1,

Fissioninvolves a new state of nuclearmatter

C.YTHIER, S. HACHEMand G. MOUZE

Faculté des Sciences, 06108 Nice cedex 2, France

PACS25.85.-w - Fissionreactions

PACS25.70 Jj - Fusionand fusion-fission reactions PACS 21.60 Gx - Clustermodel

Abstract-The rearrangementstep of nuclearfission occurs within 0.17 yoctosecond, in a new state of nuclearmatter characterized by the formationof closed shellsof nucleons.The determinationof its lifetimeis now based on the prompt neutron emissionlaw. The width of isotopicdistributions measures the uncertaintyin the neutronnumber of the fragments.Magic mass numbers,82 and 126,play a major role in the mass distributions.Arguments are presentedin favourof an all-neutron state. The boson field responsiblefor the new collectiveinteraction has to be searchedfor.

Introduction. - An overallpicture of our modelof binarynuclear fission was recently givenby R.A.Ricci in EurophysicsNews [1]. But seeing that F. Gônnenweindoes not believe[2] that fission occurs within 1.7 10-2ss,we willfirst try to justifythat this holds for all the fissioningsystems considered by J. Terrellin his work on promptneutron "nucleon emission[3], and thenwe willtry to showthat the ideaof closed shells"was alreadycontained in anotherpaper by J. Terrell t4l and can explainthe mass distributionsof binaryfission.

Fission occurs within 0.17 yoctosecond-In 1957,J. Terrellshowed that the probabilityP(u) of emittingv neutronsper fission,represented as functionof the - difference(v v), where7 is the averagenumber of neutronsemitted per fission, is a Gaussiancurve having a o - parameterof 1.08, or a full-width-at-half-maximumof 2'538 neutrons.Indeed, the data obtainedf rom the followingspontaneously 238'240'242Pu,2a2'2aaç^ 252Cf 233,235U zssp, fissioning nuclei, and and from and irradiatedwith B0 keV neutrons, were perfectly fitted by such a curve, as demonstratedby his figure4 [3],reproduced in manytextbooks, e.g. in [5].J. Terrell triedto explainthis situationas resultingfrom largevariances in totalkinetic energy and hencein excitationenergy of the fragments.

ln the nineties,the study, in particularby J.H. Hamiltonet al. 16,71,using coincidencemethods and detectorssuch as Gammasphere,of the promptgamma raysemitted by neutron-richfission fragments, revealed that the isotopicdistributions of fission fragmentscan be representedby Gaussiancurves, and J.L. DurelltB] pointedout that all isotopicdistributions encountered in fissionhave exactly the same widthas thatfound by J. Terrellfor the P(u)distribution; as an example,J.L. Durell 2

showed that all the isotopicdistributions of Zr fragmentsassociated in y-y totBa totBa, coincidenceswith each of the Ba fragmentsfrom to observedin the 2oBCm, spontaneousfission of have a width of 2.54 mass units (u) . J.L.Durell proposedthe sameexplanation as Terrell.

Let us look at the particularZr-isotopic distribution which correspondsto 148 coincidenceswith Ba, displayede.g. in ref.[B].As a consequenceof matter conservation,this distributioncannot extend beyond N=60, i.e. beyond toozr, for 'otcm the fissioningsystem. And, for the same reason,no promptneutron can have beenemitted at N=60,as notedby J.L. Durellhimself: lsotopic distributions of fission fragmentsteach us how these fragmentsare formedat the same time that prompt neutronemission occurs.

Another observationcan be made in this distribution.The abscissaN of the maximumof the Gaussiandistribution is the mostprobabte value of the "neLttron number N" of the various Zr isotopeswhich can be formed in this particular coincidence.And, as expectedfor a randomphenomenon, N is non-integer.lndeed, a value N-- 5B,4 has been found by J.L. Durell in the coincidenceswith 1oBBa, whereashe foundN- 61.B in the loz}acase.

