UNEXPECTED STRONG DECAY MODE OF SUPERHEAVY NUCLEI

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

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

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

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 1..8.6.4 (R-R i )/(R t -R i )=.25.5.75 1. 1.25 (R-R i )/R ti =.25.5.75 1. 1.25.2 Sequence of shapes. -1. -.5..5 1. 1.5 2. z / R Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.4/34

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 = 17.9439 MeV, κ = 1.7826, a c = 3e 2 /(5r ), e 2 = 1.44 MeV fm, r = 1.2249 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

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

Pairing corrections The gap and Fermi energyλare solutions of the BCS eqs: = k f k i ǫ k λ (ǫk λ) 2 + 2 ; 2 G = k f 1 (ǫk λ) k 2 + 2 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

Example: Na 148 atomic cluster -.5..5 1. 1.5 E LD, E (ev) 22 18 1-1 U, P, E (ev)2 N = 148 E LD E -.5..5 1. 1.5 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

222 Ra E Y+EM, δe shell+pair,e def PES δe sh+p (MeV) 5-5 ξ.5 1 -.5.5 η E def (MeV) 4 -.5 11.5 2 -.5.5 ξ η E Y+E (MeV) - -4.5 11.5 -.5.5 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

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

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

Unified approach: CF; HPR, andα-d -15 - ASAF 24 Ne 28 Mg Zr - log T(s) -25-3 -35-4 4 6 8 1 14 16 18 2 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

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

Prediction of heavy ion radioactivity.5ln e P 198 PREDIC: 14 ECAY of 222,224 Ra AS, DNP, WG, Part Nucl 11 (198) 528 14 C -3-4 -5 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 -6 4 6 4 6 A e was that of a 3-MeV carbon-14 emission from radium-223 by H.J. Rose and G.A. Jones in 1984. http://www.britannica.com/ebchecked/topic/465998/ Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.14/34

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

SystematicsT 1/2 : 14 C, 18, O, 23 F rad. 218 2 222 224 226 224 226 228 23 24 22 new candidate new confirm 3 28 log T(s) 18 16 14 12 Rn Fr Ra Ac Th 218 2 222 224 226 14 C 18 O 224 226 228 23 Ra Ac Th Pa U 26 24 22 18 16 Calculated lines within ASAF model and exp. points 32 32 3 3 28 28 26 24 22 O Ra Ac Th Pa U 224 226 228 23 232 23 F Ac Th Pa U Np 226 228 23 232 234 A 26 24 22 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) 5438. Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.16/34

SystematicsT 1/2 : 22,24,25,26 Ne rad. log T(s) 3 28 26 24 22 22 24 Ne Pu Ne 18 226 228 23 232 234 228 23 232 234 236 34 32 3 28 26 226 228 23 232 234 new candidate lower limit Th Pa U Np Pu Th Pa U Np 24 25 Ne 22 228 23 232 234 236 228 23 232 234 236 26 Ne 228 23 232 234 236 A Only lower limits for 18 O and 26 Ne Th Pa U Np Pu Th Pa U Np Pu 3 28 26 24 22 18 34 32 3 28 26 24 22 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

SystematicsT 1/2 : 28,3 Mg, 32,34 Si rad. log T(s) 32 3 28 26 24 22 18 232 234 236 238 24 new candidate lower limit 28 Mg U Np Pu Am Cm 232 234 236 238 24 234 236 238 24 242 3 Mg U Np Pu Am Cm 234 236 238 24 242 32 3 28 26 24 22 18 Minima at N d = 126 Strong shell effect Even-odd staggering 3 3 28 28 26 26 24 22 18 32 Si Pu Am Cm Bk Cf 236 238 24 242 244 34 Si Pu Am Cm Bk Cf 238 24 242 244 246 A 24 22 18 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

New table of experimental masses 126 162 1 152 PROTON NUMBER 82 126 82 8 184 329 nuclei, 2377 measured and 913 det. from 28 5 5 Systematics. G. Audi, W. 2 8 8 28 Meng, Private communication 2 NEUTRON NUMBER 11. Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.19/34

KTUY5 Calculated Masses N=162-, Z=1-122 9441 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

FRDM95 Calculated Masses N=17-214, Z=1-122 8979 nuclei with Z=8-136 and N=8-236. 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

Examples of time spectra (I) 222 Ra - log T (s) -5 - -15 - α 14 C - log T (s) - -15 - α 223 Ra 14 C - log T (s) - -15 - α 232 U 24 Ne -25-25 -25-3 N e 5 2 4 6 8 Z e -3 N e 5 2 4 6 8 Z e -3 N e 5 15 5 Z e Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.22/34

