v.2.1r20180507 *2018.6.26#58fe9efc HALF-LIVES OF NUCLEI AROUND THE SUPERHEAVY NUCLEUS 304 120 A. O. SILIŞTEANU 1,3, C. I. ANGHEL 1,2,, I. SILIŞTEANU 1 1 Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, RO-077125, Romania 2 University of Bucharest, Faculty of Physics, 077125 Bucharest, Romania Corresponding author : claudia.anghel@theory.nipne.ro 3 University Politehnica of Bucharest, Faculty of Automatic Control and Computer Science, 1-7 Polizu, RO-011061, Bucharest, Romania Received September 14, 2017 Abstract. Simple formulas for α-half-lives derived from the systematics of measured and calculated α-half-lives [Rom. J. Phys. 62, 303 (2017)] of superheavy nuclei, are used to predict the α-half lives of the nuclei around the expected double magic nucleus 304 120. Present α-half-life estimates for nuclei near closed shells are compared to available data and results of other methods. We get almost identical α-half-lives for decays of 104 Te, 212 Po and 308 122 leading to known 100 Sn, 208 Pb or 304 120 doubly magic nuclei. The competition between α decay and fission at the closed shells is discussed. Key words: Half-lives, α-decay, spontaneous fission. PACS: 23.60.+e; 25.85.Ca; 25.60.Cs. 1. INTRODUCTION The experimental data [1 5] and theoretical results [6 9] on synthesis and nuclear properties of elements Z=112 118 and their decay products, demonstrate an impressive increasing of nuclear stability of superheavy nuclei (SHN) with the neutron number approaching the magic number N=184. For the synthesis of new SHN is very important to know exactly the central position of the island of stability (i.e., the values of Z and N of the double magic core). The island of stability for SHN is predicted to be around the neutron number N=184 and proton number Z 120 [7 9]. The uncertainties concerning the magicity of atomic number may reveal serious limits of validity of the reaction data analysis and of theoretical results obtained by the use of phenomenological models. The experiment aimed at the synthesis of these isotopes of element Z=120 has been performed using the 244 Pu( 58 Fe,xn) 302 xn 120 reaction [10]. The sensitivity of the experiment corresponds to a cross section of 0.4 pb for the detection of one decay. Thus, the experimentally investigated nuclides 298 120 and 299 120 are still neutron deficient isotopes and therefore are expected to have a some α-branch. Otherwise, it was assumed in [10] that both isotopes of the Romanian Journal of Physics 63, 302 (2018)
Article no. 302 A. O. Silişteanu, C. I. Anghel, I. Silişteanu 2 element Z = 120 will preferentially undergo α decay (T α < T SF ). However, no decay chains consistent with fusion-evaporation reaction products ( 299 120 and 298 120) expected for the 3n and 4n reaction channels, were observed during an irradiation with a beam dose of 7.1 10 18 330 MeV 58 Fe projectiles. We want to study in detail the decay properties of these nuclei. If assuming that 304 120 is a double magic nucleus, than the nuclides 298 120 and 299 120 have six and five holes in N=184 neutron shell, and their α decaying parents should be 302 122 and 303 122. For these nuclides we make also half life estimates. In the present work we perform estimates of the α and fission half-lives for isotopes of the elements around the expected double magic nucleus 304 120. We will compare these with the experimental and calculated