REVISTA MEXICANA DE FíSICA"S S(,:)'LE:\IE~T() 2. 6.1-7.1 OCTURRE 1999

011 thc cxtcnsion 01' thc pcriodic systcm 01' c1cmcnts and relatcd topics

\Valtcr GreinerIflsrit/lljiir TheoreliJchc PhY.'lik, 1. W Goelhe-iJllil'l'r.vitiil, IJ-60054 Pral/kjilrt. GernulII)'

(,-Illai 1: g rf.'Íner@I/¡.I,hY.'lik.un i -jrall~f/I n. de

Recihido el I de fehrero de 1999; aceplado el 20 dc anril de 1999

The extcnsioll of the pcriodic ~yslem into various new arcas is investigated. Expcriments for the syntbcsis 01' supcrheavy elemcnts and thepredictions nI' magic numhers Jre reviewed, Different ways 01' nuclear decay are discusscd Iike cluster radioactivity, cold fission and coldmullifr3gmentalion. including the rccent discovcry 01'Ihe triple lission of :.lY2Cf and long-living threc-clustcr nuclear molccules. Furthcrmore.lhe possihility of production 01'cluslers 01'hypcrmattcr amI amimattcr in high encrgy hcavy-ion collisions is envisagcd. A perspeclive for (hefUlllre is givclI.

KI'YII'Ofds: Supcrhcavy clcmems: cold valleys; cold fission; temar)' fission: Illeson lIeld Ihcory: c.\lcnsion of the pcriodic (ahle

Se investiga 1.1 extensión del sislema periódico a varias arcas nuevas. Se presenta Ulla revisión lk los experimentos para la síntesis de loselementos super-pesados y las predicciones de los números mágicos. Se discuten varios tipos de dl'caimicntos lIucleares, tales como laradioactividad de cúmulo. la fisión fría y la fragmentación multiple fría, incluyendo el descuhrimiellto de la fisión triple de 252Cf y lasmoléculas nucleares de tres cúmulos. Adicionalmente se contempla la posibilidad de la proJucci(lIl de cúmulos de hipcr.malcria y anti-lllílleriJ en reacciones de iones pesados a energías altas. Se da una perspectiva para el fUluro.

/)(',\'(',-il,/ore.c Elementos super.pesados: valles fríos: tlSiÓll fría; fisión ternaria: leoría de campos rnes!Ínicos: extcnsi!Ín de la tabla periódica

PACS: 21.60.-n: 21.80.+a: 25.85.Ca: 27.9O.+h

2. Cnld \'all~)'s in lh~ I'ntential

The imporlant qlleslion \Vas how lo produce lhese superheavynuclei. Therc wcrc Illany allelllpls. hUI only ¡¡ule progrcsswas made. I! \Vas 1l0111I1lillhe lIliJdle nI' Ihe scvenlies thal the

FI(jURE l. Thc periodic SYSICJlI 01"elelllcnts as conccivcd hy thcrr:lIlkfurt SdH){)1 in the lale sixties. The islands of superheavy c1-Clllonts (2 = 11.1.N = 184, IOG) and (2 = 16.1,N = 318) areshown as dark h:Jlchcd arcas.

318

300 N

INSTABILfTY

=::::'-'Sponla.neou!.--'\

NuclearFio.síon

200

1M 196 236 2n'"100

164 /SEA / N<Z

// OF

Nud ••ar fission and114 u-dl"Cay

TIoo¡(p)=lO'°M"C82

[>t-<:~y Mod('S

1".'./-1el lJ lJ p n

Z200

N = 184 or N = 1!JG. Typical prediclions 01' their Jife timesvaried belwcen seconds :lIld Illany IhousanLl ycars. Fig. lsutl1l11arizes lhe expccl:llions al Ihe time. One can see Iheislands of superheilvy elemellls around Z = 114, N = 184:l1ll1 N = 10G. respectivcly, ¡¡mi (he olle around Z = IG4,N = :1l8.

1. 1ntroduction

There are fundamental queslions in science, likc, e.g, "howdid Jife emergc" or "how Lloes our hrain work" ano olhcrs.lIowever, lhe Illost fundamental ol' lhose queslions is "howdid lhe world originate?". Tite material world has lo exisl he.rore lile and lhinking can dcvelop. Of particular importanceare Ihe suhslances lhemsclvcs, i.e., lhe clcments. On this 1wanl lo repon loday.

Tile clelllcnts existing in nalurc are ordcrcd according\O thcir alomic (chcmical) propcrties in lhc pcriodic syslcmwhich \\'as dcvelopcd hy l\.1cndelccv anLl LOlhar Mcyer. Theheavicsl elelllent 01' nalural origin is UraniuITI. hs 1111cleusiscOlllposed 01' ?: = 92 prololls and a cerlain numher 01' neu-trons (128 S; N S; 150). They are called Ihe differenl Ura-niulll isotopcs. Thc lransuranium eleIl1cnts reach fmm Nep-lunium (2 = !.J:l) via Californium (2 = 98) and Fefmium(X = lOO) up lO Lawrcnciurn (2 = 10:1). The heavier lhe el-clllcnls are, lhe larger are Ihcir radii and lheir numher nI' pro-lons. Thus. Ihe Coulomh repulsion in their interior ¡ncreases,and Ihey undcrgo lIssion. In olhcr wonls: Ihe IransuraniufIlL'lclllcnts hecorne more inslahle as lhey gel higger.

In lhe ¡ale sixtics lhe drcam of the superheavy clelllcnlsarosc. Theorctical nuclear physicists around S.G. Nilsson(Lund) 11) and frorn Ihe Frankfurt school [2-1] predicled Iha!so-calleel ctosed proton ami neutron shells should counleracllhe rcpclling Coulomb rorces. Atornic nuclei with these spe-dal "lIIngic" P"'lOll (¡fUi f1CUlmll f1umbers and their neigh-hors could again he rather slable. These magic prolon (2)and Ileutron (N) nurnhers were Ihoughllo he Z = 11.1 and

V.'At:rER GREI:SER

Fl<iUKE 2. Thc collcclivc pOlcnlial cncrgy surfaec 01'2!i11OX ami'i\.l11.t ca1culated wilhin Ihe Iw()-cenler shcll modcl hy J.A.,\1aruhn l'f nI.. shows c1early Ihe cokl vallcys which rcaeh up lolhL' harrier and hcyond. Itere U is Ihe dislance hem'een the frag:-lllcnb ami 'I = (.'\1 - ..b)/(.'\I + ..b) denoles lhe mass asymmc-ay: '1 = O corrcsponds lo a sYl11l1lelric.JI = ::tI lo an extremel)';",Ylllllll'lric division 01'lhe nuc1L'lIsinl() projecli1e and largel. If pro-jectik ami largel approach Ihrough a c{lld valley. they do nol "con-sl;1lltly slide off" as it would he Ihe case iflhey approach along IheSlllpC." al Ihe sides 01'the valley. ('ollslanl sliding causes heatíng, solh<ltIhL'cOl1lpollnd nuclells heats IIp aml g:elSunstabJc. In Ihe coldv;llky. tll1 Ihc other hano, lhe crcateo heal is minimiled. The mI.kaglil's fHll1lFrcihurg shollld he familiar with thal: lhey appw;u.:hTilisec (in Ihe Black Foresl) mosl clegant1y lhrough Ihe llüllenlalamI not hy clímhing its slopes along lhe mOllntains al ilS sides.

'''Jl2 eN

""110

70Zn + 208Pb _ 277112 + In

G, G,11UM~V.HO~.

3. Shell slrllclllre in lhe sllpcrhea\'y re¡.:ion

Studies of lhe shcll struclurl' 01"sllperheavy e!elllenls in Ihefralllc\I.'Ork of the llleSOIl lIeld lheory and the Skyrlllc-lIartrce-Fock approach have reccntly shown that the magic shells in(he superhcavy region <Ir!.::vcry isotope Jependcnt 1101 (sceFig, 4). AccordillK 10 rllese illvesligatiolls Z =: 120 beillM ti

1II11Micprololl lIulIlher see1ll.\' 10 he as probable liS Z = 114.AdJitionally. recenl investigalions in a chirally symmelriclllean-t1eld theory (see also hclow) result also in the predic-tion of these two magic numhers 132.33]. Thus, this rcgionproviJcs an oren licld of rcscarch. R.A. Gherghescu l'( al.have ca1culated Ihe pOlenlial energy surfacc 01' the Z = 120nucleus. It utilizcs interesting isomeric and valley struclures

(Fig 5),The determinalion of the chemistry of superheavy ele-

mcnts. i.c., Ihe calculatioll of the atomic structurc-which isin the case 01' clcment I 12 the shcll structure 01' 112 cleclrons

aralOr and the posilioll sensilive detcctors. which were espc-cially dcvclopl'd hy thclIl. they produced the prc-superhcavyl'Ielllents Z = lUG, I lli,. ., 11:2, each 01' them with the Ihe-metically prediclcd pn)jcr.:tilc-target comhinations. anJ only\Vith Ihese. Evcrylhing 1'Isl' bileJ. This is an impressing suc-cess, 'l,,'hich nowllcL! the lahorious conslruction v..'ork 01"lIlaoyycars. Thc last exalllplc 01' this success, the discovery of cl-elllcnt 112 anL! its long n-t\t:cay chain, is shown in Fig. 3.Vcry rccently. whik complcling this contri huI ion, I heardfmm Yuri Oganessian Ihal Ihe rcaction .18Ca + 2HpU --+:.H!HII,¡ + 3H has Il'ad lo a ralher long living (of ordcr scc-onds) 114 isotope. This rl';Ktion also procecds lhrough a coldvalley of type spherical plus deformed nucleus. The laller hasheen predicted in Ref. l).

