NEUTRON MULTIPLICITY AND HIGH EXCITATION ENERGIES. EXPERIMENTS WITH A 4π NEUTRON MULTIPLICITY METER

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NEUTRON MULTIPLICITY AND HIGH

EXCITATION ENERGIES. EXPERIMENTS WITH A 4π NEUTRON MULTIPLICITY METER

U. Jahnke

To cite this version:

U. Jahnke. NEUTRON MULTIPLICITY AND HIGH EXCITATION ENERGIES. EXPERIMENTS WITH A 4π NEUTRON MULTIPLICITY METER. Journal de Physique Colloques, 1986, 47 (C4), pp.C4-317-C4-328. �10.1051/jphyscol:1986435�. �jpa-00225801�

JOURNAL DE PHYSIQUE

Colloque C4, supplBment au no 8, Tome 47, aoiit 1986

NEUTRON MULTIPLICITY AND HIGH EXCITATION ENERGIES.

EXPERIMENTS WITH A 4n NEUTRON MULTIPLICITY METER

U . ^JAHNKE

Hahn-Meitner-Institut fiir Kernforschung, 0-1000 Berlin 39.

F.R.G.

Abstract - The neutron multiplicity, measured for each initiated reaction in a b i l l a t o r tank,is shown to record the violence of the collision in terms of energy dissipation or linear momentum transfer. Examples for the appl ica- tion of the new tool' are Ne- and Ar-induced reactions at 10 to 20 MeVInucleon.

I - INTRODUCTION

Neutron experiments have a long and solid tradition in light- and heavy-ion induced reactions, such that there is no need for justification. However, this applies to time-of-f 1 ight (TOF) experiments only. They a1 low to extract nuclear temperatures for preequilibrium and equilibrium phases of the reaction from the slopes of the energy spectra, they allow to identify the emitting source due to the focussing of the emission in the direction-of-flight of the emitter, and, furthermore allow to extract average neutron multiplicities.

The neutron multiplicity experiments to be discussed h,ere, instead, do not offer all these advantages: they provide per se no information on the energy - and (at least till now) on the angular distribution of the neutron emission. However, they allow to count the number of neutrons from each reaction which has been initiated and whereof all kinds of charged reaction products have been observed. And even in the single mode they measure multiplicity distributions, not only average values.

The essenti a1 technical difference between these two experimental approaches is of kourse in the detection effi~iency. A typical TOF-setup detects single neutrons with a probability of to 10- , whereas for the multiplicity experiment a 4% scintil- lator tank is used with the taroet in its middle and an intrinsic efficiencv of 0.8 to 0.9.

This extremely high detection efficiency is a conditio sine qua non, since we want to deduce the violence of each reaction from the number of emitted - or rather de- tected - neutrons. The neutron multiplicity measures primarily the inelasticity of the collision, that is the amount of energy dissipated from the relative motion into intrinsic thermal excitation of the nuclei. As we shall see, the neutron number can also be calibrated to give the linear momentum transferred from the projectile to the target.

Since the multiplicity experiments yet do not have a long record in heavy-ion reac- tions, our concern here is to illustrate the new experimental possibilities of a neutron multiplicity meter by giving an overview over the experiments which have been pursued so far. We will begin with inclusive neutron multiplicity speGhra, de- monstraFg9 the relation between neutron number and excitation by means of Ar (376 MeV) + Tb, and show 2jow the neutron number c n be calibrated to record the linear momentum transfer for Ne (220 to 400 MeV) + j3'u as an example. As an application of the new parameter we will discuss the separation of fission-fragment angular distributions resulting from sequential fission and fusionlike processes.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986435

C4-3 18 JOURNAL DE PHYSIQUE

F i n a l l y , t h e r e a c t i o n 2 0 ~ e (220 MeV) + 1 6 5 ~ o i s supposed t o show how it can be made use o f t h e neutron number t o arrange d i f f e r e n t features o f t h e e x i t channel, e.g.

heavy and l i g h t evaporation residues, f i s s i o n fragments and nonequi l i b r i u m p a r t i c l e emission according t o t h e energy d i s s i p a t i o n i n t h e entrance channel.

The technique and t h e o p e r a t i o n o f t h e neutron d e t e c t o r have already been discussed b e f o r e /1/ and we repeat o n l y t h e e s s e n t i a l features: The detector i s a lm diameter s p h e r i c a l tank f i l l e d w i t h 500 1 Gd-loaded (0.5 wt %) s c i n t i l l a t o r l i q u i d . The beam t r a v e r s e s t h e tank along t h e a x i s o f a 10 cm wide vacuum tube through t h e center o f the sphere, where t h e t a r g e t s are placed. This tube has also t o accommodate a l l s o r t s o f c h a r g e d - p a r t i c l e d e t e c t o r s f o r t h e coincidence experiments.

