Experimental investigation of the cluster radioactivity
of atomic nuclei
()
S. P. TRETYAKOVAand V. L. MIKHEEV
Flerov Laboratory of Nuclear Reactions, JINR - 141980 Dubna, Russia (ricevuto il 21 Luglio 1997; approvato il 15 Ottobre 1997)
Summary. — All experimental data on the cluster decay probabilities of atomic nuclei
obtained up to date are presented. Further possibilities of experimental investigations are discussed.
PACS 23.70 – Heavy-particle decay. PACS 25.85.Ca – Spontaneous fission.
PACS 25.70.Jj – Fusion and fusion-fission reactions. PACS 01.30.Cc – Conference proceedings.
1. – Introduction
The dependence of nuclear binding energy on the mass number makes possible a two-body decay of nuclei heavier than lead with formation of any particles, from an alpha-particle and up to fission fragments. Nuclei are kept in the bound state by the potential barrier. As the first approximation, the height of this barrierV
C can be assumed to be
equal to the Coulomb energy of the two touching spherical nuclei
V C =Z 1 Z 2 e 2 =r 0 (A 1=3 1 +A 1=3 2 ); whereZ 1and Z
2are the atomic numbers of the decay products;
eis the electron charge; A
1and A
2are mass numbers; r
0is the radius parameter. The energy deficit
Erelative
to the barrier top is determined as follows: E = V C
,Q, whereQis the difference
between the masses of the initial and two final nuclei. Figure 1 presents the value of the energy deficit, E, for
232
U as a function of the atomic number Z
1 of the lighter
decay product. Due to the choice of A
1-values, we have used the highest possible Q
-values at a given value ofZ
1. The value of r
0was accepted equal to 1.44 fm. We only show
(
)Paper presented at the 174. WE-Heraeus-Seminar “New Ideas on Clustering in Nuclear and
Atomic Physics”, Rauischholzhausen (Germany), 9-13 June 1997.
Fig. 1. – The energy deficit relative to the top of the Coulomb barrier for the two-body decay of
232
U vs. the atomic number of the lighter decay productZ1.
the results of calculation for evenZ
1 because
Q-values for oddZ
1values are essentially
smaller. The quantum penetrability of the potential barrier is manifested in the maxima, which correspond to the minima ofE. Similar curves can be calculated for every cluster
emitter. The positions of the minima in these curves correspond to the values ofZ 1and A
1 for the clusters observed in experiments. Thus, in fact, the observation of cluster
radioactivity with the formation of14
C,20
O,24;26
Ne,32;34
S resulted from the sensitivity achieved in experiments. As experimental sensitivity is improved, an increasing number of clusters can be observed in the decay of any heavy nucleus.
2. – Experimental data
The experimental data on nuclear cluster decay obtained up to date are presented in table I. The measurements were performed by scientific groups from Oxford, Moscow, Dubna, Orsay, Berkeley, Argonne, Vienna, Milano and Darmstadt. In table I different data for the same nuclear decay are averaged or summed in the cases of estimation of the low limits of the decay probability (63% confidence level). The last column shows the values of the partial half-lives for cluster decay of nuclides indicated in the first column.
3. – Directions of current experimental investigations
At present, the following directions of investigations can be highlighted: 1) Study of the competition between cluster decay and spontaneous fission.
2) Study of the dependence of the cluster decay probability on the number of neutrons in the parent nucleus. According to table I this dependence has been studied mostly for the isotopes of radium and uranium. In ref. [1] it was shown that the experimen-tal value of the cluster decay probability of236
U is more than one order of magnitude higher than that predicted by theoretical calculations [2]. A general tendency in the
TABLEI. – Measured values of cluster decay probabilities.