half lives for the known trans-tin and trans-lead regions of nuclei ( 100 Sn, 208 Pb). For this purpose we use the results of experimental and theoretical studies of fundamental properties (mass, reaction energies, decay modes, half-lives and nuclear structure) of already produced SHN to make reasonable predictions for decay properties of the nuclei with Z > 118 and approaching the number 184. Many SHN has been produced in fusion-evaporation reactions and identified via the α-particle spectroscopy. Thus, the fact that the α-particle has high binding energy, zero spin, zero isospin may lead to uncomplicated interpretation of its interactions with the nuclear matter, and it may continue still to be one of the most useful probes for studying the nuclear structure and reaction mechanisms of SHN. Therefore, the important changes in the nuclear structure with increasing values of N and Z are expected to manifest itself in the α-decay energy spectra and the systematics of α-half-lives. The α-halflives have been estimated within phenomenological [11 16] and microscopic [17 22] models. These models are various generalizations of the Geiger-Nuttall law [23], (T α Q 1/2 α ) having in common the quantum penetrability factor that depends linearly on Q 1/2 α. There are also microscopic methods for calculating: the shell model cluster formation and reaction amplitudes, the folding potential [24] and scattering resonances originating from quasibound states [25, 26]. 2. CALCULATION OF HALF-LIVES The Brown fit formula for the α-half-lives is taken of the form [18]: log 10 Tα f (sec) = AZd 0.6 Q 1/2 αt B, rms (1) where Z d is the atomic number of the daughter nucleus, Q αt is the total decay energy, A and B are the fit parameters and rms is the root mean square error. The total decay energy is the reaction energy Q α (measured or calculated) plus the screening energy: Q αt (MeV) = Q α + ( 6.53Z 7/5 d 8.0Z 2/5 d ) 10 5. (2)
3 Half-lives of nuclei around the superheavy nucleus 304 120 Article no. 302 The root mean square error is defined as: N rms = [N 1/2 ][ (log 10 (T f α,i /T α,i) 2 ] 1/2, (3) i=1 where N is the number of considered α-emitter nuclei and T f α are the fitted values of T α. The values of parameters extracted from the Brown systematics of experimental and calculated (shell and one-body models, SM and ob) [18] AD-half-lives are given in Table 1. Table 1 Updated values of parameters extracted from the Brown systematics for α-half-lives [17]. The fit is performed for 80 nuclei with measured values of Q α and T α [18]. For calculated α-decay half-lives we used only measured Q α values those errors Q α 50 kev. Fit of half-lives Z,N A B rms Experimental e-e 9.746 52.236 0.493 (Tα fexp ) o-e 9.209 48.550 0.600 e-o 10.299 53.958 0.511 o-o 8.793 45.919 0.550 Calculated e-e 8.824 46.846 0.252 Shell Model o-e 8.489 44.652 0.496 (Tα fsm ) e-o 7.742 40.432 0.265 o-o 8.276 42.865 0.428 Calculated e-e 10.481 57.391 0.439 One-Body o-e 9.933 54.620 0.429 (Tα fob ) e-o 11.700 63.634 0.487 o-o 9.676 53.229 0.406 The spontaneous fission (SF) half-life is expressed as [17]: log 10 T SF (s) = 1146.44 75.3153X + 1.63792X 2 0.0119827X 3 + B f (7.23613 0.0947022X) + h e o, (4) where X = Z 2 /A, B f is the SF barrier and h e o are new even-odd corrections extracted from the fit of measured fission half lives: h e e = 0.0, h e o = 2.007, h o e = 2.822, h o o = 3.357.
