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57 CLUSTER RADIOACTIVITY and ΑLPHA DECAY of SUPERHEAVY NUCLEI D. N. Poenaru1,2, R. A. Gherghescu1,2, W. Greiner2 1 Ho

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57 CLUSTER RADIOACTIVITY and ΑLPHA DECAY of SUPERHEAVY NUCLEI D. N. Poenaru1,2, R. A. Gherghescu1,2, W. Greiner2 1 Ho CLUSTER RADIOACTIVITY AND ΑLPHA DECAY OF SUPERHEAVY NUCLEI D. N. Poenaru1,2, R. A. Gherghescu1,2, W. Greiner2 1 Horia Hulubei National Institute for Physics and Nuclear Engineering, Bucharest-Magurele, Romania 2 Frankfurt Institute for Advanced Studies, Frankfurt/Main, Germany The competition of cluster radioactivity (CR) and α decay is investigated in the region of superheavy (SH) nuclei with atomic numbers Z = 104 - 124. Calculations of half-lives within analytical superasymmetrical fission (ASAF) model are performed by using different theoretical mass tables to determine the energy released, Q. For α decay the ASAF calculations are compared with semFIS (semi-empirical fission model). A trend toward shorter half-lives and larger branching ratios relative to alpha decay for heavier SHs was observed. 1. Introduction The first theoretical explanation of α decay, as a quantum tunneling phenomenon was given by G. Gamow [1] — a famous physicist born in Ukraine. This was the first application of newly developed quantum mechanics to nuclei. Another renowned theorist who has been working in the host Institute of the present Conference was V.M. Strutinsky. I had the privilege to meet him in Kiev in 1983. Our fission models are mainly based on his macroscopic-microscopic method [2, 3]. Superheavy (SH) elements with atomic numbers Z = 104 - 118 (see the review paper [4] and the invited talks at this Conference by S. Heinz, A. Sobiczewski, G. Royer and Z. Lojewski) have been synthesized with cold fusion reactions [5, 6] or with hot fusion induced by 48Ca projectiles [7]. Many of them have already names and symbols: Rf, Db, Sg, Bh, Hs, Mt, Ds, Rg, Cn, Fl, and Lv. The elements 113, 115, 117, and 118 are still waiting to be named. Many of them are identified through the α decay chains. Previously we also discussed the competition of a decay and cluster radioactivity (CR) [8], which may be important [9, 10] in the region of the heaviest SHs. In this process, from one A Ae Ad A Ae Ad parent nucleus Z, one obtains an emitted particle Ze, and a daughter Zd: Z → Ze + Zd. Alternating theory of α- decay [11, 12] and of SH production [13 - 16] was developed by V.Yu. Denisov. A universal decay law for α emission and CR was recently introduced [17] based on R-matrix theory. Starting with 1984 [18] many CR have been experimentally confirmed [19, 20] in heavy parent nuclei with Z = 87 to 96: 14C, 20O, 23F, 22,24-26Ne, 28,30Mg, and 32,34Si. The measured half-lives are in good agreement with predicted values within the ASAF model (see the review [21] and references therein). The largest branching ratio relative to α decay, -8.9 14 223 bα = Tα /Tc, of 10 was observed for C radioactivity of Ra. Usually in this region of the nuclear chart CR is a rare 208 process in a huge background of α particles. The strong shell effect of the doubly magic daughter 82Pb 126 was observed. In order to study his importance in the region of SHs with Z > 110 we changed the concept of CR, previously max max [22] associated with a maximum Zeold| = 28. Now we allow Ze = Z - 82. 2. The ASAF model The accuracy of half-life calculation is very much dependent on the precision with which we know the Q-value Q = ⎡M −+()MMc⎤ 2 ⎣ ed⎦ (1) obtained as a difference between the parent, M, and the two decay product masses, Me and Md, in units of energy; c is the light velocity. The decay constant λ = ln2/Tc is expressed by a product of three model dependent quantities v, S and Ps where v is the frequency of assaults on the barrier per second, S is the preformation probability and Ps is penetrability of external barrier. According to our method [23] the preformation in a fission theory is given by the penetrability of the internal part of the barrier. We developed our ASAF model starting with the Myers - Swiatecki’s liquid drop model [24] adjusted with a phenomenological correction. The half-life is given by T = [(h ln2)/(2Evovs )]exp(K + K ) (2) It is calculated by using the WKB quasi classical approximation 2 Rb K= 2BRERdR ( ) ( ) (3) h ∫ Ra with B = µ, K = Kov + Ks, and E(R) replaced by [E(R) - Ecorr] - Q where Ecorr is a correction energy similar to the * 0 1/2 Strutinsky shell correction. The turning points of the WKB integral are: Rα = Ri + (Rt - Ri)[(Ev + E )/ Eb ] and 57 * 2 1/2 * * Rb = RtEc{1/2+[1/4+(Q + Ev + E )El/ Ec ] }/(Q + Ev + E ) where E is the excitation energy concentrated in the