Initial Cluster Q(MeV) cl= T
1=2, cl nucleus emitted ( cl = ) (years) 221 Fr 14 C 31.29 (1.00.2)10 ,12 9.310 6 221 Ra 14 C 32.39 (1.91.3)10 ,12 4.710 5 222 Ra 14 C 33.05 (2.30.3)10 ,10 5.310 3 222 Ra 14 C 30.44 210 ,12 610 5 223 Ra 14 C 31.85 (1.290.13)10 ,10 2.410 8 223 Ra 14 C 31.07 (7.600.56)10 ,10 4.110 7 223 Ra 14 C 30.43; 30.28 <110 ,12 >310 10 224 Ra 14 C 30.54 (4.31.2)10 ,11 2.310 8 226 Ra 14 C 28.21 (3.00.8)10 ,11 5.310 13 225 Ac 14 C 30.48 (6.01.3)10 ,12 4.610 9 228 Th 20 O 44.72 (1.10.2)10 ,13 1.710 13 230 Th 24 Ne 57.78 (5.61.0)10 ,13 1.310 17 232 Th 26 Ne 55.97 <1:210 ,12 >1:210 22 231 Pa 23 F 51.84 110 ,14 310 18 231 Pa 24 Ne 60.42 (1.30.2)10 ,11 2.510 15 230 U 22 Ne 61.40 <7:510 ,14 >7:610 11 232 U 24 Ne 62.31 (8.90.7)10 ,12 7.910 12 232 U 28 Mg 74.32 <510 ,14 >1:410 15 233 U 24;25 Ne 60.50; 60.75 (7.20.7)10 ,13 2.210 17 233 U 28 Mg 74.25 <1:310 ,15 >1:210 20 234 U 24;26 Ne 58.84; 59.47 (9.16.6)10 ,14 2.710 18 234 U 28 Mg 74.13 (1.41)10 ,13 1.710 18 235 U 24;25;26 Ne 57.36; 57.83; (8.14.3)10 ,12 910 19 58.11 235 U 28 Mg 72.20 <810 ,13 >910 20 236 U 24;26 Ne 55.96; 56.75 <310 ,14 >810 20 236 U 30 Mg 72.51 (2.00.8)10 ,13 1.210 20 237 Np 30 Mg 75.02 <1:310 ,14 >1:610 20 236 Pu 28 Mg 79.67 (2.70.7)10 ,14 1.110 14 238 Pu 28;30 Mg 75.93; 77.03 (5.63.1)10 ,17 1.510 18 238 Pu 32 Si 91.21 (1.40.6)10 ,16 6.310 17 239 Pu 28 Mg 74.10 <110 ,12 >2:410 16 240 Pu 34 Si 91.05 <1:310 ,13 >510 16 241 Am 34 Si 93.94 <6:410 ,16 >6:710 17 242 Cm 34 Si 96.53 810 ,17 610 15 114 Ba 12 C 19.3 cl = 10 ,4 10 ,4 114 Ba 4 He 3.8 alpha= <10 ,3 >10 ,5
variation of the partial half-lives for the cluster decay of uranium even-even isotopes is similar to the behaviour of the alpha-decay and spontaneous fission half-lives. The phenomenological dependence of partial half-lives on the neutron numberNin the
initial nuclei for all three modes of uranium decay exhibits a peculiarity atN=142.
In the cases of alpha-decay and spontaneous fission, this result can be explained by shell and deformation effects on both the value ofQand the shape of the exit
potential barriers. The results for236
in-dication that effects of this kind should also be taken into account in cluster decay theory. According to the phenomenological dependence of the partial half-lives for the cluster decay of uranium isotopes onN in ref. [1], the probability of
238
U decay with the emission of30
Mg or34
Si can be accessible to experimental measurements. Researchers from Dubna, Moscow and Milano have started an experiment on expos-ing track detectors usexpos-ing layers of238
U. The layers have an area of about 2000 cm2
. The necessary exposition time is more than one year for obtaining the sensitivity corresponding to the partial half-life of more than 1020
years.
3) Study of the cluster energy spectra resulting from the decay of odd nuclei and ana-lysis of corresponding hindrance factors for the decay to the ground and excited states of the daughter nucleus. Strictly speaking, only for the cluster decay of223
Ra it was specified whether it was the decay to the ground state or to the excited states of the daughter nucleus. For all the other odd nuclei shown in table I the state of the daughter nucleus involved in the observed cluster decay is not specified.