FI<,URE 3. The fusion of c1CIllClll112 with jOZn as projcclile anJ'2n~l'h as targel nucleus has hL'cn accomplishcd fm lile /irsl lime inItN:) am11996 hy S, lIofmanll. (j. r..1iinzenherg and Ihcir collahora-torso Tlle colliLiing lludci determine an enlrance lo a "colo val1cy"as rreoicled as early as 197(, hy GlIpla, Sanduleseu. anJ Grcincr.The fuseLinucleus 112 dccays succcssively via o-cmission unlil ti-nally lhe qllasi-st<lhle lluclcllS ~".JFm is reached. The n-particlcs as\Vell as Ihe l1nal nuc1cus Ila\e hecn ohscrvcd. Comhined. this ren-dcrs Ihe dcflnitc rroof 01"Ihc exis(cncc of a Z = 112 nucleu ••.

""

Frankfurt school nI' thcoretical physics logether wilh for-cigll gUl'sts (R.K. Gupta, India. and A. Sandulescu, ROllla-ni,,) 1;) 1 theoretically 1I1lderstood and sllhstantiatcd the Clln-erpl or bOlllharding 01' dOllble lIlagic lead nuclei wilh suitahleprojl'ctiles, \,l,'hich had heen prnposeJ intuitively hy lh!.::RlIs-"ian lIuclear physicist Y. Oganessian 16). The two-cenlcr shcllmOlkL which i" essenlial fm the description 01' fission. fll-si(lIl and nuclear Illolcculcs. was dcvelopcJ in 1969-197210-gL'thL'r with my lh!.::llsllldents U. t\.1osel anu l.A. Maruhn ¡il.It showed that Ih!.::slH:1I slrllcturC 01"Ihe two final fraglllcllls\VilSvisihle far heyond Ihe harrier inlo the fusioning nuclclIs.lIJc L'ollcctivc potelllial ellergy surfaces of hcavy Iluclei. astllL'y were calculatcd in the framework ofthe two-ccnter shelllll111kl. exhihit pronollnced valleys. such that these vallcysprovidc pnllnising doorways to the fusion 01' supcrheavy nu~clei f(lf certain projcctile-targcl cornhinations (Fig. 2). 11"pro-jcclill' ;¡nd target approach each other through those "cold"mI/e.".\'. Ihey get only lIlinilll<llly exl;ireJ and the harrier whichha, lo hc o\'en:ome (fusion harricr) is lowcst (as comparedto nl'ighhoring projeclile-Iargct comhinations). In this ,,,,ayIhl' ((llTl'ct projectilc-targel comhinalions for fusion C(lllldhl' predicled. Illuced, Gottfried Miinl.enherg and SigurJ Hof-11Ianll alllllhcir gmup at GSI (P. Armhruster, cl al.) [81 llaverollowcd Ihis appmach with Ihe help of the SHIP mass sep-

,-< ,:;:111.,.,.', ,,~";<-

I('o~

"".,,-;;'-,

Rel'. /11('.\.Fú ~5 S2 (1999) 63-73

()S TIIE EXTE:":SIOS (lF TlIE I'ERIODlC SYSTE~I OF El.E:\1ESTS ASI) REI.ATED TOPICS 65

¡:J(;URL 4. erey seak plots 01"prolOn gJps (len colurnn) and 111.'11-lroll g:aps (ri~hl colultln) in Ibe N-Z-planc ror spherical c"Jcula-li\l1ls \\"ilh thc forces as in¡Jic~¡lcd. Thc assigllmellt 01' scaks dil"-t'crs fo.- protol1S anJ Ileulrons. scc Ihe uppermosl ho.xes where lhes(;l!t's are indiL:atcd in unils nf ~kV. Nuclei lhal are stahlc wilh re-Sjll'ct lo ¡i-de(';l)' amI Ihe IWtl-prolon drip [ille are emphasi/.ed. TheI'nrces Wilh p:lral1lelcr seIs Skl4 ami PL-40 reproduce Ihe hindill~L'nerg:y of i~;tl0X (1IassiuJll) hesl, i.l'.,16EjEj < 0.002.1. Thusolle might assllllle Ihallhese parameler sets could give lhe besl pre*dicliolls I"or lhe supcrhcavies. Neverlhelcss. it is 1l0Iic('¡J Ihal PL*40prcdicls only Z = 120 as a magic numbcr whi le Ski'" predil.:ls holhZ = 1U alld Z = 120 as magic l1umhcrs. The lIlagirily Jepcnds-sornctimcs quilc slrongIY---()Jl Ihe I1culron llumhcr. These sluuies"re tille lo K. RUI/.. M. Hender. T. Rürvenich. PAlo ReinharJ. andJ.A. \laruhn ¡lO)

duc lo the Coulomh inleraclion of lhe electrons ami in par-¡inllar lhe calculalion 01"lhe orbitals of the ouler (valellcc)ckctrons-has nccn carricd out as carly as 1')70 by B. Pricke<lnd \'l. Greiner [11 J.

4. ASYllllllctric allll supcrasYllllllctric fission-c1ustcr radioacti\'ity

Thc Jlotcntial encrgy surfaccs, which are shown proLotypi-Gllly rOl" Z = 114 in Fig. 2. conlain cven mOfe remarkahleinforlllatioll Ihat 1 wanl 10 lIlenlion cursorily: ir a givell Illl-

•• , 1 ~()

In,l}',ic nllmhL'r~ z= I ~nN= ll'\..J

'"20;..o

~w..:

-.lO

F[(;URE). Potential cllcrgy surLK'e as a fUl1ction of rcduceu clon-g:atioll (If - l?,) / (RI - If, ) amlmass asymlTlctry '} fOl"Ihe doublemagic IltlClcllS 101120

/_pOIl'nlial

sup,'rasymml'tnc\ ftsslOn

asymml'tnc hsslOn

Fl(~Uln: h. Tlle coJ1cclive pOlenlial as a I"llnction 01' the lllass aSYI11-Ellel!"y'} = (.t1J - ..b)j( ..l¡ + .'b). A¡ dellotes the IlUc!l'Oll IllJm~hel" in rra~I1K'llt i. This qualil:llive PIlIL'lllial F(Rlixcu' '}) n)ffC-spollds lo;¡ cut throug:h lhe POICl1li:lll:lndscapc at R = Rh"f'd c10seto Ihe scissiol1 conlig:ur~llion. Thc wave fUI1Clioll is drawlI srhcmal-irally. It h;l." rnaxima wherc Ihe pnlclllial is Illinim:ll and virc versa.

clcllS. ('.g., Uraniulll, undcrgocs lIssion, it mo\'cs in ils POICIl-

tia11lHJlllllains frolllllll' interior Lothe oUlsidc. Ofcourse. thishappens quanlullllllcchanically. Thc wave funclion nI"sllch anuclcus. which decays hy 111nne1ing through lhe harriero hasmaxima \\lherc lhe pntelllial is Illinimal 31ld minillla \\-'hcre ithas Illa.xillla. This is depictcd in Fig. 6. The prohahility forflnJing a ccrtain Illass ;¡sYllllllctry IJ = (Al - A.-d( ..ll + A:dorIlle tissioll is propor\ional to If-"~(IJ)4'J(11) d1}. Gencrally, thisis cOl1lplclllentcd hy ¡¡ coordinatc dependent scalc factor rOl"

the \'olul1le clclllent in Ihis (curved) space, which I omit rol'the sakc 01"clarity. Now it hccoJl1es clear haw Ihe so-callcd{/.\"YlIIlIl('rric and supem.\'.\'I1/1llerric fission proccsses come inloheing. They result (mm the enhancctllcnt of the colleclivewave runction in the colll valleys. And Ihat is indeed, whatolle ohscrvcs. Figure 7 givcs an imprcssion of il.

