1,
Fission involvesa new state of nuclearmatter
C . Y T H I E RS, . H A C H E Ma n d G . M O U Z E
Faculté des Sciences, 06108 Nice cedex 2, France
PACS25.85.-w- Fissionreactions
PACS25.70Jj - Fusionand fusion-fission
reactions
PACS 21.60 Gx - Clustermodel
Abstract-The rearrangement
stepof nuclearfissionoccurswithin0.17yoctosecond,
in a new state of nuclearmattercharacterizedby the formationof closed shells of
nucleons.The determination
of its lifetimeis now based on the prompt neutron
emissionlaw. The width of isotopicdistributions
measuresthe uncertaintyin the
neutronnumberof the fragments.Magicmass numbers,82 and 126,play a major
role in the mass distributions.
Argumentsare presentedin favourof an all-neutron
state. The boson field responsiblefor the new collectiveinteractionhas to be
searchedfor.
Introduction. - An overallpictureof our modelof binarynuclearfissionwas recently
g i v e nb y R . A .R i c c i n E u r o p h y s i cNse w s[ 1 ] .B u t s e e i n gt h a t F . G ô n n e n w e idno e sn o t
believe[2] that fissionoccurswithin1.7 10-2ss,
we willfirsttry to justifythat this holds
for all the fissioningsystemsconsideredby J. Terrellin his work on promptneutron
emission[3],and then we willtry to showthat the ideaof closed"nucleonshells"was
alreadycontainedin another paper by J. Terrell t4l and can explainthe mass
distributions
of binaryfission.
F i s s i o n o c c u r s w i t h i n 0 . 1 7 y o c t o s e c o n d -I n 1 9 5 7 , J . T e r r e l ls h o w e dt h a t t h e
probabilityP(u) of emittingv neutronsper fission,representedas functionof the
difference(v - v), where7 is the averagenumberof neutronsemittedper fission,is a
Gaussiancurvehavinga o - parameterof 1.08, or a full-width-at-half-maximum
of
2 ' 5 3 8 n e u t r o n s .I n d e e d , t h e d a t a o b t a i n e df r o m t h e f o l l o w i n gs p o n t a n e o u s l y
f i s s i o n i n g n u c l e i , 2 3 8 ' 2 4 0 ' 2 4 2 P2ua, 2 ' 2 a a ç ^ a n d 2 5 2 C f a n d f r o m 2 3 3 , 2 3 5 Ua n d z s s p ,
irradiated with B0 keV neutrons, were perfectly fitted by such a curve, as
demonstrated
by his figure4 [3],reproducedin manytextbooks,e.g. in [5].J. Terrell
triedto explainthis situationas resultingfrom largevariancesin total kineticenergy
and hencein excitation
energyof the fragments.
ln the nineties,the study, in particularby J.H. Hamilton et al. 16,71,using
coincidencemethodsand detectorssuch as Gammasphere,
of the promptgamma
raysemittedby neutron-rich
fissionfragments,revealedthatthe isotopicdistributions
of fissionfragmentscan be representedby Gaussiancurves,and J.L. Durell
tB]
pointedout that all isotopicdistributions
encountered
in fissionhaveexactlythe same
widthas that found by J. Terrellfor the P(u)distribution;
as an example,J.L. Durell
2
showed that all the isotopic distributionsof Zr fragments associated in y-y
coincidences
with each of the Ba fragmentsfrom totBa to totBa,observedin the
spontaneousfissionof 2oBCm,
have a width of 2.54 mass units (u) . J.L.Durell
proposedthe sameexplanation
as Terrell.
Let us look at the particularZr-isotopicdistributionwhich correspondsto
coincidenceswith 148Ba, displayede.g. in ref.[B].As a consequenceof matter
conservation,
this distribution
cannotextendbeyondN=60,i.e. beyondtoozr,for the
'otcm fissioning
system.And, for the same reason,no prompt neutroncan have
beenemittedat N=60,as notedby J.L. Durellhimself:lsotopicdistributions
of fission
fragmentsteach us how these fragmentsare formed at the same time that prompt
neutronemissionoccurs.
