SYSTEMATICS OF α-decay HALF-LIVES OF THE HEAVIEST ELEMENTS

Transcription

1 Dedicated to Professor Oliviu Gherman s 8 th Anniversary SYSTEMATICS OF α-decay HALF-LIVES OF THE HEAVIEST ELEMENTS I. SILIŞTEANU 1,, A. I. BUDACA 1, A. O. SILIŞTEANU 1 1 Horia Hulubei National Institute for Physics and Nuclear Engineering, Bucharest-Magurele, RO-7715, Romania Received July, 1 The systematics of α-decay half-lives of super heavy nuclei with Z=1-1 and N=15-18 vs decay energy or number of valence nucleons is investigated in several approximation schemes. Half-lives given by self-consistent models for the α-clustering and resonance scattering are compared with empirical estimates. The calculated values of log 1 Tα th. (sec) with α-formation and resonance reaction amplitudes, plotted vs Zd.6 Q 1/ α, fall on a straight line given by log 1 Tα th. (sec)= (Zd.6 Q 1/ α ) (rms=.187), where Z d is the charge number of the daughter nucleus, Q α is the decay energy given in MeV units, and rms is the standard error. The experimental values of log 1 Tα exp. (sec) plotted vs Zd.6 Q 1/ α are shown to fall also on a straight line given by log 1 Tα exp. (sec)=9.65 (Zd.6 Q 1/ α ) (rms=.5515). The major influence of the pairing, deformed shell closures and screening corrections is evidenced and provides a convenient basis for the interpretation of observed trends of the data and for prediction of new results. The very small widths of α-resonances observed experimentally in fusion-evaporation reactions, are interpreted as resonance levels of radioactive products, and such a correlation contributes directly to the study of the nuclear structure on the basis of decay data. From the ratio between experimental and theoretical results we can obtain α-preformation factors. In few cases, the observed large discrepancies between the experimental data and theoretical results could indicate wrong data and might be eliminated by improving the accuracy of further measurements. Key words: Super heavy nuclei (SHN); α-decay, α-clustering and scattering amplitudes; Incoming/Outgoing wave boundary conditions; resonance tunneling; decay-rates systematics. PACS: 5.7.Jj; 7.9.+b 1. INTRODUCTION The super heavy nuclei (SHN) represent the very top end of the Chart of Nuclides beyond the limit of stability depending on mass, charge, and Z/N ratio. Their properties, i.e. nuclear masses, moments, half-lives, and decay modes constitute the Corresponding author: silist@theory.nipne.ro Rom. Journ. Phys., Vol. 55, Nos. 9 1, P , Bucharest, 1

2 Systematics of α-decay half-lives of the heaviest elements 189 test ground for ideas and models of nuclear structure and reaction dynamics, developed over more than four decades, on their nuclear structure and reaction dynamics as well. Recently, different groups (at JIRN-Dubna, GSI, Livermore, RIKEN, Jyvaskula) have obtained new data on the synthesis and properties of ground and excited states of SHN. For nuclei faraway from β stability on the proton rich side, binding energy rapidly decreases, due to increasing Coulomb repulsion and reaction Q-values, which leads to major difficulties in their production and also in study of decay properties. The relatively large Q-values cause high excitations in the product nuclear systems involved and open up many competing decay channels favoring the nuclei closer to stability. Damping these excitations can be very crucial for nuclei near the limit of proton stability. Alpha radioactive states of nuclei at the proton drip line and in the region Z=1-1 can be populated in fusion-evaporation processes with stable heavy-ion beams on actinide targets. Characteristic for SHN are long α-chains as well as parallel sequences of α-chains which terminate by Spontaneous Fission (SF). As a spectroscopic tool α-decay presents in SHN the following restrictions: (1) the transition rates exhibit an exponential dependence on decay energy; () it is strictly limited to neutron deficient species; (3) up to a few hundred kev, the only excited states are produced in α-decay (Fine Structure); () transition rates and energies exhibit steep variations at magic shell closure. Decay studies of heaviest nuclei close to proton drip-line are particularly interesting from the following points of view. First, the structure of these nuclei differs strongly from that of other nuclei. Secondly, by the lower levels of these nuclei are inevitably near the proton emission thresholds and consequently the proton and α- decay channels are effectively the only open ones. Thirdly, the spectroscopic studies of long chains of isotopes far away from stability, make possible the access to the basic nuclear-ground state properties of new SHN. In this work we report on the systematics evidenced in the analysis of α rates of SHN and the method of extracting information on nuclear structure from the decay data. The experimental α-decay data for isotopes of SHN with Z = 1 1, are taken from refs. [1 9]. There are known for this region of nuclides, 9 decay data points (T α,q α ) of the ground state-ground state transitions. This paper is organized as follows: in Sec. formulation is summarized and in Sec.3 numerical results for half-life systematics of SHN are presented. The comparison of results is given in Sec. and the conclusion is presented in Sec. 5.

