Permisos de usuarios

&

2 . 0 0

150

160

beam e n e r g y (MeV)

Figure 4.25 The sim ultaneous fits to the 28Si + 170E r —> 198Pb pre-scission neutron m ultiplicities of [HIN86] and the proton and alp h a particle m ultiplicities from the p rese n t study, with no ad ju stm en t of the alpha particle tran sm issio n coefficients, X d = 1 2 x l 0 - 21 s and xss= 6 0 x l0 -21 s

(dashed curves); and a 1 MeV shift in the alpha particle transm ission coefficients to lower energies, Xd=0 and xss=80xl0-21 s (solid curves).

85

S im ila r calcu latio n s w ere also perform ed for th e 28Si + l67,l70Er -> I95,l98pfc> reactio n s. T he b e st sim u ltan eo u s fits to th e 28Si + 170E r - > 198Pb pre-scission n e u tro n , p ro to n an d a lp h a p a rticle m u ltip lic ities w ith (a) no a d ju s tm e n t of th e a lp h a p a rtic le tra n s m iss io n coefficients, Xd=12xl0-21 s a n d tSs= 6 0x1 0 - 2 1 s an d (b) a 1 MeV a d ju s tm e n t of th e a lp h a p a rticle

tra n s m is s io n coefficients to low er energies, Td=0 an d xss= 8 0 x l0 -21 s are

show n in fig u re 4.25. T he m e a su re d 28Si + 167E r - > 195P b p re-scissio n p ro to n a n d a lp h a p a rtic le m u ltip lic itie s (no n e u tr o n m e a s u re m e n ts p re s e n tly exist) a re com pared to sta tistic a l model calcu latio n s w ith (a) no a d ju s tm e n t of th e a lp h a p a rtic le tra n s m iss io n coefficients, X d=12xl0-21 s an d tss= 5 5x1 0 -21 s a n d (b) a 1 MeV a d ju s tm e n t of th e a lp h a p a rticle

tra n s m is s io n coefficients to low er en erg ies, Td=0 an d xss= 8 0 x l0 -21 s are

show n in figure 4.26. T he m ea n a lp h a p article en erg ies, p red icted by th e c a lc u la tio n s sh o w n in fig u re s 4.25 a n d 4.26, a re co m p ared to th e ir ex p erim en tal v alu es in figure 4.27.

T he sta tis tic a l m odel calculations, w ith th e 1 MeV sh ift in th e alp h a p a rtic le tr a n s m is s io n co efficien ts, te n d to u n d e r- e s tim a te th e m e a n e n erg ies of th e p re-scissio n a lp h a p a rtic le s by < 0.5 MeV, w hile th e c a lc u la tio n s w ith no a d ju s tm e n t of th e a lp h a p a rtic le tr a n s m is s io n coefficients o v er-estim ate th e m ean pre-scission a lp h a p a rticle en erg ies by ~1 MeV. T his su g g ests th e tru e v alu es of th e p re-sad d le delay tim e Td and th e sa d d le-to -sc issio n tim e xss, a re so m ew h ere b e tw e e n th o se v a lu e s o b tain ed u sin g th e calcu latio n s w ith an d w ith o u t th e 1 MeV sh ift in th e a lp h a p a rtic le tr a n s m is s io n coefficients. T he a n a ly s is p re s e n te d h e re in d icates t h a t for 28Si + E r - > P b fusion-fission rea ctio n s Td < lO xlO -21 s,

tss=(70±20)x10-21 s a n d for b eam energies > 155 MeV m o st of th e p re ­

scission p a rtic le s a re e m itte d by th e com pound nuclei d u rin g th e ir tr a n s it from saddle to scission. A lthough th e calculations show n in figures 4.24 to 4.26, q u a lita tiv e ly re p ro d u c e th e o v e ra ll tr e n d s in th e p re -sc issio n

ä 0 .0 4

b e a m e n e r g y (MeV)

F ig u re 4.26 T h e e x p e rim e n ta l 2®Si + 167E r —> 195Pb p re -s c iss io n p ro to n an d a lp h a p a rtic le m u ltip lic itie s a n d s ta tis tic a l m odel c a lc u la tio n s w ith no a d j u s t m e n t o f th e a lp h a p a r t i c l e t r a n s m i s s io n c o e ffic ie n ts , T d=12xl0-21 s a n d xss= 5 5 x l0 -21 s (d ash ed curves); an d a 1 MeV sh ift in the a lp h a p a rtic le tr a n s m is s io n co efficien ts to lo w er e n e rg ie s , Td=0 a n d