Another observationcan be made in this distribution.
The abscissa N of the
maximumof the Gaussiandistributionis the mostprobabtevalue of the "neLttron
number N" of the various Zr isotopeswhich can be formed in this particular
c o i n c i d e n c eA.n d , a s e x p e c t e df o r a r a n d o mp h e n o m e n o nN, i s n o n - i n t e g e lrn. d e e d ,
a v a l u e N - 5 B , 4 h a s b e e n f o u n d b y J .L . D ur e l l i n t h e c o i n c i d e n c ew
s ith 1oBBa,
loz}a
whereashe foundN- 61.B in the
case.
Moreoverit may be asked why the wldth of the Gaussiandistributionshas a
constantvalue- 2.54 u , in so manydifferentexperiments,
and for so many different
fissioningsystems:This situationclearlyindicatesthat promptneutronemission and
fragmentformationboth occurwithinan extremelyshorttime intervalAt.
ln our opinion,due to the brevityof the fissionreaction,the energy-timeuncertainty
relationAE. At = h has to play a majorrole in its description.
To the uncertainty
AE
corresponds
an uncertainty
AA = LElc', and to AA correspond
uncertainties
AN in N
and LZ in Z. And the finiteand constantvalueof the widthAN can be interpreted
as
"uncertainty
the
in the neutronnumberN" of the fragment.With AN = (N/A)AA, and
with a value 1-6449for the mean value of A/N in the fissioningsystemstaken into
consideration
by J. Terrell,we get the followingvaluefor AJ, it AN -2.538 u.
AJ= hlcztV*l N = 1.6961o -25s
(1)
This meanvalueof the reactiontime of the fissionreactionfor the lightactinidenuclei
is now basedon the considerable
work made in the fiftiesfor determining
v and p("),
i.e. on "datawhich are of the utmostpracticalimportancein the applicationof the
chainreactionin reactorsand explosives"
[9].
A v a l u eA t = 1 . 7 71 0 - 2 s s, q u o t e d i n [ 1 ] ,h a d b e e na n n o u n c e d
i n 1 9 9 3b y G . M o u z e
and C. Ythier [10].Thisvalue was based only on cold fissiondata concerningthe
reaction235U
* flt' at the highesttotalkineticenergyI11l.A similarvaluewas recenly
deducedfrom otherold coldfissionexperiments
1121.
3
To each primaryfissionfragmentare attached,as a kindof trademark,uncertainties
AA, AN and LZ. Az is given by the difference ^Â - N = 1.6g7 proton;it is the
modernexpressionof the distribution
law of the chargein fission.
It must be pointedout that a reactiontime of 0.17 yoctosecond
is not surprisingfor a
reactionoccurringwithin an atomic nucleus.lf the reactiontime of a chemical
reaction can be defined as the ratio of range (- of interactionto velocity of
propagation
of the interaction,
its smallestvalue is ( lc, i.e.,for a reactionoccurring
b e t w e e nH a n d C l i n a H C I m o l e c u l e-,0 . 4 3 1 0 1 8s , w i t h / - 1 . 2 T 4 S S
10-1m
0 t131.
And for a reactionoccurringwithinthe most externalvalenceshellsof a nucleus,I
c a n b e a b o u t1 0 7t i m e ss m a l l e ra, n d A t c a n b e o f t h e o r d e ro f 1 1 0 - 2 5 s . l n t e r e s t i n g l y ,
t h e v a l u e a t = 0 . 1 Ty s c o r r e s p o n dtso a r a n g eo f - 5 . 0 g 1 0 - 1m
7.
T h e c l o s u r e o f n u c l e o ns h e l l s a t A = 8 2 a n d A = 12 6 . -D u r i n gt h e t i m e i n t e r v aAt t ,
an energy AE = 3.8 GeV is at disposalof the fissioningsystem.This corresponds
to
=
a temperature
T LE/k = 4.5 1013K. One may speakof extremeconditions.