3 19 I. Silişteanu, A. I. Budaca, A. O. Silişteanu 3. ESTIMATES OF α-half-lives.1. EMPIRICAL METHODS The radioactive decay law, according to which the probability to find the nucleus in the radioactive state decreases exponentially with the time, was formulated empirically by Geiger and Nuttall [1]. This was the observation that the experimental values of log 1 T α plotted vs Qα 1/, where Q α is the α-decay energy, fall on straight lines for the isotopes of a given element. Gamow [11] and independently Gurney and Condon [1] have solved the one body problem of the α-decay and derived the known Geiger-Nuttall relation from first principles of quantum mechanics. An explicit functional dependence of the halftime on the energy Q α and on the proton number of daughter nucleus Z d was introduced later in formulations [13 15]. Here we consider three phenomenological formulas. The first is the Viola- Seaborg formula [13] which writes as log 1 T α (sec) = (az d + b)q 1/ α + (cz d + d) + h e o (1) where Q α is the decay energy in MeV units, Z d is the charge number of daughter nucleus; a,b,c,d are parameters and h e o is an even-odd hindrance term [16]. The parameters used are: a = ; b = ; c = -.8; d = , h e o =. (Z=even, N=even); h e o =.77 (Z=odd, N=even); h e o = 1.66(Z=even, N=odd); h e o = 1.11 (Z=odd, N=odd). The second one is the Tagepera-Nurmia formula [1] given as log 1 T α (years) = 1.615(Z d Q 1/ α Z /3 ) h (y) The third one is the Brown formula [15] given as d e o () log 1 T α (sec) = 9.5 Z (.6) d Q 1/ α h e o (3) The effective decay energy used in the above equations is Q α = (A/(A )) E exp. α Z 7/5 d Z /5 d () where, A is the mass number of the parent nucleus, Eα exp. is the measured kinetic energy of α -particle, and the second term is the screening correction [17]. The formula (3) was tested for 119 data points (T α, Q α ) (in a range of Z d from 7 to 16), all these points falling on nearly universal line which represents the best linear fit to data [15]. In all these formulations the α-decay probability is roughly the product of the probability of particle formation and the probability of barrier penetration. The first probability is considered the same from one nucleus to another, while the second one depends only on the Coulomb term of the potential, the nuclear term being neglected.

4 Systematics of α-decay half-lives of the heaviest elements THEORETICAL METHOD In Ref. [] the cluster decay width was expressed through the clustering and scattering amplitudes, and the decay rate problem was reduced to solving the eigenfunctions and eigenvalues of the Schrödinger equation associated to the decay process. The usual quantum mechanical rules for normalizations, orthogonality and completeness have to be extended in a straightforward manner in order to take into account the bound and scattering wave functions as well. In case of the α-decay of a single resonance state k into a single decay channel n, the α-half time is []: where, the decay width is Γ k n = π T k n = ln /Γ k n (5) rmax r min rmax r min In(r)u k n(r)dr In(r)u k k. (6) n(r)dr In Eq.(6), I k n(r) is the particle (cluster) formation amplitude (FA) defined as the antisymmetrized projection of the parent wave function (WF) Ψ k > on the channel WF n = [Φ D (η 1 )Φ p (η )Y lm (ˆr)] n : I k n(r) = r Ψ k A { [Φ D (η 1 )Φ p (η )Y lm (ˆr)] n } (7) where Φ D (η 1 ) and Φ p (η ) are the internal (space-spin) wave functions of the daughter nucleus and of the particle, Y lm (ˆr) is the wave function of the angular motion, A is the inter-fragment antisymmetrizer, r connects the centers of mass of the fragments, and the symbol < > means integration over the internal coordinates and angular coordinates of relative motion. In Eq.(6) u k n(r) and u n(r) are the solutions of the systems of differential equations [ [ m m ( ) ] d l(l + 1) dr r V nn (r) + Q n u n(r) + m nv nm (r)u m(r) = (8) ( ) ] d l(l + 1) dr r V nn (r) + Q n u k n(r) + m nv nm (r)u k m(r) = In k (r) (9) describing the radial motion of the fragments at large and small separations, respectively, in terms of the reduced mass of the system m, the kinetic energy of emitted particle Q n = E E D E p, the FA I k n (r), and the matrix elements of interaction potential V nm (r). To avoid the usual ambiguities encountered in formulating the

5 19 I. Silişteanu, A. I. Budaca, A. O. Silişteanu 5 potential for the resonance tunneling of the barrier we iterate directly the nuclear potential in the equations of motion [1]. Eqs.(8 and 9) are solved numerically with usual boundary conditions for the decay problem. The lower limit in the integrals (6) is an arbitrary small radius r min >, while the upper limit r max is close to the first exterior node of u n(r). The one-body (o.b.) resonance width in the single channel problem can be expressed by means only of the the eigenvalues and eigenfunctions of the system: Γ o.b. n = π rmax r min rmax r min G n (r)u n(r)dr G n (r)u o.b., (1) n (r)dr where u o.b. n (r) is a solution of Eq.(6) in which In(r) k is merely replaced by G n (r). From Eq.(1) it follows: T n T o.b. n = ln /Γ o.b. n. (11) The critical dependence of the α-rates on energy, i.e. the Geiger-Nuttall relation, applies independently on the one body [18 ] or the many body (shell model) [ 3] treatments of the α-decay. 3. RESULTS AND DISCUSSION 3.1. SYSTEMATICS OF α-half-lives We estimate α-decay half-lives from Eqs.(1-3) and Eq.(11) using E α -data [1,] shown in Figs.1-, and Table 1. There are 9 data points (T α, E α ) for a range of Z d = 1 118, where Z d is the charge number of the daughter nucleus. The earliest systematics of α-decay lifetimes of naturally emitters from actinides region was obtained [1] by plotting the experimental values of log 1 T α vs Q 1/ α. Fig.3 shows a version of this plot for the ground state-ground state α-half-lives of known SHN calculated from Eq.(11). We see that the calculated values for a given Z d value fall on roughly a straight line and there is a large scatter between the lines for different Z d values. Further, as Eqs.(1 and ) suggest the plot log 1 T α vs Z d Q 1/ α might be different. The result is shown in Fig., where the half-lives are fit again by parallel lines for different Z d values: here the scatter is somehow less than in Fig.3 while the order of Z d lines is now reversed, and perhaps the most important,the separation between these lines is reduced. Therefore, it appears that log 1 T α vs Z d Q 1/ α is a better plot for half-lives since, the lines for different Z d values have a common slope.