86

Er ->

Er ->

beam energy (MeV)

Figure 4.27 The experim ental m ean energies of the 28Si + 167>170E r -> I 9 5 ,l9 8 p b pre-scission alpha particles and the m ean energies predicted by the calculations shown in figures 2.25 and 2.26. No adjustm ent of alpha particle transm ission coefficients (dashed curves); and 1 MeV shift in the alpha particle tran sm issio n coefficients tow ards low er energies (solid curves).

140 145 150 155 160 165 170 175 180 185

beam energy (MeV)

Figure 4.28 The measured anisotropies for the 28Si + Er -> Pb pre­ scission proton and alpha particle emission. The squares, triangles and circles are the 164Er, 167Er and 170Er target results respectively. The dashed curves are calculated anisotropies, averaged over the three reactions (see text).

87

p a rtic le m u ltip lic itie s as a fu n ctio n of b o th b e am e n e rg y a n d m ass, q u a n tita tiv e ly th e re are d iscrep an cies b etw een th e calcu latio n s a n d the e x p e rim e n ta l c h arg ed p a rtic le m u ltip lic itie s . T h ese d is c re p a n c ie s are m o st lik ely due to th e m an y sim plifying a ssu m p tio n s u sed in c alcu latin g th e m u ltip lic itie s. F or exam ple: (1) th e p a rticle em ission w as a ssu m e d to come from com pound nuclei, e ith e r a t th e ir eq u ilib riu m d eform ation or a t a p o in t h a lf w ay betw een th e sad d le-p o in t an d th e scission-point; (2) for a g iv e n b e a m e n e rg y , th e e q u ilib riu m a n d s a d d le -p o in t lev el d e n s ity p a ra m e te rs w ere assu m ed to be in d e p e n d e n t of th e spin of th e com pound sy s te m s; (3) th e level d e n sity p a ra m e te r u se d in c a lc u la tin g th e p o s t­ sad d le p a rtic le em ission w as a ssu m e d to be th e sam e as th e sad d le-p o in t lev el d e n s ity p a ra m e te r; (4) th e p a rtic le tra n s m is s io n coefficients w ere a ssu m e d to be in d e p e n d e n t of deform ation; an d (5) th e p re-sad d le delay tim e a n d th e saddle-to-scission tim e w ere assu m e d to be in d e p e n d e n t of sp in a n d ex citatio n energy.

F ig u re 4.28 show s c a lc u la te d a n is o tro p ie s for th e p re -s c is s io n p ro to n a n d a lp h a p a rtic le em issio n , av erag e d over th e th re e re a c tio n s 2^Si + 1 6 4 ,1 6 7 ,1 7 0 E r _ > 192,195,198p}-) T hese a n is o tro p ie s w ere e s tim a te d u s in g e q u a tio n s 2.80 an d 2.81 a n d m o m en ts of in e r tia a p p ro p ria te to sp h e ric a l n u clei. T he m ean n u c le a r te m p e ra tu re s of th e d a u g h te r nuclei T a n d th e m e a n sp in s of th e p a r e n t n u clei Ji w ere d e te rm in e d u s in g JO A N N E w ith th e 1 MeV s h ift in th e a lp h a p a rtic le tr a n s m is s io n co efficien ts to w a rd s low er e n erg ies, Td = 0 an d xss = 8 0 x l0 -21 s. T hese c a lc u la tio n s a re q u a lita tiv e ly in good a g re e m e n t w ith th e e x p e rim e n ta l a n is o tro p ie s , d e sp ite th e a s su m p tio n of sp h e rica l e m itte rs u se d in th e d eriv atio n of equations 2.80 an d 2.81.