Article no. 302 A. O. Silişteanu, C. I. Anghel, I. Silişteanu 4 Table 2 The calculated α-half-lives and reaction energies ( ) of the nuclei near the double magic shell closures ( 100 Sn, 208 Pb, 270 Hs, 298 Fl and 304 120). The decay data for 104 Te and 212 Po are taken from [40]. The nuclei with the double magic shell closures are predicted according to the calculated shell gaps [9]. Nucleus Q α (MeV) T fsm α (s) T fob α (s) T fexp α (s) T α (s) 104 Te 5.070 0.119 10 6 0.856 10 7 0.907 10 7 0.111 10 6 [40] 212 Po 8.954 0.915 10 6 0.432 10 7 0.327 10 6 0.299 10 6 [40] 274 Ds 11.970 0.857 10 5 0.240 10 6 0.272 10 5 302 Lv 12.180 0.907 10 4 0.630 10 5 0.355 10 4 293 Og 12.250 [9] 0.517 10 2 0.894 10 5 0.256 10 2 294 Og 12.450 [9] 0.127 10 1 0.470 10 5 0.408 10 2 294 Og 11.880 [10] 0.118 10 0 0.635 10 4 0.435 10 1 0.470 10 3 [3] 294 Og 11.820 [10] 0.151 10 0 0.845 10 4 0.564 10 1 0.690 10 3 [3] 294 Og 11.760 [10] 0.193 10 0 0.113 10 3 0.732 10 1 0.133 10 2 [3] 295 Og 12.140 [9] 0.801 10 2 0.150 10 4 0.412 10 2 294 119 13.410 [9] 0.489 10 3 0.292 10 7 0.265 10 4 295 119 13.750 [9] 0.869 10 5 0.174 10 7 0.823 10 6 298 120 12.400 [10] 0.400 10 1 0.179 10 4 0.137 10 1 299 120 12.300 [10] 0.110 10 1 0.224 10 4 0.599 10 2 298 120 13.300 [9] 0.151 10 2 0.389 10 6 0.424 10 3 299 120 13.000 [9] 0.781 10 3 0.981 10 6 0.330 10 3 304 120 12.000 [9] 0.192 10 0 0.112 10 3 0.730 10 1 296 122 14.700 [9] 0.232 10 6 0.101 10 7 0.429 10 7 0.582 10 7 [39] 302 122 14.250 [9] 0.160 10 3 0.281 10 7 0.390 10 4 303 122 14.000 [9] 0.609 10 4 0.495 10 7 0.207 10 4 302 122 12.400 [9] 0.103 10 0 0.541 10 4 0.376 10 1 303 122 12.300 [9] 0.300 10 1 0.701 10 4 0.173 10 1 308 122 14.940 [9] 0.110 10 6 0.426 10 8 0.187 10 7 0.153 10 7 [39] 3. RESULTS AND DISCUSSION The estimated α-half-lives Tα fsm, Tα fob and Tα fexp from Eq. (1) with the (Z,N) parity dependent parameters of Table 1 are shown in Table 2. The following conclusions can be drawn from our study: for the nuclei 104 Te and 212 Po the predicted α-half lives Tα fsm a very good accordance with the experimental ones [40]. and T fexp α are in
5 Half-lives of nuclei around the superheavy nucleus 304 120 Article no. 302 for all the studied nuclei, there are not important discrepancies between the values of Tα fsm and Tα fexp. the ratio between Tα fob /Tα fsm and Tα fob /Tα fexp are of order 10 2 10 3, give rough estimations for the spectroscopic factors in α-decay. the nucleus 308 122 has an α-half life almost identical with the one of 104 Te and 212 Po. because the estimated α (see Table 2) and fission (T f =0.835 10 1 (s)) half lives for 294 Og are close each other, the α and fission are expected to become competing modes. for the nuclide 304 120 we get T f =0.897 10 11 (s) which is considerably shorter than T α. Present half-life estimates for nuclei near closed shells reveal the major role of valence protons and neutrons (from Fermi surface) on decay properties. The values of Tα SM,ob calculated, need very complicated numerical procedures [27 30]. However, the results [31 38] for α-half-lives given by microscopic procedures are in a good accordance with data for all the known SHN. We shown that the results obtained with a fit formula of calculated half-lives are also in accord to data and others predicted results [39]. 4. CONCLUSIONS The α and fission half lives of nuclei with Z=118 122 have been estimated within the different approximation schemes. The results demonstrate the reasonable consistence with data and other results by using microscopic, macroscopic and empirical procedures. We prove that a detailed analysis of decay properties of known SHN may help to investigate the structure and dynamics of the new heaviest nuclei. In conclusion, the nuclide 304 120 shows decay properties specific to the known double magic nuclei. Apart from these, the main decay mode is fission not α-decay. We hope that some of our results may help in synthesis and identification of new heaviest nuclei. Acknowledgements. We thank to Prof. A. Sǎndulescu for many stimulating discussions. This work was supported from Projects Nucleu No. PN 18 09 01 01/2018 and PN-III-P4-ID-PCE-2016-0649/2017.
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