) I 9??C# 8

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