Nuclear Reactions Shape, interaction, and excitation structures of nuclei scattering expt. cf. Experiment by Rutherford (a scatt.) scattered particles detector solid angle projectile target transmitted particles http://www.th.phys.titech.ac.jp/~muto/lectures/qmii11/qmii11_chap21.pdf K. Muto (TIT)
Nuclear fusion reactions two positive charges repel each other nuclear attractive intraction compound nucleus
Why subbarrier fusion? Two obvious reasons: discovering new elements (SHE by cold fusion reactions) nuclear astrophysics (fusion in stars)
Heavy-ion subbarrier fusion reactions Inter-nucleus potential Two forces: 1. Coulomb force Long range, repulsive 2. Nuclear force Short range, attractive above barrier sub-barrier deep subbarrier Potential barrier due to the compensation between the two (Coulomb barrier)
Fusion cross sections at subbarrier energies Fusion cross sections of structure-less nuclei (a potential model) Simple potential model: OK for relatively light systems underestimates s fus for heavier systems at subbarrier energies
Strong target dependence at E < V b low-lying collective excitations?
Effect of deformation on subbarrier fusion Excitation spectra of 154 Sm 0.903 (MeV) 8 + cf. Rotational energy of a rigid body (Classical mechanics) 0.544 0.267 0.082 0 154 Sm 6 + 4 + 2 + 0 + 154 Sm is deformed
154 Sm 16 O The barrier is lowered for =0 because an attraction works from large distances. The barrier increases for =p/2. because the rel. distance has to get small for the attraction to work Def. Effect: enhances s fus by a factor of 10 ~ 100 Fusion: interesting probe for nuclear structure
Physics of superheavy elements Periodic table of chemical elements What is the heaviest element?
Periodic table of chemical elements natural elements: What is the heaviest element? Pu (Z=94) a tiny amount in nature U (Z=92) What determines these numbers??
natural elements: What is the heaviest element? Pu (Z=94) a tiny amount in nature U (Z=92) What determines these numbers?? heavy nuclei large Coulomb repulsion unstable against a decay 4 He nucleus = a particle + (Z,N) (Z-2,N-2) (Z=2,N=2)
Decay half-lives of heavy nuclei 13.7 billion years 4.6 billion years 232 Th 1.405 x 10 10 years 238 U 4.468 x 10 9 years 244 Pu 8.08 x 10 7 years 247 Cm 1.56 x 10 7 years Heavier nuclei: unstable against fission
Periodic table of chemical elements artificially synthesized ( man-made ) nuclear reactions superheavy elements (SHE)
Prediction of island of stability: an important motivation of SHE study Yuri Oganessian island of stability around Z=114, N=184 W.D. Myers and W.J. Swiatecki (1966), A. Sobiczewski et al. (1966) modern calculations: Z=114,120, or 126, N=184 e.g., H. Koura et al. (2005)
Island of stability (SHE) Thorium Uranium Lead Continent Yuri Oganessian
who is she? (*) Z=110 Darmstadtium (Ds) 1994 Germany Z=111 Roentgenium (Rg) 1994 Germany Z=112 Copernicium (Cn) 1996 Germany Z=113 No name yet 2003 Russia / 2004 Japan Z=114 Flerovium (Fl) 1999 Russia (*) Z=115 No name yet 2003 Russia Z=116 Livermoriun (Lv) 2000 Russia Z=117 No name yet 2010 Russia Z=118 No name yet 2002 Russia island of stability: Z=114, N=184 Fl discovered: Z=114, N=174-175 island not yet confirmed
How to synthesize SHE? Nuclear fusion reactions Fusion of medium-heavy systems: Fusion of heavy and super-heavy systems: re-separation
extra push Z 1 *Z 2 = 1296 Z 1 *Z 2 = 2000 C.-C. Sahm et al., Z. Phys. A319( 84)113
2-body potential before touching 1-body potential after touching The red potential has to be overcome even if the blue potential has been overcome. Re-separation if failed (quasi-fission)
contact Quasi-fission fusion evaporation ER CN n experimentally detected fission cannot distinguish experimentally CN = compound nucleus ER = evaporation residue
