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On  the  Pos si bil ity  to  Syn the size  Super heavy  Nu clei

of Higher Neu tron Num bers

Š. Šáro


De part ment  of  Nu clear  Phys ics  and  Bio phys ics,  Fac ulty  of  Math e mat ics,  Phys ics  and  In for ma tics,

Comenius Uni ver sity, 842 48 Bratislava, Slo vak Re pub lic, e-mail: saro@fmph.uniba.sk 



Ab stract: The lab o ra tory syn the sis of nu clei of atomic num bers above Z = 110 hav ing the max i mum

achiev able neu tron num ber N is con sid ered. Cold fu sion re ac tions are lim ited with mo not o nous de crease 

of the fu sion cross sec tion be low 0.01 pb for Z = 114. The cross sec tion of hot fu sion re ac tions re sult ing

in the syn the sis of nu clei of el e ments of Z = 114, 115, 116, and 118 show no ev i dence of the in flu ence of

the pre dicted neu tron subshell at N = 172. The lim i ta tions to cre ate more neu tron reach super heavy

nu clei is an a lyzed in the case of ra dio ac tive beams with half-lives lon ger than 2 s. The o ret i cal and

ex per i men tal half-life val ues for nu clei of Z = 110–118 are com pared and half-life lim i ta tions are

con sid ered. New at tempts to syn the size el e ment of Z = 120 and 122 is dis cussed.



1.  In tro duc tion

In the mid dle of the 1960s nu clei of 12 el e ments be yond ura nium were ex per i men tally

syn the sized up to law ren cium (Z = 103) and ruther ford ium (Z = 104) due to the sta bi liz ing 

ef fect of the nu clear shell struc ture. At that time the ques tion of the shell struc ture and its

ef fect on nu clear sta bil ity was ac tu ally top i cal and the pos si bil ity of the ex is tence of super -

heavy nu clei (SHN) was also con sid ered [1]. It was pro posed that in the case of closed

pro ton and neu tron shells the nu clei should have half lives long enough to be ex per i men -

tally ob served. Fur ther the o ret i cal stud ies led to the most prob a ble closed pro ton shell at

Z = 114 and closed neu tron shell at N = 184 [2-4]. Later some model cal cu la tions led to

other val ues of the closed pro ton shell, at pres ent the dom i nat ing val ues are 114, 120, and

126. The closed neu tron shell at N = 184 has a rel a tively sta bile po si tion in the the ory. An

im por tant step for ward was made in 1967 – 68 by V.M. Strutinsky [5] pre sent ing quan ti ta -

tive cal cu la tion of the mi cro scopic part of the shell cor rec tion to the bind ing en ergy of

heavy nu clei. 

The first at tempts to syn the size super heavy nu clei around Z = 114 were too op ti mis tic.

The first cal cu lated half lives were of the or der of 10

8-9

 years and at that time there were no 



re li able  es ti ma tions  of  fu sion  re ac tion  cross  sec tions.  The  avail able  ex per i men tal  tech -

nique  gave  sev eral  ba sic  pos si bil i ties  for  the  syn the sis:  a)  frag men ta tion  re ac tions  of  two

sym met ric nu clei with sim i lar pro ton num bers [7] and “gen tle fu sion” of two rare earth

nu clei [6] ; b) com plete fu sion re ac tions of the heavi est sta bile dou ble magic nu cleus 

208

Pb 


and the neigh bour ing 

209


Bi with avail able sta ble beams of Z = 26-34 [8]. This type of

com plete fu sion re ac tion led to the syn the sis of nu clei of el e ments of Z = 107-113 [9-15];

c) the third pos si bil ity was the com bi na tion of as heavy transuranium tar get nu clei as

avail able with beams of light nu clei, giv ing the de sired Z. Yu.Ts. Oganessian re al ized a se -

Acta Physica Universitatis Comenianae

Vol. XLVIII-XLIX, Number 1&2 (2007-2008) 43-50



De voted to Prof. Pavel Povinec 65-th an ni ver sary


ries of ex per i ments of this type of fu sion re ac tions choos ing the dou ble magic nu cleus of

48

Ca as pro jec tile and syn the sized the nu clei of el e ments of Z = 114, 115, 116, and 118



[16-20].

