1. B-1 Fragmentation – 0 Introduction Generalities Isotopic distributions Neck emission Participant-spectator model Fragment separators LISE of GANIL FRS of GSI Fragment selection Fragment production Spin orientation Determination of polarization Influences on polarization Kinematical model Polarization vs target size Polarization vs E inc

2. B-1 Fragmentation – 1 Generalities projectile target abraded nucleons evaporated nucleons pre-fragment fragment Definition: Formation of a unique fragment from the peripheral collision of a projectile nucleus with a target nucleus. The impact results in the abrasion of few nucleons. The excited pre-fragment decays by emitting few other nucleons.

3. B-1 Fragmentation – 2 Isotopic productions 32 S 33 S 34 S 35 S 36 S 31 P 32 P 33 P 34 P 35 P 30 Si 31 Si 32 Si 33 Si 34 Si 29 Al 30 Al 31 Al 32 Al 33 Al 28 Mg 29 Mg 30 Mg 31 Mg 32 Mg 27 Na 28 Na 29 Na 30 Na 31 Na 26 Ne 27 Ne 28 Ne 29 Ne 30 Ne 25 F 26 F 27 F 29 F 37 S 36 P 35 Si 34 Al 33 Mg 32 Na 31 Ne 31 S 30 P 29 Si 28 Al 27 Mg 26 Na 25 Ne 24 F 30 S 29 P 28 Si 27 Al 26 Mg 25 Na 24 Ne 23 F 29 S 28 P 27 Si 26 Al 25 Mg 24 Na 23 Ne 22 F 28 S 27 P 26 Si 25 Al 24 Mg 23 Na 22 Ne 21 F 24 O 26 O 28 O 23 O 22 O 21 O 20 O 23 N 22 N 21 N 20 N 19 N 193 Pb 194 Pb 195 Pb 196 Pb 197 Pb 198 Pb 192 Pb 191 Pb 190 Pb 189 Pb 192 Tl 193 Tl 194 Tl 195 Tl 196 Tl 197 Tl 191 Tl 190 Tl 189 Tl 188 Tl 191 Hg 192 Hg 193 Hg 194 Hg 195 Hg 196 Hg 190 Hg 189 Hg 188 Hg 187 Hg 190 Au 191 Au 192 Au 193 Au 194 Au 195 Au 189 Au 188 Au 187 Au 186 Au 189 Pt 190 Pt 191 Pt 192 Pt 193 Pt 194 Pt 188 Pt 187 Pt 186 Pt 185 Pt 188 Pb 187 Tl 186 Hg 185 Au 184 Pt 188 Ir 189 Ir 190 Ir 191 Ir 192 Ir 193 Ir 187 Ir 186 Ir 185 Ir 184 Ir 183 Ir 187 Pb 186 Tl 185 Hg 184 Au 183 Pt 182 Ir 186 Pb 185 Tl 184 Hg 183 Au 182 Pt 181 Ir 187 Os 188 Os 189 Os 190 Os 191 Os 192 Os 186 Os 185 Os 184 Os 183 Os 182 Os 181 Os 180 Os 185 Pb 184 Tl 183 Hg 182 Au 181 Pt 180 Ir 179 Os 186 Re 187 Re 188 Re 189 Re 190 Re 191 Re 185 Re 184 Re 183 Re 182 Re 181 Re 180 Re 179 Re 178 Re 184 Pb 183 Tl 182 Hg 181 Au 180 Pt 179 Ir 178 Os 177 Re 185 W 186 W 187 W 188 W 189 W 190 W 184 W 183 W 182 W 181 W 180 W 179 W 178 W 177 W 176 W 183 Pb 182 Tl 181 Hg 180 Au 179 Pt 178 Ir 177 Os 176 Re 175 W 182 Pb 181 Tl 180 Hg 179 Au 178 Pt 177 Ir 176 Os 175 Re 174 W 184 Ta 185 Ta 186 Ta 187 Ta 188 Ta 183 Ta 182 Ta 181 Ta 180 Ta 179 Ta 178 Ta 177 Ta 176 Ta 175 Ta 174 Ta 173 Ta 181 Pb 180 Tl 179 Hg 178 Au 177 Pt 176 Ir 175 Os 174 Re 173 W 180 Pb 179 Tl 178 Hg 177 Au 176 Pt 175 Ir 174 Os 173 Re 172 W 172 Ta 171 Ta 183 Hf 184 Hf 185 Hf 186 Hf 182 Hf 181 Hf 180 Hf 179 Hf 178 Hf 177 Hf 176 Hf 175 Hf 174 Hf 173 Hf 172 Hf 171 Hf 170 Hf 179 Pb 178 Tl 177 Hg 176 Au 175 Pt 174 Ir 173 Os 172 Re 171 W 170 Ta 169 Hf 182 Lu 183 Lu 184 Lu 181 Lu 180 Lu 179 Lu 178 Lu 177 Lu 176 Lu 175 Lu 174 Lu 173 Lu 172 Lu 171 Lu 170 Lu 169 Lu 168 Lu 178 Pb 177 Tl 176 Hg 176 Au 174 Pt 173 Ir 172 Os 171 Re 170 W 169 Ta 168 Hf 176 Tl 175 Hg 174 Au 173 Pt 172 Ir 171 Os 170 Re 169 W 168 Ta 167 Hf 167 Lu 166 Lu 181 Yb 180 Yb 179 Yb 178 Yb 177 Yb 176 Yb 175 Yb 174 Yb 173 Yb 172 Yb 171 Yb 170 Yb 169 Yb 168 Yb 167 Yb 166 Yb 165 Yb 174 Hg 173 Au 172 Pt 171 Ir 170 Os 169 Re 168 W 167 Ta 166 Hf 165 Lu 164 Yb 172 Au 171 Pt 172 Ir 169 Os 168 Re 167 W 166 Ta 165 Hf 164 Lu 163 Yb 179 Tm 178 Tm 177 Tm 176 Tm 175 Tm 174 Tm 173 Tm 172 Tm 171 Tm 170 Tm 169 Tm 168 Tm 167 Tm 166 Tm 165 Tm 164 Tm 163 Tm 162 Tm 171 Au 170 Pt 171 Ir 168 Os 167 Re 166 W 165 Ta 164 Hf 163 Lu 162 Yb 161 Tm 177 Er 176 Er 175 Er 174 Er 173 Er 172 Er 171 Er 170 Er 169 Er 168 Er 167 Er 166 Er 165 Er 164 Er 163 Er 162 Er 161 Er 160 Er 175 Ho 174 Ho 173 Ho 172 Ho 171 Ho 170 Ho 169 Ho 168 Ho 167 Ho 166 Ho 165 Ho 164 Ho 163 Ho 162 Ho 161 Ho 160 Ho 159 Ho 173 Dy 172 Dy 171 Dy 170 Dy 169 Dy 168 Dy 167 Dy 166 Dy 165 Dy 164 Dy 163 Dy 162 Dy 161 Dy 160 Dy 159 Dy 158 Dy 171 Tb 170 Tb 169 Tb 168 Tb 167 Tb 166 Tb 165 Tb 164 Tb 163 Tb 162 Tb 161 Tb 160 Tb 159 Tb 158 Tb 157 Tb 36 S+ 9 Be at 77.5 AMeV simulations for the LISE spectrometer 208 Pb+ 9 Be at 1 AGeV simulations for the FRS spectrometer

