Role of thermal fluctuations in the damping of the giant dipole resonance of spherical and deformed nuclei: 90Zr and 164Er
Abstract
We study the damping width of the giant dipole resonance (GDR) built on the ground state and on excited states of 90Zr, which is spherical at zero spin and temperature, and 164Er which is deformed. Neither of these nuclei changes appreciably their equilibrium shape when excited. Nonetheless, fluctuations due to finite temperature produce a marked increase in the width of the GDR of 90Zr, leaving essentially unchanged that of 164Er. This is because in the case of deformed nuclei thermal fluctuations imply the sampling of both larger and smaller deformations around the equilibrium shape, while spherical nuclei can only feel larger distortions. In spite of the stability of the GDR of 164Er, the angular distribution of the associated γ-rays is strongly affected by the temperature.
Full text
V01ume 191, num6e 3 PHY51C5 LE77ER5 8 11 June 1987
R0LE 0F 7HERMAL FLUC7UA710N5 1N 7HE DAMP1N6
0F 7HE 61AN7 D1P0LE RE50NANCE 0F 5PHER1CAL AND DEF0RMED NUCLE1:
9°2 AND 1~4E ~"
M. 6ALLARD0, F.J. LU15
Depa amen 0 de F151ca A 6m1ca y Nuc1ea , Facu1 ad de F151ca, Un1 e 51dad de 5e 111a, Apa ad0 1065, E-41080 5e 111a, 5pa1n
and
R.A.
8R06L1A
D1pa 1men 0 d1F151ca, Un1 e 51 a d1M11an0 and 1NFN 5e210ne d1M11an0, V1a Ce10 1a 16, 1-20133 M11an, 1 a1y
and N1e15 80h 1n5 1 u e, Un1 e 51 y 0 C0penha9en, 81e9dam5 ej 17, DK-2100 C0penha9en 0, Denma k
Rece1 ed 21 Janua y 1987; Re 15ed manu5c 1p ece1 ed 25 Ma ch 1987
we 5 udy he damp1n9 w1d h 0 he 91an d1p01e e50nance (6DR) 6u11 0n he 9 0und 5 a e and 0n exc1 ed 5 a e5 0 9°2 , wh1ch
15 5phe 1ca1 a 2e 0 5p1n and empe a u e, and 164EE wh1ch 15 de 0 med. Ne1 he 0 he5e nuc1e1 chan9e5 app ec1a61y he1 e4u1116-
1um 5hape when exc1 ed. N0ne he1e55, 1uc ua 10n5 due 0 1n1 e empe a u e p 0duce a ma ked 1nc ea5e 1n he w1d h 0 he 6DR
0 9°2 , 1ea 1n9 e55en 1a11y unchan9ed ha 0 ~64E . 7h1515 6ecau5e 1n he ca5e 0 de 0 med nuc1e1 he ma1 1uc ua 10n51mp1y he
5amp11n9 0 60 h 1a 9e and 5ma11e de 0 ma 10n5 a 0und he e4u1116 1um 5hape, wh11e 5phe 1ca1 nuc1e1 can 0n1y ee11a 9e d15 0 -
10n5. 1n 5p1 e 0 he 5 a6111 y 0 he 6DR 0 ~64E , he an9u1a d15 16u 10n 0 he a550c1a ed y- ay5 15 5 0n91y a ec ed 6y he
empe a u e.
A ecen c0mp11a 10n 0 he p 0pe 1e5 [ 1 ] 0 he
6DR can 6e 0und 1n e . [2]. F19. 17 0 h15 e -
e ence d15p1ay5 he 065e ed w1d h (FWHM) 0 he
a550c1a ed 5 en9 h unc 10n5 6a5ed 0n he 9 0und
5 a e and 0n exc1 ed 5 a e5 0 a num6e 0 nuc1e1, a5
a unc 10n 0 he ma55 num6e 1n he an9e
40~<A~< 160. A E*=0 he da a d15p1ay5 a ma ked
5 uc u e. 7he m1n1ma (F = 4 MeV) c0 e5p0nd 0
c105ed 5he11 nuc1e1 wh11e he max1ma (F < 8 MeV)
a e a550c1a ed w1 h de 0 med nuc1e1. 7h15 5 uc u e
15 wa5hed 0u 1n he ca5e 0 91an e50nance5 6u11 0n
exc1 ed 5 a e5. 1n ac , he da a 5h0w5 a un1 0 m a1ue
a 0und F = 8 MeV, 1mp1y1n9 ha he 6DR 0 nuc1e1
ha a e 5phe 1ca1 1n he 9 0und 5 a e ha e 6ec0me
c0n51de a61y 6 0ade , wh11e h05e c0 e5p0nd1n9 0
we11-de 0 med nuc1e1 ema1n app 0x1ma e1y
unchan9ed.
