COMPETITION OF ALPHA DECAY AND HEAVY PARTICLE DECAY IN SUPERHEAVY - - PowerPoint PPT Presentation

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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

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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

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Macroscopic-microscopic method

Accounting for quantum single-particle structure and classical collective properties. Liquid Drop Model: ELD 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: Edef = ELD + 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.

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Intersected spheres

R R1 R2

Two intersected spheres. Volume conservation and R2 = const. One deformation parameter: separa- tion distance R. Surface equation ρ = ρ(z). Initial Ri = R0 − R2. Touching point Rt = R1 + R2. Example: 232U → 24Ne + 208Pb Two center shell model (Frankfurt) potential

(R-Ri)/Rti=0 0.25 0.50 0.75 1.00 1.25

Sequence of shapes

• 1.0
• 0.5

0.0 0.5 1.0 1.5 2.0

z / R0

0.0 0.2 0.4 0.6 0.8 1.0

Vz / V0

1.25 1.00 0.75 0.50 (R-Ri)/(Rt-Ri)=0.25

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Liquid drop model

Nucleus considered a uniformly charged drop. Two variants: LDM and Yukawa-plus-exponential (Y+EM). LDM (surface + Coulomb) deformation energy ELDM = E − E0 = (Es − E0

s) + (EC − E0 C)

= E0

s(Bs − 1) + E0 C(BC − 1)

For spherical shapes E0

s = as(1 − κI2)A2/3 ; I = (N − Z)/A;

E0

C = acZ2A−1/3 . Nuclear fissility X = E0 c/(2E0 s). Parameters obtained by fit to experimental data on nuclear masses, quadrupole moments and fission barriers: as = 17.9439 MeV, κ = 1.7826, ac = 3e2/(5r0), e2 = 1.44 MeV·fm, r0 = 1.2249 fm.

W.D. Myers and W.J. Swiatecki, Nucl. Phys. A 81 (1966) 1

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Shell corrections

The total energy of the uniform level distribution ˜ u = ˜ U/ω0

0 = 2

˜

λ −∞ ˜

g(ǫ)ǫdǫ In units of ω0

0 the shell corrections are calculated for each

deformation ε δu(n, ε) =

n

• i=1

2ǫi(ε) − ˜ u(n, ε) n = Np/2 particles. Then δu = δup + δun.

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Pairing corrections

The gap ∆ and Fermi energy λ are solutions of the BCS eqs: 0 =

kf

• ki

ǫk − λ

• (ǫk − λ)2 + ∆2 ;

2 G =

kf

• ki

1

• (ǫk − λ)2 + ∆2

ki = Z/2 − n + 1, kf = Z/2 + n′,

2 G ≃ 2˜

g(˜ λ) ln

• 2Ω

˜ ∆

• .

The pairing correction δp = p − ˜ p, represents the difference between the pairing correlation energies for the discrete level distribution p = kf

k=ki 2v2 kǫk − 2 Z/2 k=ki ǫk − ∆2 G and for the continuous level

distribution ˜ p = −(˜ g ˜ ∆2)/2 = −(˜ gs ˜ ∆2)/4. Compared to shell correction, the pairing correction is out of phase and smaller. One has again δp = δpp + δpn, and δe = δu + δp.

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Example: Na148 atomic cluster

• 0.5

0.0 0.5 1.0 1.5

• 1

1 2

U , P , E (eV)

E P U 18 20 22

ELD , E (eV)

• 0.5

0.0 0.5 1.0 1.5 E ELD

N = 148

Ev = −333 eV was not included in ELD and E. Liquid drop and total deformation energy (top). Shell plus pairing corrections for hemispheroidal harmonic oscil- lator energy levels (bottom). Smoothing effect of pairing. Ground state shape prolate δ = 0.47 Semiaxes ratio a

c = 2−δ 2+δ

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222Ra EY +EM, δEshell+pair, Edef PES

0.5 1

• 0.5

0.5

• 5

5 ξ δEsh+p (MeV) η 0.5 1 1.5

• 0.5

0.5

• 40
• 20

20 ξ EY+E (MeV) η

00.5 11.5 2

• 0.5

0.5

• 20

20 40 ξ Edef (MeV) η

separation distance ξ = (R − Ri)/(Rt − Ri) mass asymmetry η = (A1 − A2)/(A1 + A2) Poenaru, Gherghescu, W.Greiner, Phys. Rev. C 73 (2006) 014608