In fact the prog ress in the syn the sis of nu clei with higher and higher Z was in flu enced

by sev eral fac tors. First of all the avail abil ity of the re quired beams and their in ten sity de -

liv ered from ion sources. The lack of re li able the o ret i cal ideas about the pro cess of fu sion

of heavy nu clei led to ex tremely large un cer tain ties in cross sec tion and half life es ti ma -

tions and from here to many un suc cess ful ex per i ments. 



2.  Cross-sec tion  lim i ta tion

The pro duc tion cross sec tion of com plete fu sion re ac tions of heavy ions is a re sult of

sev eral phys i cal pro cesses play ing role in this pro cess – first of all prompt fis sion, deep in -

elas tic  scat ter ing,  com plete  fu sion  and  com pound  nu cleus  sur vival  prob a bil ity.  The  pro -

cess of fu sion is in flu enced also with other ef fects, like the shell cor rec tion en ergy, nu clear 

spin, shape of the in ter act ing nu clei and oth ers. 

There are sev eral the o ret i cal ap proaches to cal cu late the cross sec tion of com plete fu -

sion re ac tions, but in gen eral the re li abil ity of these cal cu la tions is prob lem atic. In cold fu -

sion re ac tions of the dou ble magic tar get nu cleus of 

208


Pb and the neigh bour ing 

209


Bi with

neu tron reach Ti, Fe, Ni, Zn and sim i lar ions the ex per i men tal cross sec tion is steadily de -

creas ing from 5´10

-7

 barn for Z = 102 to 5´10



-14

 barn for Z = 113 [15], i.e. the de crease of

Z by one unit re sults in 6-fold de crease of the cross sec tion in av er age as is shown in Fig. 1. 

No  mea sur able  in flu ence  of  the  sta bi liz ing  shell  cor rec tion  en ergy,  iso to pic  spin  or  other

pa ram e ters on the re ac tion cross sec tion was ob served. No ex pla na tion was find for ex am -

ple for the sig 

nif 



cant jump of the 1n chan 



nel cross sec 

tion from 3.3 (

-

+

2 7



6 2

.

.



) pb for

208


Pb(

62

Ni, 1n) [12] to 15 (



-

-

6



9

) pb for 

208

Pb(


64

Ni, 1n) [21] dif fer ing only by 2 neu trons in

the Ni ions.

The hot com plete fu sion re ac tions, based on ac ti noid tar gets from ura nium to cal i for -

nium and on the dou ble magic

 48


Ca pro jec tile ions has an un ex pected fea ture. In spite of

the o ret i cal  pre dic tions  the  cross  sec tion  of  all  re al ized  re ac tions  have  very  sim i lar  val ues

dif fer ing less than one or der of mag ni tude as it is il lus trated in Fig. 2. and Fig. 3. For Z =

112-118 and for the neu tron num ber N = 170-177 no sys tem atic trend in mea sured cross

sec tion val ues was ob served. It means no ob serv able in flu ence of the pre dicted neu tron

subshell at N = 172 [23] or the in flu ence of the closed neu tron shall at Z = 184. To draw se -

ri ous con se quences for the the ory, these cross sec tion val ues need to be con firmed in in de -

pend ent  ex per i ments  and  at  higher  re li abil ity. 



3.  Tar get  –  pro jec tile  lim i ta tion

To in ves ti gate the re gion of super heavy el e ments above Z = 112, the only to day known 

ap proach is the method of hot fu sion re ac tion of ac ti noid tar get nu clei and suit able ac cel -

er ated ions. The suc cess ful chain of re ac tions based on U, Pu, Cm, Bk, and Cf tar gets and

sta ble 

48

Ca ions is ex hausted. In these re ac tions the lim its of the ra dio ac tive tar get and sta -



ble pro jec tile nu clei com bi na tions were reached in the di rec tion to more neu tron rich nu -

clei to wards to N = 184. To reach higher neu tron num bers up to the pre dicted closed

44

                                   Š. ŠÁRO




neu tron shell at N = 184 ac ti noid tar get nu clei have to be bom barded with ions heavier that 

48

Ca. But even in this case only at Z = 124 one can reach N = 184 as it is shown in Fig. 4. 