The neutrons, which are generated i n a reaction, become moderated i n t h e s c i n t i l l a - t o r and are s t o r e d f o r an average t i m e o f 11 psec. Then t h e y are i n d i v i d u a l l y , be- cause dispersed i n time, counted v i a t h e s c i n t i l l a t i o n l i g h t indues$ by t h e i r cap- t u r e i n t o Gd-nuclei. The response o f t h e detector, checked w i t h a 2 ~ f source, i s extremely h i g h (82 % f o r each neutron i n t h e present setup) and allows t o count t h e neutrons from each r e a c t i o n event n e a r l y i n f u l l number.

C e r t a i n l y , the geometry f o r t h e d e t e c t i o n o f charged r e a c t i o n products i s f a r f r o m b e i n g i d e a l . However, our d e t e c t o r has been b u i l t some 15 years ago f o r q u i t e a d i f f e r e n t purpose. We are a w a i t i n g t h e completion o f a new s c i n t i l l a t o r tank w i t h an i n n e r s c a t t e r i n g chamber.

I 1 - INCLUSIVE NEUTRON NUMBER SPECTRA Fig&- P a r t i a1 cross s e c t i o n s da/dn2$or

- t h e emission o f 1 t o 30 neutrons i n Ne (390 MeV) induced r e a c t ions.

I n c l u s i v e neutron number s p e c t r a are l i k e a d i r e c t o r y : a l l types o f r e a c t i o n s are r e - g i s t e r e d and arranged according t o i n c r e a - s i n g i n e l a s t i c i t y . Fig.1 e x h i b i t s some o f these s p ~ c t r a fo r r e a c t i o n s generated by 390 MeV Ne on a s a y l i e o f h s g ~ i e r ta r g e t n u c l e i ranging from Mo t o U. Through t h e simultaneous observation o f t h e Ruther- f o r d s c a t t e r i n g w i t h 4 monitor d e t e c t o r s a t t h e e x i t o f t h e neutron sphere these d i s - tri b u t ions could be normalized t o absolut cross sections f o r t h e emission o f n = l t o 30 neutrons. A l l spectra show two d i s t i n c t c o n s t i t u e n t s : a gaussian shaped p a r t a t h i g h m u l t i p l i c i t y and another one decrea- s i n g s l o w l y from n = 1. The former o r i g i - nates from f u s i o n o r f u s i o n l i k e processes, t h e l a t t e r i s due t o more p e r i p h e r a l t r a n s - f e r r e a c t i o n s .

With i n c r e a s i n g t a r g e t mass t h e f u s i o n l i k e processes move towards higher neutron num- bers, because w i t h i n c r e a s i n g mass t h e com- p e t i t i o n o f charged p a r t i c l e s i n t h e evapo- r a t i v e d e e x c i t a t i o n chain s t r o n g l y wea- kens. A c t u a l l y , t h e average neutron number

<n> scales r a t h e r c l o s e l y w i t h t h e neutron excess (N-Z)/A as can be seen as an example from t h e two Pt-isotopes a d j l s y t t o Au.

Also, beginning w i t h about Au (as a t a r g e t ) , t h e f i s s i o n process begins t o p r o v i d e e x t r a neutrons from i t s own energy balance. This becomes more obvious f o r

NEuTRONNUMBER(att.s~rr.) Th and U ( a l s o i n f i g . 2) where t h e

whole distribution from n=3 or 4 on is shifted by the two extra neutrons from cold fission.

z O ~ e + ^{ZJeU. Elsb} = 220 MeV

m . . . . . .

NEUTRON NUMBER (eff.corr.)

- Neutron number spectra, inclusive and in coincidence with fission fraaments detected at 720 (solid line). - -

b: ³ - Energy balance for complete ((Z~e) a n d l o m p l e t e (160) fusion.

As a first step towards confirming the rela- tion between neutron number and thermal exci- tation, we consider the energy balance for the fusionlike processes (fig. 3). From the ave- rage neutron multiplicity <n>, the neutron bindins eneraies in the cascade (7 to 8 MeV) and th; aveFge kinetic ener y <ckin> = 1.45 T, T = ((E - ^{E ~ 8 / ~ 9 ~ ~}/' ⁾the energy evaporated bv neutrons is estimated. Simi 1 arl v

the'excitation energy loss due to charged par- ticle emission can be deduced, since for all reactions the 1 ight charged particle radiation (fig. 4) has been detected with backwards- mounted counter-telescopes. When further ta- king into account the rotational energy, as calculated for' spherical bodies, this simple estimate comes close to what can be expected in these, at 20 MeV/nucleon already rather in- complete (80 %) fusion reactions. Also we see that 42 % (for Ne + Mo) to 73 % (for Ne + U ) of the total intrinsic excitation is evapora- ted by neutrons.

The inclusive neutron spectra in addition provide another insight: the relative strength of fusion1 i ke and more peripheral reactions. At 20 MeV/nucl . this re1 ation is still about 60 % to 40 % for fusionlike to other reactions, respectively, showing the mean-field dominated character of the collisions. It will be most interesting to see how the influence of the mean field fades away with increasing bombarding energy.