typical values for Ni + Pb reaction 10 11 = 100,000,000,000 10 6 = 1,000,000 99,999,000,000 very rare event!! 1 CN 999,999 ER n experimentally detected CN = compound nucleus ER = evaporation residue
Element 113 (RIKEN, K. Morita et al.) 70 Zn (Z=30) + 209 Bi (Z=83) 278 113 + n K. Morita et al., J. Phys. Soc. Jpn. 81( 12)103201 only 3 events for 553 days experiment
Theoretical treatment contact P cap Quasi-fission fusion evaporation P CN CN fission P sur statistical model ER n CN = compound nucleus ER = evaporation residue
2-body potential 1-body potential E P cap : quantum mechanics compound nucleus thermal motion energy dissipation
Theory: Lagenvin approach multi-dimensional extension of: q: internuclear separation, deformation, asymmetry of the two fragments g: friction coefficient R(t): random force
34 S + 238 U Quasi-fission (QF) CN fusion-fission ER n Y. Aritomo, K.H., K. Nishio, S. Chiba, PRC85( 12)044614
34 S + 238 U capture Quasi-fission (QF) compound ER CN fusion-fission ER n Y. Aritomo, K.H., K. Nishio, S. Chiba, PRC85( 12)044614
Element 113 Dubuna 48 Ca + 243 Am 288 115 + 3n 284 113 + a (2003) 48 Ca + 249 Bk 293 117 + 4n 189 115 + a 285 113 + a (2010) etc. Hot Fusion: 48 Ca projectile RIKEN 70 Zn + 209 Bi 278 113 + n (2004) Cold Fusion: 208 Pb or 209 Bi target
Dubna Flerov Laboratory of Nuclear Reactions, JINR, Dubna, Russia about 120 km north of Moscow 105Db (Dubnium)
fission capture evaporation survival Hot Fusion Cold Fusion Example 48 Ca + 243 Am 4n 70 Zn+ 209 Bi 1n asymmetry large small Capture large small Survival small large
113 112 277 Cn known nuclides s ~ fb = 10-39 cm 2 111 272 Rg 110 269 Ds 270 Ds 271 Ds 273 Ds 118 3 rd 114 event Aug. 12 2012 CN 282 Cn 283 Cn 286 Fl 287 Fl 290 Lv 291 Lv 294 118 117 293 117 294 117 116 a 274 Rg a RIKEN (Cold fusion) 278 113 209 Bi + 70 Zn n 115 287 115 288 115 289 115 290 115 113 282 113 283 113 284 113 285 113 286 113 278 Rg 279 Rg 280 Rg 281 Rg 282 Rg 279 Ds 281 Rg a SF 285 113 a 289 115 a 293 117 249 Bk + 48 Ca 4n CN Dubna (Hot fusion) s ~ pb = 10-36 cm 2 109 266 Mt 268 Mt 108 263 Hs 265 Hs 266 Hs 267 Hs 269 Hs 270 Hs 271 Hs 264 Hs a 270 Mt 274 Mt 275 Mt 276 Mt 278 Mt 275 Hs 107 261 Bh 262 Bh 264 Bh 266 Bh 267 Bh 106 258 Sg 259 Sg 261 Sg 263 Sg 260 Sg 257 105 Db 258 Db 259 Db 260 Db 262 Sg a 261 Db 262 263 Db Db a 104 256 257 Rf Rf 258 Rf 259 Rf 260 Rf 261 Rf 262 Rf 266 Bh 265 Sg 266 Sg 263 Rf 270 Bh 271 Bh 272 Bh 274 Bh 266 Db 267 Db 268 Db 270 Db 267 Rf 271 Sg 103 255 Lr 257 Lr 258 Lr 259 Lr 260 Lr 261 Lr 262 Lr 256 Lr 102 256 No 258 No 260 No 262 No 254 255 No No a 259 No 101 253 Md 254 255 Md Md 256 Md 257 Md 258 259 Md Md 260 Md 100 252 Fm 254 Fm 255 Fm 257 Fm 258 Fm 259 Fm 253 Fm 254 Fm a 258 Lr 257 No 256 Fm 99 251 252 Es 253 255 Es Es Es 256 Es 257 Es 254 ES 98 250 Cf 251 Cf 252 Cf 253 Cf 254 Cf 255 Cf 256 Cf 250 Cf cf. Cold Fusion: connected to known nuclei Hot Fusion: neutron-richer CN
Naming rights? Under discussions in the joint IUPAC/IUPAP Joint Working Party IUPAC = International Union of Pure and Applied Chemistry IUPAP = International Union of Pure and Applied Physics RIKEN (Japan) much less ambiguity with cold fusion Dubna (Russia) much larger number of events
Chemistry of superheavy elements Are they here in the periodic table? That is, does e.g., Lv show the same chemical properties as O, S, Se, Te, and Po?
relativistic effect : important for large Z E = mc 2 Solution of the Dirac equation (relativistic quantum mechanics) for a hydrogen-like atom: relativistic effect
Famous example of relativistic effects: the color of gold Gold looked like silver if there was no relativistic effects!
3.7 ev 2.4 ev 5s 4d Rel. Non-Rel. Non-Rel. Rel. 3.7 ev 2.4 ev 6s 5d cf. visible spectrum Silver (Ag) Gold (Au) 2.76 ev 1.65 ev
Rel. Non-Rel. Non-Rel. Rel. 3.7 ev 2.4 ev no color absorbed Silver (Ag) Gold (Au) blue: absorbed Ag Au
Chemistry of superheavy elements How do the relativistic effects alter the periodic table for SHE? a big open question