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..

, T1TL8 SL?MARY : (11’R 5[)-YEAR ODYSSEY WITH F1SS1ON

LA-uR--89-1748

DE89 012733

I)LU”I.AHMER

Ahnnm Los Alamos National LaboratorLos Alamos,New Mexico 8754 ~

,, ,’wm.l &

f #

[-, s. .%,”

on the occ~ion O( t?ris International Con ft-wcnce on Fifty Years I{esriirch in SuclrdrFission, we summarize our present understanding of the fiss~on prm-w and the rhitl-irngrs th~t lie ahead. Tile basic properties of fission arise frcm a dc]icatr corllpvtitiorlLvtwocn disruptive Coulomb forces, cohesive nuclear ftirccs, and Iluctuatirlw shell aIII!pairing forces. Th.’se static forrcs are primarily responsible for such t~xporimrntal ph(”-nornt!na ~“ deform-d gwmnci-state nuclear shapes. fission into [ragrnvnts of unequal sizc~,sawi,uoth neutron yields, spontaneously fissioning isomers, broad resonances and rlar -row intermediate structure in fissian cross sections, and cluster radioactivity. IIowcvor,inertial and dissipative forces also play decisive roles in the dynamical evolution of a fis-sioning nucleus. The energy dissip .Led between the saddle and scission points is small forlow initial excitation energy at t}le saddle point and increases with incrciusing vxritatii~llenergy. At moderate excitation enrr~ies, the dissipation of rolh~ctive rnergy into intrr -nal single-particle excitation energy procreds largely through Lhc interaction of nu(’lv~)rl~with the mean field and with each other in the vrirlity of the nuclear surface, M well asthrough the transfer of nucleons between the two portions of the evolvlng du;nbbd]l-likl,system. These uniqlle dissipation mechanism arise !=OM the }’auli exclusion prir~rl~)lrfor fcr:nions and the de~ails of the nucleon-nucleon interaction, which rnakr thv rIIViIIIfrw path of a nurleon near the Fermi surface at low excitation efl{trgy Iongrr th,~rl t!:IInucleiir radjus. \Vith ifs invergc process O( heavy .lorl fusiorl rra[ tiorls, iissioll rotltlllllt.~I(I !ItIld surprises in the study of large-amplitude collective nllcl(’ar rnoti(]ll Fllturv OI.Il-lvII~m include dtwislng experirnc=nts to unarnbiguo~ly distinglllsh {IisslpaLl~o vtrorts frorll~rl~logolls eiTects r;kused hy col!w”tive d~grees of frtwdorll drlli I olrlplltlrlg tihsit)rl t!lrt,~ 1!$f“ -r] tht~ urldrrlylrlg hadr~)nic lritc”r~ctmn

.

.. . . . .:5-.”. Ve,

-- -<

Fig. I. Fission harriers:: ‘S rnmpumd with the Gogny finite-range in[:’ractit)n.

1’ I,, ,.,, l. .Jl,. ,,, , I

I

...!., .-.-,

.-.... . ..

:, ----- ,

\ ,77, ‘

/\ ~

,J”’

\ v \J“\\ -k..-..

\.

-. --,- -.J ---~ -—- ) ..::) ‘-3 “i

\.—. —- . . . .--.—-- ------ ----- ----.. ..

. . ,..7 ..” “A--r .: ..,’ -,. . ‘“-.

barrier computed with the rrtacroscopic-mi cr(~scolJic muthcd. ;Ilust rating thtB

uyrnrnetry and mass asymmetry 32.

wopic energy, (3) Generate the single-particle potential felt by the nuclcons, (.I ) SOIVII thv

Schrikfinger equatwn for the sing! e-particle energies. [5) Calculate the microscopic [shell am,

pairing) corrections. The total potvntial energy is then given by the ,um of the rnacr,]sct];,:t

t’nergy calculated in step ? and the microscopic corr~ction~ calculated in St?p .5.