4. B-1 Fragmentation – 3 Neck emission projectile target quasi-target quasi-projectile In peripheral collisions, at intermediate energies (E inc < 100 AMeV)  The neck emission favours the n-rich LCP’s. LCP: Light Charged Particle = p, d, t, 3 He, 4 He IMF: Intermediate Mass Fragment = 3  Z  30 enhancement of the emission of LCP’s and IMF’s from the intermediate velocity region

5. B-1 Fragmentation – 4 Neck emission CHIMERA predictions for Au+Au at 80 AMeV J. Lukasik et al., Proceedings of INPC 2001 The rapidity of a particle corresponds to its velocity for non-relativistic energies J. Lukasik et al., Phys. Lett. B 566 (2003) 76 Au+Au at 40, 60, 80, 100, 150 AMeV very peripheral collisions target projectile

6. B-1 Fragmentation – 5 Participant - spectator model projectile target quasi-target (spectator) quasi-projectile (spectator) In peripheral collisions, at relativistic energies (E inc > 100 AMeV) participant region The participant region, very hot and dense, decays emitting only LCP’s, mainly nucleons.

7. B-1 Fragmentation – 6 Fragment separators Fragmentation  production of exotic nuclei LISE FRS GANIL Caen, France GSI Darmstadt, Germany

8. B-1 Fragmentation – 7 LISE of GANIL LISE = Ligne d’Ions Super Epluchés (Super Stripped Ion Line) secondary beam dipole 1 dipole 2 wedge Wien filter The primary beam ( 12 C to 238 U) have been accelerated in the two cyclotrons to energies from 5 to 95 AMeV target  http://www.ganil.fr/lise/lise.html

9. B-1 Fragmentation – 8 FRS of GSI  http://www-w2k.gsi.de/frs/index.asp FRS = FRagment Separator The primary beam ( 12 C to 238 U) have been accelerated in the synchrotron SIS to energies from 30 AMeV to 2 AGeV

10. B-1 Fragmentation – 9 Fragment selection Magnetic selection in mass, atomic number, and speed (A.v/Q). The dipoles allow a deviation of the ions of the secondary beam according to their charge state, their speed, and mass. The determination of their magnetic rigidity B  is a measure of this deviation. Non-relativistic formula: Relativistic formula: with with B  : magnetic rigidity (Tm)c: speed of light B: intensity of the magnetic field (T)A: nucleus mass (J)  : curvature radius (m)Q: positive ion charge v: speed of the nucleus (ms -1 )(Q  Z, if fully stripped) Magnetic dipoles