From the n-number spectra also the total reaction cross section can be deduced as the sum of all partial cross sections du/dn. There is one restriction, however, namely that all reactions with only charged particles or y-rays in the exit channel escape from observation. The contribution of the former reactions can be reliably evaluated from the n=O part in the neutron multiplicity spectrum in coincidence with evaporated charged particles (fig. 4), and for all target nuclei is found to be com- pletely negligible. Inel astic scattering and nucleon transfers leading to excitation energies below the neutron separation threshold, on the other hand, are more diffi- cult to assess. Their cross section might add up to 100 to 200 mb, e.g. to roughly the same seize as the one for n=l reactions in fig. 1. Principally their share once more can be determined from n-number s ectra, i.e. the n=O part therein, in coinci- dence with projectilelike fragments

(*r.

...

(*) neutron-number spectra in coincidence with projecti lel ike fragments are left out in this contribution; they have already been communicated /2/.

C4-320 JOURNAL DE PHYSIQUE

Huizenga 141 and Bass 151. We f i n d general agreement i n p a r t i c u l a r w i t h t h e most r e c e n t work 131.

NEUTRON NUMBER (eff.corr.)

Fig. 5 - Reaction cross s e c t i o n s f r o m Fig. 4 - P a r t i a l cross s e c t i o n s doldn i n W n - c o u n t i n g compared t o recent c a l -

- coincidence w i t h evaporated p a r t i c l e s . ^.- c u l a t i o n s /3,4,5/.

With respect t o a p o s s i b l e a p p l i c a t i o n o f t h i s new methode t o d e r i v e r e a c t i o n c r o s s sect ions a t h i g h e r i n c i d e n t energies, where a l t e r n a t i v e methods might become d i f f i- c u l t t o apply, i t i s important t o r e a l i z e , t h a t t h e highe t h e number k o f e m i t t e d L

neutrons, t h e h i g h e r i s t h e t o t a l p r o b a b i l i t y p = l - ( I - € ) t o d e t e c t these events- ( f o r ~ = 0 . 7 and k=4, as an example, p=0.99).

The new method may remind one t o a s i m i l a r technique used i n much e a r l i e r i n v e s t i g a - t i o n s I 6 1 i n connection w i t h f i s s i l e t a r g e t s , where t h e t o t a l f i s s i o n cross s e c t i o n was equated t o t h e r e a c t i o n cross section. From t h e comparison, i n f i g . 2, between t h e i n c l u s i v e n-number spectrum f o r Ne+U and t h e one i n coincidence w i t h f i s s i o n fragments i t i s obvious t h a t t h e new method seizes a more s u b s t a n t i a l p a r t (by about 350 mb) o f t h e t o t a l cross section. Furthermore, from f i g . 2, we can read o f f t h e s e q u e n t i a l f i s s i o n p r o b a b i l i t y pf f o r U versus n as t h e r a t i o o f t h e r e s p e c t i v e coincidence - t o i n c l u s i v e cross sections: pf i s c l o s e t o 0.1 f o r n = l and ap- proaches 1 f o r n=5, i n good agreement w i t h previous f i n d i n g s 171.

111 - NEUTRON NUMBER VERSUS INTRINSIC EXCITATION

The c o n s i d e r a t i o n o f f u s i o n 1 i ke processes i n t h e i n c l u s i v e neutron spectra has a l - ready indicated, t o what extend t h e neutron number measures higher i n t r i n s i c e x c i t a - t i o n s i n medium t o heavy systems. The r e l a t i o n between neutron number and e x c i t a t i o n over a broader range o f d i s s i p a t e d energy can be more c l e a r l y seen i n b i n a r y reac- t i o n s , where t h e t o t a l k i n e t i c energy l o s s (TKEL) can be deduced from t h e observa- t i o n o f an outgoing fragment and contrasted t o the number of c o i n c i d e n t neutrons.

Eggm a r e c e n t i n v e s t i g a t i o n 181 o f p r o j e c t i l e l i k e fragments from 376 MeV 4 0 ~ r + Tb i n t h e neutron tank, we choose an example f o r our pur ose: 8