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Basic relationships

Parent → emitted ion + daughter nucleus, AZ → AeZe + AdZd Measurable quantities Kinetic energy of the emitted cluster Ek = QA1/A or the released energy Q = M − (Me + Md) > 0. Decay constant λ = ln 2/T or Half-life (T < 1032 s) or branching ratio bα = Tα/T (bα > 10−17) Model dependent quantities (λ = νSPs ) ν frequency of assaults or Ev = hν/2 S preformation probability Ps penetrability of external barrier

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Fission theory

Shape parameters: fragment separation, R, and mass asymetry η = (Ad − Ae)/A. Our method to estimate preformation as penetrability of internal barrier: S = exp(−Kov). DNP, WG, Physica Scripta 44 (1991) 427. Similarly P = exp(−Ks) for external barrier. Action integral calculated within Wentzel-Kramers-Brillouin (WKB) quasiclasical approximation Kov = 2

• Rt

Ri

• 2B(R)E(R)dR

E – Potential barrier B = µ – Nuclear inertia = reduced mass for R ≥ Rt

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Unified approach: CF; HPR, and α-d

20 40 60 80 100 120 140 160 180 200 220

Ae

• 40
• 35
• 30
• 25
• 20
• 15
• log10 T(s)

100Zr 28Mg 24Ne

ASAF

Three valleys: cold-fission (almost sym- metrical); 16O radioactivity, and α-decay

234U half-lives spectrum

(short T up)

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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.

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Systematics T1/2: 14C, 18,20O, 23F rad.

224 226 228 230 232 20 22 24 26 28 30 32

U Pa Th Ac Ra

20O

226 228 230 232 234

A

20 22 24 26 28 30 32

Np U Pa Th Ac

23F

218 220 222 224 226 10 12 14 16 18 20 22 24

log10 T(s)

218 220 222 224 226

Th Ac Ra Fr Rn new confirm new candidate

14C

224 226 228 230 224 226 228 230 16 18 20 22 24 26 28 30

U Pa Th Ac Ra

18O

Calculated lines within ASAF model and exp. points

Zd = 84 Zd = 83 Zd = 82 Zd = 81 Zd = 80

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.

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Systematics T1/2:

22,24,25,26Ne rad.

228 230 232 234 236 22 24 26 28 30 32 34

Pu Np U Pa Th

25Ne

228 230 232 234 236

A

22 24 26 28 30 32 34

Pu Np U Pa Th

26Ne

226 228 230 232 234 18 20 22 24 26 28 30

log10 T(s)

226 228 230 232 234

Pu Np U Pa Th lower limit new candidate

22Ne

228 230 232 234 236 228 230 232 234 236 18 20 22 24 26 28 30

Pu Np U Pa Th

24Ne

Zd = 84 Zd = 83 Zd = 82 Zd = 81 Zd = 80

Only lower limits for 18O and 26Ne

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Systematics T1/2:

28,30Mg, 32,34Si rad.

236 238 240 242 244 18 20 22 24 26 28 30

Cf Bk Cm Am Pu

32Si

238 240 242 244 246

A

18 20 22 24 26 28 30

Cf Bk Cm Am Pu

34Si

232 234 236 238 240 18 20 22 24 26 28 30 32

log10 T(s)

232 234 236 238 240

Cm Am Pu Np U lower limit new candidate

28Mg

234 236 238 240 242 234 236 238 240 242 18 20 22 24 26 28 30 32

Cm Am Pu Np U

30Mg

Minima at Nd = 126 Strong shell effect Even-odd staggering

Zd = 84 Zd = 83 Zd = 82 Zd = 81 Zd = 80

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New table of experimental masses

NEUTRON NUMBER

2 2 8 8 20 20 28 28 50 50 82 82 126 152 162 108 184 126 120

PROTON NUMBER

3290 nuclei, 2377 measured and 913 det. from Systematics. G. Audi, W. Meng, Private communication 2011.

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KTUY05 Calculated Masses

N=162-200, Z=110-122

9441 nuclei with Z=2-130 and N=2-200. H. Koura, T. Tachibana, M. Uno and M. Yamada, Prog. Theor. Phys. 113 (2005) 305.

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FRDM95 Calculated Masses

N=170-214, Z=110-122

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.