11. B-1 Fragmentation – 10 Fragment selection Selection in energy loss, on the atomic mass and number (i.e. in A 3 /Z 2 ). The degrader is located in an intermediate focal plane of the beam line. The secondary beam, still composed of several ions of diverse charge states, is slowed down and purified. The energy loss in the material is characteristic of the beam particles (selection in v and Z). The relative energy loss in the degrader is given by: with K: constant typical of the degrader A: nucleus mass e: thickness of the degrader Z: atomic number Degrader (wedge) Selection in speed (v). The electrostatic tank of the filter is divided in 2 subsections which are, each of them, inside a large magnetic dipolar gap. The beam goes then through a region with cross electric and magnetic fields (the direction of the electric field is vertical and the magnetic field’s is horizontal) with intensities such that the selected nucleus can continue its trajectory without being slowed down neither deviated of the incident direction of the secondary beam (the forces due to the two fields compensate each other). The other ions are deviated. Wien filter

12. B-1 Fragmentation – 11 Fragment production LISE Beam purity: 93% FRS at the end of the beam line intermediate focus final focus M.Pfützner et al., Phys. Rev. C 65(2002)064604 31 Al 177 Ta

13. B-1 Fragmentation – 12 Spin orientation q yield target selected fragments in-flight separation 3 1 -3 Principle: transfer of momentum via nucleon removal in the projectile symmetric selection (~ 0°): alignment asymmetric selection (~ 2°): polarization rather low orientation (5-30%) In the early 90’s, it was discovered the possibility to create spin orientation in exotic nuclei via projectile fragmentation. the participant spectator model: peripheral collisions projectile fragment or “spectator” abraded part or “participant” p proj p frag p nucl target

14. B-1 Fragmentation – 13 Spin orientation Population -2 -1 0 1 2 m Z OR isotropicalignedpolarized p(m) equal  m p(m) = p(-m) p(m)  p(-m)

15. The direction in which the radiation is emitted by a radioactive nucleus, depends on the direction of its nuclear spin. This is formally described by the ‘angular distribution’ function: W( , ,t) = A k B k n (t) Y k n ( ,  ) x y z  or    I k,n 44 2k+1 radiation parameter orientation tensor spherical tensors An isotropic ensemble has B 0 = 1, all other components are zero. An aligned ensemble has B k 0 components for k=even, n  0 components and odd tensors are zero.   radiation A polarized ensemble has B k 0 components for k=odd, k=even and n  0 components are zero.   radiation for study of isomers: aligned beam for study of ground states: polarized beam B-1 Fragmentation – 14 Spin orientation

16. 32 Al 33 Al asymmetry  The amount of polarization is determined from the asymmetry of the  emissions: radiation parameter experimental loss N up /N down =  (3I/I+1) v/c A 1 Q 1 P  -NMR measurement B high /B 0 measurement Experiment E347 of July 2003 P. Himpe, private communication asymmetry  31 Al B-1 Fragmentation – 15 Determination of the polarization G.Neyens, Rep. Prog. Phys. 66 (2003) 633

17. Al isotopes 36 S + 9 Be at 77.5 AMeV the structure of the studied fragment?  32 Al ground-state: 1 +  31,33 Al ground-states: 5/2 + Influence of the crystal host B-1 Fragmentation – 16 Influences on polarization Experiment E347 of July 2003 P. Himpe, private communication

18. (pf-p0)/p0 0 polarization + - yield K. Asahi et al., Phys. Lett. B 251(1990)488, H. Okuno et al., Phys. Lett. B 335(1994)29  rot light target  rot heavy target (pf-p0)/p0 alignment + - R k R k Polarization P = J z / |J| Alignment A = ( 2J y 2 - J 2 ) / J 2 with the angular momentum J = R x k B-1 Fragmentation – 17 Kinematical model

19. Coulomb repulsion > nuclear attraction  far-side trajectory Nuclear attraction > Coulomb repulsion  near-side trajectory H. Okuno et al., Phys. Lett. B 335(1994)29  rot = -50º f = 0.05  rot = 60º f = 0.1  rot = 150º f = 0.1 15 N+ 27 Al 15 N+ 93 Nb 15 N+ 197 Au Polarization of 12,13 B from the reaction at 68 AMeV of… data model scaling factor B-1 Fragmentation – 18 Polarization vs target size

20.  rot = 10º f = 0.15  rot = 10º f = 0.07  rot = 10º f = 0.025 100 AMeV230 AMeV 400 AMeV Polarization of 12 B from the reaction 13 C+ 9 Be at… K.Matsuta et al., Hyp. Int. 120/121(1999)713 data model Increase of the incident energy  decrease of the amount of polarization (and increase of the amount of alignment) B-1 Fragmentation – 19 Polarization vs E inc