In the re gion of in ter est (Z = 114–126) higher neu tron num bers are achiev able only us -

ing  ra dio ac tive  beams  (RBs).  Con sid er ing  avail able  ac ti noid  tar get  nu clei  and  ra dio ac tive

beams of ions hav ing half lives lon ger than 2 sec onds, the achiev able front line is shown in 

Fig. 4. Even in these case the pre dicted closed neu tron shell at N = 184 is achieved at Z =

119. To day we have no idea how to reach the pro posed closed neu tron shall (N = 184) at

Z = 114.


The idea to use ra dio ac tive beams to syn the size neu tron reach super heavy el e ments is

not a new one. The ba sic prob lem is the avail able in ten sity of such beams. Suit able neu -

tron reach ra dio ac tive ions can be cre ated by frag men ta tion of high en ergy nu clei and by

con se quent in-flight sep a ra tion and deacceleration of the sep a rated high en ergy ion to

cou lomb bar rier en ergy level. With re spect to the ex pected picobarn (10-40 m

2

) cross sec -



tion level, the nec es sary beam in ten sity is of the or der of 1 pµA or 10

12-13


 ions/s. The pres -

ent ap proach able in ten sity of sin gle ion RBs is be low 10

9

 ions/s. To reach the 10



12-13

 ions/s 


level will be a very dif fi cult task. New pow er ful ion source of pri mary beams, high en ergy

ac cel er a tor  to  ac cept  such  beams,  and  prob a bly  the  pa ram e ters  of  the  frag ment  sep a ra tor

and deaccelerating ring should be spe cially ad justed to ful fill the task. 

4. Half life lim i ta tion

The first phase of a heavy com pound nu cleus cre ation in a com plete fu sion re ac tion is

a  com plex  func tion  of  many  in ter nal  and  ex ter nal  pa ram e ters  of  both  in ter act ing  nu clei.

Af ter the for ma tion of the com pound nu cleus its sur vival prob a bil ity de pends on fewer in -

ter nal pa ram e ters of the for mat ted com pound nu cleus it self. This gives for the the ory the

pos si bil ity to cal cu late more re li able half-life val ues than in the case of the fu sion prob a -

bil ity.

Half life cal cu la tions made by Sobiczewski et al. [24] show a clear de pend ence of al -

pha de cay half lives on both, the pro ton num ber Z and the neu tron num ber N of a par tic u -

lar nu cleus. With in creas ing atomic num ber Z the half lives of all iso topes of the given Z

are mo not o nously de creas ing, but there are two sig nif i cant peaks at neu tron num bers

around the pro posed neu tron subshell of N = 162 and closed neu tron shell of N = 184 (see

Fig. 5).

To check the re li abil ity of these cal cu la tions for super heavy el e ments is rather prob -

lem atic. First of all the the ory gives data only for even-even nu clei, but in the ma trix of

121 nu clei of Z = 110–120 and N = 166–176 only 9 even-even nu clei have ex per i men tally

de ter mined  al pha-de cay  half  lives.  The  com par i son  of  the  avail able  ex per i men tal  and  cal -

cu lated al pha de cay half lives are given in Tab. 1. The cal cu lated val ues are mostly un der -

es ti mated and dif fer from the ex per i men tal ones from sev eral times to two or ders of

mag ni tude.

The sec ond prob lem is the un cer tainty in the ex per i men tal data due to very low sta tis -

tics, in some cases only one or two re corded events.

