PHL424: Nuclear fusion

Transcription

1 PHL424: Nuclear fusion Hot Fusion projectiles on target compound nuclei 1 atom

2 Hot fusion ( ) successful up to element 106 (Seaborgium) Coulomb barrier V C between projectile and target nucleus has to be exceeded VV CC = ZZ pp ZZ tt ee 2 26 = MMMMMM MMMM CCCC RR iiiiii reaction: a + A C * B + b Δm = m a + m A - m CN Δm = ( ) * MeV/c 2 = MeV/c 2 excitation energy of compound nucleus E * = E kin + Δm c 2 = MeV 82.2 MeV r = 44.0 MeV approximate 4 neutrons will be evaporated to avoid fission

3 Cold fusion ( ) Coulomb barrier V C between projectile and target nucleus has to be exceeded VV CC = ZZ pp ZZ tt ee = MMMMMM FFFF + PPPP RR iiiiii reaction: a + A C * B + b Δm = m a + m A - m CN Δm = ( ) * MeV/c 2 = MeV/c 2 excitation energy of compound nucleus E * = E kin + Δm c 2 = MeV MeV r = 18.2 MeV approximate 1-2 neutrons will be evaporated to avoid fission

4 Fusion cross section Radius for fusion barrier: RR ffffffffffff = RR iiiiii ZZ pp ZZ tt ZZ pp ZZ tt < ZZ pp ZZ tt 1000 ZZ pp ZZ tt 500 ffff ddσσ ddl R i [fm] C i [fm] 58 Fe Pb R int [fm] V C (R int ) [MeV] R fusion [fm] V C (R fusion ) [MeV] l fusion l int l Total cross section for fusion: 2 σσ ffffffffffff = ππrr ffffffffffff 1 VV CC RR ffffffffffff EE cccc σσ ffffffffffff = ππ kk 2 l ffffffffffff l ffffffffffff + 1 wwwwwww EE cccc = AA tt AA tt + AA pp EE llllll wwwwwww kk = AA tt AA tt + AA pp AA pp EE llllll ffff 1

5 Interaction potential The potential between projectile and target nucleus is given by a function of the relative distance between them VV rr = VV NN rr + VV CC rr nuclear potential + Coulomb potential VV CC rr = ZZ 1 ZZ 2 ee 2 3 rr2 2 RR 2 CC RR CC rr < RR CC ZZ 1 ZZ 2 ee 2 rr rr RR CC VV NN rr = 4ππ γγ CC pp CC tt CC pp + CC tt bb ΦΦ ξξ Φ ξξ = 0.5 ξξ ξξ ξξ eeeeee ξξ 0.75 ξξ ξξ = rr CC pp CC tt /bb bb = ππ aa 1 ffff 3 wwwwwww aa = 0.55 ffff γγ = NN cc ZZ cc AA cc 2 MMMMMM ffff 2 CC ii = RR ii 1 RR ii 2 ffff RR ii = 1.28 AA ii 1/ AAii 1/3 ffff

6 The Statistical Model de-excitation of the hot compound system σ l E * n n n Yrast line no states EE = EE kkkkkk + mm cc 2 EE kkkkkk > VV CC = ZZ aa ZZ AA ee 2 RR iiiiii l mm = mm aa + mm AA mm CCCC

7 Evaporation particles cm-spectra of particles statistically emitted from CN (evaporation) are of Maxwell Boltzmann type neutrons dn de ( E E ) e B ET protons E B = Coulomb barrier T = effective nuclear temperature E B compound nucleus reactions direct reactions Typical energy spectrum of nucleons emitted at a fixed angle in inelastic nucleon-nucleon reactions.

8 Evaporation particles cm-spectra of particles statistically emitted from CN (evaporation) are of Maxwell Boltzmann type neutrons dn de ( E E ) e B ET protons E B = Coulomb barrier T = effective nuclear temperature E B Even for fixed E * the particle spectrum is continuous (Maxwell Boltzmann), except for transitions to discrete spectrum at low E ER *

9 Nuclear temperatures de-excitation of the hot compound system dddd EE ddee nn ee EE nn TT nn EE nn = 2TT max dddd ddee nn spectrum of single EE nn = TT excitation energy dddd ddee nn EE nn ee EE nn TT eeeeee spectrum of cascade of neutrons EE nn = 1.5TT TT eeeeee 0.92 TT 1 ssss ddddddddddddddd deviations at shell closures Fermi gas relations: * 2 E = a T " little a" ( E ) * de S = = 2 a E * E ρ * 2 = ρ0 e ae * * aa AA AA MMMMMM 1 8 collective states ground state

10 Fusion excitation function 2 ππrr ffffffffffff maximum l fusion due to nuclear centrifugal stability 1 VV CC RR ffffffffffff V nucl + V coul + V L r dσ d Fusion -ER Fusion Fission multinucleon transfer Elastic/quasielastic scattering 0 ER F R

