Shell effects in atomic nuclei Part 2 shapes

Shell effects in atomic nuclei Part 2: shapes and superheavy elements Laurent Gaudefroy 1, Alexandre Obertelli 2 1 CEA DAM, DIF, France 2 CEA Saclay, IRFU, France

Changes in the nuclear shell structure 126 Lecture (part 1) given by Laurent Gaudefroy protons 82 50 28 82 20 50 8 2 2 8 28 neutrons 20

Shapes of atomic nuclei Z, N = magic numbers protons 50 28 Nilsson diagram 82 28 20 82 20 50 8 2 50 sngle particle enegies Closed shell = spherical shape 126 20 28 neutrons 2 8 The vast majority of all nuclei shows a non-spherical mass distribution 8 Spherical Oblate 2 Prolate Deformed elongation

Nuclear structure description framework [Addendum to yesterday’s lecture] 1 - Shell-model: • nucleus described in the laboratory frame • the nucleus is described as a superposition of spherical configurations • « intrinsic deformation » is implicitely contained in correlations 2 - Mean-field like description: • nucleus described in its intrinsic frame • « angular momentum » is not a good quantum number • intrinsic deformation is explicit In this lecture, the deformed mean-field approach will be followed

Nilsson diagram K =7/2 K =5/2 K =3/2 - nlj=1 f 7/2 0 • core + single particle • short range & attractive int. • Pauli : orbit repulsion K =1/2 -

Shapes and “deformation” parameters Generic nuclear shapes can be described by a development of spherical harmonics alm: deformation parameters quadrupole Tetrahedral Y 32 deformation Triaxial Y 22 deformation octupole Lund convention oblate non-collective spherical hexadecapole Static rotation 2 : elongation : triaxiality prolate non-collective prolate collective oblate collective Dynamic vibration

Shapes and “deformation” from experiment Ø Quadrupole moments via low-energy Coulomb excitation Reorientation effect target quadrupole projectile excitation * Coulomb field photon de-excitation Intrinsic quadrupole moment ØMoment of inertia via rotational-band spectroscopy / model dependent J =8+ J =6+ J =4+ J =2+ J =0+ even-even

Quadrupole deformation of nuclei N=Z Oblate Pb & Bi actinides N~Z Fission fragments N~28 n-rich Prolate M. Girod, CEA Oblate deformed nuclei are far less abundant than prolate nuclei Shape coexistence possible for certain regions of N & Z

Shape coexistence M. Girod M. Bender et al. , PRC 74, 024312 (2006) 74 Kr oblate 6+ 4+ 6+ 2+ 4+ 0+ prolate 8+ 2+ 0+ Configuration mixing: electric monopole (E 0) transition

Shape coexistence in light Krypton isotopes 6+ 8+ 4+ 6+ 2+ 4+ 0+ 2+ 0+

Shape coexistence in light Krypton isotopes Coulomb excitation of 74, 76 Kr 78 Kr source 74 Kr 4. 7 Me. V/u 104 pps CSS 1 CSS 2 78 Kr 68. 5 Me. V/u 1012 pps SPIRAL beams 76 Kr 5 105 pps 74 Kr 104 pps 4. 7 Me. V/u SPIRAL ECRIS target CIME [24°, 55°] 74 Kr [55°, 74°] [67°, 97°] [97°, 145°]

Shape coexistence in light Krypton isotopes Quadrupole moments first reorientation measurement with radioactive beam SPIRAL 1, GANIL (France), 2005 Fit matrix elements (transitional and diagonal) to reproduce experimental -ray yields (as function of ) Ø 14 B(E 2) values Ø 5 quadrupole moments E. Clément et al. , PRC 75, 054313 (2007)

Comparison with ‘beyond-mean-field’ theory prolate oblate Qs<0 prolate GCM calculation axial deformation Skyrme SLy 6 M. Bender et al. PRC 74, 024312 (2006) Qs>0 oblate experimental B(E 2; ) [e 2 fm 4] E. Clément et al. , PRC 75, 054313 (2007) prolate oblate K=2 vibration GCM (GOA) calculation q 0, q 2: triaxial deformation Gogny D 1 S M. Girod et al.

