UNEXPECTED STRONG DECAY MODE OF SUPERHEAVY NUCLEI
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1 UNEXPECTED STRONG DECAY MODE OF SUPERHEAVY NUCLEI Dorin N. POENARU, Radu A. GHERGHESCU, Walter GREINER Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), Bucharest-Magurele, Romania and Frankfurt Institute for Advanced Studies (FIAS), J W Goethe University, Frankfurt am Main, Germany Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.1/34
2 OUTLINE Macroscopic-microscopic method Unified approach of cold fission, α-decay and heavy particle radioactivities (HPR) within ASAF model Experimental confirmations New mass table Audi & Meng. KTUY5 and FRDM95 α-decay and HPR of heaviest superheavies Results within ASAF, UNIV and semfis Summary Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.2/34
3 Macroscopic-microscopic method Accounting for quantum single-particle structure and classical collective properties. Liquid Drop Model: E LD Single-particle shell model (SPSM): energy levels vs. deformation. Two-center shell model for fission and fusion. Shell correction method: δe = δu +δp Total deformation energy: E def = E LD +δe The potential of SPSM Hamiltonian should admit the drop eq. ρ = ρ(z) as an equipotential surface. Semi-spheroidal shape, allows to obtain analytical results for atomic clusters on a surface. Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.3/34
4 Intersected spheres R 1 R R 2 Two intersected spheres. Volume conservation and R 2 = const. One deformation parameter: separation distance R. Surface equation ρ = ρ(z). Initial R i = R R 2. Touching point R t = R 1 +R 2. Example: 232 U 24 Ne + 8 Pb Two center shell model (Frankfurt) potential V z / V (R-R i )/(R t -R i )= (R-R i )/R ti = Sequence of shapes z / R Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.4/34
5 Liquid drop model Nucleus considered a uniformly charged drop. Two variants: LDM and Yukawa-plus-exponential (Y+EM). LDM (surface + Coulomb) deformation energy E LDM = E E = (E s E s)+(e C E C) = E s(b s 1)+E C(B C 1) For spherical shapese s = a s (1 κi 2 )A 2/3 ; I = (N Z)/A; E C = a cz 2 A 1/3. Nuclear fissility X = E c/(2e s). Parameters obtained by fit to experimental data on nuclear masses, quadrupole moments and fission barriers: a s = MeV, κ = , a c = 3e 2 /(5r ), e 2 = 1.44 MeV fm, r = fm. W.D. Myers and W.J. Swiatecki, Nucl. Phys. A 81 (1966) 1 Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.5/34
6 Shell corrections The total energy of the uniform level distribution ũ = Ũ/ ω = 2 λ g(ǫ)ǫdǫ In units of ω the shell corrections are calculated for each deformation ε δu(n,ε) = n i=1 2ǫ i (ε) ũ(n,ε) n = N p /2 particles. Then δu = δu p +δu n. Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.6/34
7 Pairing corrections The gap and Fermi energyλare solutions of the BCS eqs: = k f k i ǫ k λ (ǫk λ) ; 2 G = k f 1 (ǫk λ) k i 2 g( λ)ln( ) k i = Z/2 n+1, k f = Z/2+n 2, G 2Ω. The pairing correction δp = p p, represents the difference between the pairing correlation energies for the discrete level distribution p = k f k=k i 2vk 2ǫ k 2 Z/2 k=k i ǫ k 2 G and for the continuous level distribution p = ( g 2 )/2 = ( g 2 s )/4. Compared to shell correction, the pairing correction is out of phase and smaller. One has again δp = δp p +δp n, andδe = δu+δp. Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.7/34
8 Example: Na 148 atomic cluster E LD, E (ev) U, P, E (ev)2 N = 148 E LD E U P E E v = 333 ev was not included in E LD and E. Liquid drop and total deformation energy (top). Shell plus pairing corrections for hemispheroidal harmonic oscillator energy levels (bottom). Smoothing effect of pairing. Ground state shape prolate δ =.47 Semiaxes ratio a c = 2 δ 2+δ Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.8/34
9 222 Ra E Y+EM, δe shell+pair,e def PES δe sh+p (MeV) 5-5 ξ η E def (MeV) ξ η E Y+E (MeV) ξ η separation distance ξ = (R R i )/(R t R i ) mass asymmetry η = (A 1 A 2 )/(A 1 +A 2 ) Poenaru, Gherghescu, W.Greiner, Phys. Rev. C 73 (6) 1468 Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.9/34