T h e conclusion t h a t a t h ig h e x c ita tio n e n e rg y m o st of th e p r e ­ sc issio n p a rtic le s a re e m itte d p o st-sa d d le, is in c o n tra d ic tio n w ith th e re c e n t co n clu sio n by N a to w itz et dl. [NAT90] t h a t th e b u lk of th e p re ­ scission em issio n occurs p rio r to th e saddle-point. N ato w itz et al. claim it

88

is possible to determine first-chance fission probabilities in heavy-ion reactions using only the excitation energy dependence of total fission probability. To calculate first-chance fission probabilities at an excitation energy of Ei, Natowitz et al. use the equation

Ppst (Ei) P‘otal (Ei) - Pp0tal (E2)

1 - Pp0tal (E2) (4.2)

where PpSt (E) is the first-chance fission probability at an excitation energy of E; Pp0ta' (E) is the total fission probability of a compound system at excitation energy E formed in a heavy-ion fusion reaction; and E2 = Ei - Av

where Av is the average reduction is excitation energy caused by the emission of a neutron. Natowitz et al. have estimated first-chance fission probabilities as a function of excitation energy using equation 4.2 for the reactions 160 + 141Pr, 165Ho, 175Lu and 197Au; 12C + 169Tm and 22Ne + 159Tb. Their first-chance fission probabilities initially increase with excitation energy, reach a maximum and then decrease. Natowitz et al. attributed the decrease in their first-chance fission probabilities at the high excitation energies to a suppression of the fission decay mode caused by a transient delay. Analysis of their first-chance fission probabilities gives transient delay times that are in good agreement with delay times derived from pre-scission neutron measurements. Equation 4.2 is, however, based on the assumption that the first-chance fission probability of a given compound system is only a function of excitation energy and independent of angular momentum. This assumption is invalid. It would be better to assume that the first-chance fission probability is only a function of angular momentum and independent of excitation energy (eg see figure 2.18). At low beam energies, fusion cross sections and the maximum spins contributing to the fusion spin distribution increase rapidly with beam energy. The rapidly increasing fusion spin values produce a rapidly increasing total fission probability, because of the increase in fission probability with spin. Equation 4.2 assumes this

0 . 9

S 0 . 6

b e am e n e r g y (MeV)

F ig u re 4.29 F irs t-c h a n c e a n d to ta l fission p ro b a b ilitie s for th e re a c tio n 1 6 0 + 197A u —> 2 1 3 p r a s s u m in g B a ss m odel fu sio n c ro ss s e c tio n s;

aeq=A/8.6 MeV- 1 ; asp/aeq=1.00; kf=1.00; AL=0.0 a n d no p re -s a d d le delay tim e (so lid cu rv es). T h e d a s h e d c u rv e r e p r e s e n ts firs t-c h a n c e fissio n p ro b a b ilitie s e s tim a te d u s in g e q u a tio n 4.2 a n d th e s t a ti s t i c a l m odel c alcu latio n s of th e to ta l fissio n p ro b ab ilities, w ith Av=13 MeV as su g g ested

89

in c re a s e in to ta l fission p ro b ab ility is asso ciated w ith a n in crease in th e firs t-c h a n c e fissio n p ro b a b ility w ith e x c ita tio n e n erg y an d th u s o v er­ e s tim a te s th e tr u e firs t-c h a n c e fissio n p ro b a b ilitie s . A t h ig h b eam e n e rg ie s w h ere fusion spin d istrib u tio n s becom e re la tiv e ly in se n sitiv e to th e b e am energy, th e depletion of the high spins by first-chance fission will c a u s e e q u a tio n 4.2 to u n d e r- e s tim a te th e t r u e firs t-c h a n c e fissio n p ro b a b ilitie s. I have calcu lated first-ch an ce a n d to ta l fission p ro b ab ilities for th e re a c tio n 160 + 19,7Au —> 213F r a ssu m in g B ass m odel fusion cross sectio n s [BAS77]; a eq=A/8.6 MeV- 1 ; a sp/a eq=1.00; kf=1.00; AL=0.0 and no p re -s a d d le delay tim e. F irst-c h a n c e fission p ro b a b ilitie s e stim a te d u sin g e q u a tio n 4.2 a n d th e s ta tis tic a l m odel c a lc u la tio n s of th e to ta l fission p ro b a b ilitie s , w ith Av=13 MeV as suggested by [NAT90], a re com pared to th e s ta tis tic a l m odel calcu latio n s of th e first-ch an ce fission probabilities in fig u re 4.29. T he lack of c o rre latio n b etw een th e two sets of first-ch an ce fission p ro b ab ilities clearly d e m o n stra te s t h a t eq u atio n 4.2 can not be used