For;¡ pronoullccd mass asymmelry (11:::::::::0.8 ... 0.9) thereexisl very narrow valleys. Thcy are noL as clearly visible inFig. 2. huI they have intcresting cOllsequcllccs. Thmugh Ihcscnarrow valleys ll11clci can cmit sponLaneollsly nol on11' o-par-

Hel'. Mi'X. /'Ú. 45 S2 (1l)l)l) (¡J-73

WAL.TER GREINER

supcr-nymmclriclis"on

_I'I6Fm(s.flB(A).r¡

T.05M"V

- 1'fm(n,f)II(A) •• 9(1," b

lO'

\O'

'o A.'>Il l.' 150 200 100 ISO 21X), , , , , , 0'6 ITl , , , , , , , ~~,~4 -<12 00 02 O .• -0,6 .1.14 .()2 00 0.2 '14 "

lO"

a)

. {'[ ) ¡d.ri d.rj2/11,fJi) \ .r¡(t) - E - - dt._ di dI

B"

1I1111 ~ r I

vpalhs 11./n

.)lf = lIIi,,'::' )2/11[\'(11.11) - EJ ds'1 palhs " . S

FIGURE X Clll~lcr radi{KKlíVity 01"aetiníJc Ilucld. By cmis~ion 01"

!-le. :WO, ele. "hig Icaps" ¡!llhe pcrio<.lic s)'stem C<lnOú'ur, jusI con-

trar)' 10 Ihe ~nown (\-. ¡J-, -r-radioaclivitics. which are also partlyshown in the figurc

¡-radioactivily), hUI Illany more. Alomic nuclei CJn also de-cay IlJrough spol1taneous l.'fuster emission (thal is the "spit-ting out" of slllaller lI11dei like carhon, oxygen. ele.). Figure 8depicts SOIllCnicc exal1lplcs nI' lhese processcs .

The knowledgc (JI' Ihe l.'ollcctive potential energy surfaccand the COllcclive masscs IJij(R, '/). all calculatcu within lhelw()-center shell mode! (TCSrvO. allowed H, Klein, D. Sehn-ahe!' and J.I\. l\.'1aruhn lo cakulate lifetimes againsllission inan "oh i/litio" way 11:1]. Ulilil:ing a \VKB minimizalian forlhe penelrahilily integral P = l-I with

whcre d ..•.l = !h.i d,I"/ d.,.} ami !/ij-the rnelric tcn~;or-is inlhe wcll-Known fashioll rt:lalcd lo Ihe collcclive Illasscsflij = 2/J1,//;j, (lne explores lhe minimal paths frolll lhe nu-clear ground sl¡¡le l'onllguralioll lhrough lhe l11ultidimen-siollaf fissioll harrier (see Fig. (j). The thus ohlaincd fis-sion hall' lives are depiL'ted in Ibe lowcr pan of Fig. (j, Thcirt.Iislrihution as a functioll of lhe fragmcnt mass A:,~ l"eSClll4

hles quite \vell lhe i.lsYllllllelric mass distribulion. Clusterradioaclive dc<.:ays corresponu lo Ihe hroad pcaks around.-!, = 20. . . :\11.rcspcclivcly ..1, = 200 ..... 210. Thc con-frontatioll of lhe (akulaled lission half lives \vilh experimentsis depicrcd in Fig. 10, ()Ile notices "ncarly quanlilativc"agreelllent o\'el" 20 ordcrs 01' magniludc. which is-ror an {lb.

i'litio calculali{lll-rClllarK:¡hle ~Finally, in Fig, 11 \ve compare lhe Iifetime cakulalion

discusscd ¡¡hove \Virh one hascd on the prcforlllation clustermolle I by D. Poenaru t't al. 11'-11and recogniw an arn:1I:ingdegrec 01"silllilarily :tnl! agreclllcnt. Thc systcmati¡,;s ror theaverage 10lal kinelk ellergy releasc rOl' sponlancously Iissioll-ing isotopes 01' Cm ami No is following Ihe Viola lrend. hUI2;',IlFm and ~.-,!lFm are dcarly olltside. Thc silUalÍon is similaralso for :.!M1rv1d. wherc 1\\'0 components of tission products

10080

~~ super-/ "'-,?symmetric

/ "'A' \ ""'¡ionluyo = 7,5 McV \( ,

../ /-, '.,. j---\ ~.",1 "l¡

~ f / llOro \ r- "":tl 8,0, \]

I f \ \

I " \ \ .I I r-.... \ \ .!;~ "-.., 12MB" \ }f

'.~"I / 8,~ \ (iHtI I ,\P11I I \ \ ¡I { _ ,\ .

.. 1, /"'".... \'I I 'I t-~ \

J/20IT1\ \

1 / 7A \ t~1 I t:, J , \::'!f2\ ').

I I g \.t :f 7,4 'l..\, J 1 I'/ ~ ', 1,, \

, 1, I

I I

Fission of Nuclei with A- 200uU5P = 7-8 MeV

80 100 120 140

lO"

10'

hOY%

, 101

2IJAt"

b)

1"~11" g 10

1

120 140M,amu

FI(;lmE 7. Asymmctric (n) anJ syrnmctric (b) lissioll. For ¡he lal-¡el'. abo slIpt:fasymlllctric Ilssion is rccognizahlc. as it has hccn oh.ser\'e,'d unly a few ycars <1go by the Russian physicisl Itkis-jusl asl"\PL'ClcJ IIK'OfClicllly,

lides (lkliulll Iludci), huI al so He, ~OO, ~'INc, 'JHMg, andother 11lH':Ici. Thus, \vc arc Icad lo the cluster ml1io{fcti\'-¡tI' [121.

By now Ihis prncess has been verilled expcrimenlal!y hyrcscarch ~roups in Oxford. Moscow. Berkeley, Milan, <tndollll'!" places. Accordingly, one has lo revise wllat is Icarneoin school: Iherc are nol only 3 lypes of radioactivity (tl'-, 13-,

RCI', Me.\". 1-"':".45 S2 (1<)<)9)63-73

0;\1 TIIE EXTENS10~ OF THE !'EKIODlC SYSTEM OF ELEt-.1ENTS AND RELATED TOPICS 67

20 40 60 80 100 120 140 160 180 200 220 A,40

30

o., O' 0.4 02 00 .(l2 -0.4 .(l.' .(l8 ~f

8010

100•• 20]; 120 ()

30e¡; 140E 40 160

50 180A, 20 40 60 80 '00 120 140 160 180 200 220

~ .Hc mTh.: ' , ~ ,.~ I ~U1421.9I 20

I"M' -"11 ,1;1. l00Zr

IMTc80 81200

1• . " "

(one wilh 100vcr and one ""ilh higher kinclic energy) were oo.served by Ilulel el al. [15 l. Thc cXpl:IJ1<llion of these intcrcSI-ing ohscrvations líes in lwo dilTcrent paths thWllgh lhe col-icclivc pOlcnli:l1. One reachcs Ihe scission poinl in a slrclchedncck poSilioll (j.!' .• al a lowcr poinl of Ihe Coulomb bnrricr-thus lmvcr kinclic cnergy ror Ihe fr<lgments) whilc lhe olherone rcaches lhe scission ¡mini practically in a touching-spheres POSilioll (j.e .• higher IIp on Ihe Coulomb harricr andIherl~l'ore higl1ly cllcrgetic fraglllcllts) 11GI. The ¡alter proccssis colll lissioll; ¡.c., lIJe fissioll fraglllenls are in or c10sc lolhcir grolllld slalc (cnlt! fraglllcnts):lIld all lhe availahlc en-ergy is released as kinelic ellergy. Cold Iission is, in fact, lypi-cally a c1usler decay. The side-hy-sioe OCCllrrence of colo aminormal (hol) li.ssion has heen namcd hi-modal f1ssion IIGI.

PIGURE 11. Comparíson of Ihe lissioll half-lives calculaled in thelission lllodcl (uppcr figure-see ¡¡Iso Fig. ~) and in Ihe prcform<l-tion cluster tlloJcll14l. In hoth modcls lile deform<ltion 01'Ihe lis.SiOllfragl1lcnt.s is not includcd complclcly.