11 A limiting nuclear angular momentum rotating charged liquid drop surface energy: EE SS 0 = NN ZZ AA 2 AA 2 3 MMMMMM l IIII Coulomb energy: 0 EE CCCCCCCC = ZZ 2 AA 1 3 MMMMMM rotational energy: EE 0 RRRRRR = 1 2 ħ 2 l AA mm RR 2 = l 2 AA 5 3 MMMMMM l(ħ) l II Γ nn = Γ ffffffffffffff change of the nuclear shape mass number 0 EE RRRRRR 0 EE = XX XX XX 3 0 XX XX XX XX XX 1.0 SS with XX = EE 0 CCCCCCCC 0 2 EE SS fissility parameter 127 example: LLLL EE SS = MMMMMM EE CCCCCCCC = MMMMMM XX = EE RRRRRR EE 0 SS = EE 0 57 RRRRRR = MMMMMM l II = 67.8 ħ Cohen, Plasil, Swiatecki; Ann. Phys. 82, 557 (1974)

12 Fusion and evaporation cold fusion 50 Ti Pb 258 Rf* (HIVAP calculations) Fusion final nucleus plus neutron even-even compound nucleus n fission σ [mbarn] Fission 5-7 orders of magnitude 1n 2n 3n evaporation residues (ER) Both decay processes are determined by the level density, either from the residual nucleus or at the saddle point. level density: E lab [MeV]

13 Fusion / Fission competition liquid drop + shell corrections σσ EEEE = σσ cccccccccccccc PP CCCC PP ssssssssssssssss σσ xxnn EEEE EE = ππ l mmmmmm kk 2 2l + 1 PP CCCC EE, l PP xxxx EE, l l=0 formation survival Potential energy / MeV LD LD + shell Superheavy system: σσ EEEE σσ cccccccccccccc A. Sobiczewski et al. Deformation β 2

14 Fusion / Fission competition liquid drop + shell corrections 64 Ni Pb 271 Ds + 1n VV CC RR iiiiii = 238 MMMMMM σσ EEEE = σσ cccccccccccccc PP CCCC PP ssssssssssssssss fusion-fission

15 Synthesis of heavy elements n 70 Zn 208 Pb Fusion _1_ 10 12

16 The production cross section fusion cross section and survival probability Nucleus: 1 barn = cm 2 = m 2 fusion cross section: < 1 barn 1:10 12 Production cross section : 1 pbarn = barn Earth: -Area 1.3x10 8 km 2 1.3x10 14 m 2 Wetzlar: Area km 2 1.3x10 7 m 2 /2 1:10 7 1:10 5 Charlotte Buff s house: Area x 130 m 2 1.3x10 2 m 2 1:10 12

17 Separator for Heavy Ion Products (SHIP)

18 Separator for Heavy Ion Products (SHIP) Fusion products are slower than scattered or transfer particles vv CCCC = mm pp mm pp + mm tt vv pp ee. qq. vv pp 10.3% vv CCCC 2.2% E- and B-field are perpendicular to each other BB ρρ = EE ρρ = mm vv ee qq mm vv2 ee qq FF mmmmmm = FF eeee FF tttttt = 0 electric deflectors: ±330 kv dipole magnets: 0.7 T max

19 Separator for Heavy Ion Products (SHIP) The choice of E and B determines the transmitted velocity vv = EE BB The rejected beam will be stopped on a cooled Cu plate

20 SHIP stop detector γ α (ΔE signal) SHE will be measured in a pixel position sensitive Silicon detector determines the position an energy of SHE and α, β,... area: 27*87mm 2, thickness: 0.3mm, 16 strips energy resolution ΔE=18-20 E α > 6MeV (cooling 260K) position resolution Δx=0.3mm (FWHM) Wait for the emission of an α-particle (or β-particle) correlation method: implantation and decay event in the same pixel

21 Synthesis and identification of heavy elements with SHIP n 70 Zn 208 Pb ER MeV 280 µs 12 m 269 Hs MeV 110 µ s 265 Sg 9.23 MeV 19.7 s known 261 Rf 4.60 MeV (escape) 7.4 s kinematical separation (in flight) using electric deflectors and dipole magnets vv = EE BB velocity filter 257 No 8.34 MeV 253 Fm 15.0 s Date: 09-Feb-1996 Time: 22:37 h 8.52 MeV 4.7 s

22 Synthesis and identification of heavy elements with SHIP n 70 Zn 208 Pb cm ER MeV 280 µs 12 m 269 Hs MeV 110 µ s 31 cm known 261 Rf 265 Sg 9.23 MeV 19.7 s 4.60 MeV (escape) 7.4 s Identification by α-α correlations down to known isotopes kinematical separation (in flight) using electric deflectors and dipole magnets vv = EE BB velocity filter 257 No 8.34 MeV 253 Fm 15.0 s Date: 09-Feb-1996 Time: 22:37 h 8.52 MeV 4.7 s

23 208 Pb + 64 Ni 272 Ds * T decay E α (MeV)

24 Geiger-Nuttall relationship The average decay properties of even mass decay chains match the Geiger-Nuttall relationship Coulomb barrier nuclear potential binding energy of α-particle binding energy per nucleon in nucleus

25 The JUROGAM array + RITU + GREAT spectrometer

26 The JUROGAM array + RITU + GREAT spectrometer

27 The rotational spectrum of 254 No rotational energy: gamma energy: E J E J 2 = J J 2I ( + 1) 2 EJ = J 2I ( 4 2) 2 J 3 S. Eeckhaudt et al., Eur. Phys. J. A 26, 227 (2005)

28 Chemistry of superheavy elements Are the new elements in the same period? Does e.g. Lv show the same chemical properties as O, S, Se, Te and Po?