In 2008 Mouzeand Ythier[14] suggestedthat in so extremeconditionsa new
state
of nuclear matter could be created,in which any distinctionbetween proton
and
neutronseemsto havedisappeared.
And they showedthat the mass distributions
of
asymmetricfission,and even those of symmetricfission,could be explainedif
one
assumesthat "nucleons",
insteadof differentiated
protonsand neutrons,form, as a
c o n s e q u e n c oe f t h e s p i n - o r b ict o u p l i n gc, l o s e ds h e l l sa t m a g i c" m a s sn u m b e r s "8 2
a n d 12 6 .
Indeed, if one assumes,as proposedby Ythier and Mouze at the Karlsruhe
Symposium[15],that a fissioningsystem,such as 235U* îtn, can "clusterize"
into a
dinuclearsystem 20BPb+ "Ne, with a great energy-release,the possibilityof a
collisionof core and clustercannotbe excluded.But what can happenin such an
internalcollision?lt cannot simply be the capture,by the cluster,of 76 valence
n u c l e o n so, r l e s s ,o f t h e d e e p - l y i n g
d o u b l ym a g i c t " s n c o r e ,a s i n i t i a l l yp r o p o s e d
[16]: the hypothesisof the creationof an A = 126"nucleoncore"in 2o8pbleadsto a
betterdescription
of the massdistributions
occurringin fission.
ln the asymmetricfissionof 235U* fltn, for example,the transferof the 82 valence
nucleonsreleasedby 208Pb
allowsthe formationof an A = 82 "nucleoncore"around
the cluster,of mass numberA"1(equalto 28 in this case).Themass numberof the
lightfragment,AL, is also comprisedbetweenArt't = 82 and A'MAX- Aç1+ 82, i.e.
'1
10, whereasAHis comprisedbetweenArt't _ 126and AnMAX
_ 126_W_ (82_Act)l
= 126 + Acr,i.e.154.The widthof the regionof appreciable
yield,AA= Avnx- Axalp,
is
the same for lightand heavyfragment,and equalto A"1(firstHachemrule 7]),i.e.
[1
AA= 28u.
4
l n t h e s y m m e t r i fci s s i o no f n u c l e ih e a v i e trh a n " ' C t , e . g . i n t h a t o f 2 5 8 F m
1or'08pbtoAt),the formation
of an A -- 126"nucleoncore"becomespossibleeven in the light
fragment.This formationexplainsthe narrowwidthof the distributions.
Indeed,Art't
= 126,Arto* = Acr+ 82 = 132,Art't - 126,Arto* = 12GW - (26-A.r)] - Acr+82
- 1 3 2 . T h u s A A = ( A . r- 4 4 ) u = 6 u ( s e c o n dH a c h e mr u r e ) [g1] f o r t h e n o w s i n g r e
peakof the distribution.
The width of B u found experimentally
[19] can be justified by the uncertaintyin A
-44\
+ 2 u.
[20];in fact AA.*p (Acr
The ideaof closednucleonshellscan find itsjustification
in observations
made by J.
Terrellin 1962 [a]. First,he reportedthat fissionfragmentswith A = 82 and A = 126
do not emit promptneutrons,and that the promptneutronyield increaseslinearly
abovetheseA- values;moreprecisely,
the numberof promptneutronsemittedby the
lightfragmentcan be representedby v(L) = 0.08 (AL-82) and that emittedby the
heavyfragmentby u(H) - 0.10 (AH- 126).Moreover,concerningthe lowerlimitsof
the mass distributions,
he made the importantobservation
that "asymmetricfission
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
preferredto A = 128,because126"givesa betterlinear representation
of v(H)".