.c\s illustrafid in Fig, 2, the fiss; on barrier of a heavy actinidc nucl(ius cal(-ul~. ,!

[his IIN” Lhd cont~ins a secon{!ary minlrnum surrounded by two peaks”, Tt:r MIr(J ... ry

rllifljlnum arisrs from shell rf?ects a..socia[m! with a nuclear shap~ whosr ucs arr in , !III

r~tio 2 1. Thr dashed curve gives the potential energy for syrnrtmrlc l!dorma”.x)v~ cL\ A

tunction of thr distance r between the crIIt, crs of mass of t!lr two :;asccnt fragnwnts, In 11:111.

I)f Ihr radius k of the sphcrica] shape. Thv incluslon of axial iuiyrnmrtry at thr firs: i)i,~k

Iowrrs thr vllrrg~ hy approximately I \fe\”, wher~w the inclusion {}f [l~i~>s asylllll~rtry ,it

I

,,

. .-,-. ‘. .’. i-. -=e.

}-:g. 3. .Analj;sis of fission ,-ross scrtiuns in lcrms of rotational bands of oppositr ;)itril y “’”’

500 Ioog 1500 2000 1500 3000

;; .v

24tN WBTqRESHmQ FISSION CROSS-SECTION

‘5 ‘:1 IIx I“o L=1 A. L-ci- .$’

500 1030 ~m 2000 2500 1NEUTRONENERGYIWI

C18=-11 1 _!-.. -l_ J

Fig, I. Resona~ltos corresponding to clas~- 1 states a: :he grounci-s[ii[v minii I:um aII(l 10

class-n states at [ht~ secondary minimurnw 3’.

. . . ,,

‘*. .. ,.

‘“4....... . .

i -. .,.. .

~‘--’

!“ .-

!..=”.

<

i 4.. ,,

;

~

!.”

i

i

. . ..%. ““’ i

.,.

9

. .

‘-4#iiL;,-,,.,4-J*. ,, --

. ..” . . . . ,.. e. . .

-. .-. . .,. .”..

~c:lenlacic ,jlu~traLion of ~xp~ri~lental fission-fragment m=s distribution for IIIV~ig ~j. .-spontaneous tissiorr of heavy nurlei4S46.

? hcobald3’, .\t thu secondary minimum, scme of the energy is in the form of dcforma!mn

o:lcrgy and is therefore unavailable for forming compound states, The distance tJUt WW’f I ! !l(l

groups of strong resonances is therefore much larger Lhan the distance Lctwcen the indivillual

rtwniinces. which occur when the excitation energy is close to a compound nuclear lrvtIl fur

[hr Ilu Llrus situated at its ground state.

klxperirrlental values are now available for the heights of the relevant saddle points aml

,sutjsv.~:;orlt nlinirna in the potential-energy surface for numerous nuclei. From prrvious

I m 41, 42 between Cxperlmcntal and c~]c!l!ated ~’alll~s.(’OIIl~)drl SofiS” *(’ ConClll(l(” !hd[ ltl(i

!l~ii{ r(]~{-f ’;~:<-:::i fr[]scopic method i+ taIJ,ilJlr of reproducing the rxtrrrni+ IrI thr ;)()[t’rl[l~l-

I!:I’7K] ●’:T!,,i I’ “I) witt]ln an acrurary of dl)oli I JlcI\”. A detailed up-t~ddtv rofn~]iir;w)ll t(~r

!1’11,1’1‘ !irlJ!l~hLJut th(’ f.)erldk ta~J](’ Wollld ~M’{’Itr(}rTICl~ Vd]ll~blF.