A r g o n l i k e e j e c t i l e s (Z=18) .were detected a t an angle o f 14 and t h e i r energy s p e c t r a were s o r t e d according t o t h e neutron number ( f i g . 6). The e l a s t i c l i n e appears i n t h e n=O spectrum and from then on we see a constant d r i f t o f t h e c e n t r o i d s towards lower energy. A Gaussian curve was f i t t e d t o t h e h i g h energy s i d e o f each d i s t r i b u - t i o n ( t h e r e i s a c e r t a i n a r b i t r a r i n e s s i n t h i s procedure) i n order t o deduce t h e r e - l a t i o n between TKEL and neutron number ( f i g . 6, bottom p a r t ) . We see a n e a r l y l i n e a r r e l a t i o n between t h e d i s s i p a t e d energy and t h e number o f emitted neutrons up t o a TKEL o f about 180 MeV. Each neutron reduces t h e e x c i t a t i o n energy by about 13.5 MeV, i n good agreement t o what has been observed f o r a somewhat heavier system by Tamin e t a l . 191. I t i s n o t q u i t e c l e a r yet, what t h e reason i s f o r t h e obvious broadening o f t h e d i s t r i b u t i o n s w i t h i n c r e a s i n g n. It c o u l d be due t o t h e i n t r i n s i c d i s p e r s i o n i n t h e number o f neutrons, which would tend t o mix adjacent spectra, o r i t c o u l d b e charged p a r t i c l e emission reducing t h e energy a v a i l a b l e f o r neutrons.

We would l i k e t o add a more technical point here: an i n s u f f i c i e n t response of t h e neutron detector would also tend t o mix these spectra. Therefore the detector response should be as high as possible, in order not t o worsen the "physical' disper- sion in t h e neutron number, since i t i s obviously a d i f f i c u l t task t o correct co- incident energy spectra f o r t h e neutron detector efficiency.

. ⁶ - Energy spectra of Ar-like (Z=18) fragments sorted according t o the number o m e c t e d neutrons and t h e deduced r e l a t i o n between n (corr. for e f f i c . ) and TKEL.

9

- 1 4

-

z lo-.

-

8 -

E

2 6 -

3 C ^{4 -} 3

,

! 2 -

IV - NEUTRON NUMBER VERSUS LINEAR MOMENTUM TRANSFER (LMT)

In order t o explore t h e r e l a t i o n between neutron number and LMT, we choose a reac- t i o n with predominantly q u a s i e l a s t i c character, where excitation energy (or n) and LMT should be particulary simply correlated, namely by t h e mass qr transferred from the p r o j e c t i l e t o t h e t a r g e t nucleus (massiv-transfer picture): ON^ on 2 3 8 ~

a t 14.5 A MeV.

-150 -100 -50 0

1 " ~ ' I " " l " ' ~ I

--

0

-

ha

'

- + L

The LMT i s deduced from t h e laboratory folding angle between j o i n t l y emitted f i s s i o n fragments, which were detected in two position-sensitive s i l i c o n detectors on both sides of the t a r g e t in the middle of the neutron tank. Fig. 7 shows the r e s u l t : The folding angle d i s t r i b u t i o n ( f o r a t r i g g e r angle from 8EP t o 9 6 on the one s i d e ) with an intense bump a t small angles corresponding t o fusionlike processes and a broad shoulder towards larger angles due t o sequential fission. Along with the folding angle a fractional momentum scale i s given, as calculated f o r symmetric mass s p l i t - ting. The shape of t h i s d i s t r i b u t i o n immediately reminds one of the shape of the neutron number spectrum in coincidence with f i s s i o n fragments ( f i g . 2), only t h a t t h e s c a l e i s reversed: high neutron numbers correspond t o small folding angles. The top part in fig. 8 shows the observed average <n> f o r t h e neutron number. I t steadi- l y increases from <n> = 6 or 7 f o r low (10 %) LMT t o close t o 20 f o r f u l l LMT. The folding angle d i s t r i b u t i o n s t i l l extends about l@ beyond t h i s l i m i t due t o broade- ning e f f e c t s from neutron evaporation, whereas the average neutron number <n> re- mains constant a t the value reached a t f u l l LMT or equivalently a t f u l l energy depo- s i t , thus proving the " a r t i f i c i a l " origin of these events. Similarly, t h e dispersion in the neutron number can be demonstrated by s e t t i n g narrow gates on the momentum t r a n s f e r . For 100 % LMT t h e neutron d i s t r i b u t i o n also extends f a r beyond (and below) the average of 19.5 (second moments of t h e d i s t r i b u t i o n s a r e quoted in fig. 8).

2

Within the massive-transfer model one can now e a s i l y c o r r e l a t e t h e excitation energy or <n> t o t h e r e l a t i v e momentum t r a n s f e r bp/p0. This has been done in fig. 8 ( s o l i d l i n e ) . The agreement with t h e data, a f t e r correction f o r efficiency (E= 82%) i s quite s a t i s f a c t o r y .

-

JOURNAL DE PHYSIQUE

is[

v ---*:*:.:/ + ...-*-

...-.-

r

-.-

10

-.- -.-

$ 3\ -~-.&..-+...-?.-*-+

...

5 , ^" +corrected

t Fig. 7 - Folding-angle distributions versus correlated average neutron number

(corr. for efficiency).

Fig. 8 - First and second moments of the neu- t r o m m b e r distribution as a function of

ecoSnc lot fractional momentum transfer.