7h15 w0 k 15 pa 1a11y 5upp0 ed 6y he cA1cY7 (5pa1n) unde
c0n ac num6e 2868/83 and 6y a 9 an 0 he C0mmem0 -
1 e A550c1a 10n 0 he Japan W0 1d Exp051 10n.
7he ma1n mechan15m e5p0n5161e 0 he damP1n9
0 91an e50nance5 1n med1um and hea y nuc1e1
a 15e5 0m he c0up11n9 0 10w-1y1n9 5u ace 05c11-
1a 10n5 [ 3 ]. A 5 a 1c 4uad up01e de 0 ma 10n a5 0ne
11m1 0 h15 mechan15m (ad1a6a 1c 11m1 ), p 0duce5
a 6 eak1n9 0 he 91an d1p01e e50nance and hu5 a
6 0aden1n9 0 he a550c1a ed d15 16u 10n [ 4 ].
An9u1a m0men um (1~< 50h) 1ead5, a5 a u1e, 0
he de 0 ma 10n 0 5phe 1ca1 nuc1e1, w1 h0u e55en-
1a11y chan91n9 he 5hape 0 we11-de 0 med nuc1e1
[ 5-7 ]. 1 15 hu5 emp 1n9 0 c0nc1ude ha h15 15 he
ea50n why he 5 en9 h unc 10n 0 6DR 065e ed
1n he •/-decay 0 c0mp0und nuc1e1 ha e a c0n5 an
w1d h a5 a unc 10n 0 ma55 num6e .
1n he p e5en pape we check h15 c0njec u e 6y
5 udy1n9 he ph0 0a650 p 10n c 055 5ec 10n 0 w0
ex eme ca5e5 1n he c0mp11a 10n 0 e . [2]: 9°2 ,
5phe 1ca1 1n he 9 0und 5 a e and 164E , wh1ch 15 we11
de 0 med. We c0mpa e he d15 16u 10n 0 he d1p01e
5 en9 h 6a5ed 0n he 9 0und 5 a e and 0n he c0m-
222 0370-2693/87/$ 03.50 • E15e 1e 5c1ence Pu6115he 5 8.V.
(N0 h-H011and Phy51c5 Pu6115h1n9 D1 1510n)
V01ume 191, num6e 3 PHY51C5 LE77ER5 8 11 June 1987
p0und nuc1eu5 5 a e, de 1ned 6y he expe 1men a1
c0nd1 10n5
9°2 : 7=0,1=0 and 7=1.5MeV, 1=7.5h,
264E : 7--0,1=0 and 7=1.2 MeV, 1=21 h.
(1)
7he ca1cu1a 10n5 we e ca 1ed 0u a5 1n e . [8]. A
c anked N11550n p0 en 1a1, w1 h he pa ame e 5 aken
0m e . [6] 0 9°2 and 0m e . [9] 0 164E , 15
u5ed a5 he 51n91e-pa 1c1e 1e1d. F0
9°2
he5e
pa ame e 5 91 e a a1 d1p01e e5p0n5e a E* = 0 whe e
m05 0 he 5 en9 h 15 c0ncen a ed 1n 0ne peak a5
expe 1men a11y 065e ed. 0n he 0 he hand, a11 he
5e 5 0 pa ame e 5 we u5ed 0 164E y1e1d an an0m-
a10u5 d1p01e 5 en9 h 5p11 1n9 a 10w ene 91e5 ~. 7he
5e 91 en 1n e . [ 9 ] 15 1n any ca5e he 6e5 0ne a a11-
a61e a p e5en 0 h15 ma55 e910n.
