- Email: [email protected]
Cluster radioactivity and inverse processes
ELSEVIER
Suclear Physics A73 8 (2004)3 13-3 17
wmv.elseuier.coniilocatelnpe
Cluster radioactivity and inverse processes A.A. Ogloblin*. S.P. Trct,yakovab,R.N. Sagaidakb. S.A. Goncharovc and G.A. Pik-Pichak aKurchatov Institute, Moscow; Russia bJoint Institmutefor Nuclear Research, Dubna, kfoscow region, Russia Skobeltxin Institute of Nuclear Physics; hloscow Universit,y, Moscow, Russia The combined study of the cluster decay probability of a nucleus and fusion or elast,ic scatt,eririg of its decay products provides new information on the mechanism both of the cluster radioactivity and inverse processes. The analysis of C, I6O Pb interactions measured under some special conditions gives evidence for t,he alpha-decay-like scenario and 22JTh. 011the contrary, the j8Si of t,he cluster decay of the compound nuclei 220Ra Xi fusion poterit,ial belongs to t,he fission-type one.
+
+
Cluster radioactivit,y occupies an intermediate positmionbetween alpha-decay and spontaneous fission. There are known twenty nuclides from Fr t,o 242Cmemitting light nuclei from to 34Si, correspondingly. More than a dozen theoretical models were proposed for an explanation of this phenomenon. Differing in the det,ails they describe cluster decay either as an adiabatic fission-like process or as a sudden two-step alpha-decay-like (cluster) one (Fig. 1). However, a real mechanism of the cluster radioact,ivity still remains an open problem. The difficulty is that all the theories reproduce the measured decay probabilities quite well [l]. The reason for this paradox lies in some peculiar compensat,ion of different, factors detcrmining the decay probability. The latter can be written as Xfi, = u . Pfis for fission and Xcl = z/ . PCl. S for the cluster-type decay ( u is the frequency of assaults, P is the barrier penetrability arid S is the spectroscopic factor). The fission-like models and the alpha-decay-like ones predict completely different shapes of t,he potential barrier (Fig. 2). Clust,er-tvpebarriers normally are much more narrow than the fission-t,ype ones. and their increased penetrability is compensated by the small values of spectroscopic factors. This difference opens the way to study cluster decay mechanism by getting independent information about the barriers, especially on their internal p a r k As the both decay products are formed in their ground states, the study of inverse processes, fusion or elastic scattering, which are sensitive to the nucleus-nucleus pot,cntials can be used for this purpose. Notc that this is not the case for normal spontaneous fission which results in formation of highly excited and deformed fragments. The work was partly supported by Russian Foundation for Basic Researches, grant 02-02-17297 0375-9474s see front matter C 2004 Published by Elsevier B.V doi:10.1016/j.nuclphysa.2004.04.052 -
314
4 . A . Ogloblin et 01. /Niicleur Plijaics A738 (2004) 313- 31 7
Fission-like mechanism
35j
"Ne + "’Pb POTENTIALS
0-0-0-m-*-..