This direct comparison between the traditional folding angle technique and the neu- tron number counting has been realized only recently 1101. Before,we used a forward- backward detector arrangement, which did not exhaust so much the tight geometry in- side the beam tube through the tank. It seems, however, worthwhile to mention be- cause of its advantage when studying fission-fragment angular distributions: for forward and backward emitted fission fragments the recoil velocity of the targetlike nucleus, or the LMT, manifests itself in a drastic shift in the fragments energy and

- less subject to experimental inconvenience - in the laboratory intensity as com- pared to the center-of-mass quantities. Both effects are demonstrated in fig. 9 and 10, which show the energy spectra and the ratio of the laboratory cross sections as a function of n. With increasing recoil velocity of the targetlike nucleus under- going fission the forward emitted fission fragments aquire more and more energy and become strongly focussed into the forward hemisphere. For the backward emitted ones the contrary happens: with increasing n the energy distributions shift downwards and the laboratory solid angle is depopulated. We use this simple kinematic effect on the laboratory solid angles to deduce the recoil velocity VR. For symmetric angles with respect to 9 6 in the center-of-mass system the ratio R of lab. differential cross sections is inversely proportional to the proper Jacobians only, and, close t o 6 and 1 8 6 simplifies to:

where vff are the fragment velocities taken from systematics (11). Thus from this ratio VR can be determined , or, as indicated in fig. 10, in a further step VR can be translated to a transferred mass mtr with the help of the massiv-transfer picture. Once more, we have thus calibrated n in units of mtr .or LMT. We will make use of this calibration in order to observe angular distributions of fission frag- ments as a function of LMT.

V - ANGULAR DISTRIBUTION OF FISSION FRAGMENTS AS A FUNCTION OF LMT

In the past, the analysis of fission-fragment angular distributions from fissile targets often was hampered (with one exception in the more recent work, by Lesko et al. /12/), because contributions from sequential fission could not easily be separa- ted from the ones following fusion or fusionlike processes.

neutron number n

Fig. 9 - ^{2 0 ~ e} (290 MeV) + 2 3 8 ~ : Energy

- - ^{F i 10} - ^{2 0 ~ e} (400, 290 and 220 MeV) + s p e c t r a o f f i s s i o n fragments detected a t - 2 8 e U ? R a t i o s o f forward (ef) t o back- 1 7 6 and $, i n c l u s i v e and decomposed ac- ward ( e b ) l a b o r a t o r y cross sectlons f o r c o r d i n g t o t h e number o f detected neutrons. f i s s i o n fragments versus n (detected).

'ONe + 2 3 8 ~ a t 220 MeV i n f i g . 11 gives an example o f how these d i f f e r e n t c o n t r i b u - t i o n s can be observed s e p a r a t e l y w i t h t h e h e l p o f t h e neutron number n. Gaussian shapes have been f i t t e d f o r t h i s purpose t o t h e s e q u e n t i a l (mtr ,= 4) and t h e f usion1 ik e (mtr = 18.5) c o n s t i t u e n t s i n t h e neutron-number-spectra i n coincidence w i t h f i s s i o n events observed a t d i f f e r e n t angles (see f i g . 2 f o r 1 3 ~ ~ 7 2 0 1.

de see t h a t sequential f i s s i o n ( i t s cross s e c t i o n amounts t o about 22% o f t h e t o t a l f i s s i o n cross s e c t i o n ) e x h i b i t s a much l e s s pronounced v a r i a t i o n w i t h angle than f i s s i o n a f t e r n e a r l y complete fusion. This i s n o t t o o s u r p r i s i n g , though, when com- pared w i t h two observations: The sequential f i s s i o n can best be compared t o a-in- ,duced f i s s i o n o f U a t 43 MeV 1131 where a u i t e s i m i l a r a n i s o t r o p y w ( @ ) / w ( ~ @ ) = 1.55 has been found. Also, t h e a n i s o t r o p y w ~ @ ) / w ( ~ @ ) = 3.0 observed f o r t h e f u - i i ~ ~ n l i ~ p ~ c o n t r i b u t i o n i s i n agreement, f o r instance, w i t h t h e value 2.6 r e p o r t e d f o r

0 + U a t an i n c i d e n t energy o f 215 MeV /14/.

I n view o f t h e whole range o f LMT's which c o n t r i b u t e t o t h e f u s i o n l i k e r e a c t i o n s , we would have p r e f e r r e d t o r e c o r d t h e angular d i s t r i b u t i o n as a f u n c t i o n o f each s i n g l e neutron number, however, t h e s t a t i s t i c s i n t h e present experiment i s t o o poor t o do so. We leave t h i s more c h a l l e n g i n g task f o r t h e new t o o l , as w e l l as t h e i n t e r p r e -

$ @ t i o n f& t h e f i s s i o n ani s o t r o p y w i t h i n t h e t r a n s i t i o n - s t a t e model t o t h e r e a c t i o n Ne + Ho t o be discussed next.