\\P ti~,ar(i fr(,rn several speakers ,lbI)II[ fh~ Irilportant r,)]c’ ttidt sing] v-par ti[”!r !dh’[= [)l,iy

iII !i~sli)n.fragment maw and kinctlr-vrrergy distributions, :\s (llscllss(’d lJy ltki:~43. rtu~,rll

rrlvasureInvnts show that at sut!irlt-n?ly low c’xcltation rnrrgy thv rII~ss dis[rlljlltl{}!)+ !f)r

1“1”!~rl(j ,)th(. r Ilg}]t nuc]el ar~ ~~~rr:rr~~’trl( \\”dg:lrr]~nsa4 prf’stinlt’(i 11{’w rvsll~l~, -!III\\ ‘: l!i

}’:g ‘,. [rllllcallrlg [hat Irl thv sp,)llt,ifl,,):,s !ls~.il,rl of plutorlllllll lso(t,pw. III() dti,jllio!i I,! ,:,.

,i:rl,rl> I,:; !IA:I( t+ 1}11,tj{)III)~\ ::. iig. I !:‘.,\() fit ,Lg::II, rIl ~tlt’11*I!~cw!* ,il ‘)() ~lr(]!{~rl~,~rl(! ●J ::1 ‘. ’: I,:.

*

— . a:. . . . . . . . . . . . . . .

LK ‘“

E

?“m

lEo50 “. ..-. . . ... ______ ... . .. . .-_. .. . . ... . . . . . . .0 ?5 1Oc I 25 150 175 200

Distance between Mass Centers r (Units of R9)

Fig. 7. Calculated potential-energy surface for 2W3Fm, showing a new fission va]h?~ leading

to compact scission shapes :- the lower right-hand corner’”.

sufficiently co Clramatica]]y shift the peak in the mass distribution and increase the kinetic

energy,

Hoffman45 told us about the abrupt transition that occurs at 25UFm in fission-fragment

msss distributions, kinetic-energy distributions, and half-lives for the spontaneous fissh.m

of heavy nuclei’s ’47. As illustrated in Fig. 6, for 258Fm and certbin nuclei beyond, the

m~s distribution becomes very narrow, with a single peak at symmetry. The kinetic-energy

distribution for some of these nuclei becomes skewed, with a peak at high energy and a broad

low-energy tail.The spontaileous-fission half-iife decreues by several orders of magnitude,

.411 three of these phenomena arc explained qualitatively by a new fission valley in the

multidimensional pot. “ial-energy surface.

As discussed by Brusa’a and others, this new valley is associated with doubly magic frag-

ment shell effects at 50 protons and 82 neutrons. Since these shell effects are maximum for

spherica! shapes, it is essential for an accurate calcula~ion that the shape parameterizatit-)n

tJe capable of describing touching spherical fragments and that the finite range of the nuclear

forrc ~JPtiikrn into account in calculating the macroscopic energy, These items are ill(llldvd

111 [!:(l ~~(][t’:ltiai-i’nergy surface’w for 25uFm shown in Fig. 7.

l~t(~~j~~l tht~ swidle point leading into the new “’~sion vallry in LIlc Iowcr rig]lt-hllllll

porclr)n i~f Fig. 7 is lower than that Icading into the oid ftssion valley in t},e upper right-harl(i

porLlo[l of the figure, spontaneous figsion will prorccd prinlarily into thv new val](~y, l[owos~,r.

thvre is also a switrhback path, which is lowered by mass- ~symrml[ric dcform;l[l,)llk. I tl,it

I)ranchcs off from the new path arl(! tra(ls into the old va]l~y arross arlotht,r sii(ltll(’ ~)IIIrIT

‘~)IIs swltchback path is probably r(vip(Jrl~lLi(’ ft)r thr Iow-vnvrgy tail ~~fthv kir:(’t;( tr~l:g:,

(l,?!rlLll[llJrl for [his nucl[’us’”

3 “-----O 5 ‘c ~5

Fragment Charge Z ‘

Fig. 8. Fission-barrier height as a function of the charge of the lighter fragment5’jS1’S3.