5. Fissiun uhserved with Ihe Gamma-sphere:lung living nuclear mulecules

Thcrc has now hcetl pUl forwanl ;¡ I'antastic idea (171 in or-del" lo sluLly colo lission (cluster dccays) and other exotic fis-sioll processcs (Icrnary, l11ultiple lission in general) very eleganlly: hy llle:J.suring wilh, e.g, lhe Gamma-sphcrc. cilarac-teristic 1'-lransilions of individual fragmcnts in coincioence,onecan idelllil'y all lhcse processcs in a dircct and simplc wayway (Fig. 12). Firsl continnalion 01" lhis IIlcthol1 hy J. lIamil.Ion, V. Ramaya et al. workcd oul excellently in Ref. 18. ThisIllethod has high pOlential rOl"rcvolutionizing tission physics!\Vilh SOIllCphysical intuilion olle can imagine thal triple and

"

"

"" l>'",.,

'00

C3 = O.20/fm232U92

Vfm

10 12 14 16 18 20

Vmm

= 9,752 MeV

E~1Jl = 1 MeV

232 2J6 240 244 248 252 Z56A

FUjt'RE 9. The uppcr pan of the Iigure shows the rollcrtive po-tcntialcllcrgy surface for 231U wi!h Ihe ground slatc POSilioll anuvariolls lissioll palhs through Ihe harrier. Thc middlc pan showsvarious collective masses. all ealculateu in Ihe TCS1\1. In Ihe lowcrpar! lIJe calculatcd lissioll hall".livcs are JcpiclcJ.

soA2 21) 4.0 60 80 100 120 14.0 lW ¡SI) 200

10° ---.- .------------o Uo ru• Cm• CfO Fm

1\,'.,..~ ., .,/ •..... ;.

'7- .,... ;~.~ ..---' ,~/ ''1 ~ •

FI(jURE 10. Fission hall" li\'es for various isotopes 01"Z :;::;:92 (U),Z = 91 (l'u), Z = 9G (Cm), Z = 98 (Cn nnd Z = lIJO (['m). Tileopell s)'lllhoJs rcprcsCllt Ihe experimcntal valuc.s. The fu]] symbolswilh fulJ anJ Jashcd li!les correspond lO calculalions with difrcr-elH choiees of Ihe harrier parnmclcr in Ihe Iwo-ccnler shell model(f-'l :::: 0.2 anJ C.1 ::::::0.1. rcspcclively).

Rell• Ale.\". 1'-':". 45 S2 (1999) 63-73

FI(¡Ul{l I J. Tllc ~f.lransili{)ns (Ir (he Ihree tission products nr '2,',2cr

llleasured in C()iIKi(kllCC. V:lfi(lllS c(lrnhinalions orlhe coilKidenceswcre studied.

6X

Cold Fission

WALTER GREINER

IJn."II'l.I f4

77.5 1

336H.O

~1'¡.7

FJ(;URI. 12. llluql'atioll 01' cokl amI htlt (normal) fissioll idcntiti-c:llioll llll'ough mulliple l'-coinciuenccs 01' phOIOllS fmm Ihe frag-l1lCllh. Thc pIHl\OIlS serve lo idcntify lhe fragmcnts.

l/lIt/drll/,/e ¡¡"sion proccsscs ano cvcn Ihe proct::ss 01'co!d IIlII!-

'i/mgl1lcl/fatioll \\'ill he tJisco\'crcLl-ahsolulcly fascinaling!\\'c ha\(.' (hus ..•cen ¡hat I1ssion physií:s (c(lld fission, clu,lclradio;lcti\'ity. ele.) and fusion physics (cspccially lhe prolÍm:-¡ion tlf sUjlcrhe:l\'Y ch=mcnts) are intimately conllcclcd.

Indccd. \'l:-ry rcccl1tly. lhe triple flssion proccsscs

:!'-".!Cf --t J.ICoBa + !lI;Sr + IOBc

htl\'L' bcen idL'ntilicd hy IIlcasuring the various Ay.transitioll'\

or Ihcsl' IllKki in coinciticncc (sce Fig. 13). Evcll lhoughlhe 11ll: ,[alislical evitiellce for lhe JOBr li!le is ....mall (;:;; ,jUl'\.CIl[..;) Ihe \ariou, eoincil!enccs s('em 10 pnHlf [hal :-,poI11a-11l'tIU'"Iriple li ..•,ion oul 01' [hc ground slale of :!~':!cr\\ilh [hebe;I\.Y c111:-.ll'rJ('lk as a lhirl! fragmcllI cxists. Also oll1L'r IripleIraglllclllaliolls can he e'{pectcl!. One 01"tbose is also dellolcd¡¡hm.L'. 111laet. Ihere are tirst inl!icalions, Ihal [his brcak-up is¡¡IStlllh:-'L'l"\cd. The mosl <lm3zing ohscrvalioll is. h(l\\'l'VrL Ihej"ollowing: Ihe LTOSScoincidentes secm lo suggesl Il1al OlleLlrals wilh a silllllllaneous threc-hol!y hrcakup ami nol wilba ea.,cade proCCSS. For Ilw.t onc cxpeCls a cOllfiguralioll assbowll in Fig. l-l. Consequclllly Ihe J(lBe will ohtain killelicL'llel'g~' whilc 1"1I1111illgdown Ihe eomhined Coulomh barrierof Ill'H;! ;llld %Sr and, Ihercforc. Ihe JJ6X Kl:V line 01"llllk~hould tw J)pppkr-hroilJencJ. Amazingly. howe\'er, il is nolallll, IllOreO\"L'L il :-'CCIllSlo be abouI 6 KL'V smallcr Iban IheIreL' llllk -,-lr;lll ..•ilioll. Iflbis lurnsollllO he lrue, Ibe only cx-planalioll \\ill hc lbat l!le ; is cmiuL'd whilc Ihe nuclear 11101-

'@', II I1 II I

" I

FIGURE 14. Typicd lincar cluslt'f L"Onliguration Icauing lo [ripIelission of :2!",2Cf. The inlluL'IKL' of holh cluslers !Cad s lo a soJ'ten-ing of lhe rOBe pOIl.?n(i:lI :llld [hus [n a somewhat srnaller Iransi-[ion cl1ergy. RL'Cl.?rltIheOlClil'al invcs(igalions indicale thatthe axialsymmetry 01' Ihis contiguratioll is orokcn (lowcr Icft-hamJ tlgurc)

C'cule 01"lhe lYIlL'shown in Fig. 14 holLis. The molcculc has 10li\'e longlo'r Ihan aholll IO-l:! s. The nuclear forccs fromlhcllCoBo alHI "hSll clusll'r lo Ihe Iefl ami righl from IOBe lcadlo a softL'ning 01" ils polelllial and Ibereforc lo a sotllcwhalsmallrr Iransilioll lo'lh.'rgy. Thus. il"experimenlal rcsulls bold,(lIlC has disco\'cl"ed long living (::::::1()-u s) complex nuclearIllolecllles. This is fanlasliL:~ 01" cnurse. 1 do imllledialelywondel" \VhClher 'lIch l'ol1li~llratioIlS Jo also e.üsI in. (',g.,

U + Cm sof! cllcoulllns direclly al Ibe Coulomb harricr. This\\/ould llave [relllclldous imporlance ror Ihe obscrvaliun orIhe observa[ioll uf IhL' Spollt;llll'()US \'acuum decay 1:20], furwhich "slicking gianl lIlulecllles" ",ilb a lirelime of Ihe onlcr(Jf 1()-1~1s are nel'del!. The nuclear phy,ics 01"such heav)' ioncol1ision, al IhL' Coulomb harricr (gianl Illlch.'ar l11olccuks)shollld indl'ed be invcsligatL'd ~

Thlo' .'cokl \'alleys" in 111L'colkcli\'c po(cnlial energy ••ur-race are hasir fOI"undcrslandil1,b lhis exciling arca of Iluckarpbysics~ It is a masler l'xalllplc for lJlldersIJllding lhe slruc-tllre ni c/C'IIIt'IIU1ry /I/(/lter, which is so importanl ror olllerliclds. espccially <lslrophysil"s, hui c\"Cn more so rOl"cnrich-ing 0111""\Veltbild". ¡.c.. 111L'slallls ofour unJerslanding (Ir IhewmlLl (lround liS.

6. Extcnsinn ••1'tltc Jlcri ••dk systcm int •• tltc sce-ti••ns ••1'hYJlcr- ami antimatter

i'\uclei Ihal are fOlllld in naturc cOllsi"t of nuclcolls (prolOIl.'>ami nCU[WllS) \\hich Ihlo'lll:-'clvc.s are maLlc of 11 (lIpJ and ti(dO\\'IIJ qll;lIb. !fO\\'l'Vl'i". Ihefe also c.xi,,1 ,.• ("Irange) quarks

UN TlIE EXTENSIOt'\ nFTllE I'ERIO[)l(' SYSTE~l ()F ELE\IE¡"¡TS A:"JI) I<ELATE!> TOPICS fJ9

y

N

"h -'>:;;Ñ :7 N

Q".•.•z S

c1uslCr. This happcns indecd ralha frcquently for one or Iwo,\-particles. 1I00\'C\'l'L lIIore of Ihclll get huill into nuclci withrapidly decrL'asing prohahility only. This is duc to Ihe lowprohabililY for linding. lhe right condilions for such a l'aplurein lhe pitase space uf lhe parliclcs: lhc llUIllCroUS partklcslravel wilh L'\'cry possihlc mOlllcnla (\"clacitics) in all direc.lions, The c1wnces rOl"hypcrons and anliharyol1s lo meel getsrapidly worse wilh inncasing nurnhcr. In urder lo producernuhi-.\ Illlclci ami antim<lllcr nuclei. one has to look rOl" tidilTell'JlI SOUrt:c.

