COMPETITION OF ALPHA DECAY AND HEAVY PARTICLE DECAY IN SUPERHEAVY NUCLEI Dorin N. POENARU, Radu A. GHERGHESCU, Walter GREINER National Institute of Physics and Nuclear Engineering (IFIN-HH), Bucharest-Magurele, Romania and Frankfurt Institute for Advanced Studies (FIAS), J W Goethe University, Frankfurt am Main, Germany CLUSTER C D Dorin N. POENARU, IFIN-HH DECAYS 18th Nuclear Physics Workshop Maria and Pierre Curie, 28 Sept - 02 Oct 2011, Kazimierz Dolny, Poland – 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. KTUY05 and FRDM95 α -decay and HPR of heaviest superheavies Results within ASAF , UNIV and semFIS Summary CLUSTER C D Dorin N. POENARU, IFIN-HH DECAYS 18th Nuclear Physics Workshop Maria and Pierre Curie, 28 Sept - 02 Oct 2011, Kazimierz Dolny, Poland – 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. CLUSTER C D Dorin N. POENARU, IFIN-HH DECAYS 18th Nuclear Physics Workshop Maria and Pierre Curie, 28 Sept - 02 Oct 2011, Kazimierz Dolny, Poland – p.3/34
Intersected spheres Two intersected spheres. Volume conservation and R 1 R 2 R 2 = const. One deformation parameter: separa- tion distance R. Surface equation ρ = ρ ( z ) . Initial R i = R 0 − R 2 . Touching point R t = R 1 + R 2 . 0 R (R-R i )/(R t -R i )=0.25 Example: 232 U → 24 Ne + 208 Pb 1.0 0.50 0.75 1.00 0.8 1.25 Two center shell model (Frankfurt) potential V z / V 0 0.6 0.4 (R-R i )/R ti =0 0.25 0.50 0.75 1.00 1.25 0.2 0.0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 Sequence of shapes z / R 0 CLUSTER C D Dorin N. POENARU, IFIN-HH DECAYS 18th Nuclear Physics Workshop Maria and Pierre Curie, 28 Sept - 02 Oct 2011, Kazimierz Dolny, Poland – 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 0 = ( E s − E 0 s ) + ( E C − E 0 C ) = E 0 s ( B s − 1) + E 0 C ( B C − 1) s = a s (1 − κI 2 ) A 2 / 3 ; I = ( N − Z ) /A ; For spherical shapes E 0 C = a c Z 2 A − 1 / 3 . Nuclear fissility X = E 0 E 0 c / (2 E 0 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 = 3 e 2 / (5 r 0 ) , e 2 = 1 . 44 MeV · fm, r 0 = 1 . 2249 fm. W.D. Myers and W.J. Swiatecki, Nucl. Phys. A 81 (1966) 1 CLUSTER C D Dorin N. POENARU, IFIN-HH DECAYS 18th Nuclear Physics Workshop Maria and Pierre Curie, 28 Sept - 02 Oct 2011, Kazimierz Dolny, Poland – p.5/34
Shell corrections The total energy of the uniform level distribution � ˜ λ u = ˜ U/ � ω 0 ˜ 0 = 2 −∞ ˜ g ( ǫ ) ǫdǫ In units of � ω 0 0 the shell corrections are calculated for each deformation ε n � δu ( n, ε ) = 2 ǫ i ( ε ) − ˜ u ( n, ε ) i =1 n = N p / 2 particles. Then δu = δu p + δu n . CLUSTER C D Dorin N. POENARU, IFIN-HH DECAYS 18th Nuclear Physics Workshop Maria and Pierre Curie, 28 Sept - 02 Oct 2011, Kazimierz Dolny, Poland – p.6/34
Pairing corrections The gap ∆ and Fermi energy λ are solutions of the BCS eqs: k f k f ǫ k − λ 2 1 � � 0 = ( ǫ k − λ ) 2 + ∆ 2 ; G = ( ǫ k − λ ) 2 + ∆ 2 � � k i k i � � g (˜ 2 2Ω k i = Z/ 2 − n + 1 , k f = Z/ 2 + n ′ , G ≃ 2˜ λ ) ln . ˜ ∆ The pairing correction δp = p − ˜ p , represents the difference between the pairing correlation energies for the discrete level distribution p = � k f k ǫ k − 2 � Z/ 2 k = k i ǫ k − ∆ 2 k = k i 2 v 2 G and for the continuous level g ˜ g s ˜ ∆ 2 ) / 2 = − (˜ ∆ 2 ) / 4 . Compared to shell correction, distribution ˜ p = − (˜ the pairing correction is out of phase and smaller. One has again δp = δp p + δp n , and δe = δu + δp . CLUSTER C D Dorin N. POENARU, IFIN-HH DECAYS 18th Nuclear Physics Workshop Maria and Pierre Curie, 28 Sept - 02 Oct 2011, Kazimierz Dolny, Poland – p.7/34