4) Cluster radioactivity of nuclei close to the nuclear shells ofZ=50,N=50. The decay
of114
Ba with the emission of12
C is the most favourable opportunity for experimen-tal investigations of cluster radioactivity in the nuclear domain close to the nuclear shells withZ=50,N=50. The cluster decay probability of
114
Ba calculated by Kad-mensky et al.[3] proved to be 106
–107
times higher than that calculated in [2, 4] with the same values ofQ. However, more recently Poenaru and Greiner [5] showed that
due to a reasonable change in their model parameters one can obtain agreement between different theoretical approaches and preliminary experimental results. The Dubna group was the first to carry out experiments on the cluster decay of114
Ba [6, 7]. Then similar experiments were performed in Darmstadt [8]. Both in Dubna and in Darmstadt the nuclear reaction58
Ni(58
Ni, 2n) was used. The mean cross-section for the production of a12
C emitter was estimated to be of about 10,34
cm2
. The Dubna exper-iments allowed the registration of about 17 events that could be attributed to the decay of114
Ba. The experiments carried out in Darmstadt resulted in 3 registered events. But owing to very hard experimental conditions it is necessary to check the obtained results both in Dubna and Darmstadt. It is worthwhile to note that the currently available exper-imental data on theQ( )values in the trans-tin region [9] allow one to estimateQ( )and Q(
12
C) for114
Ba. They are respectively (3.80.2) MeV and (19.30.2) MeV. We are going
to continue the investigations of the cluster decay of114
Ba. Besides 114
Ba, the cluster decay 118
Ce! 16
O+102
Sn offers good prospects for ex-perimental investigations. The most favourable reaction for synthesizing this nucleus is
64
Zn(58
Ni, 4n).
4. – Search for the cluster decay of242
Cm and for spontaneous fission of226
Ra The researchers from Dubna, Moscow and Milano have joined their efforts in order to study the decay242
Cm! 34
Si + 208
Pb. The main difficulty encountered is that the spontaneous fission probability of242
Cm is 109
–1010
times higher than the expected prob-ability of the cluster decay. 242
Cm was produced from241
Am irradiated with thermal neutrons at the Kurchatov Institute reactor. Chemical separation was used. Two sources of242
Cm have been prepared. The amount of242
Cm was 0.46 mg at the beginning of the measurements. The242
Fig. 2. – Cross-section for fusion-fission in the system208
Pb +16
O as a function of the bombard-ing ion energy. The energy error bars are equel to0.3 MeV due to the thickness of the target. present work,2Murakami et al.[14],4Videbaek et al.[13], —– results of calculation [12].
of hemispheres of 190 mm in diameter. The interior surface of the hemispheres was in-laid with phosphate glass track detectors. The detectors were covered with 20m thick
polyimide film absorbers to prevent an action of the spontaneous fission fragments on the detectors. The setup was placed in a vacuum chamber. The experimental sensitivity is expected to allow the detection of one cluster per 1017
of alpha-particles. The242
Cm isotope falls in the nuclear domain where spontaneous fission suppresses the cluster decay. In contrast, in the essentially lighter nucleus226
Ra spontaneous fission can be supposed to be suppressed due to a relatively high probability of cluster decay. The groups from Dubna and Orsay are presently searching for spontaneous fission of226
Ra. The theoretical estimations of the spontaneous fission probability are much more difficult as compared with the case of cluster decay and alpha-decay. Especially this is true for nuclei withZ90, which have fission barriers of very complicated forms. The
systemat-ics oflog( = s:f: )in relation toZ 2
=A[10, 11] allows one to expect that the spontaneous
fission partial half-life of226
Ra is about 1017
–1018
years. It is worth noting that the data of work [11] on the spontaneous fission of232
Th fit well into this systematics. To date we have established the low limit value of the spontaneous fission partial half-life for226
Ra: T 1=2(s.f.) 10 18 years.
5. – Fusion-fission in the system208
Pb +16
O
Figure 2 presents the results provided by the investigation of deep subbarrier fusion-fission in the reaction 208
Pb+16
O [12] which formally is reverse to the cluster decay
224
Th! 16
O atE
lab= 50.07 MeV. For energies
72 MeV of the 16
O ions the behaviour of the fission cross-section deviates from the exponential drop which testifies the fact that structural effects have influence on the fusion cross-section in the deep subbarrier
inter-action of two spherical nuclei. The track detector method enables one to go down in the cross-section measurements to several orders of magnitude. The interest in further in-vestigations in the low-energy range is explained by the possibility to find some effects connected with the coupling of the cluster states in the224
Th compound nucleus with the states of a double nuclear system208
Pb +16
O involved in the cluster decay. However, to analyze the total fusion cross-section from this point of view a careful theoretical treat-ment taking into account the contribution of the cluster states is required.
6. – Conclusion
A 13-year experimental investigation has supplied a lot of data on cluster radioactivity. Combined with the data on alpha-decay and spontaneous fission, these data provide a good basis for the progress in theory. One can hope that a unified microscopic description of all the decay channels with the formation of complex particles will be elaborated.
The financial assistance from the Russian Fund of Fundamental Research, Grant No. 96-02-17975 is acknowledged with thanks.
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