In Ihe fralllework of llleSOll lield lheory the energy spec-Irlllll 01' haryolIs has ti peculiar slruclurc, dcpicted in Pig. 17.It consists of:ln lIpper and a lowcr continul1J11, as il is knmvnfmm lllL' l'leclrons (see. e.g. Rcf. 20). 01' special illteresl inIhe case 01' lhe baryon spectllll1l is Ihe pOlenlial \\'el!. buillof Ihe scalar and Ihe \'CClor pOlcnlial, which rises fmm Ihe100ver cOlllinllulIl.11 is knowll sincc P,A.M. DiraL' (1930) Ihallhe llcgati\"C L'llcrgy q¡¡les 01' Ihe 10\\'1..'1'colltinuum have lohe llLTupied hy particles (eleL'trons 01', in our case. haryons).Ol!lcrwi<.;c OlJl"world would he unslahle, hecausc Ihe "ordi-nary" ptlrticlcs are found in the lIpper slales \vhich can de-l'ay [hmllgh [11('cllli<.;sion or pholollS into lo\\'cr Iying st:llcs.1I00vevcr. ¡flhe .'undcrworld"' is occupicd,lhc Pauli.principle\\"ill prc\'cnl Ihis lkcay, Holcs in lhe occupied "lIndcrworld"(Dir,lc sca) are ;lIl1iparlicks,

FIGU f.: L 16. The e.'i:lellsionof Ihe perioLlic system into lhe scclors 01"slr,mgeIK'.S\ (,'-" ,S') ;lIld anlim<lller (2, i\.'). Thc slah!c valley winds(lul of the ~nO\\1l pHllon (x) ami nelllron LV) plane inlo Ihe S anu8 sector. respectivel)", The same can ht.~ohservcd for Ihe antimat.ler seclor. In the uppcr par! 01' lhe figure only lhe stahle valley inIhe usual prolon (Z) :llld lIeutron LeY) planc is plotted. howcvcr. l"-tended In[o lhe seclor (Ir antíprolons and :mlinelllrons, In lhe sccundpan nf [hc li~urc i[ has nl'cn indi(',Hed. Ilo\\' Ihe slahle valley wimlsout oftlle Z.X-plane imolhe strangellcss se('lnr.

:1:+ (su u)T,

1 P(uud)

(ssd) =:- -1

[8 J

(sdd));--1

FI(jlll{E 15. Imp0rl,llll haryorh are ordercd in [his oclet. Thc t¡uarkCOlllcnl ¡" (iL'ric!cd. Protons (JI) and nClllrons (11). musl importall!ror Illll' "nowll world. contain (ln!y 11- ,lIld d-quarks. lI)'pl'fons con-[;lill dl'.;o al] ~-qllark. Thc llumbcr 01",~-quarks is a lIlcasllt"c for Ihestr;ll1!!CllcSS.

;¡nd C\"L'Jlhca\'icr Ilavors. calleo charm. notlolTI. top. Thc !atta

has ju,t recently OL'CI1 discovcred. Lel liS stick lo lhe s-quarks.They ¡¡fe fOllnd in lhe: "s(range" rclativcs (JI' lhe IlUCICOllS, Ihe

so-callcd hypcrons (.\. ~. =. ~n.Thc ,\.parti< ..']c. e.g .. C0l14

,siSIS (Ir (lile //-, d. ;¡nd .'i-quark, the =-paniclc cvcn of <11111_and IW(l .....-quarks, while thL' fl ( ..•......••) cOlllains slrange quarksonly. Fig. 15 gives an o\"erview of Ihe haryons, which arL' 01"intcn:sl hCTL'.ami lheir quark contcnt. Ir sllch a hyperoll isl;¡kcn up hy ;¡ nuclclIs, a hypem/lclc/l.\" is crealed. HYPCrllll-clci '.vilh onc hypcron have heen knowll ror 20 ye;¡rs 110\\',¡¡nd wcre eXlcnsivcly studicd hy B. Pavh ¡:tI], Sevcral yearsago, C. Greiner, J. SchatTner, and H. SlÜcker [:!:!] thcoreti-cally illvcsligalcd nuclei wilh lllilJlY hypcrons, hYIJcmw!fer,and fOlllld Ihat Ihe hinding energy per haryoll of slrangc mal-Icr is in lllany cascs evcll highcr Ihan thal 01"ordinary 1I1aller(composcd onl)' 01" /1 ami d qua!"ks). This Jcads (o the idca ufc\lcllding: thc periodic systclll al' CICIllCIlIS in the dirccliun ofslr:lllgclless.

One call also ask for lhe possihilily 01' huilding atomicl1uclei out 01"(lfl1iIJ/(/lter, thal mcans scarching, e.g., for anli-heliulll. anli-carhon, ;¡nti-oxygcn, etc. Fig. 16 depicts thiside;l. Duc lo the chargc conjllgation symlllctry ¡¡nlillllcleishollld have Ihe samc Illagic nUlllhers and the sanlL' spcclra asordinary nllclci. Ho\\"cvcr, as soon as Ihe)' get in IOllch wilhordinal")' maller, Ihcy annihilalc wilh il and lhc systern cx-plndes.

Now Ihe importanl qlleslioll arises how lhese slrange lJ1al-ler alld <lnlimaltcr clusters can he produced. First. OIlClhinksnI' collisiolls 01' hca\'y nuc!l:i, e.g., lead 011 Icad. at high ener-gies kncrgy pe!" nllcJcoll 2:" 200 GeV). Calculatiolls wilh lheUR()f\ID modcl of Ihc Frankfurt sc!lool sho\\' thal Ihmugh111/( '¡{'U,. slu/{'J..: ll'm'('.\" I :2:3-:'!:; 1 lluclear maller gels compresscdlo 5-10 times of ils usual \'aluc, {Jo ::::::O. J '; fm:l, and hcatcdup lo tL'mpcr;l1ures 01' Ff:::::: 200 ~fcV. As a cOIl<.;cquellceahOll[ lO ()()() pions. lOO ,\ 's, 40 2::'s and ::::'s, amI aholll :1<';

1Il<lIlYantiprololls allll lIlilny olllL'r p;miclcs are crcated in ti

....ill~k, collisioll, JI secms L'ollcci\'ahlc lhat ir is possihle insllch a scenario ror sume .\'s lo gel caplurcd h!' ti ll11ck';lr

1\1'\'.,\1('\, 1-/\ -15 S~ (l{){jl)) (l.1-n

70 WALTER GREINER

-V,G1=

Ql(¡ 1 -¡. -120 ,.

Q2(}~ ".--"~ :> ,." 'Olr, \lPpt" " .YO Jow<'r~ ¿

wcll

~/wdl

2' QOO

¥. '001_ ~ .l60". ~"~O"~

"~'"'~ .1MO

"o 1"O 4CJ{¡

r, " " e " "r[rm] r[fro]

FUiUI{I; IX. The lowcr wclJ r¡ses slfOngly wilh incrcasing primarylludcon t1cnsilY. amI cven gels supcn:ritical (spolllancous nudeonCIllISsi(l1lantl nealioll 01'nound antinllcleons). Supcrcrilic.i1ily de-lIotes (he silllalion. whcll Ihe lower well cnlcrs Ihe uppcr conlin-utlm

"

-- ~ld<:n\II)(AllP. -1 Al

--- p.-4A1- - P.-I>AI

P. -11 S Po

r [rrJI]

.M..l"

r(rmJ"""••.---.-• •

•I".