6 6 Systematics of α-decay half-lives of the heaviest elements 193 Fig. 1 Chart of the heaviest nuclei produced in cold-fusion reactions with 8 P b and 9 Bi-targets, in hot-fusion reactions with 8 Ca and heavy actinides targets, and in radioactive decays. The measured half-lives T 1/ and reaction energies E are given by Oganessian [1, ] for dominant decay modes. The nuclei undergo α-decay are shown in yellow squares.

7 19 I. Silişteanu, A. I. Budaca, A. O. Silişteanu 7 Fig. Observed decay chains interpreted as originating from the isotopes A=9 (single event) and A=93 (average of five events) of the new element Z=117. The deduced [1] and predicted [59] lifetimes (τ = T 1/ /ln) and α-particle energies are shown in black and blue, respectively. This suggests a possible interpolation between Fig.3 and Fig., so that by reversing and compressing Z d lines to obtain a single line for a some Zd x Q 1/ α value, where x 1. The fit of theoretical values for log 1 Tα th. vs Zd x Q 1/ α where x=.5,.6,.7 is shown in Figs. (5-7). The best linear fit is obtained when theoretical values log 1 Tα th. are plotted vs Zd.6 Qα 1/. The root-mean square (rms) deviation of the calculated values of log 1 Tα th. for 9 SHN with Z d =1-118, from the straight line is rms=.157. The similar result has obtained first by Brown [15] (see Eq. (3)) from the analysis of 119 data points (T α,e α ) for a range of Z d from 7 to 16. In this case the rms deviation of data from the straight line was.333. Further, in analysis of decay properties of SHN we make use of this simple functional dependence of the decay rate on Zd.6 Qα 1/.

8 8 Systematics of α-decay half-lives of the heaviest elements 195 logt th (s) - - Z=1 Z=13 Z=1 Z=15 Z=16 Z=17 Z=18 Z=19 Z=11 Z=111 Z=11 Z=113 Z=11 Z=115 Z=116 Z=117 Z=118 Z=1-6 -8,6,8,3,3,3,36 Q -1/ (MeV) -1/ Fig. 3 Calculated values from Eq.(11) for log 1 Tα th. (sec) are plotted vs the effective decay energy Q 1/ α. The Eα exp data [1, ] are shown in Figs.(1,)and Table 1. log T th (s) Z=1 Z=13 Z=1 Z=15 Z=16 Z=17 Z=18 Z=19 Z=11 Z=111 Z=11 - Z=113 Z=11 Z=115 Z=116 Z=117 - Z=118 Z= Z d * Q -1/ (MeV) -1/ Fig. Calculated values from Eq.(11) for log 1 Tα th. (sec) are plotted vs Z d Q 1/ α, where Z d is the charge number of the daughter nucleus,and Q α is the effective decay energy. The Eα exp data [1, ] are shown in Figs.(1,) and Table 1.

9 196 I. Silişteanu, A. I. Budaca, A. O. Silişteanu 9 6 log T th (s) - - Z=1 Z=13 Z=1 Z=15 Z=16 Z=17 Z=18 Z=19 Z=11 Z=111 Z=11 Z=113 Z=11 Z=115 Z=116 Z=117 Z=118 Z= , 3, 3, 3,6 Z.5 d Q-1/ (MeV) -1/ Fig. 5 The same as in Fig. but for Zd.5 Q 1/ α log T th (s) Z=1 Z=13 Z=1 Z=15 Z=16 Z=17 Z=18 Z=19 Z=11 Z=111 Z=11 Z=113 Z=11 Z=115 Z=116 Z=117 Z=118 Z=1 y=a+b*x a= b=9.681 rms=.157,6,8 5, 5, 5, 5,6 5,8 Z.6 d * Q -1/ (MeV) -1/ Fig. 6 Calculated values from Eq.(11) for log 1 Tα th. (sec) are plotted vs Zd.6 Q 1/ α, where Z d is the charge number of the daughter nucleus,and Q α is the effective decay energy. The Eα exp data are shown in Figs.(1,) and Table 1. The straight line represents a best Fit to the log 1 T α (sec) values.