For compact dumbbell-like shapes, which are present both in the new fission valley and

at the fission saddle points for medium-weight nuclei, the finite range of the nuclear force

substantially ]owers the macroscopic energy relative to that calculated in the liquid-drop

model. This is illustrated in Fig. 8, which was shown by Schr6der50 in his talk. Th(!

solid curve, calculated by Sierk51 with previously determined constants42 in th~ Yukawa-

plus-exponential mode152, satisfactorily reproduces tile experimelltalss fission-barrier heigh!s

for asymmetric mass divisions. [n contrast, the liquid-drop model yields barriers that arc

approximately 10 MeV too high.

\lorettoS4 stressed in his talk that msss-~ymmetric fission of the type shown in

Fig. 8 evolves continuowly with decre~ing maas asy~etry into the statistical evapora-

tion of complex fragments. The spontaneous emission of complex fragments was discussed

14C to Si have been ob-by Pricess and Poenaru5’. As shown in Fig. 9, clusters ranging from

served cxperimenta]]y55, with half-lives ranging from 1011 s to 102S s. Since cluster emission

is intermediate between fission and a decay, theoretical approaches based on both tissim

theory and the preformation of ctusters have been used. The emitted clusters arc nvutrorl-

rkh because this leads to tightly bound daughter nuclei close to 20uPb, with Iargr rrlrrgy

reletie.

3. XL-CLEA,I IN LRT1,4

3.1. Role in spontaneous fission

\Ve turn rIow to the nuc]par incr[ia, w}lich at low ~,~ci[dtion {~llcrgy is ~,x[)t)rilrl,,lll,iil)

tusted primarily by spontaneous fission Ilvrv’nt progress in sclfcunsistrrlf rllirros(ol)l(” I rtii’

,, J

?0 I m I

20

“5

“cl 1.. 1 I—.....——— — —.- ----1+- :lF Ye v g SI

Fig. 9. Half-life for c“ .er emission:.

ments of spontaneous fission w= discussed by Xegeleze, who IIsed a Fcynmdn path intvgr,t!

to formulate an imaginary-time mean-field theory of tunneling in many-body systems. ‘1’tlis

approach has the nice feature that the contributing paths in deformation space arc deter-

mined aummatica]ly by the system’s Hamiltonian. For a 32S nucleus without spin-(lrt)it

interaction and with the charge artificia])y Increued to cause fission to occur, the result illg

wrninant path is significantly different from that corresponding to constrainml mran-fit’1{1

theory. However, because Gf computational difficulties, this approach h= no! ‘ 1)11’11

applied to the spontaneous fission of a realistic heavy nucleus,

As discussed by 5obiczewski57, actual calculations of spontaneous-fission half -livl’s ,irv

IIsually performed by use of the semiclassical WKR approximation applied to a partiruldr

mm-dimensional path through the multi-dimensional deformation space. ‘1’his pi~tt~ is ill

practice clctermirlcd either from cortsiderations of statics alone or dynamically by rnfixillli~ing

the penetrability. which is related to an integral along the path involving the pmduc[ [Jf !Ili’

incrtla with respect to this path and the potrntial cnprgy relative to the gr[)und-st,tto t,n~rg}

:!,2. \fi,ros(opic and semi-empirical in~rti~~

Thv nuclmr inertia tensor for spontaneous Iission is frrquvntly ( alculattv! flii~ row (JPI

(’ill ly”~ “~ ~J~ IJSP of the lnglis cranking model, As illustrate] by tho solid drld shf)rt -l!, L\hl’11

pafllrbvs III Fig, I(J, the microscopic inertia with rosprct to thr {~istancc LVLWVPII II I,L+\ ~I’11.

1~- r IS ~11 oscillating function of deformation and for St:lall d!,for!rlatiorls is s~’v~lr,:] I i:lli,~

[l,,’ Irr:jt. a[iondl value. Three prop~rtim arise from tho rriirrangrrrl(’nt ,If HOII.11 ~! ril ‘ tri’

in ~lrlglc-particlu w , 10 functions which IJf”(”llr!i at thp near (“-,Jgsin~S of siflglr-pd: ‘ :1‘t’ ~tI”.I ~.