V I - FISSION AND EVAPORATION I N 2 0 ~ e + ' 6 5 ~ o AT 220 MeV

2 0 ~ e + 1 6 ' ~ o a t 220 MeV has been thoroughly i n v e s t i g a t e d b e f o r e i n our Lab. The angular d i s t r i b u t i o n o f f i s s i o n had r e s i s t e d 1151 a t r a d i t i o n a l a n a l y s i s w i t h i n t h e

C4-324 JOURNAL DE PHYSIQUE

.

OI

Fission

P-+

framework of the t r a n s i t i o n - s t a t e model. Evaporation and f i s s i o n decay modes a r e nearly equally strong (aev ⁼ 700 + 100 mb, of = 900 + 100 mb), and the balance between them obviously i s rather delicate, because also 5 neutrons on the average are emitted prior t o scission /16/.

Our new findings f o r the fission channel are sumnarized in figs. 12 and 13. In f i g . 12, a t t h e top i s t h e neutron number spectrum in coincidence with f i s s i o n fragments detected at 7 9 . This spectrum i s not distorted by the laboratory observation, be- cause the Jacobians f o r a l l mass t r a n s f e r s are close t o one a t t h i s angle; i t i s ca- librated, so t h a t t h e sum over a l l neutron numbers gives t h e t o t a l f i s s i o n cross section. The middle part of f i g . 12, shows t h e transferred mass mtr versus neutron number, deduced in t h e forward-backward geometry (see Chapt. IV): i t increases from about 17 t o 19.5, t h e average being 18.6. However, even a t the highest neutron num- bers complete fusion (mtr=20) i s not q u i t e reached, in contrast with what has been observed f o r Ne + U a t the same energy ( f i g . 10). I t seems only naturally t o f i l l t h i s gap with evaporation. The f i s s i o n angular d i s t r i b u t i o n with no selection on t h e neutron number n i s shown in f i g . 13. I t i s much more anisotropic than f o r Ne + U, because due t o the lower f i s s i l i t y X = 0.66 t h e system has t o a t t a i n a more elonga-

ted shape - t h e shape parameter in t h e liquid-drop model i s J ~ ~ = /1-86 J - ~ ~ ~ f o r t h e escape through the f i s s i o n channel. With t h e neutron f i l t e r applied ( f i g .

12, below) the anisotropy, expressed here as ~ ( 1 @ ) / ~ ( 9 @ ) , seems t o be rather con- s t a n t with n, eventually decreasing (*) with increasing n or increasing LMT.

Within t h e peripheral picture (breakup fusion, massive t r a n s f e r ) of t h e incomplete fusion process, where lower mass t r a n s f e r s are associated with higher impact para- meters, one arrives a t a p a r t i a1 wave 1 -population as indicated schematically (with sharp c u t o f f ) i n f i g . 14, top part. Evaporation with 700 mb exhausts do/dl up t o 45 4i,followed by t h e p a r t i a l f i s s i o n cross sections da/dn in the order of decreasing n or mtr.

For t h e comparison of the observed anisotropies with the t r a n s i t i o n - s t a t e theory t h e 11 n-bins were compressed into 3 mass bins ( f i g . 12) with average mass t r a n s f e r s ranging from 17.2 t o 19.3. The compound-nucleus spin I-population i s deduced from t h e ?-distribution using t h e simple scaling r u l e I = l-mtr/m(project.) I t ends a t 8 1 6, rather close t o the limiting value 84 4, where t h e f i s s i o n b a r r i e r vanishes.

The r e s u l t of t h e calculation, with shape parameters taken from the r o t a t i n g liquid- drop model (RLDM) as further ingredients, i s shown as the dashed lines in f i g . 12.

-- --

(*) the variation might be stronger in r e a l i t y , in the experiment i t appears f l a t t e n e d by t h e dispersion in n.

20

! ⁷⁸

IE' 16

, I - d l s t r b a

D

4 5 10 15

exp neutron number n

-

Fig. 12 - ^{2 0 ~ e (220 MeV) +} 1 6 5 ~ o : from

- -

the top: n-number spectrum for fission, average transferred mass mtr and obser- ved fission angular anisotropy versus neu- tron number (not corrected for efficiency) .

Fig. 13 - Angular distribution of

- -

fission fragments from Ne + Ho.

The agreement between experiment and calculation is not quite satisfactory. Also, the use of spin-independent shape parameters (1 iquid-drop description) would sti 1 1 increase the calculated anisotropy somewhat, and so would the considerat ion of pre- fission neutron evaporation, since it tends to lower the temperature of the fission- ing nucleus relativ y strqn er than its angular momentum.

In comparison with "Ne + 3 a ~ we have to face another inconsistency: For He + U the average transferred mass q r for fusionlike reactions is about 18.4, whereas for Ne + Ho it would come out to be 19.2, if the whole evaporation residue cross section of 700 mb is assigned to complete fusion. Therefore we decided to measure the velo- city distributions of the evaporation residues and the associated neutron multipli- city; and the result came quite as a surprise.