10 Basic relationships Parent emitted ion + daughter nucleus, A Z A e Z e + A d Zd Measurable quantities Kinetic energy of the emitted cluster E k = QA 1 /A or the released energy Q = M (M e +M d ) >. Decay constant λ = ln2/t or Half-life (T < 32 s) or branching ratio b α = T α /T (b α > 17 ) Model dependent quantities (λ = νsp s ) ν frequency of assaults ore v = hν/2 S preformation probability P s penetrability of external barrier Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p./34
11 Fission theory Shape parameters: fragment separation, R, and mass asymetry η = (A d A e )/A. Our method to estimate preformation as penetrability of internal barrier: S = exp( K ov ). DNP, WG, Physica Scripta 44 (1991) 427. Similarly P = exp( K s ) for external barrier. Action integral calculated within Wentzel-Kramers-Brillouin (WKB) quasiclasical approximation E Potential barrier K ov = 2 Rt R i 2B(R)E(R)dR B = µ Nuclear inertia = reduced mass for R R t Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.11/34
12 Unified approach: CF; HPR, andα-d ASAF 24 Ne 28 Mg Zr - log T(s) A e Three valleys: cold-fission (almost symmetrical); 16 O radioactivity, andα-decay 234 U half-lives spectrum (short T up) Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.12/34
13 Fine structure of 14 C radioactivity Martin Greiner and Werner Scheid, Radioactive decay into excited states via heavy ion emission, J. Phys. G: Nucl. Phys. 12 (1986) L229. Experiments with SOLENO spectrometer at Orsay, France: E. Hourany, M. Hussonnois et al., C. R. Acad. Sci. Paris 39 (1989) 15. E. Hourany et al., Phys. Rev. C 52 (1995) 267: the transition from the gs of 223 Ra to the first excited state of the daughter 9 Pb is stronger than that to its gs. A transition with an excited state of 14 C was not observed. Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.13/34
14 Prediction of heavy ion radioactivity.5ln e P 198 PREDIC: 14 ECAY of 222,224 Ra AS, DNP, WG, Part Nucl 11 (198) C The New Encyclopaedia Britannica: Heavyion radioactivity. In 198 A. Sandulescu, D.N. Poenaru, and W. Greiner described calculations indicating the possibility of a new type of decay of heavy nuclei intermediate between alpha decay and spontaneous fission. The first observation of heavy-ion radioactivity A e was that of a 3-MeV carbon-14 emission from radium-223 by H.J. Rose and G.A. Jones in Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.14/34
15 Experimental confirmations Rare events in a strong background ofαparticles Detectors: Semiconductor telescope + electronics Magnetic spectrometers (SOLENO, Enge split-pole) Solid state nuclear track det. (SSNTD). Cheap and handy. Need to be chemically etched then follows microscope scanning Experiments performed in Universities and Research Institutes from: Oxford; Moscow; Orsay; Berkeley; Dubna; Argonne; Livermore; Geneva; Milano; Vienna, and Beijing. Table: R. Bonetti and A. Guglielmetti, Rom. Rep. Phys. 59 (7) 31. Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.15/34
16 SystematicsT 1/2 : 14 C, 18, O, 23 F rad new candidate new confirm 3 28 log T(s) Rn Fr Ra Ac Th C 18 O Ra Ac Th Pa U Calculated lines within ASAF model and exp. points O Ra Ac Th Pa U F Ac Th Pa U Np A Z d = 8 Z d = 81 Z d = 82 Z d = 83 Z d = 84 new confirm A. Guglielmetti et al., J Phys: Conf Ser 111 (8) 15 One of the new candidates from our paper: Poenaru, Nagame, Gherghescu, W. Greiner Phys. Rev. C 65 (2) Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.16/34
17 SystematicsT 1/2 : 22,24,25,26 Ne rad. log T(s) Ne Pu Ne new candidate lower limit Th Pa U Np Pu Th Pa U Np Ne Ne A Only lower limits for 18 O and 26 Ne Th Pa U Np Pu Th Pa U Np Pu Z d = 8 Z d = 81 Z d = 82 Z d = 83 Z d = 84 Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.17/34
18 SystematicsT 1/2 : 28,3 Mg, 32,34 Si rad. log T(s) new candidate lower limit 28 Mg U Np Pu Am Cm Mg U Np Pu Am Cm Minima at N d = 126 Strong shell effect Even-odd staggering Si Pu Am Cm Bk Cf Si Pu Am Cm Bk Cf A Z d = 8 Z d = 81 Z d = 82 Z d = 83 Z d = 84 Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.18/34
19 New table of experimental masses PROTON NUMBER nuclei, 2377 measured and 913 det. from Systematics. G. Audi, W Meng, Private communication 2 NEUTRON NUMBER 11. Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.19/34
20 KTUY5 Calculated Masses N=162-, Z= nuclei with Z=2-13 and N=2-. H. Koura, T. Tachibana, M. Uno and M. Yamada, Prog. Theor. Phys. 113 (5) 35. Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p./34
