This content has been downloaded from IOPscience. Please scroll down to see the full text.

Download details:

IP Address: 129.21.35.191

This content was downloaded on 18/12/2014 at 16:37

Please note that terms and conditions apply.

Cluster-fission, a new fission mode

View the table of contents for this issue, or go to the journal homepage for more

2002 Europhys. Lett. 58 362

(http://iopscience.iop.org/0295-5075/58/3/362)

Home Search Collections Journals About Contact us My IOPscience

Europhys. Lett., 58 (3), pp. 362–367 (2002)

EUROPHYSICS LETTERS 1 May 2002

Cluster-fission, a new fission mode

G. Mouze

Faculte des Sciences, 06108 Nice cedex 2, France

(received 20 December 2001; accepted in final form 5 February 2002)

PACS. 23.70.+j – Heavy-particle decay.PACS. 25.85.-w – Fission reactions.

Abstract. – Clusters heavier than those observed in the cluster-radioactivity of heavy nucleican not only be formed in superheavy compound nuclei but also be immediately expelled,because the clusterization energy is very great. This process differs from cluster-radioactivityand constitutes a new type of fission reaction. Its reality is confirmed by recent experimentalobservations.

Clusterization of nuclear matter and cluster-radioactivity. – The discovery of the phe-nomenon of cluster-radioactivity by Rose and Jones in 1984 [1] has opened a new field ofresearch in nuclear physics. Rose and Jones found that 223Ra emits a 14C cluster according to

223Ra −→ 209Pb + 14C. (1)

As in alpha-radioactivity, the daughter of an odd-A emitter is often left in an excited stateand it is the case of 223Ra [2].

Let us consider the simpler case of even-even emitters: Here, the maximal energy releasedin the cluster emission is usually given by the difference of ground-state binding energies

Q = [EB (core) + EB (cluster)]f − [EB (emitter)]i. (2)

A positive value of Q means that the formation of a cluster within the emitting nucleus isenergetically possible, and the small probability of the cluster emission, i.e. the great partialhalf-life of the phenomenon, results from the smallness of this possible energy release Q ascompared with the Coulomb barrier of the core-cluster system.

Equation (2) can also be written as

Q = [EB (cluster)] − [EB (emitter) − EB (core)]. (3)

This relation shows that the formation of a cluster within a nucleus is energetically pos-sible —i.e., that the phenomenon of clusterization is possible— only if this nucleus containsan underlying strongly bound core having the following property: The valence nucleons sur-rounding such a core win energy if they condense into a cluster; in other words, the energy ofthese valence nucleons is greater if they become bound in a cluster than if they remain boundto the core.c© EDP Sciences

G. Mouze: Cluster-fission, a new fission mode 363

300

250

200

150

100

50

90 94 98 102 106 110 114 118 122

z

E (

MeV

)

B

QQ*

c

BcSH

Fig. 1 – Variation of clusterization energies Q and Coulomb barriers Bc for even-even isotopes ofheavy nuclei (see text).

In heavy nuclei, such a strongly bound core is normally the doubly magic 208Pb core, with82 protons and 126 neutrons; but in all nuclei it can happen that the favoured core-clusterconfiguration nevertheless involves a core differing slightly from 208Pb.

The aim of the present letter is to ask: Can the clusterization energy become very greatin superheavy nuclei or in superheavy compound nuclei, and what can happen in this case?

Prediction of the existence of a new kind of fission reaction. – T h e c l u s t e r i z a t i o ne n e r g y. We first observe that the clusterization energy Q defined by eq. (3) increases regu-larly as a function of the atomic number of the emitting (or virtually emitting) nucleus: Forall isotopes for which the necessary mass data are available, the clusterization energies of theeven-even heavy nuclei with Z in the range 92–110, calculated in this way, are represented byopen circles in fig. 1. One observes that their variations as a function of A are approximatelyparabolic, and that the greatest Q values increase regularly as a function of Z. Assuming alinear law of variation for QMAX(Z), which can be written:

QMAX = (9.168Z − 783.56)MeV, (4)

a superheavy nucleus of Z = 112 and having a normal N/Z ratio could have in its groundstate a QMAX of about 243.3MeV.