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Examples of time spectra (I)

5 10 2 4 6 8

• 30
• 25
• 20
• 15
• 10
• 5

222 Ra Ne Z

e

• log T (s)

14C

α

5 10 2 4 6 8 10

• 30
• 25
• 20
• 15
• 10

223 Ra

Ne Ze

• log T (s)

1 4

C α

5 10 15 5 10

• 30
• 25
• 20
• 15
• 10

232 U

N

e

Ze

• log T (s)

24

N e

α 18th Nuclear Physics Workshop Maria and Pierre Curie, 28 Sept - 02 Oct 2011, Kazimierz Dolny, Poland – p.20/34

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Examples of time spectra (II)

• 25
• 20
• 15
• 10
• 5
• log10 Tc(s)

0 10 20 30 40 50

Ae

4Be

C

15N 16O e 14Ce

20 40 60 80 100

even Ae

e

Be C Ni Zn Ge Se Kr Sr 222Ra 288114 288114 → 80Ge + 208Pb. D.N. Poenaru, R.A. Gherghescu, W.

Greiner, Phys. Rev. Lett. 107 (2011) 062503.

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Superheavies as cluster emitters

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 Emitted Heavy Particles

Z = 120 N = 184

New concept: for Z > 110 Ze > 28 to get a daughter around 208Pb. D.N. Poenaru, R.A. Gherghescu, W. Greiner,

• Phys. Rev. Lett. 107 (2011) 062503.

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HIR of SH nuclei (I)

• 10

10 20 30

log10 Tc(s)

150 160 170 150 160 170 180 190 200

N

104 106 108 110 112 114 116 118 120 122 124

AME11 KTUY05

• 20
• 15
• 10
• 5

5 10

log10 b

150 160 170 150 160 170 180 190 200

N

104 106 108 110 112 114 116 118 120 122 124

AME11 KTUY05

Half-lives Branching ratios

Branching ratio with respect to α decay: bα = Tα/Tc. Usually bα << 1. Trend: shorter Tc and larger bα. For larger Z > 120 there are SHs with Tc < 1 ns and bα > 1.

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HIR of SH nuclei (II)

150 160 170 180 190 200

• 20
• 10

10 20 30

126 124 122 120 118 116 114 112 110

e-o e-e

• -e
• 20
• 10

10 20 30

log10 Tc(s)

150 160 170 180 190 200 170 180 190 200

N

• 20
• 10

10 20 30

125 123 121 119 117 115 113 111

170 180 190 200

• 20
• 10

10 20 30 160 180 200 220

• 20
• 10

10 20 30

126 124 122 120 118 116 114 112 110

e-o e-e

• -e
• 20
• 10

10 20 30

log10 Tc(s)

160 180 200 220 160 180 200 220

N

• 20
• 10

10 20 30

125 123 121 119 117 115 113 111

160 180 200 220

• 20
• 10

10 20 30

KTUY05 FRDM95

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HIR of SH nuclei (III)

150 160 170 180 190 200

• 20
• 15
• 10
• 5

5 10 15

126 124 122 120 118 116 114 112 110

e-o e-e

• -e
• 20
• 15
• 10
• 5

5 10 15

log10 b

150 160 170 180 190 200 170 180 190 200

N

• 20
• 15
• 10
• 5

5 10 15

125 123 121 119 117 115 113 111

170 180 190 200

• 20
• 15
• 10
• 5

5 10 15 160 180 200 220

• 20
• 10

10 20

126 124 122 120 118 116 114 112 110

e-o e-e

• -e
• 20
• 10

10 20

log10 b

160 180 200 220 160 180 200 220

N

• 20
• 10

10 20

125 123 121 119 117 115 113 111

160 180 200 220

• 20
• 10

10 20

KTUY05 FRDM95

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SH nuclei as cluster emitters

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

EMITTED CLUSTERS

Z = 120 N = 184

FRDM95 Ze ≤ Z − 80 (freq. daughter around 208Pb) Most probable emitted clusters with different colors.

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Universal curves (I)

Approximations: log S = [(Ae − 1)/3] log Sα, ν(Ae, Ze, Ad, Zd) = constant. From fit to α decay: Sα = 0.0160694 and ν = 1022.01 s−1. log T = − log P − 22.169 + 0.598(Ae − 1) − log P = cAZ

• arccos √r −
• r(1 − r)
• cAZ

= 0.22873(µAZdZeRb)1/2, r = Rt/Rb, Rt = 1.2249(A1/3

d

+ A1/3

e ), Rb = 1.43998ZdZe/Q, and µA =

AdAe/A.

DN Poenaru, W Greiner, Physica Scripta 44 (1991) 427.

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Universal curves (II)

10 20 30 40

• Log10 Ps

10 20 30

• decay

0.4 0.5 0.6 0.7

Q

• 1/2(MeV
• 1/2)

10 20 30

• decay

25 30 35 40 10 15 20 25 30

Log10 of half-life in sec.