I_ Fission (Royer) Cluster (Blendowski)
Alpha-decay-like mechanism
r, fm
Figure 1. Visualization of "fission-like" [2] and "alpha-decay-like" mechanisms of the cluster radioactivity
Figure 2. Examples of fission- [a] and cluster-type [3] potentials. The horizontal lines indicate t,he p r t s of t8hepot,eiit,ials probed by fusion at different levels of cross section values
Our proposal t o invest,igatc the clust,er radioactivity mechanism cont>ernplatest,he study of deep sub-barrier fusion a,rid (or) elastic scat>teringof decay products of some part>icular nuclei with known cluster decay probabilities. It is expected that, empirical barrier shapes extract,ed from such measurements will allow making selection between different t)lieoretical predictions. Obviously, the penetrability of t8heempirical barrier t,ogether wit,h the other relevant’ fact,ors (S and v) calculated or taken from systematics, should be able t80 reproduce the partial half-life of the parent nucleus. On the ot,her hand, such combined st,udy of cluster decays and the corresponding inverse processes could give some new informatmionon the mechanism of the latter ones becausc the barrier penetrability at’ t’he energy determines the potential far beyond the top of t,he harrier (see Fig. 2). To fulfill this program one has t o solve two problems. The first onc comes from t,he fact tha,t it is not so easy to arrange the projectile-t#argetcombinat,ion leading t o t>he compound nucleus with the measured cliister decay probability. At present t,iriie it is realistic to study only two such combinations:
In all other cases tlie known cluster decaying nuclei emit, the products which cxinot, bt: obtained as "good" b e a m or targets. Fortunately, more or less reliable theoretical predictions of t,he decay probabilities can be made for some of tlie nuclides decaying by emission of stable fragmeiit,s (e.g., ’"Ra +lZC ’’*Pb and z24Th+l60 208Pb)!and t,his allows one to use some other projcct,ile-target combin, t,’ ions. Secondly, most, of fusion experiments are able to determine t,he shape of the barrier only close t o its top. The situa,tion is even worse in the case of the near-barrier elast,ic scattering which is sensitive, as a rule. only to t,he outer part, of the potential almost completely determined by t,he Coulomb interaction.
+
+
315
A.A. Oglohlin et ul. /Miclear Physics A738 (2004) 313-317
Vcry effect,ive incthotl to study ext,reinely deep sub-barrier fusion occurred to be the measurements of heavy-ion fission excitation functions using solid-state track det,ectors (SSTD) [4]. The use of SSTD allows one to go down t,o the cross-section level of nib or even lower and probe t,he potent,ial far beyond t,he top of the barrier as shown in Fig. 2. Similarly, the evidence was obtained [5]t,hat if one managed t>omeasure the elastic lop4 and observe the deviation from the typical cross-sect,ions at the level ceel/c~utlr Fresnel diffraction t,he data become sensitive t o the inner parts of the barrier. We analyze in this paper some data on the near-barrier elastic scatt,ering of 12C, I 6 0 on "’Pb [6] and sub-barrier fusion react,ions 12C + ’"Pb + ’"Ra and 160 2"8Pb 224Th[7] satisfying the aforementioned conditions. It demonstrat,es The 12C "’Pb e1ast)icscattering was measured in [6] at 75.7 some deviation from Fresnel diffract,ion pattern at the cross-sect,ions level o e l / c ~ u t h l o p 4 including the appcarancc of tiny back angles oscillations. This part of the angular dist,ribution occurred to be serisitivc to the distances of -10 fm t,hat is approximat>elyequal to the slim of the 12C "’Pb radii. Thc fits were done iising the st,andard Woods-Saxon forin for the real part, of the poterit,ial and combined (volume plus surface) imaginary part. The scattering potential belongs to tzhenarrow "cluster-type" family of tmhebarriers (Fig. 3). An interesting feat,ure of the pot,ential is t,he existence of a shallow pocket containing the touching point, of t,he interacting nuclei. This indicat,es on the possibility t,o form a quasi-molecular st,ate during cluster decay of 22"Th and t,he inverse pro The "C 208Phfusion excita,tioii funct,ion was const,ructed as the sun1 of fission [7] and evaporat>ionresidues [8] cross-sections. For the data analysis we used the HIVAP code [9] wit>hphcnomciiological exponential potential (nuclear part): N
+
+
---f
-
+
+
Coupling to ot,lit:r inelastic channels was taken into account with the fluctuating barrier method [lo]. Good agrccment with thc experiment was obt,ained for t,he potential parameter values V" = 80 MeV/fm and d = 0.8 fni. The exponential fusion potential is shown in Fig. 3. It practically coincides wit$hthe above-mentioned scattering one. On the other hand, the potential obtained in [8] rcmarkably differs from them. The choice can be made on the basis of comparison with the ’"Ra + 12C ’"’Pb cluster decay probability. Taking the penet,rability of our empirical barriers, a reasonable value of the frequency of assaults I/ = 2 . lo2’ s-’ and the theorct,ical valiie [13] of the corresponding spectroscopic fact80ronc obtains the partial half-life for ’"Ra logTl,z = 10.3 (s). in excellent agreement wit811the predicted valuc logTI12 = 10.5 (s) [14]. On t,he other hand. the "fission-like" calculation of the decay probability, which omits the spectroscopic factor, would fail to reproduce t,he theoretical log TI,, by many orders of magnitude. It, is evident that any uncert,ainties in our approach cannot, be compensated by this alternative suggestion. So! our analysis of the fusion rcaction gives a serious argument in favor of thc "alpha-decay-like" scenario of the ""Ra cluster radioactivity. As for the potent,ial [8], one can sce (Fig. 3) that being t,oo shallow it, is inconsist>entwith the cluster radioactivity data (the minimum produccd by the sum of nuclear and Coulomb potentials is located above the decay Qvaliic). The Ifi0 ’"Pb elastic scattering differcnt,ial cross-section measured at. 95 MeV is
+
+
A.A. Oglobliiz et al. /Nuclear Physics A738 (2004) 313-317
316
!