10 1 Systematics of α-decay half-lives of the heaviest elements log T th (s) - - Z=1 Z=13 Z=1 Z=15 Z=16 Z=17 Z=18 Z=19 Z=11 Z=111 Z=11 Z=113 Z=11 Z=115 Z=116 Z=117 Z=118 Z= , 7,6 7,8 8, 8, 8, 8,6 8,8 9, 9, Z.7 d * Q -1/ (MeV) -1/ Fig. 7 The same as in Fig.6 but for Zd.7 Q 1/ α. 3.. α-decay CHAINS OF 93,9 117 NUCLEI The experimental and calculated values of log 1 T α vs Zd.6 Qα 1/ for the α- chains originating from the 93,9 117 nuclei are presented in Figs.(8-9). The results given by Eqs.(1-3), i.e. by Viola-Seaborg [13] and Brown [15] formulas, are almost the same and are somewhat higher than the experimental ones. The results calculated from Eqs.(1-3) and those from Eq.(11) with the added even-odd term h e o are very close, and in general, are lower than the experimental ones up to an order of magnitude. This is of course due to the overestimation of the formation factor in our model and a improve treatment of this factor would raise the half-time estimation []. The Geiger-Nuttall rule applies to the both experimental and calculated half-lives, excepting the two data points (T α, Q α ) for the and 8 Rg nuclides COMPARISON OF CALCULATED HALF-LIVES TO THE DATA The estimated α-decay half lives from Eqs.(1-3,11) using E α -data from the Figs. 1-, are presented in Table 1. In general, the half-lives obtained from Eqs.(1,3) and Eqs.(,11) are overestimations and underestimations of the deduced [1,] halflives, respectively. Our estimations are in a good agreement to the available data only for the proper α-transitions unperturbed by others competing channels. The calculated α-half-lives in the decay chains of Z=18,11 (Hs, Ds) and Z=11,116 isotopes have well-defined energies, pointing the absence of hindrance in the observed decay,

11 198 I. Silişteanu, A. I. Budaca, A. O. Silişteanu 11 which is a characteristic of the α-decay of spherical nuclei. The large differences of the α-decay energies and half-lives are observed in Table 1 at the crossing of the proton Z=18,11 shells and N = 15,16,17 neutron shell. log T (s) Experimental data Eq.(11) prezent work Viola-Seaborg Tagepera-Nurmia Brown ,1 5,15 5, 5,5 5,3 5,35 5, Z.6 d * Q -1/ (MeV) -1/ Fig. 8 Experimental [1] and calculated values from Eqs.(1-3,11) of log 1 T α vs Zd.6 Q 1/ α for the α-decay chain of the nuclide. log T (s) Experimental data Eq.(11) prezent work Viola-Seaborg Tagepera-Nurmia Brown Rg 5,1 5, 5,3 5, 5,5 5,6 Z.6 d * Q -1/ (MeV) -1/ Fig. 9 Experimental [1] and calculated values from Eqs.(1-3,11) of log 1 T α vs Zd.6 Q 1/ α for the α-decay chain of the nuclide.

12 1 Systematics of α-decay half-lives of the heaviest elements FIT OF EXPERIMENTAL AND CALCULATED α-half-lives If one plots log 1 Tα exp. (sec) vs Zd.6Q 1/ α as shown in Fig.(1), the data points fall nearly on a universal straight line. This line represents a best fit to the data. It is given by log 1 Tα exp. (sec)=9.65*(z.6 d Q 1/ α ) (rms=.5515). (1) If one plots log 1 Tα th. (sec) vs Zd.6Q 1/ α, we obtain a straight line which represents a best fit to theoretical results given by Eq.(11). Now, this line is given by log 1 Tα th. (sec) = *(Z.6 d Q 1/ α ) (rms=.187). (13) We can see that we have almost identical parameters in Eqs.(3, 1, 13). The same behavior we obtained in the case of theoretical method Eq.(11) with even-odd corrections as well in the case of empirical formulas Eqs.(1-3) (Viola-Seaborg, Tagepera- Nurmia, Brown). We see in Figs.(11-1) that the even-odd corrections separate the straight line in two. The one below represents the even-even nuclei. Since, the slopes of these universal Gamow lines from Figs.(1,11) are almost identical, the difference between experimental and theoretical half-lives arises only from the difference (of about one order of magnitude) between the structure constants. It is interesting that our theoretical predictions are in good agreement to the existing data. It appears that Figs.(1,13,1) are very similar, but their parameters (a,b) of Gamow lines, as well as predicted half-lives, considerably differ from those of Figs.(1,11) α-spectroscopic FACTOR (α-sf) From the ratio of the calculated and the measured half-time a spectroscopic factor for α-decay is deduced. This factor is given in the 9-th column of Table 1 and is plotted vs N d in Fig.15. The values of SF are expected to be less than unity as the ground state FA contains contributions from many other internal configurations than the resonance one with the α-particle already at the surface of the parent nucleus. The result of fit is seen to follows the smoothly increasing behavior with N d. The scatter in Fig.15 may be connected to the crossing the neutron shells N=15, 16, 17, and the proton Z=18,11, and large oscillations of the clustering amplitude near this shell closure. This means that the SF incorporates effects of shell closure. The most important decay quantities as Q α, T α [] and SF [37] have been plotted vs the Casten-Zamfir factor N p N n /(N p + N n ) [38]. While for SHN, the α-sf and T α increase with the Casten-Zamfir factor, the Q α decreases monotonically as we can see in Figs.(16,17). From the Figs.(16,17) it is clear that the Casten-Zamfir factor represents the number of valence α-particle formed from the valence nucleons. Moreover, this appears as a dominant controlling factor in evolution of structure and α-decay properties with the nuclear mass and deformation.