Extreme shapes and intruder orbitals 152 Dy 108 Cd single-particle energy (Woods-Saxon) i 13/2235 U N+3 shell N+2 shell N+1 shell N shell Z=48 Energy Fermi level Deformation ND SD quadrupole deformation HD Ø (N+1) intruder normal deformed, e. g. 235 U Ø (N+2) super-intruder Superdeformation, e. g. 152 Dy, 80 Zr Ø (N+3) hyper-intruder Hyperdeformation in 108 Cd, ?

The quest for high-spin superdeformation: 152 Dy TESSA 3 (12 detectors), Daresbury (UK) P. Twin et al. , Phys. Rev. Lett. 57, 811 (1986) Ø first discrete superdeformed band Ø energy spacing: E = 47 ke. V TESSA Ge array Extracted moment of inertia 8+ 6+ 4+ 2+ 0+ even-even

The quest for high-spin superdeformation: 152 Dy Properties of the superdeformed band firmly established 20 years later Argonne National Lab. Gammasphere 108 Ge detectors T. Lauritsen et al. , Phys. Rev. Lett. 88, 042501 (2002)

Pushing the limits: The quest for nuclear hyperdeformation Hyperdeformation favored at high-spin Competition with fission Need for intense neutron-rich beams Spiral 2 : intense Kr and Sn neutron-rich beams Fission barrier vs. High spin n-rich beam stable beam

The AGATA germanium array New generation gamma-detection array based on the tracking method > Efficiency ~ 40 % Huge gain in γγ, γγγ, … efficiency > Cristal rate up to 50 k. Hz Allow larger beam intensity • 180 large volume 36 -fold segmented Ge crystals in 60 triple-clusters • Digital electronics and sophisticated signal processing algorithms (PSA) • Operation of Ge detectors in position sensitive mode -ray tracking http: //www-w 2 k. gsi. de/agata/

Existence and structure of heavy elements Limits of stability ? Shell structure ? Next magic number ? 238 U ~4. 5 109 y 208 Pb Chart from http: //www. nndc. bnl. gov/chart/

Synthesis of heavy elements in the universe Why SHE do not exist on earth ? 1 - not stable 2 - not formed during the r-process B. Pfeiffer et al. , NPA (2001) Cassiopea A supernova

Upper limit of stability : positron emission Nuclei for Z larger than 173 become unstable against positron emission. The most deeply bound electrons from the 1 s 1/2 shell reach an energy of -511 ke. V W. Pieper, W. Greiner Z. Phys. A 218 (1968) 327 J. Reinhardt et al, Z. Phys. A 303 (1981) 173

Limits of stability : fission Surface prefers spherical nuclei Coulomb favours deformation If BE(ε) -BE(ε=0)> 0: gain in energy with deformation fission • B(A, Z) = av A - as A 2/3 - ac Z 2/A 1/3 - aa (A-2 Z)2/A +δ A-1/3 volume – nuclear attractive force less binding at the surface Coulomb – proton repulsion asymmetry pairing b R V= 4/3 R 3 S=4 R 2 a a=R(1+ ) b=R(1+ )-1/2 V=4/3 ab 2 S=4 R 2(1+2/5 2+…)

Liquid drop energy (Me. V/A) Fission barrier – liquid drop Deformation β

Limits of stability from liquid drop model Stability = balance between surface and coulomb • Fissility parameter x = Ecoulomb/ 2 Esurface • • • ~ 1/50 Z 2 / A scaling of the fission barrier x > 0. 8 : no survival • Possible definitions of SHE : No macroscopic fission barrier Bf < 1 Me. V x > 0. 8

State of the art Superheavy elements synthesized in laboratory Shell effects balance fission and are responsible for the existence of superheavies! Superheavy elements Z 104

Chemist point of view H 1 Li Be 3 4 Na Mg 11 K 19 12 Point of view of chemist : Actinides 90 Z 103 Transactinides 104 Z 121 (? ) Arbitrary point of view : Superheavies: existence due to shell effects Ca Sc Ti 20 22 Rb Sr 21 23 2 B C 5 6 Al Si 13 14 N 7 P 15 O 8 S 16 F Ne 9 10 Cl Ar 17 18 Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 24 36 25 26 27 28 29 30 31 32 33 34 35 Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te 40 41 42 43 49 50 Cs Ba La Hf Ta W Re Os Pt Au Hg Tl Pb Bi Po At Rn 55 72 73 74 75 78 81 82 37 38 56 Y V He 39 57 44 76 45 Ir 77 46 47 79 48 80 51 83 52 84 I 53 85 Xe 54 86 Fr Ra Ac Rf Db Sg Bh Hs Mt Ds Rg 112 113 114 115 116 117 118 87 88 89 104 105 106 107 108 109 110 111 119 120 96 004 9 2 1 10 007 0 2 2 Cn (2010) copernicium Lanthanides Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Actinides Th Pa 58 90 59 91 60 U 92 61 62 63 64 65 66 67 68 69 70 71 Np Pu Am Cm Bk Cf Es Fm Md No Lr 93 94 95 96 97 98 99 100 101 102 103