""

F[(;U[{E 17. B,lryoll spt'«(rulll in a IlW,:!cus. Bc!o\V the posilive en-l'fg:y l'tllllinU1I1l1cxists lile pot('nlj~1 wcll (JI"rcalnucleons. It is L1ctcr-lllíncd h)' Ihe SUIllorille sellar and vector potcnlials (l's + "v) inrncsol\ licld thcor)'. It is 01' onlcr 50-60 i\tcV and shows lhe correelsl1cll slrurtmc. Tlle shcll modcl of Ilude! is rcalizcd here. Furlhcr.more. fromlhc Ilegali\'c conlinuum anolhcr pOlcntial \.l/el! ariscs. inwhich aholll .tO noo hound parliclcs are found. hcJong:ing lo (heVaClltllll, A P:lfl or lhe sllc]] slructure 01' Ihe upper wcll ami (helo\\'er (V:lClIlll1l)wcll is dcpiclcd in lhe 10\'icr figures. The dcpth ofIhis "Iowcr" potclllial is-within mcson licld Ihcory--dclcrrníncJhy \-~ - \'v ~ (j;)O~lcV, The precise magnitudc of Ihm is an im-portanl oP':1l qucslioll. Evenlllally OIlCcan determine it lhrough ¡¡

dClaiIcd stuJy 01'Ihc .•.pin-orhit inlcraclion, which is propurlionallo("/,h)(", - F,,).

The occlIpied slalcs of Ihis lIndcrworld including up lo-w (lOOol'Cupied hounu stalcs 01"Ihe lower pOlcnlial well rcp-resellllhe 1'(/CfIItIll. The peculiarily 01' Ihis strongly correlated\'aclIurn s(rm:lure in Ihe region 01' alOmic nuclci is Iha(-depending on Ihe si!.e 01"Ihc Iluclcus-morc Ihan 20000 IIp 1040000 (occupict!) hound nucleon slalcs contrihute 10 Ihis po-iarisalioll ellec!. Ohviously, \Ve are dealing hcre with a !Jig"'.\'corrl'!med l'lICltllfll. A pronounccd shcll struclurc can he rec-ogni/cd 12G. 271. lIoles in Ihese slales have lo be inlerpretcdas h(Hllld anlinuclcons (anliprotons, anlineutrons). If lhe pri-lllar)' ll11dcar tlcllsity rises tlue lo comprcssion. Ihe lo\Vcr \VcllinCl"eases while lhe uppcr dccrcases an.d soon is convcrtedinto a repulsive harrier (see Fig. IH). This compression ofI1lH:lcar maller can onl)' he earricd out in relalivistic nuclclIs-IlIIClcus collisioll wilh Ihe hclp 01' shock waves, which ha veheell proposcd hy lhe Frankfurt school [23,241 and whichhave sillce ¡!len heen conlirmcd cXlcnsivcly (for rcferenccs

seco e.l-:. Rd, 2X). Thesc nue/ear shock u'm'es are accolll-panicd hy heating of Ihe nuclear malle!". Indced. dcnsily amiIcmperalure are il1timalely cOllplcd in lams 01' the hydmdy-!lamic RankitH.~~Hugol1iol-equalions. Healing as well as Ihe\'iolenl dynamics cause Ihc crcation of many holes in Ihevery dCL'P (mcasurcd I"mm -iHu(,"2) vacuum \\'cll. These nu-l1lerous hound holes rescmhle anlimmler c1ustcrs which arehound in the lllediulll; Iheir wave funclions have large overlapwil!l anl illlatlL'r e luslers. \\lhcn Ihe primary rnatter Jensily de-creases during the expansion stage 01"the heavy ion collision,lhe p(l1enlial wclls. in particular the lower one. disappear. ThehOllnd anlillucleons are then pullcd down into Ihe (Iower)L'()fllinllLJm. In Ihis way :tntim<tlter clusters may be set free.Of course, a large par! nI" Ihe antimattcr ",'ill annihilale onordinary maller presenl in Ihe course 01"Ihe expansion, How-ever, it is illlpOrlanllhal this Illechanism for lhe productioll ofanlimaltcr dllsters out of the highly corrclaled vaCUUlll Lloesnot proCL'l'd \"ia lhe phase space. The required eoalesccnce 01"many partieles in phase spaec surpresses rhe proJuclion 01"duslers, while it is favorcd hy Ihe direct production out ofIhe highly [OlTelalcd V;;lCUUIll.In a certain sen se, the highlycorrelatcd vaClllI1ll is a kind of cluster vacuum (vacuum wilhduslcr slructure). The shell struclure of the vacuum levels(see Fig. 17) supports this lalter suggcstion. Figure 19 ¡lIus-Irall'S Ihis idea,

The lllcehanislll is similar ror Ihe produclion oí" mlllti-hyper Illlclei (,\. ~, =. U). Meson f¡eld theory predicts alsorOl"the 1\ cncrgy speclrulll al linite primary 1l1lcJeoll densityIhe exislellce of llpper ami lower \Vclls, The lower weJl he-longs to lhe V:l(tllllll ami is fully occupicJ by A 's. Dynami(samllelllper:tlure then induce lransilions (1\;\ crealion) anJ de-

(>N TIIE EXTENSION OF TIlE PERIODIC SYSTEr\1 OF ELEr-.'1ENTS ANI) RELATE!) TOPICS 71

{\'ce =

E

I2m~o

-m~ _

.•.E

o

-m:-,r _

quesliolls. Prohlcllls 01' lhe llleSOIl IIcld lhcory (e.g., Land<lupoles) can Ihen hc rccollsidered. An cffcctivc mesan ficld thc-orv has to he eOllslrucletl. Various cffcctivc lheories. e.~.,01'\V:llecka Iype on lhe tlne side amI lheories wilh chiral in-\'ariam:e IHl lhe olher sidc. seem lo givc diffcrent slrenglhsnI' Ihe potclllial \\.'clls ami also dilTcrent depcndence 011 theharyoll dcnsily ¡:lOJ, Thc Lagrangians 01' lhe Dürr-Tcller-\\'alecka Iypc antl 01"lhe chir~l1ly symmetric mean fleld tl1eo-ries look quite dillerenlly. \Vc e:xhihil them-without furthcrdisclIssioll-in Ihe folll)wing equaliolls:

N01H.:hiral Lagrangian:

[. _ l.) ')'1, 1 ') ~ ("lll ~ 1 [J [J''"kin - 2"( /1"<;( ,<;+ 2( W'.u - - ~ '11'

- ~C' GJIV - ~F F"".¡'LV' ..:¡ IV ,

fll"l = ¿0u [¡'II¿}II - !J",'¡lI'IIWII

- Ye>lJ"Y,14il

1/

l' 1 (1 )A" • 1 I-.IIJ'I/-""TUI' -(>~1J12 +TB -1I111J~'n,

I :2, l' 1:2 I1 1 :2. 112//1 .•..'-'-'1, .•••' + 2"1¡,II,dl + 211100JI1I •

fRM = ¿0/1 [ir'Jli)!1 - Y..•.../JI'¡IW" - Y¡)LJ"Yp.ljJJI1/

- Y"U1JITUI'1' - ('''Y/I~(I + Tn)A'1

- mñJ1.l'n,

, - 1O 0" lO (0" e lO 01'[kin - 2 ¡JT rr + "2 JI +"2 11\ X

I!J l?JII' 1G (,"01 1 F FJIV- ~ . JII'. ~ ~ '10" - 4" 111'

Fl(iU]{E ll). Duc lo the high Icmpcrature and Lhe violent dynamic~.1llany i'lollnd h()lc~ (alHilluclcon c1uslcrs) are createJ in lhe highlyrorrelalCd V¡¡CUlIl1l. which can !"le sel free during the expansionslage illlo Ihe lowcr continulllll. In this way. anlimaller c1usters canIx: produced dircctly fWlll Lhe vacuUnl. Thc horizontal arrow in lhelower par! of lhe ligure denotes lhe sponfancolls crealion of haryon-illlliharyon pairs. while lhe anliharyons o<.'l:'UpYhound sLates in Lhehl\\"cr potential well. Sllch a ~illlation. where Ihe IO\l.'er pOlenlialweJJ reachcs inLo Lhe uppcr cOIlLinulIlll. is calJcd sllpercritical. POllr(lf the bOlll1d hoJes states (houml antinuclcons) are encircled lo í1~IUslr;lte a "quasi-¡llItiheliulTl" forrned. It may he sel free (drivcn inloIhe lowcr confilltllllll) hy lhe violclH nuclear dynarnics.

• l., .,L, = --;;11I:.<;--

Chiral Lagrangian:

1 .,.} I 3-11I:::'- - -b8' -~ - :J

1-cs".4

posillll<lny .\ 's inlhe upper wcll. These IlUlIlerous oound A'sare silting ctose 10 Ihe primary haryol1s: in a ccrtain sensc agiant ll1ulti-.\ hypcrIlueleus has heen crcated, \Vhen Ihe sys-Icm disinlegralcs (expansioll slage) Ihc.\'s distrihute over thellllcleon c1usters (which are 1I10s1ahundant in peripheral col-lisions). In Ihis \vay mu1ti-A hypernuelei can he formcd.