However, a (Z = 112)-nucleus formed in a heavy-ion reaction with a heavy projectile 48Caand a heavy target 238U, such as 286(112), may have a great N/Z ratio. Figure 1 showsthat the Q-values of the heavy U- and Pu-isotopes considerably decrease as their N/Z ratioincreases; for example, Q(Pu) decreases by 19MeV in going from 236Pu to 244Pu. It maycertainly be assumed that Q(286112) departs from the extrapolated value 243.3MeV by atleast 10MeV, and in a first approach we will adopt for 286(112) a Qeff of about 233.3MeV.But this effective value might be even smaller, perhaps 30MeV smaller than the extrapolatedvalue of 243.3MeV.

Let us now imagine the formation of 286(112) by the reaction 48Ca + 238U as an excitedcompound nucleus, 286(112)∗, with an excitation energy of ∼ 30MeV. Since its clusterization

364 EUROPHYSICS LETTERS

according to286(112) −→ 78Zn + 208Pb (5)

should release, in the ground state, about 233.3MeV, the final excitation energy of 286(112)∗

can be as great as ∼ 263.3MeV.But can such an excited clusterized nucleus remain bound? We have to evaluate the

Coulomb barrier of the system 208Pb-78Zn.

C o u l o m b b a r r i e r a n d t h e p h e n o m e n o n o f c l u s t e r - f i s s i o n. Let us assumethat the Coulomb barrier is given by

Bc =Z1Z2e

2

r1 + r2(6)

and thatr = r0 10−13A1/3 cm; (7)

the expression of the Coulomb barrier is [3]

Bc (MeV) =1.44Z1Z2

r0

(A

1/31 + A

1/32

) . (8)

The value 1.48 of r0 has been found suitable for describing the phenomena of α-radioactivity [4],and the (208Pb-78Zn) system is similar to the (208Pb-4He) system. Many Bc-tables are basedon an r0 value of 1.50.

However, a value of 1.48 has to be rejected, because it would lead to a value of 225.08MeVfor the Coulomb barrier of the system 208Pb-64Ni in which 272(110) clusterizes with an energyrelease of about 225.1MeV: Indeed, in such a situation, 272(110) would immediately fissionand expel a heavy cluster; however, such a phenomenon has not been observed. Thus it isclear that r0 has to be smaller than 1.48, and at most equal to 1.47. Let us adopt this value.

The Bc energies, calculated according to eq. (8) with r0 = 1.47, of the same even-evenclusterized heavy nuclei with Z in the range 92–110 are represented, too, in fig. 1 (opentriangles). They vary slowly as a function of A.

One sees that their mean value, for a given Z, increases approximately linearly as a functionof Z, according to

Bc = (7.673Z − 615.55)MeV. (9)

An extrapolation of this law for the range Z = 112–122 is represented in fig. 1. This linecrosses the QMAX- line at Z = 112.39.

Thus a clusterized superheavy nucleus of Z = 112 having a normal N/Z ratio is expectedto have in its ground state a Bc-value of about 243.87MeV.

This value is very near to the QMAX-value of Z = 112 nuclei, Q = 243.3MeV. As aconsequence, two new phenomena can come about: a radioactive emission, with very shorthalf-life, of a very heavy cluster, and a fission releasing a variety of cluster-like fragments andof core-like fragments.

This new kind of fission might be called cluster-fission, or primordial asymmetric fission,since the fragments are always preformed as a consequence of the tendency of nuclear matterto clusterize.

C l u s t e r - f i s s i o n o f s u p e r h e a v y c o m p o u n d n u c l e i. The foregoing predictiondoes not hold for superheavy nuclei having an important N/Z ratio, because their Q-values

G. Mouze: Cluster-fission, a new fission mode 365

are probably strongly reduced by the N/Z-ratio effect (see the first paragraph of the secondsection). This effect, on the contrary, does not considerably reduce the Bc-value of the su-perheavy elements: For superheavy nuclei, such as those recently synthesized in Dubna [5],namely 286(112), 292(114), 296(116), 294(118) and 306(122), we find, according to eq. (8), thefollowing Bc-values: 236.31; 249.45; 263.28; 274.69 and 304.98MeV, represented by closedtriangles in fig. 1, and which follow the variation law

BSHc = (6.953Z − 542.62)MeV. (10)

These effective Bc-values are only somewhat smaller than the values calculated using eq. (9):243.87; 259.22; 274.56; 289.91 and 320.60MeV.