32Si 28Mg 24Ne 20O 14C

25 30 35 40

• Log10 Ps

10 15 20 25 30

34Si 30Mg 26Ne 22Ne

25 30 35 10 15 20 25

28Mg

25 30 35

30Mg

25 30 35

32Si

25 30 35 40

• log10 Ps

34Si

10 15 20 25

22Ne 24Ne 25Ne 26Ne

10 15 20 25 30

log10 T(s)

14C 20O 23F

Geiger-Nuttal plot Tα = f(range of α in air) log T = f(1/Q−1/2)

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Single Universal curve: α and HIR

15 20 25 30 35 40 45 50

• log Ps
• 10
• 5

5 10 15 20

log T(s) + log S

34Si 32Si 30Mg 28Mg 26Ne 25Ne 24Ne 22Ne 23F 20O 14C

26 28 30 32 34 36

• log10 Ps

2 4 6 8 10 12 14

34Si 32Si 30Mg 28Mg 26Ne

2 4 6 8 10 12 14

log10 T(s) + log10 S

26 28 30 32 34 36

25Ne 24Ne 22Ne 23F 20O 14C

16 decay m. ee parents 27 decay m. ee, eo, oe p. ee, eo, oe p.

D.N. Poenaru, R.A. Gherghescu, W. Greiner, Phys. Rev. C, 83 (2011) 014601.

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α-decay Z = 92 − 118, fission models

130 140 150 160 170 180

• 5

5 10 15 20 25

• 5

5 10 15 20 25

log10 T (s)

130 140 150 160 170 180 190

e - e e - o

130 140 150 160 170 180 190

N

• 5

5 10 15 20 130 140 150 160 170 180 190

• 5

5 10 15 20 25

• - e
• - o

15 20 25 30

• 5

5 10 15

• 5

5 10 15

log10 T (s)

15 20 25 30

e - e e - o

15 20 25 30

• log10 Ps
• 5

5 10 15 15 20 25 30

• 5

5 10 15

• - e
• - o

Vertical bars: Nd = 126, 152, 162 Poenaru, D.N., Plonski, I.H., and Greiner, W., Phys. Rev. C 74 (2006) 014312

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α-decay: ASAF, semFIS & UNIV

60 80 100 120 140 160

Nd

• 2
• 1

1

SemV-S

• 2
• 1

1

SemFIS

• 2
• 1

1

UNIV

• 2
• 1

1

log T/Texp

60 80 100 120 140 160

ASAF

STANDARD DEVIATION Group σ-ASAF σ-UNIV σ-semFIS 47 e-e 0.402 0.267 0.164 45 e-o 0.615 0.554 0.507 25 o-e 0.761 0.543 0.485 25 o-o 0.795 0.456 0.451 Poenaru, D.N., Plonski, I.H., Gherghescu, R.A., Greiner, W.,

• J. Phys. G 32 (2006) 1223

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UNIV and UDL curve for e-e nuclei

• 5

5 10 15 20

log T(s) + log S

15 20 25 30 35 40

• log Ps

15 20 25 30 35 40 45

log T(s) - b (s)

100 110 120 130 140 150 160

(MeV

• 1/2)

UNIV = 0.354

hee=0.030

UDL = 0.329

cUDL=-20.796

• 1.0
• 0.5

0.0 0.5 1.0

log TUNIV/ Texp

60 80 100 120 140 160

N

• 1.0
• 0.5

0.0 0.5 1.0

log TUDL/Texp

Vertical bars: N = 50, 82, 126, 152, 162, 172 UDL: C. Qi, F .R. Xu, R.J. Liotta, R. Wyss Phys. Rev. Lett. 103 (2009) 072501.

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Compare UNIV, UDL, semFIS for α decay

Standard deviations of log T values of semFIS, UNIV and UDL formulae for 173 even-even, 134 even-odd, 123 odd-even, and 104 odd-odd α emitters with atomic numbers Z = 52 − 118. n σUNIV hUNIV σUDL cUDL σSEM 173 0.354 0.030 0.329 −20.796 0.222 134 0.640 0.528 0.606 −20.327 0.501 123 0.565 0.379 0.538 −20.481 0.434 104 0.826 0.961 0.804 −19.904 0.567 σ = n

i=1[log(Ti/Texp)]2/(n − 1)

1/2

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Summary

ASAF model predictions have been confirmed for parent nuclei with Z = 87 − 96 The magicity of the daughter 208Pb 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

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