Moreoverit may be asked why the wldth of the Gaussiandistributions has a - constantvalue 2.54u , in so manydifferent experiments, and for so manydifferent fissioningsystems: This situationclearly indicates that promptneutron emissio n and fragmentformation both occur within an extremelyshort time intervalAt.

ln our opinion,due to the brevityof the fissionreaction, the energy-timeuncertainty relationAE. At = h has to playa majorrole in its description.To the uncertaintyAE correspondsan uncertaintyAA = LElc',and to AA corresponduncertainties AN in N andLZ in Z. And the finiteand constantvalue of the widthAN can be interpretedas "uncertainty the in the neutronnumber N" of the fragment.With AN = (N/A)AA, and with a value 1-6449for the mean value of A/N in the fissioningsystems taken into considerationby J. Terrell,we getthe followingvalue for AJ, it AN -2.538 u. -25 AJ= hlcztV*l N = 1.696 1o s (1)

Thismean value of the reactiontime of the fissionreaction for the lightactinide nuclei is now basedon the considerablework made in the fiftiesfor determiningv p("), "data and i.e. on which are of the utmostpractical importance in the applicationof the chainreaction in reactorsand explosives" [9]. -2ss A valueAt = 1.7710 , quotedin [1],had been announced in 1993by G. Mouze and C. Ythier[10].This value was based only on cold fissiondata concerningthe 235U reaction * flt' at the highesttotal kinetic energy I1 1l.A similarvalue was recenly deducedfrom other old coldfission experiments 1121. 3

To each primaryfission fragment are attached,as a kindof trademark,uncertainties AA, AN and LZ. Az is given by the difference ^Â - N = 1.6g7proton; it is the modernexpression of the distributionlaw of the chargein fission.

It mustbe pointedout thata reactiontime of 0.17yoctosecond is not surprisingfor a reactionoccurring within an atomic nucleus.lf the reactiontime of a chemical reaction can be defined as the ratio of range (- of interactionto velocity of propagationof the interaction,its smallestvalue is ( lc,i.e., for a reactionoccurring betweenH and Cl in -0.43 a HCImolecule, 1018s, with/ - 1.2T4SS10-10 m t131. And for a reactionoccurring within the most externalvalence shells of a nucleus,I can be about107 times smaller, and At can be of the orderof 1 10-25s.lnterestingly, thevalue at = 0.1Tys correspondsto a rangeof -5.0g 10-17m.

The closureof nucleonshells at A = 82 and A =126.- During the time intervatAt, = an energy AE 3.8 GeV is at disposalof the fissioningsystem. This corresponds to a temperatureT = LE/k = 4.5 1013K. One may speakof extremeconditions. In 2008 Mouzeand Ythier[14] suggested that in so extremeconditions a new state of nuclear matter could be created,in which any distinctionbetween proton and neutron seemsto havedisappeared. And they showedthat the massdistributions of asymmetric fission,and eventhose of symmetricfission, could be explainedif one assumes "nucleons", that insteadof differentiatedprotons and neutrons,form, as a "mass consequenceof the spin-orbitcoupling, closed shells at magic numbers"82 and 126.

Indeed,if one assumes,as proposedby Ythier and Mouze at the Karlsruhe 235U "clusterize" Symposium[15], that a fissioningsystem, such as * îtn,can intoa 20BPb "Ne, dinuclearsystem + with a great energy-release, the possibilityof a collisionof core and clustercannot be excluded.But what can happenin such an internalcollision? lt cannotsimply be the capture,by the cluster,of 76 valence t"sn nucleons,or less,of the deep-lyingdoubly magic core,as initiallyproposed "nucleon 2o8pb [16]: the hypothesisof the creationof an A = 126 core"in leadsto a betterdescription of the massdistributions occurring in fission. 235U ln the asymmetricfission of * fltn, for example,the transferof the 82 valence 208Pb "nucleon nucleonsreleased by allowsthe formationof an A = 82 core"around the cluster,of mass numberA"1 (equal to 28 in this case).Themass numberof the lightfragment, AL, is also comprisedbetween Art't = 82 and A'MAX- Aç1+ 82, i.e. '1 10,whereas AH is comprisedbetween Art't _ 126and AnMAX _ 126_W_ (82_Act)l = 126+ Acr,i.e. 154. The widthof the regionof appreciableyield, AA= Avnx- Axalp,is the samefor light and heavyfragment, and equalto A"1(first Hachem rule [17]),i.e. AA= 28u. 4

"'Ct, 258Fm ln the symmetricfission of nucleiheavier than e.g.in thatof 1or'08pb- toAt), -- "nucleon the formationof an A 126 core"becomes possible even in the light fragment.This formation explains the narrowwidth of the distributions.Indeed, Art't = = 126,Arto* Acr+ 82 = 132,Art't - 126,Arto* = 12G- W - (26-A.r)] - Acr+82 -132. Thus AA = (A.r- 44) u = 6 u (secondHachem rure)[1 g] for the now singre peakof the distribution.

The widthof B u foundexperimentally [19] can be justified by the uncertaintyin A [20];in fact AA.*p- (Acr-44\ + 2 u.