01' coursc t!lis vision has to he workcLl out and prohahlyrelincd in many respecls. This mean s mueh more and thor-ough illvestigalion in lhe fUlurc. h is particularly importantlo gain more t:xpcrilllt:111al inforrnation 011 the propcrties ofIhe lowcr wcll hy (f'. (JI') or (l'. l:'JlfJ') and also (¡JC¡Jh' ¡¡Ci¡h)reaclions (Pc denoles an incidenl anliproton from the conlill-uum, ¡Ih is a prolOIl in a hound Slale; for Ihe reaction protl-llcts (he silualion is just the opposilc) 120). Also the reaction(/I./,'d), (/I,},"lIo), (/I,},'llIo), ami othors 01' similar typc!leed lo he invesligaled in this contcxt. The systcm<llic SGIl.Il'ring 01' anliprololls on nuclei can cOlltrihutc lo clarify Ihese

The Ilon.chirallllodel eonlains the scalar-isoscalar ficld s anLlils strange coulllerparl .:. Lhe \'eclnr-isoscalar flclJs w1' and1J'I' amI Ihe Ihe II-I11eSOIl('JI as wcll as thc photon AJI' Pormore dcl;¡ils sec ReL 30. In contrast (o (he Ilon-ehiral J11odel,lile SU(3 )},x SU(J)/I I.agrangian conlains the dilaton l¡cld \

Re!'. Me.\". Fú . ..:tSS2 (]()()l») ().\-7.\

72 \VALTER (i]{EINER

""""""--

III

,... .¡ II ~ 1) h.n

¡ljtn,-'1 .10,1

-_.-l." ~¡I

'" -\

'"(1, •

'"'"

,"

until l!l¡.;cllcrts nI lh¡.; corrclalcd \'acuum are strong cnoughso l!lal lhl' 1l1l..'L'!lanisms dcscrihcd herc hccome cllcctive.In tllhL'r wonls. arcording lo chirally symll1elric IllcsonI¡cld lheorics Ihe anlilllauer-c111slcr produclion and multi .hYJll'l"lllaltcr-c1l1Sler prodllClioll OUI of [he highly correlalcd\'aCtllltn lakcs placl' al considerahly highcr heavy ion cn-l'I"gies as compared tn Ihe prcdiclions of Ihe Diirr- Tellcr.\Valeeka-Iypc Illesnn licld Ihcories. This in ilself is a moslinlcrcsling, quasi-rundatllelllal qucstion lo he clarificd.l\1ore-o\'¡.;r, the queslinll 01' lhe ll11clcOllic suhstruclUl"c (form rac.lors. quarks, gluons) and its illllucncc on the highly corrc-lal¡.;d VaCUllll1slrUL'lure has to he studied. The nuclcolls arepossihly slJ"Ongly polarised in Ihe correlaled vacuum: the ~-reS(Jnallcc l'{JlTe[;¡li(lIlS in [he vaClllllll are prohahly importanl.Is [his highly corrclated V;¡Clllllll slate, especially during thecOlllpn:ssioll. a preliminary slagc to thc quark-gluon c1us-ler plasma'!. To which cxtcnt is il similar or pcrhaps cvcnidcnlical \\-'ilh it'!. 11 is \\'ell kllOWIl rOl' !llorc Ihan 10 yearsIha[ Ill('SOIl ti¡.;ld Ihcorics prcdü':l a phasc Iransilion qualita-I¡vely and lJuanlilali\'¡.;ly similar lO that 01' Ihe quark-gluonplasma I:n ]-scc.:: Fig. 21.

F[(;IJI~L].I 'rile ....,lrung rilase lransi!ion inherent in Dlirr-Tdlcr-\\!alcrl...a-typc Illt'SOIl l¡cld 1l1corics. ,IS rrCt!iCled hy J. Theis (,(

al. 1:\11. Nole lh:!l lbefe is a lirsl order tr:msitioll along the ¡I-axis(¡,l'., wilh dCllsity). huI a .simple Iransition along Ihe IcmpcralureT-axis. NolC :ds(l 111:11Ihis is \'ery similar 10 lhe rhase lransitinnllhlaincd rcccntly rrlll1l the ;S¡;¡mhu-Jona-Lasínio arrroxim;)lioll 01'()CIJ 1.111.

\'!Im)

.._._~~--r,

""'1

"111'1

~"'~'E;

"'1J""" , • ~_

'1''''1

'> ,!~",

- - -~~~I'''''~-

~ ' .. 1 "'"

!J•... 1

\

p.up,

i,_ ------l. .

'1""1

'11'''1

illlrot!lIccd lo lllimÍl: lhe tracc <lllomaly 01' QCD in <Incllec-tiVL' I.agrangian al ln:c Icvcl (fur ¡m cxplanatioll of lhe (hirallllotkl scc Rl'rs. JO <lmI32).

'1'1IL'L'1l11IlL'Cliollof lhe (!Jiral Lagrangian wilh Ihe \Vakekalypl' can he cslahlishcd by lhe suhstilution a = 170 - .•• (andsilllilarly rOl' llll.' slrange condensale (l. Then. e.g .. [he dil"-krcnL"l..~in the definition of Ihe t:lTecli\'e nucleon Illa~s in hothlllodl'ls (noll-chiral: 1I1~. = 111 .•••. - !/ss:io. chiral: /11..~. = .rJs.\'fT)

can he 1"L'1ll0VC(1.yielding:

F[{al~L 20 The pOIL'ntial struclurc of [he shell modcl <lnu Ihe\;Il.:11umfor \"ilriuIlS primary ucnsitics fl = [Jo, .lpo.14po. Al ll'fttlll' prcJlCll011S (Jf nrdinary Dürr-Tcl1cr-WaJccka-typc thcorics 3rc"JHmn~ :11ri~hl l!lose for :1 rhiral]y syrnmclric rnesoll licld l!lenry<1"dl'\dopcd hy 1'. Pap:1/.oglu 130.32).

''''1"

'''''.~'.."I~'"

~.,..,<j:::

1'01thl' IlUC!L'ollIllass in Ihe chiral moJel.Nl'\'l'rlhekss, ir lhe parametcrs in oOlh cases are aLljusteJ

surh [hat ordinary nurlci (hinding cnergies, radii. shell struc-Iml'. elc) and properties 01' inlinite nuclear maller (equilih-riulll dl'llsily. eomprcssioll constant 1\-, hinding encrgy) are\\'1.'11n:pnldlH.:ed, Ihe prediction of holh cffectivc Lagrangiansror tlll' depL'lldence (JI' Ihe propcrties of lhe correlatcd vacuulll011dCllsily amllcmperalurc is remarkahly different. This is il-11IsIraled lo SOllle extend in Fig. 20.

An:t1nlingly. lIJe chirally SYllllllctric mesOIl ¡¡eld lheoryprcdicl.s llllJ('11 highcr primary dcnsities (and tempcratures)

7. Conc!lIding remarks-Olltlook

The cXlcnsioll of Ihe pcriodic SYSlelll inlO the scctors hy-pc.::nnaltcr (slrangcllcss) ami anlimaller is 01"general and as-lrophysical illlportancc. Indecd. microscconds after the highang Ihe nc\V dilllcnsions of Ihe periodic syslem, \Ve havelouchcd upon, ccrtainly havc hecn populatcJ in thc courseof Ihe baryo- and nlJclco-gencsis. Of course, for Ihe creation01"the univers\:, eVCIl highcr dimensional extcnsions (chaTIll,bollOlll, IOp) nHIlC i!llo play, which we did nol pursue here.It is an open question. how the depopulation (lhe <lecay)nf lhcse sL'clors inllucllces the dislrihulion 01' clclllcnts 01"

Re\'. Afex. F/s. 45 S2 (]l)(JI)) 6,~-73

ON TI lE EXTENS10N ()F THE PERIODlC SYSTEt>.l ()F ELE~lENTS AND RELATEI) T()I'ICS

ollr \\'orld toJay. Gur conceplioll 01' lhe \vorld \vill cerl~inlygain a 101through the clarification 01' thcse qucstions. rorlhe Cicsel1schaft für Sdnvcrionenrorschllng (GSI). which 1hL'lpcd iniliating in lhe six.(ies. Ihe qllestions raiseo herc could¡lOinl lo lhe way ahcao. \Vorking grollps hav(: heell inslrucl(:l!hy Ihe board of dircctors nf GSI. lo l!link ahout lile future oflile lahoratory. 011 that occasioll, very concrete (almost tooCOIlLTele)slIggcstions are disclIss(:d-as far as il has heenprL'~cnt(:dlo Ihe puhlic. \Vha! is missing, as il secms. is a vi-sio/l 011(/ long le1"m b(/sis. The ideas proposed here. the verili-l':Lli(11lnI"which wi11need the cOll1l11il11/ellt Jor 2-4 decmles of

I'c.H'lIIrh. cOllld he slIch a vision with considerahle atlractiollrOl'lhe hest YOllngphysicists. The new diJllensions of the p(:-r¡odie SYS!ClllmaJe of hyper. ami antimalter cannot he ex.am-illel! in lhe "~Ii.lIld-by" moJe aLCERN (Geneva); a dedicateJ

1. S.(j I"'ils~(ln e/ al .. N/ld. I'hy.\. A J 15 (19Mn 545 IJI (llJ6lJ) 1;I'{¡n. Ll'l/. 2XB (1969) 45K.

,) t1. ~doscl. B. Fink. and W, GrcinL'r. COlltrihulion te ,\1('11101'(//1-

dI/m Ik\.\;\'cl/l'r KemphYJikl'l'. Darmsladt. Frankfllrt. Marhurg1 1tJ()()).

