CENTRAL INSTITUTE OF PHYSICS INSTITUTE FOR PHYSICS AND NUCLEAR ENGINEERING Bucharest, P.O.Box MG-6, ROMANIA BUCHAREST UNIVERSITY, FACULTY OF PHYSICS Bucharest, P.O.Box MG-6, ROMANIA ^\tf ~ FT-350-*fta9 March Plonic radioactivity versus spontaneous fission in decay of superheavy nuclei D.B.ION*. R.ION-MIHAI** M. IVASCU* \* ^^ Ab4.f./iac-t» In this paper ,th3 pionic radioactivity as dominant decay mode of superheavy elements (SHE) is investigated. The dynamical thresholds as well as the competition between the ground state pionic radioactivity and the spontaneous fission are discussed. It is shown that the usual island of stability around the double magic nucleus 29 8[114 ] is destroied via a deep instability due to the spontaneous -,ion emission. An is­ land of relative stability against the pionic dominant decay mode is predicted to be around the magic nucleus [120],The pionic radioactivity dominance in the SHE region can be con­ sidered as one of the possible reasons why SHE nuclei have not been synthesized and/or identified using heavy ion reac­ tions. 1. INTRODUCTION In some recent papers [1-13J we have initiated the investi­ gation of the spontaneous pion emission from the ground state of a nucleus as a new possible natural radioactivity called pionic nuclear radioactivity. Then, the Q^ - systematics, the definitions of the "width" (T^) and the Lorentz invariant statistical factors of the pionic nuc>ear radioactivity are presented [1-3]. It was shown that this new type of nuclear radioactivity is energetically possible via two (or many)-body fragmentation of the parent nucleus and that the most statistically favoured pionic emitters are those with Z > 92. Experimental detection of the neutral and charqed pions as well as some possible two step mechanisms for the spon­ taneous pion emission are also discussed in ref. [1-6]. An Optical Theorem for the inclusive pionic radioactivity was- proved [6]. Ex­ tensions of these results to other possible natural radioactivi­ ties, such as muonic nuclear radioactivity, lantbdonic (\°) nuclear radioactivity, hyperfission, etc., are also presented in refs. [2, 7, 13]. The dynamical predictions for the pionic nuclear radioac­ tivity were obtained in refs. [ 8-12 ]. The credibility of these predictions is verified by applying the same fission-like model [ see e.g. refs. [ 11-13 ]] to the light-charged-particle (LCP) emis­ sion data. Moreover, the absolute predictions for the yieldr /rs are in agreement with the experimental upper limits obtained at Bucharest [14-16] for charged pions and also with those measured at: CEN - Saclay [17], ORNL [18], and TRIUMF-Vancouver [19]for neutral pions. Also, it is important to note that, recently [21], the unusual background observed experimentally by Wild et al El ] in the (AE, E) - energy region below that characteristic of LRA's - 2 - 257 emission from Fm is interpreted by us as being produced by 257 negative pions emitted spontaneously by Fm. If this interpreta­ tion is correct then the inferred value of the negative pionic 257 -3 yield of Fm is r /rCc = 1° • This result is with ten orders II or of magnitude higher than that predicted by us in ref. [10]. Now, we remember that in refs. [5,12] we pointed ^ut that: the discovery of the pionic radioactivity will contribute to a much deeper understanding of the nuclear instabilities in the region of the superheavy elements where the ground state jnowic ra­ dioactivity is expected to be one of the dominant nuclear decay m ode. Consequently a detailed investigation of this last conjec­ ture is needed. So, in this paper, the fission-like model [ 12] is applied for the calculation of the pionic yields (^-„/^cc) for the superheavy elements in terms of their spontaneous fission half-lives. The Q -systematic for the superheavy elements (SHE) is presented in Section 2, wm'le the dynamical thresholds for the ground state pionic radioactivity are discussed in Section 3. The competition between tK« pionic radioactivity ind spontaneous fission in decay of the superheavy element' is investigated in Section 4 while the conclusions are sutmarized in Section 5. 2. Q - SYSTEMATICS FOR SUPERHEAVY ELEMENTS IT Superheavy elements (SHE) have been postulated in 1955 by Wheeler [22] and in 1967 by Scharf Goldhaber [231. But the inter­ national interest in detection and synthesizatlon of these elements began in the latter part of 1960's as a result of the theoretical predictions [23] for their localization around the doubly magic nucleus 292[H4]. So predictions given by Myers and Swiateckl [24], Strutlnsky [25], Meldner *.26], Nilsson [27], N1x [28] and their - 3 - co-workers, have given the naif-lives we can expect for the nuclei from the island of stability arcund element 114. They rar.qe in 9 294 this island as high as 10 years e.g. for 110 . Another .