+
Figure 3. ’"’Pb potentials. Solid and dash-dotted lines were obtained from scatteririg and fusion, correspondingly. The dash line is taken from [8].
58
"1
il
Ni+58Nipotentials , \ ,
%
... ......
6
8
ID
12
r,
11
18
16
fm
Figure 4. 58Ni+58Nipotentials. The dash line corresponds to the fission model [19]. Others are related to the Woods-Saxon potential with differmt values of the diffuseness parameter.
+
’o’Pb demonstrating deviation from the exponential fall-off at similar to that of "C large angles. The obtained potential clearly shows all the features of the cluster-type one. Again, the analysis of the 160 "*Pb fusion excitation function (see for the details [ l l ] ) results in the exponential potential with the same parameters V, = 80 MeV/fni and d = 0.8 fm and fluct,uating paranieter ( T ( T ~ ) / Q = 2.3%. The barrier shape occurred to be of the clust,er type and is consistent with the predict,ions [14]for the z24Th+ l60 "’Pb decay logTl/’ = 14.7 (s). The 160 ’"’Pb fusion data [15] limited by a few orders of magnitude higher crosssections could not select bet,ween two potent,ials. One of them approximated by the Woods-Saxon form wit,h a normal value of the diffuseness (a = 0.65 fm) is rather close to our potential. It gives for the cluster decay half-life more or less reasonable value log TI/;? = 15.9 (s). On the contrary, the other potential with an abnorrnally large value of tmhe diffuseness a = 1.005 fm, which oRen is considered as the most adequate to fusion; leads to logTl,z = 19.1 (s); that is inconsistent, with the theoretical cluster decay probability. + "’Pb and 160+ ’08Pb fusion and elastic scattering gave So, the study both of similar results and provided serious evidence of the "alpha-dec;~y-like" scenario of the emission of clusters with A = 12-16. This conclusion correlates with the old result, of tmhe st,udy of the fine structure of the z’3Ra + 14C decay spectrum [16]. General analysis of cold decays including t~hecluster radioactivity and cold fission indicates that the transition between the "alpha-decay-like" and "fission-like’’ mechanisms inevit,ably should take place: and most probably it occurs in the vicinit,y of the masses 35 of the emitting clusters [l].For this reason the study of the inverse processes of A with heavier projectiles becomes very interesting. As was mentioned above, especially important, is the "Ne 208Pbprojectile-target combinatmion.The extremely deep sub-barrier fusion data were obt,ained very recently as
+
+
+
N
+
A.A. Oglohliii et al. /Nuclear Physics A738 (2004) 313-31 7
317
dcscribed in the accompanying paper [17]. The main result, is that the potential belongs t,o the cluster-type f a d y . In order t o gct inforniation about the fusion potential for even heavier projectiles we looked t o the recent data on "Xi + j8Ni fusion [18].The authors claimed that thc best fit to the data is obt,ained with the Woods-Saxon pokntial with a,n abnormally large value of the diffuseness pammeter a = 1.3 fin. We doubt the given explanation of this finding and plot in Fig. 4 the barriers proposed in [18]for three different a values. As was expected the widths of the barriers increase wit,li the diffuseness. However, the most inkresting result is that the potent>ialwith u = 1.3 fm coincides in its main part) wit,h the "fission-like" potential [19] for the ’16Ba compound nucleus decay (the difference of the upper parts of the barriers is riot important because the model [19] uses zero-range nuclear forces). So, the most natural explanation is that, symmetric decay of ’I6Ba,+ ’*Ni "Ni is governed by the fission-like potential and can be considered as the cold fission. The authors are grateful to G. Royer for the calculation of the 22Ne 208 P b fission-like potential in the framework of his model and Yu.M. Tchuvilski for providing some values of theoretical spectroscopic factors and discussions.