13 11 I. Silişteanu, A. I. Budaca, A. O. Silişteanu 13 Table 1. Experimental [1 9] and calculated α-decay properties of the all known SHN. The data for Eα exp and Tα exp are also included in Figs.(1,). Elem. Z N A Eα exp Q α log 1 Tα exp log 1 Tα at α a exp /Tα log 1 Tα b log 1 T α clog 1 T α d (MeV) (MeV) (sec) (sec) (sec) (sec) (sec) No No No No No No Lr Lr Lr Lr Lr Lr Lr Rf Rf Rf Rf Db Db Db Db Db Db Db Db Sg Sg Sg Sg Sg Sg Sg Bh Bh Bh Bh Bh Bh Bh Hs Hs Hs Hs a - Eq.(11), log 1 Tα=log a 1 Tα th + h e o b - Viola-Seaborg formula [13] c - Tagepera-Nurmia formula [1] d - Brown formula [15]

14 1 Systematics of α-decay half-lives of the heaviest elements 111 Table 1. Sequel Elem. Z N A Eα exp Q α log 1 Tα exp log 1 Tα at α a exp /Tα log 1 Tα b log 1 T α clog 1 T α d (MeV) (MeV) (sec) (sec) (sec) (sec) (sec) Hs Hs Mt Mt Mt Mt Mt Mt Ds Ds Ds Ds Ds Ds Rg Rg Rg Rg Rg Cn Cn Cn a - Eq.(11), log 1 Tα a=log 1Tα th + h b e o - Viola-Seaborg formula [13] c - Tagepera-Nurmia formula [1] d - Brown formula [15]

15 11 I. Silişteanu, A. I. Budaca, A. O. Silişteanu 15 log T exp (sec) Z=1 Z=13 Z=1 Z=15 Z=16 Z=17 Z=18 Z=19 Z=11 Z=111 Z=11 Z=113 Z=11 Z=115 Z=116 Z=117 Z=118 Z=1 y=a+b*x a= b=9.65 rms=.5515,6,8 5, 5, 5, 5,6 5,8 Z.6 d * Q -1/ (MeV) -1/ Fig. 1 Experimental values for log 1 Tα exp (sec) are plotted vs Zd.6Q 1/ α, where the data [1, ] for Eα exp and Tα exp are shown in Figs.(1,) and Table 1. The straight line represents a best Fit to the all known data. log T th (s) Z=1 Z=13 Z=1 Z=15 Z=16 Z=17 Z=18 Z=19 Z=11 Z=111 Z=11 Z=113 Z=11 Z=115 Z=116 Z=117 Z=118 Z=1 logt=a+b*x a= b= rms=.187,6,8 5, 5, 5, 5,6 5,8 Z.6 d * Q -1/ (MeV) -1/ Fig. 11 Calculated values from Eq.(11) for log 1 T th. α h e o [16] plotted vs Z.6 d Q 1/ α (sec) plus the even-odd corrections. The straight line represents a best Fit to the values log 1 Tα th (sec).

16 16 Systematics of α-decay half-lives of the heaviest elements 113 log T calc. F.1 (s) Z=1 Z=13 Z=1 Z=15 Z=16 Z=17 Z=18 Z=19 Z=11 Z=111 Z=11 Z=113 Z=11 Z=115 Z=116 Z=117 Z=118 Z=1 y=a+b*x a=-5.97 b=1.356 rms=.3966,6,8 5, 5, 5, 5,6 5,8 Z.6 d * Q -1/ (MeV) -1/ Fig. 1 Calculated values for log 1 T α (sec) by using Viola-Seaborg formula [13] (Eq.(1)) plotted vs Zd.6Q 1/ α. The Q α values are taken from Refs. [1, ]. The straight line represents a best Fit to the calculated log 1 T α (sec) values. log T calc. F. (s) Z=1 Z=13 Z=1 Z=15 Z=16 Z=17 Z=18 Z=19 Z=11 Z=111 Z=11 Z=113 Z=11 Z=115 Z=116 Z=117 Z=118 Z=1 y=a+b*x a= b=1.831 rms=.17,6,8 5, 5, 5, 5,6 5,8 Z.6 d * Q -1/ (MeV) -1/ Fig. 13 Calculated values for log 1 T α (sec) by using Tagepera-Nurmia formula [1] (Eq.()) plotted vs Zd.6 Q 1/ α. The Q α data are taken from Refs. [1, ]. The straight line represents a best Fit to the calculated log 1 T α (sec) values.

17 11 I. Silişteanu, A. I. Budaca, A. O. Silişteanu 17 log T calc. F.3 (s) Z=1 Z=13 Z=1 Z=15 Z=16 Z=17 Z=18 Z=19 Z=11 Z=111 Z=11 Z=113 Z=11 Z=115 Z=116 Z=117 Z=118 Z=1 y=a+b*x a=-8.15 b=9.165 rms=.17-8,6,8 5, 5, 5, 5,6 5,8 Z.6 d * Q -1/ (MeV) -1/ Fig. 1 Calculated values for log 1 T α (sec) by using Brown formula [15] (Eq.(3)) plotted vs Zd.6Q 1/ α. The Q α data are taken from Refs. [1, ]. The straight line represents a best Fit to the calculated log 1 T α (sec) values. T th T exp Z=1 Z=13 Z=1 Z=15 Z=16 Z=17 Z=18 Z=19 Z=11 Z=111 Z=11 Z=113 Z=11 Z=115 Z=116 Z=117 Z=118 Z=1 y=a+b*x a=-.536 b=. rms= N d Fig. 15 The ratio Tα th. /Tα exp. plotted vs the neutron number of the daughter nucleus N d. The Tα exp. values are taken from Refs. [1, ]. The straight line represents a best fit to this ratio against N d.