Peninsula vs island of stability Spherical 298114 238 U ~4. 5 109 y Deformed 254 No, 270 Hs LDM 152 LDM 162 LDM 184 LDM

Modern-theory predictions Z N W. S 114 184 HFB 126 184 RMF 120 172 M. Bender et al. PL B 515 (2001) 42 Note 1 : Up to 208 Pb : proton and neutron magic numbers identical. Note 2 : Models rely on extrapolations –parameters are adjusted on known cases

Level density increases with A, Z 132 Sn : Large gap Super-heavies : Gap function of models and not marked M. Bender et al. , Phys. Lett. B 515 (2001) 42 Theoretical challenges

Why is it so difficult to get information on SHE? 1 second times needed to observe on 1 minute average 1 event 1 hour present sensitivity: 1 day 10 days limit 1 pbarn beam dose: 1. 5 1018 projectiles

Synthesis and Identification of SHE n 70 Zn 208 Pb 277112 273110 269 Hs 265 Sg known kinematic separation in flight 257 No 253 Fm 8. 34 Me. V 15. 0 s Date: 09 -Feb-1996 Time: 22: 37 h 261 Rf 8. 52 Me. V 4. 7 s CN 11. 45 Me. V 280 s 11. 08 Me. V 110 s 9. 23 Me. V 19. 7 s 4. 60 Me. V (escape) 7. 4 s identification by - correlations to known nuclides

State-of-the-art worldwhile RIKEN Tokyo, Japan GSI JINR/FLNR Dubna, Russia 294118: Yu. Oganessian et 294117: Yu. Oganessian et al. , J. Phys. G R 165 (2007) al. , Phys. Rev. Lett. 104, 142502 (2010)

Spectroscopy of Transfermium elements (courtesy of P. -H. Hennen) Access to high j deformed orbitals : probe of higher lying spherical orbitals Prompt and/or decay spectroscopy R. -D. Herzberg et al. , Nature 442, 896 -899 (2006) S. K. Tandel et al. , PRL 97, 082502 (2006)

Bridging the gap from heavies to superheavies 253, 254, 255 No mass measurement Cyclotron resonance curve of 253 No 2. M Block et al. , Nature 463, 785 -788 (2010)

The S 3 spectrometer at SPIRAL 2 A spectrometer for the high intensity stable ion beams of SPIRAL 2 (from 2012) New elements 54 Cr+248 Cm 299120+3 n S 3 (I=10 pµA) 1 evt/month@σest~0. 01 pb ? Isotopic exploration 40 -48 Ca+238 U 275 -283112+3, 4 n S 3 (I=20 pµA) 40 evt/week/pb Closed-shell deformed nucleus ? ? ? 40 Ar+238 U 274 Ds (+4 n) 270 Hs + α S 3 (I=50 pµA) 190 evt/week@σth=2 pb

Summary Ø most nuclei are deformed Ø prolate quadrupole deformation are the most common Øshape coexistence: interplay between shell effects and macroscopic properties Øessential to constrain collective nuclear models Ø Very large deformations encoutered at high spin Ø superdeformation evidenced / hyperdeformation still to be discovered Ø AGATA high-resolution germanium array Ø superheavy elements exist only because of shell effects Ø theory predicts deformed + spherical shell gaps Ø next proton magic number still to be discovered Ø very low production cross sections Ø direct production and undirect experimental techniques Ø SPIRAL 2 and S 3 spectrometer

Key questions and shell effects in nuclei • How does shell structure evolve away from stability? magic numbers, shell-model, spin-orbit, tensor • How do nuclear clusters and molecules form? few-body systems, halos, clusters • What is the shape of a nucleus, how large can be nuclear deformation? hyperdeformation, shape-coexistence • Is there any island of stability for superheavy elements? Next proton magic number, stabilizing deformed shell gaps • Next-generation facilities and innovative detectors worldwhile built this decade