+
+
REFERENCES 1. A. Ogloblin, G. Pik-Pichak, S.P. Tretyakova, in: Exotic Clustering, CRIS 2002, eds. S. Costa! A. Insolia, C. Tiwe; Melville, Tew York: 2002, p. 122. 2. G. Royer, R. Moustabchir, Nucl. Phys. A 683 (2001) 182. 3. R. Blendowski, H. Walliser, Phys. Lett. 61 (1986) 1930. 4. S.P. Tretyakova, A. Ogloblin, in: Exotic Clustering, CRIS 2002, eds. S. Cost’a, A. Insolia, C. Tuve, Melville, S e w York, 2002, p. 132. 5. A. Demyanova, et al., in: Exotic Nuclci and Atomic Masses, ENAM’95. ed. M. d e Saint Simon, Edition Frontiers, p. 401. 6. V. Rudakov, et al., Izv. RAN, Ser. Fiz. [Bull Acad. Sci. Russia, Phys. Ser.] 65 (2001) 11. 7. S.P. Tretyakova, et al., in: Nuclear Shells 50 Years, eds. Yu.Ts. Oganessian, R. Kalpakchieva. World Scientific, p. 151. 8. S. Santra, et al., Phys. Rev. C 64, 024602 (2001). 9. W. Reisdorf, Z. Phys. A 300 (1987) 227; W. Reisdorf, M.Shadel, Z. Phys. A 343 (1992) 47. 10 W. Reisdorf, et al., Nucl.Phys. A 438 (1985) 212; Nucl.Phys. A 444 (1985) 154. 11. S.P. Tretyakova et al.. contribution to the Conference on Nucleus-Niicleus Collisions. "2003, Moscow (2003), Xucl. Phys. A (to be published). 12. C.R. Morton. et al., Phys. Rev. C 60, 044608 (1999). 13. S.G. Kadmenskii, et al., Sov. J. Nucl. Phys. 51 (1990) 32. 14. D.K.Poenaru, et al., At. Data Xucl. Tables, 48 (1991) 231. 15. C.R. Morton. et al., Phys. Rev. C 60, 044608 (1999). 16. E. Hourani, et al., Phys. Lett. B 160 (1985) 375. 17. S.P. Tretyakova, et al., contribution t o t>hisConference. 18. K. Hagino, et al., Phys. Rev. C 67, 054603 (2003). 19. G.A. Pik-Pichak, Sov. .I. Nucl. Phys. 44 (1987) 923. <.
Suclear Physics A73 8 (2004)3 13-3 17
wmv.elseuier.coniilocatelnpe
Cluster radioactivity and inverse processes A.A. Ogloblin*. S.P. Trct,yakovab,R.N. Sagaidakb. S.A. Goncharovc and G.A. Pik-Pichak aKurchatov Institute, Moscow; Russia bJoint Institmutefor Nuclear Research, Dubna, kfoscow region, Russia Skobeltxin Institute of Nuclear Physics; hloscow Universit,y, Moscow, Russia The combined study of the cluster decay probability of a nucleus and fusion or elast,ic scatt,eririg of its decay products provides new information on the mechanism both of the cluster radioactivity and inverse processes. The analysis of C, I6O Pb interactions measured under some special conditions gives evidence for t,he alpha-decay-like scenario and 22JTh. 011the contrary, the j8Si of t,he cluster decay of the compound nuclei 220Ra Xi fusion poterit,ial belongs to t,he fission-type one.