Example: Na 148 atomic cluster -0.5 0.0 0.5 1.0 1.5 E LD 22 E v = − 333 eV was not included E E LD , E (eV) in E LD and E . Liquid drop and 20 total deformation energy (top). Shell plus pairing corrections for 18 hemispheroidal harmonic oscil- U 2 E (eV) P lator energy levels (bottom). E 1 Smoothing effect of pairing. P , 0 Ground state shape prolate U , δ = 0 . 47 -1 N = 148 Semiaxes ratio a c = 2 − δ -0.5 0.0 0.5 1.0 1.5 2+ δ CLUSTER C D Dorin N. POENARU, IFIN-HH DECAYS 18th Nuclear Physics Workshop Maria and Pierre Curie, 28 Sept - 02 Oct 2011, Kazimierz Dolny, Poland – p.8/34
222 Ra E Y + EM , δE shell + pair , E def PES δ E sh+p (MeV) 40 E def (MeV) 5 20 0 0 -5 -20 0 η ξ 0.5 00.5 11.5 2 0.5 0 1 -0.5 η 0.5 ξ 0 -0.5 E Y+E (MeV) separation distance 20 0 ξ = ( R − R i ) / ( R t − R i ) -20 mass asymmetry -40 0 0.5 1 η η = ( A 1 − A 2 ) / ( A 1 + A 2 ) ξ 1.5 0.5 0 -0.5 Poenaru, Gherghescu, W.Greiner, Phys. Rev. C 73 (2006) 014608 CLUSTER C D Dorin N. POENARU, IFIN-HH DECAYS 18th Nuclear Physics Workshop Maria and Pierre Curie, 28 Sept - 02 Oct 2011, Kazimierz Dolny, Poland – p.9/34
Basic relationships Parent → emitted ion + daughter nucleus, A Z → A e Z e + A d Z d Measurable quantities Kinetic energy of the emitted cluster E k = QA 1 /A or the released energy Q = M − ( M e + M d ) > 0 . Decay constant λ = ln 2 /T or Half-life ( T < 10 32 s) or branching ratio b α = T α /T ( b α > 10 − 17 ) Model dependent quantities ( λ = νSP s ) ν frequency of assaults or E v = hν/ 2 S preformation probability P s penetrability of external barrier CLUSTER C D Dorin N. POENARU, IFIN-HH DECAYS 18th Nuclear Physics Workshop Maria and Pierre Curie, 28 Sept - 02 Oct 2011, Kazimierz Dolny, Poland – p.10/34
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 � R t K ov = 2 � 2 B ( R ) E ( R ) dR � R i E – Potential barrier B = µ – Nuclear inertia = reduced mass for R ≥ R t CLUSTER C D Dorin N. POENARU, IFIN-HH DECAYS 18th Nuclear Physics Workshop Maria and Pierre Curie, 28 Sept - 02 Oct 2011, Kazimierz Dolny, Poland – p.11/34
Unified approach: CF; HPR, and α -d ASAF -15 24 Ne 28 Mg 100 Zr -20 - log 10 T(s) -25 -30 -35 -40 0 20 40 60 80 100 120 140 160 180 200 220 A e 234 U half-lives spectrum Three valleys: cold-fission (almost sym- metrical); 16 O radioactivity, and α -decay (short T up) CLUSTER C D Dorin N. POENARU, IFIN-HH DECAYS 18th Nuclear Physics Workshop Maria and Pierre Curie, 28 Sept - 02 Oct 2011, Kazimierz Dolny, Poland – p.12/34
Experimental confirmations Rare events in a strong background of α particles 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 (2007) 301. CLUSTER C D Dorin N. POENARU, IFIN-HH DECAYS 18th Nuclear Physics Workshop Maria and Pierre Curie, 28 Sept - 02 Oct 2011, Kazimierz Dolny, Poland – p.13/34
Systematics T 1 / 2 : 14 C, 18 , 20 O, 23 F rad. 218 220 222 224 226 224 226 228 230 24 30 new candidate new confirm 22 28 log 10 T(s) 20 26 Calculated lines 18 24 Rn Ra 16 22 within ASAF model Fr Ac 20 14 Ra Th 14 C 18 O Ac Pa 12 18 and exp. points Th U 10 16 218 220 222 224 226 224 226 228 230 32 32 30 30 28 28 Ac 26 26 Z d = 80 Ra Th Ac Z d = 81 24 24 Pa Th 20 O 23 F Z d = 82 U 22 Pa 22 Np U Z d = 83 20 20 Z d = 84 224 226 228 230 232 226 228 230 232 234 A new confirm — A. Guglielmetti et al., J Phys: Conf Ser 111 (2008) 012050 One of the new candidates from our paper: Poenaru, Nagame, Gherghescu, W. Greiner Phys. Rev. C 65 (2002) 054308. CLUSTER C D Dorin N. POENARU, IFIN-HH DECAYS 18th Nuclear Physics Workshop Maria and Pierre Curie, 28 Sept - 02 Oct 2011, Kazimierz Dolny, Poland – p.14/34
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