separation degree of freedom, Ri = R0 - Re is the initial separation distance, Rt = Re + Rd is the touching point separation 1 3 distance, Rj = r0 Aj (j = 0, e, d; r0 = 1.2249 fm) are the radii of parent, emitted, and daughter nuclei, respectively, and 0 Eb = Ei - Q is the barrier height before correction. The interaction energy at the top of the barrier, in the presence of a 2 2 2 non-negligible angular momentum, lħ, is given by Ei = Ec + El = e ZeZd/Rt + ħ /(l + 1)/(2µ Rt ). The two terms of the action integral K, corresponding to the overlapping Kov and separated Ks fragments, are calculated analytically [10, 22]. The potential barrier shape similar to that which we considered within the ASAF model was calculated by using the macroscopic-microscopic method [25]. 3. Mass tables Half-life calculations are very sensitive to the Q-values. The closest to reality are the updated table of evaluated experimental masses AME11 [26], but many masses are still not available for new SHs in this table. We have also used some calculated masses: LiMaZe01 Liran - Marinov - Zeldes [27, 28] (semi empirical shell model), KTUY05 Koura - Tachibana - Uno - Yamada [29] (phenomenological) and FRDM95 the finite-range droplet model [30] (macroscopic- microscopic). To these we may add: MySw94 Myers-Swiatecki [31] (macroscopic-microscopic), APDT95 Aboussir- Pearson-Dutta-Tondeur [32] (microscopic), DuZu96 Duflo-Zuker [33] (shell model). Other alternatives are presented by A. Sobiczewski at this Conference. We show in Figs. 1, 2, and 3 the nuclides for which Z=126 calculated masses are available according to the tables LiMaZe01, KTUY05, and FRDM95, respectively. For the region of interest Z = 104 - 124 the beta stability line goes through Ng = 106 for Z = 104 and Ng = 206 for Z = 124. It is clearly seen that the most complete mass table of these three is FRDM95. The other two will allow us to make calculations only for some of the neutron deficient heaviest SHs. When using calculated masses for parent and daughter nuclei we take into account the nuclides stable against one proton, two protons, one neutron and two neutrons spontaneous emissions which leads to a smaller number of Z=82 parent nuclides than those shown in Figs. 1, 2, and 3. N=126 N=184 4. Shorter half-lives for heavy superheavies Fig. 1. Chart of nuclides with calculated LiMaZe01 Besides the emitted clusters with Z ≤ 28 (Be, C, Ar, masses. 1969 masses for Z = 82 - 126, N = 126 - 184. The e Ti, V, Cr, Mn, Fe, Co, and Ni), many other types of new Green approximation of the beta stability is marked by full CR with Z > 28 appear when we use the FRDM95 squares. e calculated mass table to determine the Q-values: Cu, Zn, Ga, Ge, As, Se, Br, Kr, Rb, Sr, Y, Zr, Nb, and Mo. Many of the SH nuclides are 8Be emitters, but they have a very low 78 branching ratio bα. Most frequently occurs the doubly magic Ni radioactivity. Z=124 Z=104 N=200 Fig. 2. Chart of nuclides with calculated KTUY05 masses. 9441 masses for Z = 2 - 130, N ≤ 200. The Green approximation of the beta stability is marked by full squares. 58 Z=124 Z=104 N=206 Fig. 3. Chart of nuclides with calculated FRDM95 masses. 8979 masses for Z = 8 - 136, N ≤ 236. The Green approximation of the beta stability is marked by full squares. An even-odd staggering of CR half-lives was observed [10] leading to shorter Tc for even N nuclides compared to the neighboring odd N ones. In order to avoid such a complication we consider in Fig. 4 for cluster decay only the odd N isotopes. Two important trends are observed: (1) both Tc and Tα are shorter for SHs with larger atomic number, and (2) for some of the isotopes of Z = 123 and Z = 124 elements cluster decay half-life may be shorter than that of a decay: Tc < Tα (or the branching ratio bα = Tα/Tc becomes larger than unity when the atomic number of the parent nucleus increases over 122). We observed [10] that large differences in Q-values for α decay calculated with various mass tables occur very frequently and make an important contribution to the broad range of branching ratios bα for any particular nucleus. Even the most probable emitted cluster can differ as in the case of the 304124 parent for which 98Mo results in calculations of released energy based on LiMaZe01, 95Zr based on KTUY05, and 96Zr based on FRDM95. More elaborate models should be used (see, e.g., [34]) in order to estimate the competition of spontaneous fission. Fig. 4. Decimal logarithm of the half-lives of superheavy Fig. 5. Comparison of alpha-decay half-lives calculated nuclei with atomic numbers 121 - 124 against α decay with ASAF (open circles) and semFIS (full squares) (open circles) and CR for odd-neutron isotopes (stars) models vs.
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