21 FRDM95 Calculated Masses N=17-214, Z= nuclei with Z=8-136 and N= P. Möller, J.R. Nix, W.D. Myers, W.J. Swiatecki, At. Data Nucl.Data Tables 59 (1995) 185. Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.21/34
22 Examples of time spectra (I) 222 Ra - log T (s) α 14 C - log T (s) α 223 Ra 14 C - log T (s) α 232 U 24 Ne N e Z e -3 N e Z e -3 N e Z e Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.22/34
23 Examples of time spectra (II) - log T c (s) Be C 15 N 16 O e 14 Ce 222 Ra e Be C Ni Zn Ge Se Kr Sr A e even A e Ge + 8 Pb. D.N. Poenaru, R.A. Gherghescu, W. Greiner, Phys. Rev. Lett. 7 (11) Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.23/34
24 SHs as cluster emitters. AME11 Emitted Heavy Particles Be C Ne Mg Si P S Cl Ar Ca Sc Ti V Cr Mn Fe Ni Cu Zn Ga Ge As Se Br Kr Z = 1 N = 184 Z = New concept: for Z > 1, Z e > 28, daughter around 8 Pb. D.N. Poenaru, R.A. Gherghescu, W. Greiner, Phys. Rev. Lett. 7 (11) Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.24/34
25 SHs as cluster emitters. FRDM95 EMITTED S Be Ar Ca Ti V Cr Mn Fe Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Z = 1 N = 184 Z = Z e Z 8 (freq. daughter around 8 Pb) Most probable emitted clusters with different colors. Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.25/34
26 HIR of SH nuclei (I) log T c (s) N AME11 KTUY5 - Half-lives log b AME11 KTUY N Branching ratios Branching ratio with respect to α decay: b α = T α /T c. Usually b α << 1. Trend: shorter T c and larger b α. For larger Z > 1 there are SHs with T c < 1 ns and b α > 1. Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.26/34
27 HIR of SH nuclei (II) e-e o-e e-e o-e 3 log T c (s) - - log T c (s) e-o o-o e-o o-o N KTUY N FRDM95 Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.27/34
28 HIR of SH nuclei (III) log b e-e e-o o-e o-o N KTUY log b e-e e-o o-e o-o N FRDM Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.28/34
29 Universal curves (I) Approximations: logs = [(A e 1)/3]logS α, ν(a e,z e,a d,z d ) = constant. From fit to α decay: S α = and ν = 22.1 s 1. logt = logp (A e 1) logp = c AZ [arccos r ] r(1 r) c AZ =.22873(µ A Z d Z e R b ) 1/2, r = R t /R b, R t = (A 1/3 d + A 1/3 e ), R b = Z d Z e /Q, and µ A = A d A e /A. DN Poenaru, W Greiner, Physica Scripta 44 (1991) 427. Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.29/34
30 Universal curves (II) Log of half-life in sec decay 14 C O 24 Ne 28 Mg 32 Si Log P s -decay 22 Ne 26 Ne 3 Mg 34 Si log T(s) C O 23 F 22 Ne 24 Ne 25 Ne 26 Ne Mg 3 Mg 32 Si 34 Si Log P s Q -1/2 (MeV -1/2 ) log P s Geiger-Nuttal plot T α = f(range of α in air) logt = f(1/q 1/2 ) Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.3/34
31 Single Universal curve: α and HIR log T(s) + log S C O 23 F 22 Ne 24 Ne 25 Ne 26 Ne 28 Mg 3 Mg 32 Si 34 Si log P s log T(s) + log S decay m. ee, eo, oe p. 16 decay m. ee parents log P s 14 C O 23 F 22 Ne 24 Ne 25 Ne 26 Ne 28 Mg 3 Mg 32 Si 34 Si D.N. Poenaru, R.A. Gherghescu, W. Greiner, Phys. Rev. C, 83 (11) Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.31/34
32 UNIV and UDL curve for e-e nuclei log T(s) - b (s) UDL =.329 c UDL = (MeV -1/2 ) log T UDL /T exp log T(s) + log S UNIV =.354 h ee =.3 log T UNIV / T exp log P s N Vertical bars: N = 5,82,126,152,162,172 UDL: C. Qi, F.R. Xu, R.J. Liotta, R. Wyss Phys. Rev. Lett. 3 (9) Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.32/34
33 Compare UNIV, UDL, semfis forαdecay Standard deviations of logt values of semfis, UNIV and UDL formulae for 173 even-even, 134 even-odd, 123 odd-even, and 4 odd-odd α emitters with atomic numbers Z = n σ UNIV h UNIV σ UDL c UDL σ SEM σ = { n i=1 [log(t i/t exp )] 2 /(n 1) } 1/2 Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.33/34
34 Summary ASAF model predictions have been confirmed for parent nuclei with Z = The magicity of the daughter 8 Pb was not fully exploited: new experimental searches can be performed The ASAF, semfis and universal curves UNIV and UDL provide good estimation of half-lives For some superheavies HIR half-lives could be shorter than that of α decay Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.34/34
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