‘I”tlc’rlli( r(]wopir inertia osclllat~’s atlout it svrlli-vlrlplriral i[lort ia, which is rl’l,itv[l ‘,) :1,1 .: “II

t,illf)flal Irll)rtia in sur)l a way []1~1 I)olh i~~)~)rr)ll~~l[Ill, rt,(]llf III] rlli~+s for •f![l,~r,lll,(! !r,lg”, t ‘ o

II

,.

L..-

—

.:

. .

,=

, :. ..:.:.. :~.a.>.

r j,. . . . ,,-..- ,. -.. FT.

..1! :’.:1’ .:“%=.”. : :!F . .

.● ’ .% ..

*

..

:.

.,! ,.

.

,,..“.

G.. -: .,. -..

.,

primarily in the sllr[d(.t~ regloI1 from IWO iil~!ln(~ rIlt~r}larllsliLs.

Thc tir+t rrl!~c!l,trll.~rll is onv-t.m~!y ciissipa[ion, but with a rniig.’:[l~~c ttla[ is sulmtitl]ti,ill}

Wdllced fl’;dli~c’ tII l!id[ of tttt~ wail (jrr’nll]a. III c~]cll]a[ions i)ds(l~ ,)n the ran(jolll-phas~

approximation for spherical : lei, Grif%n, Dworzccka, and ~annOll]pW }Iavp S]IIXVII that the

r!rect of rrplacing three idt’alizations of the wall formula by n, )rc realistic fea[urcs appro-

priate to real nuclei is to reduce the t-me-body tlissipation coeffiricrtt to roughly IOv: ,~f thr

wall-formula valuc~z 73. .llternatively. the reduction could arisv hccausc the nuchwns rtltairl

some memory of th~ir previous collisions with the wall, which invalidates the assulylp[i(]n 01

a random velocity distribution that w- used to derive the wall formula.

The second mechanism is twmbody collisions in the surface r~gion. ‘rh~ Pauli t-xclusion

principle, which supprcssm tw~body collisions in I hti nuclear interior “sappvars M 01111

proses through the nuclear surface to the extcrior:4, In addition, the I. , l]u(.leon-ll(lrl~’{)11

cross section itself incre~es aS one passes through the surface to the exterior hccause of

its increase with decre~ing kinetic energy, Since the density decreases to zero outside the

nucleus, the probability for tw~body collisions peaks in the nuclear surface.

[under the assumption that the surface dissipation irr local, it can be calculated from thr

Itw!ing term in an expansion of the time rate of change of the collective Hamiltonian H in

w This ]eading ter M call ~J4’powers of the surface diffuseness divided by the nuclear radius ,

written m

lit{()lfi /Ir,pl” [n - D)’tfs .

murrue(?)

wherp h is the vp]oci~y of a surf~~ e]cmcnt d.$, f) is the normal drift v~lority of II Url{II~IIS

~bout to strike the surface ●lement d.~”, w is the average speed of the nuclcons insidu thr

II IIClOUS, P is thr nuclear m-g &nsity, and ~, is J dimensionlcsa parameter that wprc iiilw

the total strength of the interaction of ei’. ner onc or two nuclcons with the moving nuchwr

surface. A value O( k, I would correspond to the wall formula, but stworal typw of

~xp~rirtlrntal data indicate that for real nuclei its value in mbt:h !ess than unity. ‘1’hc vitluv

of k, roul~ depend upon both the ●xcitation energy and type of collective rrmt. ion irlv(]lvrvi,

For dumbb~li.likr shapm, the transfer of nurlcr.ms throuRh tlw wIIIdow swpiiri~tillg ltlv

IW(I pl)r[ii)ris of th~ systrrrl lt~alls to art A(jtlltional (Iissipalion I Ilat is allml[)golls to tll~~iIM*II, II

WI II I!I)W fl)rillilla i)f swlatprkl~”r’ 7’) ‘1’hp rl,qlllt IS

fill() I

(fly’uw”(q,q) ,

911,1 ●

1:1]