18 18 Systematics of α-decay half-lives of the heaviest elements α-spectroscopic STUDIES The α-radioactive SHN are deduced from fusion-evaporation reactions or by decay of other nucleus. However, the reaction channel of interest in their production typically represents only a very small fraction (down to 1 8 ) of the total cross section. Therefore, special devices and methods are needed to resolve radiation of interest from the vast background due to dominant reaction channels. For more detailed spectroscopic studies of SHN two experimental developments are very promising. Resonant-particle emission method (RPE) The observation of resonant-state products in nuclear reactions by measurements of coincidences between decay partners was proposed [39] as a general spectroscopic tool for nuclear physics. The detection technique currently available could, however, be used to detect a system which is internally excited to an excitation energy corresponding to resonant states which can decay by particle emission. In particular, a coincidence measurement of the two fragments emitted may be an adequate identification system. The particle decay of a resonant system always produces a certain amount of kinematic focusing for the emitted pair in the laboratory reference frame. Such kinematics focusing is particularly strong when the resonating system has a decay energy for a particular pair fragments which is small relative to the kinetic energy of the c.m. of resonating system. In fact, our approach for α-rates from Sect.., is a foundation of the RPE method. RDT-method A major breakthrough was achieved when large Ge detector arrays where combined with a high-transmission recoil separator for Recoil-Decay-Tagging (RDT) experiments []. Thus, it was shown that in beam γ-ray spectroscopic studies of exotic α-decays nuclei with very low production cross (down to 1 nanobarn) are possible. The RDT technique provides high confidence correlations between prompt γ -rays and subsequent radioactive decay under optimal conditions of short decay half-lives and high branching ratios α-half-lives OF MAGIC NUCLEI Theoretical calculations with the inclusion of higher order of deformation suggested that the ground state correction energy of deformed nuclei around 7 18 Hs 16 and which reach similarly large values. The relatively long partial SF halflives for both these nuclei make the α-emission to appear as the main decay mode. The increased stability leads to local minima at the N=16,18 neutron shells and large difference in Q α energy between Ds and Hs [9] and 116 and 11 [31] isotopes, respectively.

19 116 I. Silişteanu, A. I. Budaca, A. O. Silişteanu Hs 16 AND 66 16Sg 16 NUCLEI Theoretical calculations predict 7 18 Hs 16 to be a doubly magic deformed nucleus, decaying mainly by α-particle emission. The emission energy Q exp. α = 9. ±.3 MeV and Tα exp. = s have been measured for 7 18 Hs 18 [9]. Thus, 7 18 Hs 16 is the first nuclide in SHN region for which experimental nuclear decay properties have become available for comparison with theoretical investigations of the N=16 neutron shell. Several theoretical calculations of Q α for this nucleus have been performed and most of them ( e.g. [9] and References, Q α =8.69; 8.83; 8.87; 8.9; 9.5; 9.13 MeV) are in agreement with the measured value of Refs. [9]. The value Q α =9.33 MeV used in our estimation from the Table 1 is somewhat higher than the measured one, and therefore, the deduced half-time Tα exp. =.9 s is lower by one order of magnitude than the reported results [, 1]. The reported partial α-decay half-life of 66 Sg is T α = s [,1], which suggests the α-decay as the likely decay mode. But, the assignment of experimental findings [9] of T exp. SF = + 18 ms for 66 Sg is in contradiction to the interpretation of earlier works, where 66 Sg was reported to decay only by α-emission COMPETITION α-fission Minimum value of T SF (N) is for N= [1] where the effect of nuclear shells is the smaller. The Ds isotopes, with N=169 and 171, as the Cn ones, with N=17 and 17, are expected to undergo spontaneous fission [1] rather than α-decay. Indeed, for the 79 Ds isotope we get from Table 1: T a α =.69s; T b α =.61s; T c α =.39s; T d α =.187s; while the estimated total half-life is of about T t =.138s. In other words, the α-decay and the SF are competing modes having close halflives. Such a competition is pregnant at the even-even nuclei as we can see in Fig.. Systematic studies of SF versus α-decay in SHN are given in Refs. [33 36] 3.1. COMPARISON TO OTHER PROCEDURES Prompted by the recent experiments, a number of theoretical and phenomenological studies are aimed at reproducing the and α-decay data and further extrapolating calculations into the region of SHN. The generalization of the Geiger- Nuttall law is presented starting from the microscopic mechanism of the chargedparticle radioactivity [ 5]. The α-decay and SF half-lives are estimated either by phenomenological formulas [51] and shell and reaction energies of KUTI-formulas, or by approximate [5 55] or shell model [56 58] form-factors. In spite of a number of recognized simplifications in the present model, the qualitative and quantitative Fits to the T α - data are generally within the expected [59,6] or measured [61] errors in Q α -values.