This means that the strong reduction of the Q-value resulting from the N/Z ratio effectshould considerably reduce the probability that the recently synthesized superheavy nucleiundergo a cluster-fission already in their ground state.

But an excitation of about 30MeV resulting from the reaction of formation changes com-pletely this prediction. For example, a total excitation energy of 243.3 + 30 = 273.3MeV for286(112)∗ should be greater than the effective Bc-value of 236.3MeV, by as much as 37MeV,and no N/Z-ratio effect smaller than 37MeV could hinder cluster-fission from coming about.

As long as the hypothesis made on r0 is correct, excited superheavy compound nuclei areexpected to undergo a cluster-fission as soon as they are formed.

Experimental evidence of the existence of a the new fission mode in superheavy compoundnuclei. – An international team working in Dubna [5] recently succeeded in synthesizingsuperheavy compound nuclei having up to 30 protons more than 92U, namely 286(112)∗,292(114)∗, 296(116)∗, 294(118)∗ and 306(122)∗, using 48Ca, 58Fe or 86Kr as projectile and 208Pb,238U, 244Pu or 248Cm as target. Furthermore, they succeeded in studying the disintegrationof these excited nuclei, in particular the mass distributions of the reaction products. Theyhave interpreted the most intense of these mass distributions as resulting from a quasi-fissionreaction.

A careful examination of the mass spectra published by Itkis et al. [5] shows that theyresult in reality from the superposition of two kinds of distribution. One of these kinds couldeffectively result from a quasi-fission reaction. Indeed, it is known since the discovery of quasi-fission by Lefort et al. [6] that quasi-fission is a transfer reaction in which a projectile a, in acollision with a target B, captures a number of nucleons of B, thus giving a heavy projectile-likefragment A, while the target is changed into a lighter nucleus b, according to a + B → A + b;and a careful examination of the mass spectra of the reactions

48Ca + 238U −→ 286(112)∗, (11)

or86Kr + 208Pb −→ 294(118)∗, (12)

shows that each of them contains two continuous spectra, one beginning at A ∼ 48 or at A ∼ 86and the other ending at A ∼ 238 or at A ∼ 208, as expected for quasi-fission reactions, if theexperimental mass resolution of about 3 atomic mass units [5] is taken into consideration.

However, each of these mass spectra contains a discrete spectrum made of two peaks,culminating at A = 78 and A = 208 for eq. (11), and at A = 86 and A = 208 for eq. (12).Such discrete spectra cannot result from a quasi-fission reaction, because it is not possible thathigh-energy projectiles as different as 48Ca and 86Kr lead to only one and the same target-likefragment; and in the case of the second reaction, there is no transfer of nucleons, since theexit channel is the same as the entrance channel.

366 EUROPHYSICS LETTERS

Table I –

Reaction Maxima Predicted fission mode

I 48Ca + 238U → 286(112)∗ 78-208 286(112)∗ → 78Zn + 208PbII 48Ca + 244Pu → 292(114)∗ 84-208 292(114)∗ → 84Ge + 208PbIII 48Ca + 248Cm → 296(116)∗ 88-208 296(116)∗ → 88Se + 208PbIV 86Kr + 208Pb → 294(118)∗ 86-208 294(118)∗ → 86Kr + 208PbV 58Fe + 248Cm → 306(122)∗ 98-208 306(122)∗ → 98Zr + 208Pb

The discrete spectra occurring in these reactions, and those occurring in the reactionsof 48Ca with 244Pu and 248Cm, or in the reaction of 58Fe with 248Cm, all need anotherinterpretation than quasi-fission.

But table I shows that the maxima of these discrete spectra coincide perfectly with themasses of the fragments of the fission mode predicted in the second section.

The extremely great intensity of the reaction IV [5] could result from a resonance effect, asa consequence of the precouplage between the exit channel and the identical entrance channel.

Superheavy cluster-fission and spatial conformation of superheavy nuclei. – It is wellknown that the concept of nuclear radius is not completely independent of the conditions ofits use. It is the reason of the great variety of recommended expressions for r.

Now that the cluster-fission of excited superheavy compound nuclei has been observed, itmay be asked whether this observation could furnish some information on the height of theCoulomb barriers of their core-cluster systems, and in this way on the size of clusterized nucleialong their symmetry axis.