Examples of time spectra (II) - log T c (s) -5 - -15-4 Be C 15 N 16 O e 14 Ce 222 Ra 288 114 e Be C Ni Zn Ge Se Kr Sr -25 3 4 5 A e 4 6 8 even A e 288 114 8 Ge + 8 Pb. D.N. Poenaru, R.A. Gherghescu, W. Greiner, Phys. Rev. Lett. 7 (11) 6253. Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.23/34

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 = 94 118. 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) 6253. Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.24/34

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 = 4 118. 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

HIR of SH nuclei (I) log T c (s) 3-15 16 17 15 16 17 18 19 N 4 6 8 1 112 114 116 118 1 122 124 AME11 KTUY5 - Half-lives log b 5-5 - -15 AME11 KTUY5 15 16 17 15 16 17 18 19 N Branching ratios 4 6 8 1 112 114 116 118 1 122 124 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

HIR of SH nuclei (II) 15 16 17 18 19 3 e-e 17 18 19 o-e 3 3 16 18 2 e-e 16 18 2 o-e 3 log T c (s) - - log T c (s) - - - 3 - - e-o 1 112 114 116 118 1 122 124 126 o-o 111 113 115 117 119 121 123 125-3 - - - 3 - - e-o 1 112 114 116 118 1 122 124 126 o-o 111 113 115 117 119 121 123 125-3 - - 15 16 17 18 19 17 18 19 N KTUY5 16 18 2 16 18 2 N FRDM95 Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.27/34

HIR of SH nuclei (III) 15 16 17 18 19 17 18 19 16 18 2 16 18 2 log b 15 5-5 - -15-15 5-5 - -15 - e-e e-o 15 16 17 18 19 1 112 114 116 118 1 122 124 126 o-e o-o 17 18 19 N KTUY5 111 113 115 117 119 121 123 125 15 5-5 - -15-15 5-5 - -15 - log b - - - - e-e e-o 16 18 2 1 112 114 116 118 1 122 124 126 o-e o-o 16 18 2 N FRDM95 111 113 115 117 119 121 123 125 - - - - Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.28/34

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 =.16694 and ν = 22.1 s 1. logt = logp 22.169+.598(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 = 1.2249(A 1/3 d + A 1/3 e ), R b = 1.43998Z 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

Universal curves (II) Log of half-life in sec. 3 25 15 3 25 3 35 4 -decay 14 C O 24 Ne 28 Mg 32 Si 25 3 35 4 - Log P s -decay 22 Ne 26 Ne 3 Mg 34 Si 3 25 15 3 log T(s) 3 25 15 25 15 14 C O 23 F 22 Ne 24 Ne 25 Ne 26 Ne 25 28 Mg 3 Mg 32 Si 34 Si 15 3 4 - Log P s.4.5.6.7 Q -1/2 (MeV -1/2 ) 25 3 35 25 3 35 25 3 35 25 3 35 4 - 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

Single Universal curve: α and HIR log T(s) + log S 15 5-5 - 14 C O 23 F 22 Ne 24 Ne 25 Ne 26 Ne 28 Mg 3 Mg 32 Si 34 Si 15 25 3 35 4 45 5 - log P s log T(s) + log S 14 12 8 6 4 2 14 12 8 6 4 2 26 28 3 32 34 36 27 decay m. ee, eo, oe p. 16 decay m. ee parents 26 28 3 32 34 36 -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) 1461. Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.31/34

UNIV and UDL curve for e-e nuclei log T(s) - b (s) 45 4 35 3 25 15 UDL =.329 c UDL =-.796 1 1 13 14 15 16 (MeV -1/2 ) log T UDL /T exp 1..5. -.5-1. log T(s) + log S 15 5-5 UNIV =.354 h ee =.3 log T UNIV / T exp 1..5. -.5-1. 15 25 3 35 4 -log P s 6 8 1 14 16 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) 7251. Symposium on Exciting Physics, Makutsi Safari Farm, South Africa, 13- November 11 p.32/34

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 = 52 118. n σ UNIV h UNIV σ UDL c UDL σ SEM 173.354.3.329.796.222 134.64.528.66.327.51 123.565.379.538.481.434 4.826.961.84 19.94.567 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

Summary ASAF model predictions have been confirmed for parent nuclei with Z = 87 96 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