Pa1 1n9 15 n0 1nc1uded 1n he ca1cu1a 10n5. A he
empe a u e5 0 1n e e5 1 5 e ec 15 expec ed 0 6e
5ma11 [ 10]. F0 n0n-2e 0 empe a u e5, he 0ccu-
pa 10n pa ame e 5 0 he 51n91e-pa 1c1e 1e e15 a e
91 en 6y he Fe m1 d15 16u 10n [ 11 ]. 7he e51dua1
1n e ac 10n 15 app 0x1ma ed 6y a 5epa a61e
d1p01e-d1p01e 0 ce. 7he c0up11n9 5 en9 h5 a e ch0-
5en 0 1 he expe 1men a1 ene 9y cen 01d5 0 he
6DR a 7=0, 1=0
(x/x5c=0.765,
0.697 0 ~64E
and
9°2 ,
whe e he 5e1 -c0n515 en a1ue5 [4] a e
x5c=0.102, 0.274 MeV/ m :, e5pec 1 e1y).
7he d1p01e c 055 5ec 10n 1n he 1a60 a 0 y ame c
15 ca1cu1a ed 1n he 11nea e5p0n5e he0 y [ 12,13]
(c . a150 e . [ 8 ] and n0 e an e 0 0 a m1551n9 ac 0
1/3 1n e45. (12) and (15)). 7he ma1 1uc ua 10n5 0
he nuc1ea 5hape a e 1nc1uded 1n he ca1cu1a 10n5.
7hu5 he 0 a1 c 055 5ec 10n 15 w 1 en a5 [ 8]
( a(1,7) ) ;
e de d7 P(e, 7; 1, 7)a(e, 7; 1, 7)
e de dy P(e, y; 1, 7)
whe e
P(e, y; 1, 7) ~exp[
-F(e, 7; 1, 7)/7].
(2)
(3)
~J we n0 e ha he unpe u 6ed d1p01e e5p0n5e 1n he 9 0und
5 a e need5 0 6e 5 ud1ed m0 e ca e u11y. A11 he ea115 1c 51n91e-
pan1c1e p0 en 1a15 91 e, 1n 9ene a1, a 6ad de5c 1p 10n 0 1 .
7he 4uan 1 y F(e, y; 1, 7) 15 he ee ene 9y 0 a 91 en
empe a u e 7, 5p1n 1 and de 0 ma 10n pa ame e 5
(e, 2:). N0 hexadeCap01e de 0 ma 10n5 a e c0n51d-
e ed. 7he ee ene 9y 5u ace5 F a e ca1cu1a ed w1 h
he 5 u 1n5ky me h0d [ 7]. F19. 1 5h0w5 he5e 5u -
ace5 0 he w0 nuc1e1 unde 5 udy and 0 he a1-
ue5 0 7 and 1 d15p1ayed 1n (1). 7he e4u1116 1um
de 0 ma 10n5 ema1n 1n 60 h ca5e5 e55en 1a11y
unchan9ed. C0n5e4uen 1y, he 065e ed 6 0aden1n9
0 he 6DR 1n 9°2 15 n0 due 0 a chan9e 1n 5hape,
a5 wa5 he ca5e 1n 1°85n [8], 6u mu5 a 15e 0m he
5amp11n9 0 1n1 e d15 0 10n5 unde he 1n 1uence 0
he ma1 1uc ua 10n5.
F0 5y5 em5 wh1ch d15p1ay n0n-5phe 1ca1 e4u1116-
1um 5hape5 a 7,1# 0 11ke 164E , he 01e 0 he 5hape
1uc ua 10n515 n0 50 1mp0 an . 7he he ma1 en5em-
61e 1nc1ude5, w1 h 51m11a we19h 5, 60 h 5ma11e and
1a 9e de 0 ma 10n5 han he 0ne a550c1a ed w1 h
e4u1116 1um, he 5ummed e ec 6e1n9 5ma11.