A value of r0 as small as 1.23 can be excluded: it should correspond to a Bc-line havingalmost the same slope as that of Q + 30MeV = Q∗ given by

Q∗ = (9.168Z − 753.56MeV), (13)

but lying ∼ 17MeV higher than the Q∗-line represented in fig. 1. For all values of r0 < 1.23,the Bc-lines have a smaller slope than the Q∗-line. As a consequence, as soon as 286112 isexpected to fission, a fortiori heavier superheavy compound nuclei are expected to fission,too: we have to discuss only the 286(112)∗ case.

For the superheavy nuclei synthesized in Dubna, we have to compare the values of Q∗eff

and of Bc(SH)(eff), but Bc

(SH)(eff) is a function of r0. For the following values of r0 : 1.269;1.317; 1.369 and 1.425, B

286(112)c (eff) becomes equal to, respectively: 273.3MeV (the value

of Q∗ without correction for the N/Z-ratio effect); 263.3MeV (Q∗ with a −10MeV effect);253.3MeV (Q∗ with a −20MeV effect); and 243.3MeV (Q∗ with a −30MeV effect).

We may conclude that all r0-values of the range 1.32–1.47 are acceptable, but those ofthe range 1.37–1.47 are the most probable. Further work on the onset of cluster-fission insuperheavy compound nuclei is to be wished for; it could furnish exact information about thediameter of the primordial diclusteric molecules.

Conclusion. – The considerable increase of the clusterization energy in going from heavyactinide to superheavy nuclei leads to predict that this clusterization energy, added to theexcitation energy of the compound nucleus, can become greater than the Coulomb barrier,and make possible the immediate expulsion of the partners of the primordial diclusteric con-figurations, made of the doubly magic 208Pb core and of the cluster formed from its valence

G. Mouze: Cluster-fission, a new fission mode 367

nucleons. And these predictions are confirmed by a careful analysis of the recent work madein Dubna.

The phenomenon of cluster-radioactivity expected in the ground state of superheavy nucleifor which Q is almost equal to Bc (see second paragraph in the second section) is discussedelsewhere.

Additional Remark. – Assuming that the variation of Q as a function of A is the samefor nuclei with Z in the range 92–110, a better determination 1) of QMAX, 2) of the A-valuecorresponding to QMAX, 3) of the effects on Q of the neutron excess in heavy isotopes canbe obtained. With QMAX = (8.99009Z − 764.584)MeV, QMAX(Z = 112) becomes equalto 242.3MeV, instead of 243.3MeV. The mean value of Bc, Bc, is advantageously replacedby the Bc-value calculated for the A-value at which Q is maximum, BQMAX

c = (7.39592Z −586.5109)MeV, so that the BQMAX

c -line crosses the QMAX-line at Z = 111.78. And thedifferences between the Q-values corrected for the neutron excess, Qeff , and the Bc-valuesgiven by eq. (8), Qeff − Bc, can be found equal to about +12.4; +7.7; +6.9; +20.5 and9.6MeV, respectively, for the superheavy compound nuclei 286(112)∗, 292(114)∗, 296(116)∗,294(118)∗ and 306(122)∗ at an excitation energy of 30MeV.

REFERENCES

[1] Rose H. J. and Jones G. A., Nature, 307 (1984) 254.[2] Sheline R. K. and Ragnarsson I., Phys. Rev. C, 55 (1997) 732.[3] Mayer-Kuckuk T., Kernphysik (Teubner B. G., Stuttgart) 1994.[4] Perlman I. and Ypsilantis T., Phys. Rev., 79 (1950) 30.[5] Itkis M. G., Oganessian Yu. Ts., Kozulin E. M., Bogatchev A. A., Itkis I. M., Jan-

del M., Kliman J., Kniajeva G. N., Kondratiev N. A., Korzyukov I. V., Krupa L.,

Pokrovski I. V., Ponomarenko V. A., Prokhorova E. V., Rusanov A. Ya., Giardina

V. M. and Moody K. J., Proceedings of the International Conference Fusion Dynamics at theExtremes, Dubna, May 25-27, 2000 , edited by Oganessian Yu. Ts. (World Scientific, Singa-pore) 2001, p. 93.

[6] Lefort M., Ngo C., Peter J. and Tamain B., Nucl. Phys. A, 216 (1973) 166.