On the Pos si bil ity to Syn the size Super heavy Nu clei
of Higher Neu tron Num bers
. áro
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 = 110118 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
i
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.
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50
Š. ŠÁRO
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