+
+
Cluster radioactivit,y occupies an intermediate positmionbetween alpha-decay and spontaneous fission. There are known twenty nuclides from Fr t,o 242Cmemitting light nuclei from to 34Si, correspondingly. More than a dozen theoretical models were proposed for an explanation of this phenomenon. Differing in the det,ails they describe cluster decay either as an adiabatic fission-like process or as a sudden two-step alpha-decay-like (cluster) one (Fig. 1). However, a real mechanism of the cluster radioact,ivity still remains an open problem. The difficulty is that all the theories reproduce the measured decay probabilities quite well [l]. The reason for this paradox lies in some peculiar compensat,ion of different, factors detcrmining the decay probability. The latter can be written as Xfi, = u . Pfis for fission and Xcl = z/ . PCl. S for the cluster-type decay ( u is the frequency of assaults, P is the barrier penetrability arid S is the spectroscopic factor). The fission-like models and the alpha-decay-like ones predict completely different shapes of t,he potential barrier (Fig. 2). Clust,er-tvpebarriers normally are much more narrow than the fission-t,ype ones. and their increased penetrability is compensated by the small values of spectroscopic factors. This difference opens the way to study cluster decay mechanism by getting independent information about the barriers, especially on their internal p a r k As the both decay products are formed in their ground states, the study of inverse processes, fusion or elastic scattering, which are sensitive to the nucleus-nucleus pot,cntials can be used for this purpose. Notc that this is not the case for normal spontaneous fission which results in formation of highly excited and deformed fragments. The work was partly supported by Russian Foundation for Basic Researches, grant 02-02-17297 0375-9474s see front matter C 2004 Published by Elsevier B.V doi:10.1016/j.nuclphysa.2004.04.052 -
314
4 . A . Ogloblin et 01. /Niicleur Plijaics A738 (2004) 313- 31 7
Fission-like mechanism
35j
"Ne + "’Pb POTENTIALS
0-0-0-m-*-..
I_ Fission (Royer) Cluster (Blendowski)
Alpha-decay-like mechanism
r, fm
Figure 1. Visualization of "fission-like" [2] and "alpha-decay-like" mechanisms of the cluster radioactivity
Figure 2. Examples of fission- [a] and cluster-type [3] potentials. The horizontal lines indicate t,he p r t s of t8hepot,eiit,ials probed by fusion at different levels of cross section values
Our proposal t o invest,igatc the clust,er radioactivity mechanism cont>ernplatest,he study of deep sub-barrier fusion a,rid (or) elastic scat>teringof decay products of some part>icular nuclei with known cluster decay probabilities. It is expected that, empirical barrier shapes extract,ed from such measurements will allow making selection between different t)lieoretical predictions. Obviously, the penetrability of t8heempirical barrier t,ogether wit,h the other relevant’ fact,ors (S and v) calculated or taken from systematics, should be able t80 reproduce the partial half-life of the parent nucleus. On the ot,her hand, such combined st,udy of cluster decays and the corresponding inverse processes could give some new informatmionon the mechanism of the latter ones becausc the barrier penetrability at’ t’he energy determines the potential far beyond the top of t,he harrier (see Fig. 2). To fulfill this program one has t o solve two problems. The first onc comes from t,he fact tha,t it is not so easy to arrange the projectile-t#argetcombinat,ion leading t o t>he compound nucleus with the measured cliister decay probability. At present t,iriie it is realistic to study only two such combinations:
In all other cases tlie known cluster decaying nuclei emit, the products which cxinot, bt: obtained as "good" b e a m or targets. Fortunately, more or less reliable theoretical predictions of t,he decay probabilities can be made for some of tlie nuclides decaying by emission of stable fragmeiit,s (e.g., ’"Ra +lZC ’’*Pb and z24Th+l60 208Pb)!and t,his allows one to use some other projcct,ile-target combin, t,’ ions. Secondly, most, of fusion experiments are able to determine t,he shape of the barrier only close t o its top. The situa,tion is even worse in the case of the near-barrier elast,ic scattering which is sensitive, as a rule. only to t,he outer part, of the potential almost completely determined by t,he Coulomb interaction.