20 Systematics of α-decay half-lives of the heaviest elements 117. SUMMARY AND OUTLOOK We have investigated the systematics of α-half-lives for SHN as predicted by theoretical self-consistent models for clustering and resonance scattering and by representative phenomenological models. The major influence of the pairing, resonance continuum, deformed shell closures, resonance scattering, and screening corrections was evidenced and provides a convenient basis for the interpretation of observed trends of the data and for prediction of new results. The following conclusions can be drawn from our study: 1) The spin-parity and energy information can be accurately extended, with support from theoretical investigations, from the daughter to parent. Thus, the decay chain can be rebuild from the bottom and this helps to identify new nuclides through their α-decay characteristics and measured α-α, parent-daughter space-time correlations. ) Characterized by their energy and lifetime the nuclear decay can be enhanced due to the collective behavior or forbidden by internal selection rules. 3) The nuclides just above Z=18, Z=11 and N=16 and N=18 present characteristics typical for deformed and spherical α-emitters. The shortest α-half-lives estimated for these nuclides are in the range of tens of ms,and µs, respectively. ) The Q α and T α -values of the homologues from the same groups are periodic functions of the number of valence α-particles, as it is shown in Figs.(16-17). Therefore, it was possible to deduce the properties of nuclides above Z = 11 from what we know in the regions above Z = 8 and Z = 5, by using the symmetry arguments associated to the α-periodicity. 5) The very small widths of α-resonances observed experimentally in fusion-evaporation reactions, are interpreted as resonance levels of radioactive products, and such a connection contributes directly to the study of the nuclear structure on the basis of decay data. Acknowledgements. We thank to Profs. Yu. Ts. Oganessian, V. K. Utynkov, S. Hofmann, W. Scheid, M. Rizea, Dr. Hab. S. Mişicu, M. Cristu and V. Grecu for many stimulating discussions. This work was supported from Contracts: PN Part.71-11; Idei 9/7; PN

21 118 I. Silişteanu, A. I. Budaca, A. O. Silişteanu n +n 3 n Q ( MeV) Po 8 Pb+ 1 Te 1 Sn At 18 Rn Fr 1 Ra 18 Po 11 I 11 Te 1 At 1 Rn 3 Fr Ra 11 Xe 11 Cs 113 Ba 113 I 113 Xe 115 Cs 116 Ba 1, 1,5,,5 3, 3,5, P=N p *N n / [N p +N n ] Fig. 16 Experimental Q α values for the trans- 1 Sn, trans- 8 P b nuclei and the calculated Q α values for the trans nuclei [31] vs. the Casten-Zamfir factor P [38]. log T (s) n 1 Sn -1 8 Pb Po 1 Te 18 Po 11 Te I 18 At +n 113 I 11 Xe At Rn Xe 1 Rn 11 Cs Fr n 115 Cs 3 Fr 113 Ba 1 Ra Ba Ra 1, , 1,5,,5 3, 3,5, P = N p *N n / [N p + N n ] 3 Fig. 17 Experimental α-halflives of the trans- 1 Sn and trans- 8 P b and the calculated α half-lives of the trans vs. Casten-Zamfir factor P [38]. Many body α-fa is given by shell model [,9]. REFERENCES 1. Yu. Ts. Oganessian, F. Sh. Abdulin, P. D. Bailey et al., Phys. Rev. Lett. 1, 15 (1).