ON THE POS SI BIL ITY TO SYN THE SIZE SUPER HEAVY NU CLEI           45



5. Pres ent at tempts 

At pres ent new at tempts are made to go fur ther in SHN syn the sis. The syn the sis of Z =

120 el e ment is on the pro gram in two lab o ra to ries. In JINR Dubna the re ac tion of 

244


Pu +

58

Fe ® 



299

120 + 3n is go ing on [22] and at GSI Darmstdat [25] the re ac tion of 

238

U + 


64

Ni

® 



299

120 + 3n is on the way. Both re ac tions are lead ing to the same com pound nu cleus

302

120* and the 3n evap o ra tion chan nel will cre ate the same evap o ra tion res i due of 



299

120. 


The ex pected al pha de cay chain of 

299


120 af ter one un known mem ber (

295


118) will fol low

the path of al ready syn the sized al pha de cay nu clei - 

291

116 ® 


287

114 ® 


283

112 ® 


279

110 as


it is il lus trated in Fig. 6.

The cross sec tion of both re ac tions lead ing to 

229

120 is un cer tain. The hot fu sion syn -



the sis of all nu clei of el e ments of Z = 112, 114, 116, and 118 were based on the in ter ac tion

of the neu tron reach dou ble magic 

48

Ca ions with transuranium tar get nu clei. If the closed



shells in 

48

Ca played a sub stan tial sta bi liz ing role in the pro cess of fu sion then the cross



sec tion of both re ac tions, lead ing to 

299


120 can fall sig nif i cantly be low 1 pb. The cal cu -

lated al pha de cay half life of 

299

120 is about 1 µs [24] or higher [26]. The time of flight of



the  evap o ra tion  res i dues  from  the  tar get  to  the  an a lyz ing  de tec tor  ar ray  is  sev eral  µs,

there fore  the  de tec tion  ef fi ciency  may  be  crit i cal.



6.  Per spec tives

The cross sec tion s of the cold fu sion re ac tion at Z = 113 is only 0.05 pb [15]. The mo -

not o nous  de crease  of  s from Z = 102 to Z = 113 pre dicts the ex pected value of s for

Z = 114 0.01 pb. This is be low the ac cept able beam time of sev eral months to syn the size

one nu cleus of el e ment Z = 114. There are ex pec ta tions to de sign ECR ion sources de liv er -

ing heavy ion beams of the or der of 10

14

 ions/s which should al low to reach the 0.01 pb



level at rea son able beam time. But at such a heavy ion beam in ten sity sev eral sec ond ary

prob lems will ap pear. First of all the en ergy de po si tion in Pb or Bi tar gets is lim it ing at

pres ent the ac cept able beam in ten sity to about 10

12

 ions/s. The sec ond prob lem will be the



back ground. The method of iden ti fi ca tion of new nu clei based on the al pha – al pha cor re -

la tion method re quires as low back ground count rate in the sen si tive part of the en ergy

spec tra as pos si ble. To avoid dif fi cul ties of this type spe cial ef fort should by paid to the

con struc tion and shield ing of all parts of the equip ment from the tar get cham ber to the de -

tec tor  ar ray  be yond  the  sep a ra tor. 

Prop erly de signed transuranium tar gets will be able to ac cept beams of ions of the or -

der of 10

14

 but the prob lem of the back ground will be se ri ous also here, es pe cially in the



case of gas filed sep a ra tors.

7.  Con clu sion

The ar ti fi cial syn the sis of nu clei heavier than ura nium was, all the time, a front-line ex -

per i ment  re quir ing  the  most  ad vanced  lab o ra tory  equip ment  and  novel  phys i cal  ap -

proaches. The method used to syn the size the first transuranium nu clei ex hausted its

pos si bil i ties  at  men de le vium  Md  (Z  =  101).  The  next  gen er a tion  of  ex per i ments  post -

poned the fron tier to siborgium (Z = 106). A new ap proach was needed to con tinue, the

46

                                   Š. ŠÁRO




cold fu sion con cept, which shifted the fron tier to el e ment 113, where the cross sec tion of

the 1n evap o ra tion chan nel fall to 0.05 pb. An un ex pected suc cess of hot fu sion re ac tions,

based of the dou ble magic 

48

Ca ions and trasuranium tar gets pushed the fron tier to el e ment 



118. The pres ent at tempts to go fur ther are not based on novel phys i cal ideas but on the ex -

pec ta tion that the 3n hot fu sion evap o ra tion chan nel will work as well as in the case of the

dou ble  magic 

48

Ca ions. To get closer to the pre dicted closed pro ton shell at Z = 114, 120,



or 126 and closed neu tron shell at N = 184 new phys i cal ideas and more ad vanced and

pow er ful  ex per i men tal  tech nique  should  be  in volved. 



