Nuclear shapes. The question of whether nuclei can rotate became an issue already in the very early days of nuclear spectroscopy

Transcription

1 Shapes

2 Nuclear shapes The first evidence for a non-spherical nuclear shape came from the observation of a quadrupole component in the hyperfine structure of optical spectra The analysis showed that the electric quadrupole moments of the nuclei concerned were more than an order of magnitude greater than the maximum value that could be attributed to a single proton and suggested a deformation of the nucleus as a whole Schüler, H, and Schmidt, Th, Z Physik 94, 457 (1935) Casimir, H B G, On the Interaction Between Atomic Nuclei and Electrons, Prize Essay, Taylor s Tweede Genootschap, Haarlem (1936) The question of whether nuclei can rotate became an issue already in the very early days of nuclear spectroscopy Thibaud, J, Comptes rendus 191, 656 ( 1930) Teller, E, and Wheeler, J A, Phys Rev 53, 778 (1938) Bohr, N, Nature 137, 344 ( 1936) Bohr, N, and Kalckar, F, Mat Fys Medd Dan Vid Selsk 14, no, 10 (1937) Can perfectly spherical nucleus rotate?

3 Nuclear deformation: Jahn-Teller effect The Jahn Teller theorem (1937) states that any nonlinear molecule with a spatially degenerate electronic ground state will undergo a geometrical distortion that removes that degeneracy, because the distortion lowers the overall energy of the species Cs 3 C 60 Theory: Hartree- Fock experiment: (e,e ) Bates The intrinsic shape of the deuteron by combining the results from experiments at JLab Shape of a charge distribution in 154 Gd

4 How to describe nuclear shapes? z y x ( λ + R(θ,ϕ) = c(α)r 0 * 1+ α * λµ Y λµ (θ,ϕ)- )* λ=1 µ = λ,- volume conservation radius of the sphere with the same volume deformation parameters For axial shapes µ=0 β λ α λµ

5 a) λ=1 (dipole); µ=-1,0,1!r d 3 r = 0 b) λ= (quadrupole); µ=-,-1,0,1, V 3 conditions, they fix α 1µ center of mass conservation α 1 = α 1 = 0, α =α 3 conditions, they fix three Euler angles Only two deformation parameters left (Hill- Wheeler coordinates): α 0 = β cosγ, α = 1 β sinγ c) λ=3 (octupole) d) λ=4 (hexadecapole) e)

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7 S Raman et al, Atomic Data & Nuclear Data Tables 78, (a) N =8 N =0 N =8 N =50 N =8 N =16 5 Energy of + 1 (MeV) LINES CONNECT ISOTOPES B(E) (e b ) Neutron Number N ~400 spu ~1 spu (b) N =50 N =8 N =16 N =8 N =8 N =0 LINES CONNECT ISOTOPES Neutron Number N

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9 triaxial band noncollective states 114 superdeformed bands (48 ) (46 ) (44 ) (4 ) (54) (5) (50) (48) (56) (54) (5) (50) (49 ) (47 ) (45 ) (43 ) (48 ) (46 ) (44 ) (4 ) (5 ) (50 ) (48 ) (46 ) E fission/fusion exotic decay heavy ion coll (40 ) 93 (46) 1049 (48) (41 ) 9787 (40 ) 9538 (44 ) (38 ) (39 ) (38 ) (44) (46) 990 (4 ) (36 ) 970 (37 ) 998 (36 ) (40 ) (4) (44) (34 ) (35 ) (34 ) (518) (38 ) (3 ) (40) (4) (33 ) (3 ) (36 ) (30 ) (38) (40) (31 ) (30 ) (8 ) (34 ) (38) (8 ) 851 (36) (9 ) (6 ) (3 ) (6 ) 858 (7 ) (36) 613 (34) 1114 (4 ) E Q 0 shape coexistence Q (4 ) ( ) Dy Q 1 Q Q

10 Fission

11 Fission

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13 N,Z 1938 Hahn & Strassmann 1939 Meitner & Frisch 1939 Bohr & Wheeler 1940 Petrzhak & Flerov elongation necking split N=N 1 +N Z=Z 1 +Z N 1,Z 1 N,Z Fission yields (fragments)

14 Understanding the fission process is crucial for many areas of science and technology: Fission governs the production and existence of many transuranium elements, including the predicted long-lived super-heavy species Fission influences the formation of heavy elements in a neutron rich environment Fission produces reactor antineutrinos Improved understanding of the fission process will enable scientists to enhance the safety and reliability of nuclear reactors Fission is important for stockpile stewardship The new phase in fission theory is expected to rely heavily on advanced modeling and simulation capabilities utilizing massively parallel leadership-class computers

15 1939: Bohr s paper on fission 1939 Nature Publishing Group

16 Deformed liquid drop (Bohr & Wheeler, 1939) fission of nuclear droplet E LDM B S ( def ) = E S 0 ( def) = E def S E S 0 x = E 0 C E S 0 ( ) ( ) B S ( def) 1+ x B C ( def) 1 [ ] ( ) ( ), B ( def ) = E ( def ) C C E C ( 0) ( ) ( ) = Z / A Z / A ( ) crit Z 50 A x: fissility parameter

17 The nuclear droplet stays stable and spherical for x<1 For x>1, it fissions immediately For 38 U, x=08 Realistic calculations Nature 409, 785 (001) All elements heavier than A= are fission unstable! But the fission process is fairly unimportant for nuclei with A<30 Why?

18 40 Pu Realistic calculations

19 38 U lives 45 billion years 50 No fissions after 4 µs 10 6 U N = Pu N = T sf / s 10 6 Cm 10 1 Cf TKE EM fission of RNBs at GSI, E*~11 MeV K-H Schmidt et al, NPA 665, 1 (000) Status: Fm Hs No Rf Sg Neutron number

20 Third minimum around 3 Th? Phys Rev C 87, (013) E (MeV) 8 (a) (b) 6 4 SkM* 6 Th 8 Th 30 Th 3 Th 8 (c) (d) 6 4 UNEDF1 SkM* UNEDF1 8 U 30 U 3 U 34 U Q 0 (b) Phys Rev C 85, (01)

21 180 Tl β + /EC Curious Fission of 180 Hg step process: β + /EC decay of a parent 180 Tl nucleus populates an excited state in the 180 Hg daughter, which then might fission (in competition with the γ decay to the gs) Low-energy fission! (E*<Q EC =108 MeV) 10 cases know so far (neutron-def Uranium region) Q EC γ β + /EC γ γ B f 180 Hg deformation Phys Rev Lett 105, 550 (010); Rev Mod Phys (013) Before the ISOLDE experiment: expected SYMMETRIC split in two semi-magic 90 Zr The most probable fission fragments are 100 Ru (N=56,Z=44) and 80 Kr (N=44,Z=36)

22 Fission half-lives: depend on potential, friction, and inertia terms WKB: The action has to be minimized! collective inertia (mass parameter) multidimensional space of collective parameters Phys Rev C 80, (009)

23 Low-energy fission: theoretical strategy Quality Input Large- scale Simula0ons on Leadership- class Computers Dynamics PRC 84, 05431(011) PRC 85, (01) PRC 80, (009) Numerical Techniques PRC 78, (008) Confronta0on with experiment; predic0ons PRC 80, (009)