7h15 p1c u e 15 60 ne 0u 6y he e5u1 5 0 he ca1-
cu1a 10n5 d15p1ayed 1n 19. 2.7he e 15 a 519n1 1can
1nc ea5e 1n he w1d h 0 he 6DR 0 9°2 w1 h exc1-
a 10n ene 9y. 0n he 0 he hand, he d1p01e 5 en9 h
0 ~64E d15p1ay5 w0 peak5 and hu5 a 512ea61e w1d h
a 7= 1= 0. 7h15 15 6ecau5e 164E ha5 a 5 a61e de 0 -
ma 10n (e=0.26, y=0 °) 1n he 9 0und 5 a e. A
7= 1.2 MeV and 1=21 h, 60 h peak5 6ec0me 50me-
wha 6 0ade due 0 he a e a91n9 e ec 0 he ma1
1uc ua 10n5. 7he 0 a1 w1d h 15, h0we e , 11 1e
a ec ed 6e1n9 5 111 c0n 011ed 6y he 5epa a 10n
6e ween he peak5 and e 1ec 1n9 he m05 p 06a61e
5 a 1c de 0 ma 10n (e = 0.19, y = 0 ° ).
Ca1cu1a 10n5 0 he 6DR u51n9 a pu e ha m0n1c
05c111a 0 p0 en 1a1 a5 he 51n91e-pa 1c1e ham11 0n1an
[14] a e 5h0wn 1n 19. 3.7he a550c1a ed e5u1 5 d0
n0 d15p1ay Landau damP1n9. C0n5e4uen 1y, he
e ec 5 0 0 a 10n and empe a u e appea c1ea e 1n
h15 51mp1e m0de1.
70 06 a1n a a1 de5c 1p 10n 0 he 6DR 1n he
9 0und 5 a e, he e5u1 5 0 he ca1cu1a 10n5 we e
01ded 6y a 10 en 21an unc 10n w1 h an emp1 1ca1
ene 9y dependen w1d h ~2 [ 15 ]
:2 8ecau5e 0 he 5 0n9 Landau damp1n9 p e5en 1n he ca1cu1a-
10n5 w1 h he N11550n p0 en 1a1, he 01d1n9 p 0cedu e w111 n0
1mp 0 e he e5u1 5. 7he e 0 e we ha e n0 pe 0 med 1 1n ha
ca5e.
223
V01ume 191, num6e 3 PHY51C5 LE77ER5 8 11 June 1987
60*
a 970~ 0 MeV 0~k~hk ~
/ 2(111(4 •,00
C 161~E
7:0M 0y)
/•60*
/50*
/40*
•1-30*
20*
10*
"••-•" 0*
1"
/ 60*
04~ /50*
/60•
0.4~ /50~
-10
---~00
Y
F19. 1.5 u 1n5ky ee ene 9y 5u ace5 a5 unc 10n 0 he de 0 ma 10n pa ame e 5 0 9°2 a 7=1=0 (a) and a 7= 1.5 MeV, 1=7.5 h
(6) and L64E a 7=1=0 (c) and 7= 1.2 MeV, 1= 21 h (d). 7he e4u1p0 en 1a111ne5 a e ep e5en ed 1n 5 ep5 0 0.5 MeV away 0m he
m1n1mum wh1ch 15 den0 ed 6y a u11 d0 .
6
10
06
02
06
02
902 6
5 75 25 5 15 25
E (MeV)
F19. 2. Ph0 0a650 p 10n c 055 5ec 10n 1n he 1a60 a 0 y 5y5 em 0
he 6DR 0 9°2 and 164E a he c0nd1 10n5 91 en 1n (1). A
c anked N11550n p0 en 1a1 15 u5ed a5 he 51n91e-pa 1c1e ham11 0n-
1an. 0 7# 0 he 0 a1 c 055 5ec 10n 15 ca1cu1a ed acc0 d1n9 0 e0.
(2).
F=F0(E/Ec) 1"9 •
(4)
7he 4uan 1 y F015 ch05en 0 1 he expe 1men a1 da a
a 7=1=0, wh11e Ec 15 he ene 9y cen 01d 0 he
d1p01e 5 en9 h d15 16u 10n. 7he5e pa ame e 5 a e
kep 1xed h 0u9h0u he ca1cu1a 10n5.7h15 15 50me-
wha e4u1 a1en 0 a55um1n9 ha he e ec 0 he
c0up11n9 0 2p-2h 5 a e5 0 he 91an 16 a 10n d0e5
n0 chan9e ne1 he w1 h empe a u e [ 16 ] n0 w1 h
5p1n.