Ac knowl edge ment

This work was sup ported by the Slo vak Sci en tific Agency VEGA un der Con tract No.

1/4018/07.

120


 

 

 



 

 

?



 

 

 



 

 

 



1-2 ms

118


 

 

 



 

 

 0.9 ms



 

 

 



 

 

 



0.05 ms

116


 

 

 



 

  15 ms


18 ms

 

 



 

 

 



 

  8 ms


114

 

 



 

160 ms


800 ms

 

 



 

 

 



    8 ms

200 ms


 

112


 

 

0.50 ms



101 ms

 

 



 

 

 



7 ms

    1 ms


 

 

110



9.7 ms

 

 



 

 

 



 

0.2 ms


 

 

 



 

 

Z / N



166

168


170

172


174

176


ON THE POS SI BIL ITY TO SYN THE SIZE SUPER HEAVY NU CLEI           47

Ta ble  1.  Mea sured (up per data) and cal cu lated (Sobiczewski et al. [24]) half-lives of the syn the sized

el e ments of Z = 110-118.



Fig. 1. Ex per i men tal cross sec tion for cold fu sion re ac tions for evap o ra tion res i dues of Z = 102-113

and  1n  evap o ra tion  chan nel.




48

                                   Š. ŠÁRO



Fig. 2. Ex per i men tal  cross  sec tion  for  hot  fu sion

re ac tions  for  evap o ra tion  res i dues  of  Z  =  112-118 

and 3n, 4n evap o ra tion chan nels [16-20].

Fig. 3. Ex per i men tal  cross  sec tion  for  hot  fu sion

re ac tions  for  evap o ra tion  res i dues  of  N  =  170-177

and Z = 112-118 [16-20].

Fig. 4. Chart of super heavy nu clei. The full line rep re sents the max i mum pos si ble num ber of neu trons

in  the  par tic u lar  nu clei,  cre ated  in  3n  evap o ra tion  chan nel  hot  fu sion  re ac tions  of  ac ti noid  tar get  nu clei

and sta ble pro jec tiles. The dashed line rep re sents the same, but for ra dio ac tive pro jec tiles hav ing

half-lives >2 s.




ON THE POS SI BIL ITY TO SYN THE SIZE SUPER HEAVY NU CLEI           49

Fig. 5. Al pha de cay half life cal cu la tion for iso topes of heavy el e ments from fer mium (Z = 100) to el e -

ment of Z = 124 (af ter Sobiczewski et al [24].



Fig. 6. The ex pected de cay chains of evap o ra tion res i dues 

299


120 and 

305


122.


Ref er ences

  [1]


W. D. Myers, W. J. Swiatecki: Nu clear Phys. 81 (1966) 1.

  [2]


A. Sobiczewski, F. A. Gareev, B. N. Kalinkin: Phys. Lett. 22 (1966) 500.

  [3]


H. Meldner: Ark. Fys. 36 (1967) 593.

  [4]


U. Mosel, W. Greiner: Z. Phys. 222 (1969) 261.

  [5]


V. M. Strutinsky: Nu clear Phys. A 95 (1967) 420; Nu clear Phys. A 122 (1968) 1.

  [6]


W. Nörenberg: GSI-95-08 Preprint. Januar 1995.

  [7]


A. Sandulescu et al.: Phys i cal Let ters, 60B 3 (1976) 225.

  [8]


A. S. Ilionov, Yu. Ts. Oganessyan, E. A. Cherepanov: Sov. J. Nucl. Phys. 36(1) (1982) 69.

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G. Münzenberg et al.: Z. Phys. A300 (1981) 107.

[10]


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