The velocity spectrum, measured with solid-state telescopes behind the neutron sphere at an angle of 8 and at a distance of 72 cm from the target is shown in fig. 15 and the average neutron multiplicity for 0.02 cmlns velocity bins is on top of it. From the comparison of the spectrum with the expected recoil velocities following the capture of mass-12, -16, and -20, as indicated by arrows below the ve- locity scale, one immediately realizes that the fusion-evaporation process is far from being complete fusion. And, more importantly in this context, there are strong components pertinent to mass-16 and even mass-12 capture, i.e. lower masses than have been observed in the fission channel. The neutron number <n> confirms this ob- servation: the maximum <n>= 9.6 coincides with the velocity expected for complete fusion, as one would expect, because this process creates the hi hest excitations.

Ye have noticed this matching before in 3 similar reactions 1 1 7 L For lower velo- cities <n> strongly decreases; for qr = 16 and 12 <n> has diminished to roughly 415 and 3/51 of its maximum value, respectively, i.e. in the same relation as ttie in- trinsic excitation should be reduced.

C4-326 JOURNAL DE _PHYSIQUE

Initial o r b i t a l ang. momentum li Ih l

Fiq. 14- Two p o s s i b l e angular

-. -

momentum 1 - d i s t r i b u t i o n s da/dl

.

< .

Fig. 15 - 20 Ne (218 MeV) + "'Ho:

-- fusion:m+,= 12 16 19,20

Evaporation-residue v e l o c i t y spectrum and c o r r e l a t e d avarage neutron number <n>.

From t h e n-spectra i n coincidence w i t h forward e m i t t e d a - p a r t i c l e s and p r o t o n s ( f i g . 16) we get more i n d i c a t i o n s f o r t h e existence o f these low-mass t r a n s f e r s . These spectra c o n s i s t o f 3 components which have been s t u d i e d b e f o r e i n s i m i l a r r e a c t i o n s /18,19/ :

( i ) a and D released from o r o i e c t i l e breakuo a f t e r t a n q e n t i a1 c o l l i sions connected w i t h low e x c i t a t i o n o r low n ( i n d i c a t e d by t h e hached area i n f i g . 16)

( i i ) a r a t h e r small component (blackened) due t o evaporation f o l 1 owing near-compl e t e f u s i o n and l o c a t e d i n t h e same range o f n-numbers as t h e backward e m i t t e d l i g h t par- t i c l e s ( f i g . 17).

( i i i ) and t h e dominant preequi 1 i b r i um component ( w h i t e p a r t o f t h e histogram i n f i g . 16).

The l a s t component i s t h e c o u n t e r p a r t o f t h e incomplete f u s i o n r e a c t i o n s w i t h mtr

= 19 t o 12 i n t h e v e l o c i t y spectrum i n f i g . 15. The neutron number r e v e a l s t h e i r common o r i g i n : mass-19 t r a n s f e r s are accompanied by about 9 neutrons and so are t h e forward w i t h beam v e l o c i t y e j e c t e d protons. Nonequilibrum a's, on t h e o t h e r

hand, show a much broader asymmetrical neutron d i s t r i b u t i o n . It i s n o t t o o d i f f i c u l t t o imagine t h a t t h i s broad spectrum c o n s i s t s o f twf componegts centered near n=8 and 6, where one expects t h e l i g h t residues from t h e ^2~ and 0-capture processes seen i n t h e r e c o i l v e l o c i t y spectrum.

That f i s s i o n i s not 1 ik e l y t o be i n s e r i e s w i t h these s t r o n g l y incomplete channels i s once more suggested by t h e r e l a t i v e l y small overlap o f t h e r e s p e c t i v e neutron number spectra i n f i g . 16 and 17.

Once we have seen t h a t f i s s i o n i s associated predominantly w i t h mtr= 18 and 19, whereas t h e e v a p o r a t i v e decay f o l l o w s f u l l LMT as w e l l as much lower t r a n s f e r s w i t h mtr=16 and 12, we can no longer m a i n t a i n t h e angular momentum 1 - d i s t r i b u t i o n d i s - cussed b e f o r g and sketched as No. 1 i n f i g . 14. Instead, an arrangement l i k e No. 2 seems more appropriate. Now o n l y t h e mtr=20 p a r t (estimated t o be a t most 400 mb from t h e observation o f t h e residues a t P and o n l y ) and some minor qr'19,18 and 17- components o f t h e whole evaporation r e s i d u e cross s e c t i o n are l o c a t e d more inward f r o m t h e f i s s i o n reactions; whereas t h e q r = 16 and 12 p a r t s of t h e evapo- r a t i o n decay come beyond f i s s i o n , beginning w i t h 1= 83 h. I n s p i t e o f t h e q u a l i t a - t i v e n a t u r e o f t h e new order i n t h e i n c i d e n t angular momentun 1, which w i l l , have t o be s o l i d i f i e d by i n v e s t i g a t i n g t h e composition o f t h e heavy-residue spectrum over

the whole angular range, it is still challenging to consider the consequences for the f ission-fragment angular distribution: Since the average angular momentum I for the f ~ s s i o n channel is reduced now, the calculated anisotropy is also reduced, in particular for mtr=19.3 (solid lines in fig. 12). The transition-state model under these conditions would fully account for the observed angular distribution.