1n 195. 3a, 36 and 3d, 3e we c0mpa e he 6DR
6u11 0n he e4u1116 1um de 0 ma 10n a 2e 0 and n0n-
2e 0 exc1 a 10n ene 91e5.7he he ma1 5hape 1uc ua-
10n5 a e 1nc1uded 1n he e5u1 5 ep0 ed 1n 195. 3c
and 3 0 9°2 and 164E , e5pec 1 e1y. A e5ume 0
he d1 e en w1d h5 15 c011ec ed 1n a61e 1.
51m11a c0mmen 5 0 h05e made 1n c0nnec 10n
224
V01ume 191, num6e 3 PHY51C5 LE77ER5 8 11 June 1987
0.4
0,2
0
6- 04
0.2
F: 0 ° ~
5 15 25 5 15 25 5 15 25
E(MeV)
a2
02
01
-01
-0.2
.....
91
16/~ E 7 =1.2 MeV, 1 =21 ~
w1 h0u 1uc .----
w1 h ....
5 1L0 1•5 2J0 25
E (Me•C)
F19. 3. Ph0 0a650 p 10n c 055 5ec 10n 0 he 6DR 1n he 1a60 a-
0 y 5y5 em ca1cu1a ed w1 h he ha m0n1c 05c111a 0 m0de1. (a)
and (d) 5h0w he 6DR 6a5ed 1n he 9.5.0 9°2 and 164E . 1n (6)
and (e) he 6DR 15 6u11 0n he e4u1116 1um de 0 ma 10n a550-
c1a ed w1 h he exc1 ed 5 a e5 7= 1.5 MeV, 1=7.5 h 0 9°2 and
7= 1.2 MeV, 1=21 h 0 J64E . 7he e ec 0 he 5hape 1uc ua-
10n5 can 6e n0 ed 1n (c) and ( ) wh1ch 5h0w he a e a9e c 055
5ec 10n (e4. (2)) 0 he ca5e5 91 en 6e 0 e. (9) ep e5en 5 he
an9u1a d15 16u 10n 0 J64E a 1= 21 h, 7= 1.2 MeV a550c1a ed
0 he e4u1116 1um de 0 ma 10n ( h1n 11ne) and he 0ne ca1cu-
1a ed c0n51de 1n9 5hape 1uc ua 10n5 ( h1ck 11ne). (A5 1 15 e y
we11 kn0wn, he c0e 1c1en a2 15 e1a ed w1 h he an9u1a d15 1-
6u 10n,
W(0),
0 he 7- ay5 a 151n9 0m d1p01e decay e1a 1 e 0
he 6eam ax15, 6y
W( 0) 0c 1 + a2P2( c05( 0) ). )
7a61e 1
Damp1n9 w1d h (FWHM) 0 a a 1e y 0 91an d1p01e e50nance5. 1n c01umn5 4 and 5 he a 105 6e ween he w1d h F 0 he 6DR
e5p0n5e unc 10n 6a5ed 0n a 5 a e w1 h empe a u e 7 and an9u1a m0men um 1 and 0n he 9 0und 5 a e a e ep0 ed (c . 19. 3). 7he
ca1cu1a 10n5 0 he ca5e 0 m85n we e ca 1ed 0u 01d1n9 he a550c1a e d1p01e e5p0n5e unc 10n aken 0m e . [ 8 ] w1 h a 10 en 21an
unc 10n 0 w1d h P = 5 MeV wh1ch 15 a55umed 0 51mu1a e he c0up11n9 0 2p-2h 5 a e5. 1n he 1a5 w0 c01umn5 he w1d h F(0) 0 he
6DR e5p0n5e unc 10n 6a5ed 0n he 9 0und 5 a e 15 5h0wn. 7he ca1cu1a 10n5 0 9°2 and 2°85n a e 06 a1ned e11m1na 1n9 he e ec due
0 Landau damp1n9 0 he e5u1 0 e1". [ 3]. whe e he c0up11n9 0 he 91an 16 a 10n 0 2p-2h 5 a e5 c0n a1n1n9 a 5u ace 16 a 10n 15
c0n51de ed. 7he w1d h 0 he 6DR 0 ~64E e5u1 5 0m he c0n 01u 10n 0 he 5 en9 h unc 10n e5u1 1n9 0m he ca1cu1a 10n 0 he
16 a 10n 1n he de 0 med p0 en 1a1 ( ¢ = 0.2 6 ) and a 10 en 21an w1d h
F = F 0 ( E/Ec ) (
c . he ex 0 m0 e de a115 ).