I “)

deforming fragments There IS ilo need [J renormalize this part of thr dissipat!t~rl “~ICaUSI’

nuckons that have’ passed through a small window have a IOW probability of rt’tl~rnlng

through IL itrlilt’Still retaining mtvnory of their pre~ious passage. The combination of tll(,s(~

two rnecharlisms leads to slirfact~-pills-window’ dissipation.5~Jbo~h discussed dynaml~a] calcu]a[ioris of hSSIOIl t hat hiiy(’pa.~kevirh’u and Schr&jer .

been performed }vith surface-plus-window dissipation~i. For values of the streng!! corre-

sponding to dynarxlical motion that is somewhat overdampeu, these calculations s,itlsfac to-

rily reproduce the average kinetic enrrgies for the fission of nuclei throughout t}le pvriodir

table at moderate excitation energies’1.

4.3. Generalized F’okker-Plank equation

~hus far we have been considering the effect of dissipation ‘n meal iantities in fissi~

AS {iiscussed by Weidenm Gller67 and Pashke~ich68, the coupling between t}~e collective’

find internal degrees of freedom also gives rise to residual fluctuating forces, which diffuse

Lne dy,~amical paths in phase space. When these stochastic forces are treated under the

\larkovian assumption that they do not depend upon the system’s previous history, one

arrives at the generalized Fokker-Planck equation

for the dependence upon time t of the distribution function f(q, p,t) in ph~e spa(t) 01

(ollt)ctive coordinates and momenta, The lastterm on the right-hand side of this cquiltior)

describes the spreading of the distribution function in phase space, with a rate that i+

proportional to the dissipation q and the nuclear temperature r, which is me~urml hvr~’ if]

energy units,

i.ly solving a stationary Fokker-Planck equation in one dimension for t},e probability IIOW

~~ showed in 1940 that dissipation increaae8 the Mynlptoti(” ~~111~’over the barrier, Kramers

of the fission lifetime relative to thr Bohr-Wheeler transition-state valuee, As discusswi I)y

\Veidenmilller*’ an i Paahkevicbos, this important result has only recently been incorpori~tvf!

into stutlics of fission.

,1.1. Stiutrort emission prior to fission

Solil~l,lfl of the Fokker. P]anck ~qllation (<~) for tw(jot~]er sltuation~ ha llla(~(i I( \)()\\ItIl(* to

vxtra(t information on fission time scales and nuclear dissipation from rlcutron Pmission I)rlor

to fission, u disruswd by liinde’e, (;avmn”, [)ietrich’e, and Schr6der “), First, ill) ilniil~tll’fil

solutlor) for the me~n saddle-t(~scission time has been obtain~d from ii ot)o-(llrll{’risll)li,ll

79 0() $e~ort(j a numprl~al sr~lutioft for the tri~nslrut I Irlll’stationary Fokkvr-Planck ~quation ,

rtv~ulrtd to build up the qu~i-statll)nary prf)hahl]lty i][)w r)v?r l}]t! f]wrion barrlt!r }1,L\ }It’1111

!~t)tdlr)e{~ froml a ()~e-~lmensl()n~l tl;]i!*-ot$\)~*l\(l~*rlt F(~kkor.l)lan( k ptill~tlt)r)”” ‘1

I)llrlrlg thw4~’ ~adfil~-t(>srlssi{)r~ AIId f ranslont lIIIIt*q, AIj(j II IOIIAl flo~i[r{)rl 011, II\ SII If I I *I:

Ifi

cake piace relative [f} Ihdt Calculateli from evaporation in a standard statistical !IIL1{](’I.$IJCh

enhanced neutron t,rnission has been ot)servt’d expt~rin)entalls in 4eavy-ion-ir](!ll~~i~~ fi~~io!l

reactions;’ 77. .41thuugh some important differcncm In the exper~rncnta] results still remain.

the analysis O( this enhancement in terms of neutron emission during tilt) sad(ilc-to-s(’ issif)n

iin(i transient times nevertheless suggests that fission is somewhat ovtlrdampedX”.

t..;. .Additional experiments related to dissipation

W)cquetg? described mez+uremcnts of the odd-evt~n efTec+ “: fission-fragment charge (ii+

tributions for the neutroli-induced fission of nuclei r~nging [rem thorium to cii]ifofllilJI~l.