22 Systematics of α-decay half-lives of the heaviest elements 119. Yu. Ts. Oganessian, Pure. Appl. Chem. 78, 889 (6). 3. Yu. Ts. Oganessian, V. K. Utyonkov, Y. V. Lobanov, et al. Phys. Rev. C 7, 6 (6).. Yu. Ts. Oganessian, Eur. Phys. J. A, 361 (9). 5. S. Hofmann et al., Eur. Phys. J. A 1, 17 (). 6. S. Hofmann and G. Münzenberg, Rev. Mod. Phys. 7, 733 (). 7. S. Hofmann et al., Zeit. Phys. A 35, 9 (1996). 8. K. Morita, K. Marimoto, D. Kaji, et al., Jap. Phys. Soc. J. 73, 593 (). 9. J. Dvorak, W. Bruchle, M.Chelnokov et al., Phys. Rev. Lett. 97, 51 (6) and therein references. 1. H. Geiger and J. M. Nuttall, Philos. Mag., 613 (1911). 11. G. Gamow, Z. Physik, 51, (198). 1. R. W. Gurney and E. U. Condon, Nature (London), 1, 39 (198). 13. V. E. Viola and G. T. Seaborg, J. Inorg. Nucl. Chem. 8, 71 (1966). 1. R. Tagepera and M. Nurmia, Ann. Acad. Sci. Fenn. Serie A 78, (1961). 15. B. Alex Brown, Phys. Rev. C 6, 811 (199). 16. A. Sobiczewski, Z. Patyk, S. Cwiok, Phys.Lett., 1 (1989); Z. Patyk and A. Sobiczewski, Nucl. Phys. A 35, 9 (1996). 17. J. O. Rasmussen, Alpha-, beta- and gamma-ray spectroscopy, K. Siegbahn (Ed., North-Holland, Amsterdam) 1, 71( 1968). 18. G. Breit, Encyclopedia of Physics, Vol. XLI, Nuclear Reactions II: Theory, Springer-Verlag (Ed S.Flugge), H. Feshbach, Ann. Phys. 5 (NY), 357 (1958).. I. Silişteanu, W. Scheid and A. Sǎndulescu, Nucl. Phys A 679, 317 (1). 1. I. Silişteanu, W. Scheid, Phys. Rev. 51, 3 (1995).. M. Ivaşcu, I. Silişteanu, Nucl. Phys., A 35, 5 (1988). 3. A. Sǎndulescu, I. Silişteanu, R. Wuensch, Nucl. Phys., A35, 5 (1978).. V. Ledoux, M. Rizea, M. Van Daele, G. Vanden Berghe, I. Silişteanu, J. Comput. App. Math. 8, (9). 5. I. Silişteanu, M. Rizea. B. I. Ciobanu et al., Rom. J. Phys. 53, (8). 6. I. Silişteanu, A. Neacşu, A. O. Silişteanu et al., nd Carpathian Summer School of Physics 7, AUG -31, 7 Sinaia ROMANIA, EXOTIC NUCLEI AND NUCLEAR /PARTICLE AS- TROPHYSICS (II) 97, (8). 7. I. Silişteanu, Rom. J. Phys. 5, (7). 8. I. Silişteanu, A. Sandru, A. O. Silişteanu et al., Rom. J. Phys. 5, 87-8 (7). 9. I. Silişteanu, A. Neacşu, A. O. Silişteanu et al., Rom. Rep. Phys. 59, (7). I. Silişteanu, A. Sandru, A. O. Silişteanu et al., International Summer School in Nuclear Physics, AUG 8-SEP 9, 6, Predeal ROMANIA, COLLECTIVE MOTION AND PHASE TRANSI- TIONS IN NUCLEAR SYSTEMS, (7). 3. Yu. Ts. Oganessian et al., Phys. Rev. C 79, 63 (9). 31. P. Möller, J. Nix, K. L. Kratz, At. Data and Nucl. Data Tab. 66, 131 (1997). 3. I. Muntian, Z. Patyk, and A. Sobiczewski, Acta Phys. Pol. B 3, 691 (1). 33. K. P. Santhosh, R. K. Biju and S. Sahadevan, J. of Phys. G: Nucl. and Part. Phys. 36, (9). 3. Chang Xu, Zhongzhou Ren and Yanging Go, Phys. Rev. C 78, 395 (7). 35. A. Baran, Z. Lojewski, K. Sieja, and M.Kowal, Phys. Rev. C 7, 31 (5). 36. G. Royer, J. of Phys. G: Nucl. and Part. Phys. 6, ().

23 111 I. Silişteanu, A. I. Budaca, A. O. Silişteanu G. Gangopadhyay, J. of Phys. G: Nucl. and Part. Phys. 36, 9515 (9). 38. R.F. Casten and N.V. Zamfir, Phys. Rev. Lett. 7, (1993). 39. D. Robson, Nucl. Phys. A, (197).. R. Julin, Nucl. Phys. A 83, 15c-1c (1). 1. Yu. A. Lazarev et al., Phys. Rev. Lett. 73, 6 (199).. C. Qi, F.R.Xu, R.J. Liotta et al., Phys. Rev. C 8, 36 (9). 3. V. Yu. Denisov and H. Ikezoe, Phys. Rev. C 7, 6613 (5).. P. Mohr, Phys. Rev C 73, 3131 (6). 5. P. Roy Chowdhury, C. Samanta and D. N. Basu Phys. Rev. C73, 161 (6). 6. Chang Xu and Zhongzhou Ren, Phys. Rev. C 7, 13 (6). 7. Takatoshi Ichikawa et al., Phys. Rev. C 71, 68 (5). 8. T. R. Routray et al., Nucl. Phys. A 86, 3-9 (9). 9. D. S. Delion, A. Sǎndulescu, and W. Greiner, Phys. Rev. C 69, 318(). 5. H. Zhang, J. Li,, W. Zuo, et al., Phys. Rev. C 8, 5731 (9). 51. H. Koura, J. Nucl. Radiochem. Sci., 3, 1-3 (). 5. M. Rizea and N. Cârjan,, Rom. Rep. Phys. 6, 7- (8). 53. M. Mirea, D. S. Delion, A. Sǎndulescu, Rom. J. Phys. 55(3-), (1). 5. M. Mirea, R. C. Bobulescu, M. Petre, Rom. Rep. Phys. 61, 65 (9). 55. M. Mirea, L. Tassan-Got, Rom. J. Phys. 5, 331 (9). 56. I. Silişteanu, A.O. Silişteanu, W. Scheid, et al, Carpathian Summer School of Physics, JUN 13-, 5 Mamaia Constanta, ROMANIA, Exotic Nuclei and Nuclear/Particle Astrophysics, 3,(6). 57. I. Silişteanu, W. Scheid, M. Rizea, et al., International Workshop on New Applications of Nuclear Fission, SEP 7-1, 3 Bucharest, ROMANIA, NEW APPLICATIONS OF NUCLEAR FISSION, PROCEEDINGS, 197(). 58. R. Nazmitdinov, I. Silişteanu, Sov. J. Nucl. Phys. 3, 36(1986); I. Silişteanu, R. Nazmitdinov, Rev. Roum. Phys. 3,59(1987). 59. A. Sobiczewski, Acta Phys. Pol. B 1, 157 (1). 6. J. Dong, W. Zuo et al., Phys. Rev. C 81, 639 (1). 61. Ch. E. Düllmann et al., Phys. Rev. Lett. 1, 571 (1). 6. B. A. Brown, private communication (1).