+
+
315
A.A. Oglohlin et ul. /Miclear Physics A738 (2004) 313-317
Vcry effect,ive incthotl to study ext,reinely deep sub-barrier fusion occurred to be the measurements of heavy-ion fission excitation functions using solid-state track det,ectors (SSTD) [4]. The use of SSTD allows one to go down t,o the cross-section level of nib or even lower and probe t,he potent,ial far beyond t,he top of the barrier as shown in Fig. 2. Similarly, the evidence was obtained [5]t,hat if one managed t>omeasure the elastic lop4 and observe the deviation from the typical cross-sect,ions at the level ceel/c~utlr Fresnel diffraction t,he data become sensitive t o the inner parts of the barrier. We analyze in this paper some data on the near-barrier elastic scatt,ering of 12C, I 6 0 on "’Pb [6] and sub-barrier fusion react,ions 12C + ’"Pb + ’"Ra and 160 2"8Pb 224Th[7] satisfying the aforementioned conditions. It demonstrat,es The 12C "’Pb e1ast)icscattering was measured in [6] at 75.7 some deviation from Fresnel diffract,ion pattern at the cross-sect,ions level o e l / c ~ u t h l o p 4 including the appcarancc of tiny back angles oscillations. This part of the angular dist,ribution occurred to be serisitivc to the distances of -10 fm t,hat is approximat>elyequal to the slim of the 12C "’Pb radii. Thc fits were done iising the st,andard Woods-Saxon forin for the real part, of the poterit,ial and combined (volume plus surface) imaginary part. The scattering potential belongs to tzhenarrow "cluster-type" family of tmhebarriers (Fig. 3). An interesting feat,ure of the pot,ential is t,he existence of a shallow pocket containing the touching point, of t,he interacting nuclei. This indicat,es on the possibility t,o form a quasi-molecular st,ate during cluster decay of 22"Th and t,he inverse pro The "C 208Phfusion excita,tioii funct,ion was const,ructed as the sun1 of fission [7] and evaporat>ionresidues [8] cross-sections. For the data analysis we used the HIVAP code [9] wit>hphcnomciiological exponential potential (nuclear part): N
+
+
---f
-
+
+
Coupling to ot,lit:r inelastic channels was taken into account with the fluctuating barrier method [lo]. Good agrccment with thc experiment was obt,ained for t,he potential parameter values V" = 80 MeV/fm and d = 0.8 fni. The exponential fusion potential is shown in Fig. 3. It practically coincides wit$hthe above-mentioned scattering one. On the other hand, the potential obtained in [8] rcmarkably differs from them. The choice can be made on the basis of comparison with the ’"Ra + 12C ’"’Pb cluster decay probability. Taking the penet,rability of our empirical barriers, a reasonable value of the frequency of assaults I/ = 2 . lo2’ s-’ and the theorct,ical valiie [13] of the corresponding spectroscopic fact80ronc obtains the partial half-life for ’"Ra logTl,z = 10.3 (s). in excellent agreement wit811the predicted valuc logTI12 = 10.5 (s) [14]. On t,he other hand. the "fission-like" calculation of the decay probability, which omits the spectroscopic factor, would fail to reproduce t,he theoretical log TI,, by many orders of magnitude. It, is evident that any uncert,ainties in our approach cannot, be compensated by this alternative suggestion. So! our analysis of the fusion rcaction gives a serious argument in favor of thc "alpha-decay-like" scenario of the ""Ra cluster radioactivity. As for the potent,ial [8], one can sce (Fig. 3) that being t,oo shallow it, is inconsist>entwith the cluster radioactivity data (the minimum produccd by the sum of nuclear and Coulomb potentials is located above the decay Qvaliic). The Ifi0 ’"Pb elastic scattering differcnt,ial cross-section measured at. 95 MeV is
+
+
A.A. Oglobliiz et al. /Nuclear Physics A738 (2004) 313-317
316
!