For the fission of uranium isotopes, this odd-even effect decreaes from about 23Y for zero

excitation energy at the saddle point to about .l&o for 4 \leV excitation energy at the saddle

point. This dramatic decrease in odd-even effect with such a small incre~e in excitation

energy led Bocquet to conclude that the energy dissipation between the saddle and scission

points is very small at low excitation energies. In particular, he found that the energy dissi-

pated between saddle and scission ranges from about 3 NleV for thorium to about 10 \lv\”

for californium,

‘s G6nnenwein showed highly resolved scattt?r plotsPresenting a paper of Signarbieux ,

~f fission fragments vers~s their mass and kinetic energy. In the extreme high-energy tails

of these distributions, essentially all of the energy released in fission goes into the kinrtir

energy of the fragments, with zero neutron emission, Although these high-energy events arc

only a tiny !’raction of the total events, they nevertheless correspond to situations in which

there is no dissipation of energy ~!tween the saddle and scission points.

Scveral other experin,ents were discussed at the conference whose proper analysis could

in principle yield information on nuclear dissipation, These include fission induced by rli(lotls,

iintiprotons, and lam bda,ss’, light-particle-accompanied fission esed, scission rmutronss’, iind

the emission of charged particles and gammaa prior to scission,

Although several issues still remain to be clarified, our present picture is that ttlc vnrrgy

dissipated between the saddle and scission points is small for low initial excitation (Int’rgy

at the saddle puirtt and increaaea with increasing excitation energy, At moderate e)((iti~tioll

onvrgies, the dissipation of large-amplitude nuclear collective energy into internal singlw

i)articlc excitation energy arises primarily from the interaction of nuclcons with Ihv trit~iit)

tIPld ~n~ with each other in the vicinity of the nuclear surface, as w(’II M from tht’ tr,lnsf’vr

of nU(lW)rIS thr~ug}l tl)e win(~ow ~rparat:ng the two portions of a dulnbbvll-lik(l systt~lll, ‘1’}1(1

rrlii~tlitude of dissipation at moderate excitation energies corresponds to dynarr II(Al rIIOI io[i

thdt 1~ somewhat overdamped,

turned to the birthplace of our odyssey and completed o~lr asscssrncnt, we S(VI I\IAt II i>

not yet over. Fisslor) continues to surprise us, and important cha]lcrrges lie it};(’i~{l. “l’!lt,>f)

iflclude devising t“xperirnents to unambiguously distinguish dissipative effec[s from Alldl-

ogous effects caused b}’ collective degrees o! freedor~, further refinirlg the prc(ii(’tions of

the macroscopic-microscopic method, and computing fission directly from the underlying

hadronic interaction,

In the last area, much remains to be done even within the restriction of an effective t\vo-

nucleon interaction treated ic the nonrelativisric approximation. But it is also important

to extend this work by using a more realistic interaction, as well as in another direction I)y

!~sirtg a relativistic approximation suitable for spin- ~ nucleons. The ultimate challenge is

of course to start at ‘he level of quantum chromodynamics, with explici[ quark and gluon

degrees of freedom taken 1,.’o account.

Large-amplitude collective nuclear motion, as exemplified by fission, should continue LO

provide an invaluable testing ground to; nuclear many-body theories. The next sO years

could be even more exciting than the first!

.4 CKSOW’LEDGEMEST

I am grateful to D, C. Hoffman, J. Ylachen, P. !L!oller, and R. ~’o~.denbosch for stimulating

discussions while writing this summary,

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