Nuc1eu5 7 (Me )
1 (h) F(E*)/F(0)
F(0)(MeV)
expe 1men he0 y expe 1men he0 y
90 2 1.5 7.5 2 1.4 4 4.6
1°85n 2 60 2.1 1.9 5 5
J64E 1.2 21 1 0.9 8.2 7
225
01ume 191, num6e 3 PHY51c5 LE77ER5 8 11 June 1987
w1 h 19. 2 a150 app1y he e. 70 6e added 15 ha e en
1 he a650 p 10n c 055 5ec 10n5 0 64E when he -
ma1 1uc ua 10n5 a e n0 1nc1uded ( 19. 3e) and when
hey a e 1nc1uded ( 19. 3 ) a e e y 51m11a , he ),-
decay an9u1a d15 16u 10n 5h0w5 a p 0 0und chan9e
1n he 1a5 ca5e. 7h15 15 appa en 1n 19. 39 whe e he
c0e 1c1en a2 15 p10 ed. 1 15 ca1cu1a ed 0m he
exp e5510n
a2 = 1 ( 3a10/ -
1 ) (5)
whe e 7 15 he 0 a1 d1p01e a650 p 10n c 055 5ec 10n
and 7~0 he 0ne a550c1a ed w1 h he d1p01e an51-
10n5 ca Y1n9 n0 an9u1a m0men um w1 h e5pec 0
he ax15 0 0 a 10n (a55um1n9 0 a1 5p1n 1>> 1h).
7he he ma1 a e a9ed e5u1 ( h1ck 11ne 0 19, 39),
ca1cu1a ed 0m he c0 e5p0nd1n9 d1p01e c 055 5ec-
10n, d15p1ay5 0 e a11 a9 eemen w1 h he expe 1men-
a1 da a [17]. 1 1mp11e5 a d1m1nu 10n 0 he
an150 0py w1 h e5pec 0 he ca5e w1 h n0 1uc ua-
10n5 ( h1n 11ne), a1 h0u9h a p 01a e 5hape 0 he
nuc1eu5 can 5 1116e 5u99e5 ed. 1 1511ke1y ha he 5 udy
0 he •/- ay an9u1a d15 16u 10n5 15 he 5pec1 1c 001
0 1ea n a60u he 5u ace he ma1 1uc ua 10n5 0 he
c0mp0und nuc1eu5 [ 18 ].
We c0nc1ude ha he ma ked a 1a 10n5 0 he
w1d h 0 6DR ec0 ded a5 a unc 10n 0 empe a u e
and an9u1a m0men um a e due 0 chan9e5 1n de 0 -
ma 10n and/0 0 he ma1 5hape 1uc ua 10n5. 7he
e ec 0 he C0 10115 0 ce 15 n0 0und 0 6e 1mp0 -
an . F 0m he kn0w1ed9e 0 he ee ene 9y 5u ace5
a5 a unc 10n 0 /and 71 5eem5 hu5 p055161e 0 1n e
he a550c1a ed e 01u 10n 0 he ph0 0a650 p 10n c 055
5ec 10n.
Re e ence5
[ 1 ] J.E.D ape e a1., Phy5. Re . Le . 49 (1982) 434;
J. 8a e e and A.M. 5and0 1, C0mm. Nuc1. Pa . Phy5. 12
(1983) 57;
8. Haa5 e a1., Phy5. Le . 8 120 (1983) 79;
W. Henne 1c1 e a1., Nuc1. Phy5. A 396 (1983) 329;
A.M. 5and0 1 e a1., Phy5. Le . 8 130 (1983) 19;
L. La22a 1n1 e a1., Phy5. Re . Le . 53 (1984) 1045;
J.J. 6aa dh0je e a1., Phy5. Le . 8 139 (1984) 273;
J.J. 6aa dh~je e a1., Phy5. Re . Le . 53 (1984) 148;
D. 5chwa1m e a1., F 0n 1e 51n nuc1ea dynam1c5, ed5. R.A.
8 0911a and C.H. Da550 (P1enum, New Y0 k, 1985) p. 33.