?

NEUTRON NUMBER (eff.corr.)

I 1

mt,=12 16

F' 16 - Differential cross sections

$ u ~ ; 8 f p ; v p y;o: ( 6 L = 1 9 ) from

n e u t r o n n u m b e r (.Irn.o'-r.)

Fig. 17 - Compilation of neutron number sp7ct-n coincidence with : a, p, eva- poration residues and fission fragments.

Returning to fig. 15, we like to continue the discussion of the evaporation process.

From its maximum value reached for full LMT the neu.tron number <n> decreases also towards higher recoil velocities ver.. This is generally expected, because the fil- ter on ver selects processes where h~gher-energy particles, in particular p and a, are emitted in the opposite direction, thus providing the higher recoil velocity very but at the same time leaving less energy for the neutrons to carry off. The arrows in the upper part of fig. 15 indicate the most probable recoil velocities, when a proton or an a-particle is ejected backwards, and the associated <n> as known from the n-spectra in coincidence with these p, a (fig. 17). For the reaction at hand, the decrease in <n> is relatively small (about In) because the average multi- plicity for p and a is larger than 1 and therefore already the maximum <n> for full LMT is reduced by their competition.

With a filter on the energy of evaporated light particles (a's as an example in fig. 18) we observe a similar effect: the higher their energy is the lower is <n>.

The decrease of <n> is, however, only half as much as one would expect, namely 0.5 instead of 1 unit in n for an increase in the a-energy of 12 MeV: We ascribe this to the compensating effect of other charged particles emitted simultaneously.

From the n-spectrum in coincidence with all heavy evaporation residues observed at

@ (fig. 17) we tried to reconstruct the one for complete fusion by selecting only recoils with ver > ^{ver(mtr = 20).} It is considerably smaller, shifted by In and in reasonable agreement with the result of a statistical model calculation (Gaussian shaped line in fig. 17). The fission n-number distribution (top row in fig. 17) in turn, has a broader width than the experimental complete fusion spectrum below, because fission originates from a broader range (mtr=18 and 19) of capture processes. But its avarage <n> is even enhanced by 0.5n relativ to the mtr=20 eva- poration residue n-spectrum. Since for this system fission by itself is not likely to provide extra neutrons, this indicates that indeed the p,a -evaporation is mainly in coincidence with heavy evaporation residues, thus reducing the respective neu- tron-number, and rather competes with fission.

C4-328 JOURNAL DE PHYSIQUE

Fig. 18

-

V I I - CONCLUSION

The neutron m u l t i p l i c i t y meter i s a new t o o l i n t h e f i e l d o f heavy i o n experiments. The new observable, t h e neutron number, records t h e v i o - lence o f each i n i t i a t e d r e a c t i o n i n terms o f energy d i s s i p a t i o n o r LMT. It thus s p e c i f i e s t h e i n c i d e n t channel, however, w i t h an i n t r i n s i c (and r a t h e r inconvenient) d i s p e r s i o n r e s u l t i n g from t h e spread o f neutron evaporation energies, t h e charged p a r t i c l e p a r t i c i p a t i o n and from t h e 1 -dependence o f t h e r o t a t i o n a l energy, which i s not a v a i l a b l e f o r evaporation.

We have t r i e d t o o u t l i n e t h e use and a p p l i c a t i o n o f t h e neutron number i n t h e i n c l u s i v e measure- ments and i n evaporation and f i s s i o n studies,as f a r as we have experienced it so f a r i n t h e

E ,[ ~MeV I lower energy domain below 20 MeV/nucl.

With i n c r e a s i n g bombarding energy t h e s i g n i f i - cance o f t h e neutron number f o r t h e t o t a l l y created i n t r i n s i c e x c i t a t i o n w r l l become l e s s s t r i n g e n t , unless i t i s supplemented by analogous i n f o r m a t i o n on t h e evaporated charged p a r t i c l e s . I n t h i s respect t h e neutron counting provides an e s s e n t i a l advan- tage, i n t h a t an i n t e r i o r 471 charged p a r t i c l e d e t e c t o r would h a r d l y e f f e c t t h e neu- t r o n measurement performed i n an o u t e r second d e t e c t o r s h e l l .

F i n a l l y I would 1 i k e t o thank my colleagues A.Budzanowski (Crakow), B.Cramer, H.Fuchs, J.Galin (GANIL), D.Hilscher, H.Homeyer, G.Ingold, M.Lehmann, H.Rossner, E.Schwinn and P .Zank. T h i s r e p o r t summarizes p a r t o f t h e i r work.

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