-.land of stability has been predicted 1291 to exist around element V21164 1. The continuing progress "n synthesis and study of the pro­ perties of the heaviest nuclei 130-33: demands further improvements in the theoretical predictions of these r;UCiiJes. Various methods of calculations of the ground state o.t:-rqy and fission barriers and various models for description of the internal structure of these nuclei have been used, leading to many different estimates of their lifetime [see e.g. reviews |36-39)| . Most searches for SHE's in nature and at heavy ion accelerators have used spontaneous fission as detection methods Isee e .q . ref. [35]] . This is because of extreme sensitivity ana iow b-trkground offered by this method and the expectation that superheavy nuclei will either decay by spontaneous fission themselves or at least r!<-cay by another nuclide which will decay by spontaneous fission. 1,'nfor tunatel y to date no superheavy elements have been discovered. Several possible reasons why SHE's have not been synthesized and/or identified using heavy ion reactioni are analysed in ref. 140]. Here, we analyse in more detail the possibility of the competition between the spontaneous pion emission and the sponta­ neous fission in the decay of superheavy elements suggested in refs. [5,12], As we can see in Section 4, this new hypothesis can explain why the efforts to synthesize and identify superheavy elements using heavy-.on reactions have been unsuccessful up to present time. - 4 - The ground state pion radioactivity is energetically pos­ sible only accompanied by the spontaneous fission of the parent nucleus. Hence, we start our discussion with the following nuclear reaction: (A,Z) > •: • (Aj. Zj) + (A2, Z2) (2.1a) with A = AL + A2, Z = Z^ + Z, + Z2 (2.1b) where A, A,, A- and Z, Z., Z2 are the usual mass numbers and charge numbers of the involved nuclei, while Z« denotes the pion charge. If the nuclear masses: H(A,Z) - M, M(A.,Z.) = n., i = 1,2, and also the pion rest mass m , are given in units of energy, then the total energy liberated in the reaction (2.1a,b) is given by Q = M - m, - m0 - m = Q0 - m = LW - m, - m0 - m (2.2) v XTI 1 2 ^ 2 ^ 1 2 TI ' where .'-M , Am-, i = 1,2,are the nuclear mass decrements. Here, usinq the nuclear masses from ref. 1411 we calculate the Q , when the .i° emission is accompanied by symmetric fission rr (A1 = A2 = A/2, Zj = Z2 = Z/2) for the heavy nuclei with even Z = 106 T 108 and A = 251 r ?10. The results for Q are given in Table 1. 3. DYNAMICAL THRESHOLDS FOR GROUND STATE PION RADIOACTIVITY OF THE SUPERHEAVY NUCLEI A nuclear theory based on an exact Hatniltonian (which includes a complete knowledge of the nuclear constituents and the interconstituents forces) could in principle provide us a complete explanation of all nuclear phenomena i r,c 1 ud 1 ng : fission, alpha emission, etc., and also the ground state pion radioactivity. - 5 - But we do not know all these ingredients in sufficient detail and then it is necessary to replace the exact Hamiltonian with a simpler oae which we can solve. Hence, recently [8-12] assuming that the pionic nuclear radioactivicy is a fission-like process in which EJ|(nF) i E° - ran , E°(*F) " E° (3.1) we introduced the pionic f.ssility parameter E (irF) C x m 2E o Xwc = "^ = r " ,r/ £ (3-2) 2ES(TTF) where E° , =* yZ2/A1/3, E^ = 6A2/3 are the usual Coulomb e**<$H . and the nuclearfctCwjiA, respectively, for the spherical shape corresponding to the parent nucleus. In th€. case r ; ' that the pion rest mass is considered as originated froâ both energies, the electromagnetic and the nuclear one, then we can write •% = mţj + m^ = otm^ + (1 - a)m^ , a ~ m^/m^ , (3.3a) and F F E"C (0) = E£ - an, , E* (0) - E| - (1 - a)*, (3.3b) c s where n, 3 am , m* = (1 -<*)"% are the contributions of the Conlomb energy and the nuclear energy to the pion rest mass. Consequently we obtain the following general definition of the w- fissilUy parameter F Ej (0) E° - «m, (3#4) X* F * r»Fr 2E* (0) 2lE|-(l-a)m1tl - 6 - This is the essential parameter for the discussion of the nuclear stability with the respect to the * - fission just as in case of usu:al fission. Indeed, assuming that we si ightly deform a spherical parent nucleus into an elipsoidal one with the aid of a small symmetrical distortion of eP2(cos 8) type, then it can be shown that F F 2 Ec (c) = E£ (0) II - I E + hioher powers of e] (3.5») ESF(G) = ESF(°* ll + I e2 * ni1ner powers of e] (3.5b) and therefore the total change of energy is qiven by F F AE^ = AEJ • AEj = F 2 F - Y- C<(0) - Ej (0)] - | e E; (0) 11 - Xj»>] (3.6) IT F T[ F The AEC and AE$ arr the differences between the Coulomb a'nd the surface energies for the elipsoidal and for the spherical configurations, while x|p' is the n - fissility parameter defined by eq.