The ideaof closednucleon shells can find itsjustification in observationsmade by J. Terrellin 1962[a]. First,he reportedthat fission fragments with A = 82 and A = 126 do not emit promptneutrons, and that the promptneutron yield increaseslinearly abovethese A- values;more precisely, the numberof promptneutrons emitted by the lightfragment can be representedby v(L) = 0.08 (AL-82) and that emittedby the - heavyfragment by u(H) 0.10 (AH- 126).Moreover, concerning the lowerlimits of "asymmetric the mass distributions,he made the importantobservation that fission seems to be characterizedby the relation At define quite accurately the region of appreciableyietd. They a/so seem to be the point at which neutron yield nearly vanishes".He noted that AH = 126 has to be "gives preferredto A = 128,because 126 a betterlinear representationof v(H)". "nucleons" Could the nucleonphase be an all-neutronstate ?.- The of thisphase deserveto be callednucleons since mass-numbers, rather than proton-and neutron- numbers,without doubt play a majorrole. But what are these nucleons? The survival, "spin- in this phase,of the magicnumbers 82 and 126 clearlysuggests that the orbit couplingstill plays a role,and consequentlythat theseparticles still have a sprn.But it may be asked:Are they all protons,or all neutrons?We presentat least two argumentsin favour of a neutronstate, i.e. in favour of a disappearanceof the charge'First we observedthat in ordinarynuclear matter, it is fhe Coulomb potential of the protonsthat is responsiblefor the particularseries of energy states of the protonphase. lndeed, the seriesof statesof the neutronphase result from the sole spin- orbit coupling.Thus, the disappearanceof the protons,because they are changedinto neutrons,would lead to a pure neutronphase, and this justifies "mass that magic numbers"such as 82 and 126intervene. Secondly, an all-neutronstate duringthe rearrangementstep seems necessaryfor the formationof fragmentsin conditionsin whichtheir neutron-numberis affectedby a considerableuncertainty. Moreoverat the end of thisstep, as protonsare presentagain, the ratioN/Z is stillso greatthat a seriesof betadecays is necessaryin orderto get the finalmuch smaller value.

Could the creationof the new phase be relatedto an interactionwith W* and -boson W fields? - lt may be askedwhether the all-neutronstate can be explained by the knowninteractions encountered in high-energyphysics, e.g. by the interaction 5 withthe Wt -bosonfield . lt is well knownthat the W bosonfield is involvedin the p- decayof the fissionproducts. There, a d-quarkbecomes changed into a u- quark at each step of the decaychain. lf the chargeof Z protonsof the fissioningsystem disappears,and then reappears,it meansthat now a numberZ of u-quarksare changedinto a numberZ of d- quarks,which then reappear,changed into a number Zotu-quarks.

But can the interactionwith the W- fieldshave such a collectivecharacter that, insteadof only one, in fact Z quarkscan be changed?Moreover, what happensto the leptonsinvolved in thesequark-changes? ls it necessaryto assumethat these changesoccur within a so shorttime intervalthat no leptonis emitted?ln fact,the lifetimeof the new phaseis equalto 1.69710-25s: it is remarkablyshorter than that of the Wt -boson,i.e. 3.074 10-25 s , and evenshorter than that of the Zo-boson, i.e. 25 2.637810 s l21l; maybe,such a lifetimeis shortenough for explainingthat no one leptonis observed. Moreover,this extremelyshort lifetimesuggests that it could correspondto a veryheavy intermediary new particle.lndeed, one observesthat the ratio R = Mi r of mass and energy-widthis almost constantfor the Wt and Zo - bosons,and equalto 35.74and 36.548 respectively. with I- equalto h/ at = 6.58210 " GeVsI 1.6971O-25 s, i.e.to 3.878GeV, for the nucleonphase, a mass equalto 3.B7B X 36.1 46 = 140 .17 4 GeV/ c' ,or even greater, cou ld be predicted for the intermediaryparticle; but, why not a massgreater than M(2W)= 160.8GeVic2, the massof the W* -W- bosonpair ? An interactionof the fissioningsystem with W* and W-fields could so be justified.

Conclusion.-One seesthat the extremebrevity of the fissionreaction can no more be contested.Fission occurs more than thousand times fasterthan betievedsrnce seventyyears.

Symmetricas well as asymmetricmass distributionscan now be explained.This explanationreveals that spin-orbitcoupling is a fundamentalproperty of nuclear matter,since it survivesin extremeconditions.

The fact thatthe chargeof all protonsdisappears and reappearsin the ephemeral new phase stronglysuggests that they interactwith the ltll and W boson fields,But whatdo we reallyknow about the truenature of the chargel22l?

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