:1 lJ. t\lost:l and \V. Grciner, Z. "h.rs. A 217 (1968) 256: Z. Ph,,\ ..222 (llJ()9) 261.

'\. J. Cilllrnanl1. lJ. ~losC'1. n. Fink. amI W. Grciner. Z. "hy.\", A22X (19()9) 371: J. Grumann. T. 1\lorovic. and W. Greiner. Z.NtllUlfol"Sch. 2(,.1 (1971) 643.

.• t\. S:ll\dllh.'s{'u. R.K. Gupln, \v, Scheio. ami W. Grciner. "I,rs.1.('1/. flUB (1976) 225: R.K, (iupt,l. A. S;inoulescu. nnd W.(ileínl'r. Z. N(//III!ol".\cl1. J2a (1977) 704: I'hys. /..l'I/, 64B(11J77) 257: R.K. GUpln. C. 1\-lrvu1cscu. A. S~lll¡julescll. ano \\'.(irl'Íncr. Z. I'IIys. A 2X_' ( 1(77) 217.

(j. (; .•\1. TC'r-AKopian ct al., NI/el. PI/y.\". A255 (1975) 509; y.T.()~;lnl.'~~ian ('/ 01.. NI/el. "".1'.\', ABI) (1975) 353: r\239 (11)75)157.

,. D. Scl1al'l1wchcr, U. ~1oscl. anu W. Greiner. 1'11)'.1". Rel'. Lel1. 2O:¡(JlJ7()) (lO 1: U. Mose!' lA. Maruhn. amI \\1. GreillC'r."IIy.\. Ll'l1.

.QB (1~71) 5X7.~ (j, ~liin/l'llhcrg e/ (/1., Z. I'ltr.\". A 3WJ(1992) R9: S. Hoflllanll 1'1

(/1.. 1. "h."\. A _'5U (1995) 277: .'5U ( 19t)5) 2XX~J R K. (,upla. A SiílllJlI!cSClI,amI \\'. Grciner. Z. NlI/l/r(on'd¡

32.1 ( 1IJ77) 704.

lO K. Rul/. ('/ al .. Phys. Rc\~e 5() (1{)t)7) 23S1L B Fridc ;¡nd \V. Grcincr. 1'1t)'.I".U'I/. 3UB (1969) 317: B,

Frickl'. \V. Grcincr. and J.T. Waher. Tltcor('(. Cltimin/ Ac/olIk'rlill) 21 (1971) 135.

12. A. S:indulcsclI. D.N. Pocnaru. amI W. Greincr. SOl' . .1. !'tll"!.,vll( 1. I J (19XO) 51X.

l:~ 11. Klcin. PIt.D. Ihesis. J.\\.'.-Gocthc UnivcrsiWt. Frankfurt a.:\1. (]tJ92); D. Schnahe1. Pb,D thcsis. J.\\'.-Go('ll1e Univcrsitil.F!",ll1Kt'Urta. ,\1. (1992).

11. D.N. I'ocn;lru ct al.. Z. Ph."s. A .12X( ¡t)S7) 309: 332 (19S9) 2t) l.1,•• E.K, Ilull'l f'/ al. Ph.\'.I". Rl'l~LJ.'11. 56 (19X(I) 313.10. K. (kpta. f'/ (/1.. Int..I. Moti. "hy.\'. A 5 (1990) 3901: K. ()cpla,

R, Iknnallll. l.A. ~larllhn. and W. Grl'illC'r. in Dyntllllic.I"o{Col."'('r;I'" l'h,'II01I/('//o. edited hy 1'. D,lVid. (World Sciclltilir. Sin-¡.!:I¡lorc. JlJS7) r. 29

racilily is Ilecessary rOl' this lielJ of rescarch. which can in!üturc serve as a !lome rol' the llnivcrsitics, Thc GSI-whichhas llnforlllnately hccollle lllllCh loo sclf-sufficient-could heslIch ;¡ home for l1e\\'gcncraliolls of physicists, \vho are inlcr-csted in Ihe strtlclltn' (!l elell/Clltal)' IIW1tcr. GSI would then1101develop jusI ¡nlo a delcctor lahoratory for CERN. ami assllch hccome ohsolete. I can already see Ihe cnthusiasm inlh(:eyes (Ir Y(Hll1gscienlisls, \••..'hen illllfold these ideas lo Ihclll-similarly as il \Vas 30 years ago. whcn lhe nuclear physicislsinlhe slate nf lIesscn initialeJ Ihe construclion ofGSI.

,\ckllowledgments

I al1l gralcful lo Dr. Klclllens Rutl. rnr his hclp in preparingIhis reporto

17. ,\. S;intiu1esclI. \V. Greinl'r. amI J,II. Ilamillon. prívate discus-sions ( 1992-199~)_

1S. 1.11. lIamilton ('/ (/1...1. l'¡'ys. G 211(1994) L85.

EJ. E.K. lIukl ('/ al. I'/n'.\. R('\ ..e 40 (19R9) 770.

20. W, Greincr. B. Müller, ami J. Rafelski, QED of Stmllg Fie1d.'l,(Springer Verlag. llciddhcrg. 19X5); Fora ilIOn' /'l'cnlt /'l'\'it'll'

\l'l' W. Grcillcr. J. Rcinhardt. SIlI'enTificol Fieltl.\' in 1/£'(1\')'-lo" l'I1y,\I('.I". Procecdings of Ihe 151h Aovnnecd (CFA I1camDYll<lrnics\Vmkshop 011 QlIanlllrn AspcclS of Beam Physics.(Wmld Scicnlillc, Singaporc, 19tJX).

2.1. B. 1'0vl1.R£'I'. I'rog!: ""y,I, JI) (1976) 823; Ami. Rel', NI/el. !'l/r(,Sci. 28 (1t)78) 1: NI/el. I'''-rs. '\.'-'5 (1980) 233: I'mgl" I'(/r/.NI/(l !,".rs. 5 ( 19X1) 245; "!ly.\', l/liittcr 4U (1984) 315.

22. J. Schafrner. C. Grcincr. amllf. Stilckcr. P!lys. Re\'. C.t5 (1992).U2: NI/el. PhY.I. B2.t (1991) 246: 1. Schaffner el tll.. AI/II. ,.ltrs.235(19~4)35. .

:.u. W. Schcíd anJ W. (;rcincr, A/III. "!Ir.\" . .tX (i96K) 493; Z. "!lr.\',i\ 22<, ( 1()69) 3()4. . .

2.1. W, Schcid. 11. f\1¡¡llcr. ami W. Greiner. Pltys. Re\'. l.A'II. U(1974) 741.

2r. 11. Slóder. W. Greincr, and W. Schcid. Z. Pltys. A 286 (197X)I ~ 1.

:l(j. 1. ~li~hllstill ef (/1.. .1. I'''y.\. G 19 (1993) 1303.

27. 1'.K. Panda el al,. II/t . .1.AfrJ(1.l)h)'.I". E () (1997) 307.

2R. 11.Slikl\cr amI W. Greincr, "")'.\'. Rel', 137 (19X6) 279.

:!!). J. Rcinhardl ami W. Grciller. to he published.

:JO 1'. l'apalOglou el ,,1 . .1. "".1'-" G 2.\ (1997) 2081: 1'.l'apawglou('( al., Pltys. Rl'l'. e 57 (1')98) 2576.

:ll. J. Theis f'l al .. P"r\'. 1<1'1'. f) 2X(1983) 2286.

:J2. P. Papa/ogloll f'! al.. /'lty.\. I<el'. e 59 (1999) 411.:.n P. Papa/Oglou. Ph.D. Illcsis, J. W.-Goelhe Universil:it. Frank-

flirt a . .\1. (19tJ8): C. BecKrnann et al.. in prcparation.

:~l. s. KliJllt. M. LUll.. <lnd\V, Wl.'ise, /'hrs. Len. B 249 (1990) 3X6.

Rel: AII'.\. Fi.\ . ..JSS2 ( 1(J91J) (13-7~