C.A. 6055e e a1., Phy5. Re . Le . 54 (1985) 1486;
7h.
A c aed1u5 e a1., Phy5. Le . 8 158 (1985) 205;
J.J. 6aa dh0je e a1., Nuc1ea 5 uc u e 1985, ed5. R.A.
8 0911a, 6. Ha9emann and 8. He 5k1nd (N0 h-H011and,
Am5 e dam, 1985) p. 519.
[2] K.A. 5n0 e , Annu. Re . Nuc1. Pa . 5c1.36 (1986) 1.
[3] P.F. 80 19n0n and R.A. 8 0911a, Nuc1. Phy5. A 371 (1981)
405;
6.F. 8e 5ch, P.F. 80 19n0n and R.A. 8 0911a, Re . M0d.
Phy5. 55 (1983) 287.
[4] A. 80h and 8. M0 e150n, Nuc1ea 5 uc u e, 01 11 (8en-
jam1n, New Y0 k, 1985).
[5] 6. Ande 550n, 5.E. La 550n, 6. Leande , P. M011e , 5.6.
N11550n, 1. Ra9na 550n, 5. A6e 9, R. 8en9 550n, J. Dudek,
8. Ne 10-P0m0 5ka, K. P0m0 5ky and 2. 52yman5k1, Nuc1.
Phy5. A 268 (1976) 205.
[6] 5. A6e 9, Phy5. 5c . 25 (1982) 113.
[7] M. D1e6e1, K. A16 ech and R.W. Ha55e, Nuc1. Phy5. A 355
(1981) 165.
[ 8 ] M. 6a11a d0, M. D1e6e1, 7. D0551n9 and R.A. 8 0911a, Nuc1.
Phy5. A 443 (1985) 415.
[9] R. 8en9 550n and 1. Ra9na 550n, Nuc1. Phy5. A 436 (1985)
14.
[ 10] 0. C1 1 a e5e, 6.6. Du55e1 and R.P.J. Pe a220, Nuc1. Phy5.
A404 (1983) 15.
P. R1n9, J. Phy5. (Pa 15) C6, 5upp1. 6, . 45 (1984) 247.
[ 11] A. 80h and 8. M0 e150n, Nuc1ea 5 uc u e, V01.1 (8en-
jam1n, New Y0 k, 1968);
C. F101ha15 and J. da P 0 1denc1a, Nuc1. Phy5. A 435 (1985)
190.
[ 12] J.L. E91d0 and P. R1n9, Phy5. Re . C 25 (1982) 3239; Nuc1.
Phy5. A 388 (1982) 191;
J.L. E91d0, H.J. Man9 andP. R1n9, Nuc1. Phy5. A 339 (1980)
390;
P. R1n9, L.M. R061ed0, J.L. E91d0 and M. Fa6e , Nuc1. Phy5.
A 419 (1984) 261;
P. R1n9, Nuc1. Phy5. A 421 (1984) 205.
[ 13] M. Fa6e , J.L. E91d0 and P. R1n9, Phy5. Le 8 127 (1983)
5, and e e ence5 he e1n.
[ 14] K. Nee 9a d, Phy5. Le . 8 110 (1982) 7.
[ 15 ] P. Ca 105, R. 8e 9e e, A. 8e11, A. Lape e and A. Vey551e e,
Nuc1. Phy5. A 219 (1974) 61;
K.A, 5n0 e , p 1 a e c0mmun1ca 10n.
[ 16] P.F. 80 19n0n, R.A. 8 0911a, 6,F. 8e 5ch and J. Pachec0,
Nuc1. Phy5. A 460 (1986) 149.
[ 17 ] J.A. 8eh , 6. Fe1dman, C.A. 6055e , J.H. 6und1ach and K.A.
5n0 e , Annua1 ep0 , Un1 e 51 y 0 Wa5h1n9 0n ( 1985 ).
[ 18] A. 8 acc0, M. 6a11a d0, J.J. 6aa dh0je and R.A. 8 0911a, 0
6e pu6115hed;
M. 6a11a d0 and R.A. 8 0911a, 0 6e pu6115hed.
226