+
Figure 3. ’"’Pb potentials. Solid and dash-dotted lines were obtained from scatteririg and fusion, correspondingly. The dash line is taken from [8].
58
"1
il
Ni+58Nipotentials , \ ,
%
... ......
6
8
ID
12
r,
11
18
16
fm
Figure 4. 58Ni+58Nipotentials. The dash line corresponds to the fission model [19]. Others are related to the Woods-Saxon potential with differmt values of the diffuseness parameter.
+
’o’Pb demonstrating deviation from the exponential fall-off at similar to that of "C large angles. The obtained potential clearly shows all the features of the cluster-type one. Again, the analysis of the 160 "*Pb fusion excitation function (see for the details [ l l ] ) results in the exponential potential with the same parameters V, = 80 MeV/fni and d = 0.8 fm and fluct,uating paranieter ( T ( T ~ ) / Q = 2.3%. The barrier shape occurred to be of the clust,er type and is consistent with the predict,ions [14]for the z24Th+ l60 "’Pb decay logTl/’ = 14.7 (s). The 160 ’"’Pb fusion data [15] limited by a few orders of magnitude higher crosssections could not select bet,ween two potent,ials. One of them approximated by the Woods-Saxon form wit,h a normal value of the diffuseness (a = 0.65 fm) is rather close to our potential. It gives for the cluster decay half-life more or less reasonable value log TI/;? = 15.9 (s). On the contrary, the other potential with an abnorrnally large value of tmhe diffuseness a = 1.005 fm, which oRen is considered as the most adequate to fusion; leads to logTl,z = 19.1 (s); that is inconsistent, with the theoretical cluster decay probability. + "’Pb and 160+ ’08Pb fusion and elastic scattering gave So, the study both of similar results and provided serious evidence of the "alpha-dec;~y-like" scenario of the emission of clusters with A = 12-16. This conclusion correlates with the old result, of tmhe st,udy of the fine structure of the z’3Ra + 14C decay spectrum [16]. General analysis of cold decays including t~hecluster radioactivity and cold fission indicates that the transition between the "alpha-decay-like" and "fission-like’’ mechanisms inevit,ably should take place: and most probably it occurs in the vicinit,y of the masses 35 of the emitting clusters [l].For this reason the study of the inverse processes of A with heavier projectiles becomes very interesting. As was mentioned above, especially important, is the "Ne 208Pbprojectile-target combinatmion.The extremely deep sub-barrier fusion data were obt,ained very recently as
+
+
+
N
+
A.A. Oglohliii et al. /Nuclear Physics A738 (2004) 313-31 7
317
dcscribed in the accompanying paper [17]. The main result, is that the potential belongs t,o the cluster-type f a d y . In order t o gct inforniation about the fusion potential for even heavier projectiles we looked t o the recent data on "Xi + j8Ni fusion [18].The authors claimed that thc best fit to the data is obt,ained with the Woods-Saxon pokntial with a,n abnormally large value of the diffuseness pammeter a = 1.3 fin. We doubt the given explanation of this finding and plot in Fig. 4 the barriers proposed in [18]for three different a values. As was expected the widths of the barriers increase wit,li the diffuseness. However, the most inkresting result is that the potent>ialwith u = 1.3 fm coincides in its main part) wit,h the "fission-like" potential [19] for the ’16Ba compound nucleus decay (the difference of the upper parts of the barriers is riot important because the model [19] uses zero-range nuclear forces). So, the most natural explanation is that, symmetric decay of ’I6Ba,+ ’*Ni "Ni is governed by the fission-like potential and can be considered as the cold fission. The authors are grateful to G. Royer for the calculation of the 22Ne 208 P b fission-like potential in the framework of his model and Yu.M. Tchuvilski for providing some values of theoretical spectroscopic factors and discussions.
+
+
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