C o u l d t h e n u c l e o n p h a s e b e a n a l l - n e u t r o ns t a t e ? . - T h e " n u c l e o n so"f t h i s p h a s e
deserveto be callednucleonssincemass-numbers,
ratherthan proton-and neutronnumbers,withoutdoubtplaya majorrole.But whatare thesenucleons?The survival,
in this phase,of the magicnumbers82 and 126 clearlysuggeststhat the "spin-orbit
couplingstill playsa role,and consequently
that these particlesstill 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'Firstwe observedthat in ordinarynuclearmatter,it is fhe Coulomb potential
of the protons that is responsiblefor the particularseries of energy states of the
protonphase.lndeed,the seriesof statesof the neutronphaseresultfrom the sole
spin- orbit coupling.Thus, the disappearanceof the protons,becausethey are
changedinto neutrons,would lead to a pure neutronphase,and this justifiesthat
magic"massnumbers"such as 82 and 126 intervene.
Secondly,an all-neutron
state
duringthe rearrangement
step seems necessaryfor the formationof fragmentsin
conditionsin which their neutron-number
is affectedby a considerable
uncertainty.
Moreoverat the end of this step,as protonsare presentagain,the ratioN/Z is stillso
greatthat a seriesof betadecaysis necessaryin orderto get the final much smaller
value.
Could the creation of the new phase be relatedto an interactionwith W* and
W -boson fields? - lt may be askedwhetherthe all-neutron
statecan be explained
by the knowninteractions
encountered
in high-energy
physics,e.g. by the interaction
5
with the Wt -bosonfield . lt is well knownthat the W bosonfield is involvedin the
p- decayof the fissionproducts.There,a d-quarkbecomeschangedinto a u- quark
at each step of the decaychain.lf the chargeof Z protonsof the fissioningsystem
disappears,and then reappears,it means that now a numberZ of u-quarksare
c h a n g e di n t oa n u m b e rZ o f d - q u a r k s w
, h i c ht h e n r e a p p e a rc, h a n g e di n t oa n u m b e r
Zotu-quarks.
But can the interactionwith the W- fields have such a collectivecharacterthat,
insteadof only one, in fact Z quarkscan be changed?Moreover,what happensto
the leptonsinvolvedin these quark-changes?
ls it necessaryto assumethat these
changesoccurwithina so shorttime intervalthat no leptonis emitted?ln fact, the
lifetimeof the new phaseis equalto 1.69710-25s:
it is remarkably
shorterthan that of
b
o
s
o
n
,
the Wt
i . e . 3 . 0 7 41 0 - 2 s5 , a n d e v e n s h o r t e rt h a n t h a t o f t h e Z o - b o s o n ,i . e .
25
2.637810 s l21l; maybe,sucha lifetimeis shortenoughfor explaining
that no one
leptonis observed. Moreover,this extremelyshort lifetimesuggeststhat it could
correspond
to a veryheavyintermediary
new particle.lndeed,one observesthat the
ratio R = Mi r of mass and energy-widthis almost constantfor the Wt and Zo bosons,and equalto 35.74 and36.548respectively.
with I- equalto h/ at = 6.582 10
" GeVs 1.697
1 O - 2s5, i . e . t o 3 . 8 7 8G e V , f o r t h e n u c l e o np h a s e ,a m a s s e q u a lt o
I
3.B7B X 36.146 = 140.174 GeV/ c' ,or even greater,could be predicted for the
intermediary
particle;but, why not a mass greaterthan M(2W)= 160.8GeVic2,the
massof the W* -W- bosonpair ? An interaction
of the fissioningsystemwithW* and
W- fieldscouldso be justified.
Conclusion.-One sees that the extremebrevityof the fissionreactioncan no more
be contested.Fission occurs more than thousand times faster than betievedsrnce
seventyyears.
Symmetricas well as asymmetricmass distributions
can now be explained.This
explanationreveals that spin-orbitcoupling is a fundamentalproperty of nuclear
matter,sinceit survivesin extremeconditions.
The fact that the chargeof all protonsdisappearsand reappearsin the ephemeral
new phase stronglysuggeststhat they interactwith the ltll and W boson fields,But
whatdo we reallyknowaboutthe true natureof the chargel22l?
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