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Resonance Scattering Technique and break-up to study nuclear structure

ISOLDE Nuclear Reaction and Nuclear Structure Course. Resonance Scattering Technique and break-up to study nuclear structure. A. Di Pietro. Outline of the lecture:  Resonance scattering method in reverse kinematics.  Advantages of the technique.

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Resonance Scattering Technique and break-up to study nuclear structure

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  1. ISOLDE Nuclear Reaction and Nuclear Structure Course Resonance Scattering Technique and break-up to study nuclear structure A. Di Pietro

  2. Outline of the lecture: • Resonance scattering method in reverse kinematics. •  Advantages of the technique. •  Resolution. Discrimination of different processes and energy reconstruction. • Resonant break-up • 3-body kinematics

  3. 12O 13O 14O 15O 16O 17O 18O 19O 20O 21O 22O 11N 12N 13N 14N 15N 16N 17N 18N 19N 20N 21N 8C 9C 10C 11C 12C 13C 14C 15C 16C 17C 18C 19C 20C 8B 9B 10B 11B 12B 13B 14B 15B 17B 19B 7Be 8Be 9Be 10Be 11Be 12Be 14Be 6Li 7Li 8Li 9Li 11Li 3He 4He 6He 8He 1H 2H 3H n core core Exotic structures in light nuclei triangle α α α 3-2 in 14C α α α dilute gas C 0+2 in 12C B Decoupling of Proton and neutrons Be 10C, 16C Li He α α H excited states α α neutron skin Be isotopes 8He,C molecular neutron halo vanishing of magic number From Y. KanadaEn’yo 6He,11Li,11Be

  4. Conventional cluster structure Cluster structure is a well established feature of many light NZ nuclei both in their ground and excited states. Ikeda diagram Weak coupling picture: Clusters are formed by tightly bound nucleons (cluster is stiff, i.e. not easy to excite); Weakly coupled inter-cluster motion is considered. Threshold rule: i.e. these states appear close to the threshold for breaking-up into the cluster constituents. Ex. Hoyle state in 12C K. Ikeda et al. Supp.Progr.Theo.Phys. 68(1980)1 4

  5. Possible ways to study cluster structures: • transfer and decay into the constituents • inelastic scattering followed by break up 3-body processes Ex: 10Be+9Be->15C*+a->11Be+a+a • Resonant elastic scattering2-body process Ex: 10Be+b->6He+a+b Ex: 10Be+a->14C*->10Be+a Experimental signature: • large reduced width for cluster decay • rotational bands with band head around the threshold for cluster decay (measurement of Eexc and Jπ moment ofinertia)

  6. thick solid or gasous target gaseous target (H, He) easy to change target thickness (changing gas pressure) more homogeneous target Resonant scattering method (RSM) in invese kinematics K.P.Artemov et al. Sov.J.Nucl.Phys. 52(1990)408 Elastic scattering of heavy projectiles B on a light targets b (protons or as) in order to study properties of the compound nucleus C resulting from B+b C B+b Excitation function measured at qcm180º enhanced visibility of resonances with respect to potential and Coulomb scattering. Used in the last ten years to measure excitation functions with radioactive beams.

  7. Allows to measure excitation function in a wide energy range without changing beam energy  reduces running time of the experiment Allows precise measurement of resonance properties:Er, Jp, Gtot, Gp, Ga Allows to measure recoil particles around q c.m.~180° light heavy beam recolil particle  Very useful in experiments with low intensity beams (104÷ 106 pps).

  8. Direct kinematics Inverse kinematics Q Q T0 E0 T3 E3 Advantages of using inverse kinematics E0 e T0 = laboratory projectile energy in direct and reverse kinematics respectively E0' e T0' = c.m. energy in direct and reverse kinematics respectively Θ =laboratory scattering angle of light particle E3 e T3 = light particle laboratory energy in direct and reverse kinematics respectively

  9. Some trivial equations (see previous lecture) direct inverse For the same c.m. energy: T0' = E0' For: θlab = 0° (= 180° in the c.m.) light particle enrgy is:

  10. In the current notation : E3=E2L recoil energy in the Lab system E1L=E0 projectile energy V1L V1B VBL V2L V2B at q1B=180°

  11. Excitation function from measured recoil energy: B+b C*B+b

  12. Laboratory energy resolution for light recoil particles in inverse kinematics. ∆E=beam energy straggling in the laboratory (dE/dx)li= stopping power for light particles (dE/dx)HI= stopping power for beam particles z= charge of light recoil particles Z=charge of beam particles

  13. Dependence of energy resolution from energy straggling q>00 q=00 32S+a G. RogachevPh.D thesis. Moscow1999 Energy resolution depends also from: • Beam spot size • Detectorenergy resolution • Detector angular resolution • Kinematical spread within dq • Beam angular straggling •  Recoil angular straggling (small) Due to energy straggling, to the same Ec.m. correspond different Edet. due to different paths. Effect larger at q>00 due to additional contribution of different scattering angles. Dx DEstraggDx 13

  14. Problems of using this technique: Sources of background  inelastic scattering events  Precise knowledge of stopping power to extract correctly the resonance parameters Need to measure de/dx with radioactive beams (but not only!)

  15. How to discriminate elastic from inelastic scattering events? From a or p spectrum no possibilities to discriminate the process which produces recoil particles.  In experiment with a gasous extended target is possible to discriminate elastic from inelastic from time of flight measurement or tracking (active targets).

  16. Example:9Be + 4He Calculated TtOF- ∆E 2d-spectrum 16

  17. 9Be* 9Begs Experimental Ttof-∆E 2d-spectrum Inelastic Elastic Projecting on time axis Time resolution ΔT~1 ns

  18. Problems with stopping power calculations. Excitation function 9Be+4He at Ecm<4.5MeV  Excitation function 9Be + α with RSM on infinite target and energy loss calculated using Monte Carlo code SRIM M. Zadro et al, NIM B259 (2007). — Excitation function α+9Be measured with thin target method varying beam energy at small strepsJ. Liu [NIM B 108,(1996) 247] , J.D. Goss [PRC 7,(1973) 247] Different energy resonance with the two techniques !

  19. Using measured energy loss data Note: changing stopping power date changes also extracted resonance cross-section

  20. Excitation function 9Be+a at Ecm>4.5 MeV Using measured energy loss data  Excitation function 9Be + α with RSM on infinite targetM. Zadro et al, NIM B259 (2007). — Excitation function α+9Be measured with thin target method varying beam energy at small strepsR.B.Taylor [NP 65,(1965) 318] Need to measure stopping power with RIBs but not only!

  21. Some example of experiments performed using RIBs and RSM technique.

  22. Level scheme of p-rich nuclei unknown for many species. By bombarding a 1H enriched target with a p-rich radioactive beam  possibility to study levels in the p-rich compound nucleus which are proton unbound. RSM on thick target Curtsy of C. Angulo

  23. b background Experiment performed at CRC Louvain-la Neuve 18Ne+p @ Elab=21, 23.5 and 28 MeV Average beam intensity ~4  106 pps Target 0.5 mg/cm2 polyethylene Detection set-up C. Angulo et al. Nucl. Phys. A 716(2003)211

  24. R-matrix analysis Level scheme Very large Coulomb shift (~0.73 MeV) typical of deformed states in nuclei near the drip-line.

  25. Beamprofile P=700 mbar T=295 K 50 mm 50 mm E8Li=30.6 MeVI≈5x104pps beam 8Li+4He12B • ΔE : quadrants 50x50 mm2 quadrants Si detectors 50 μm thick. • E DoubleSidedSilicon Strip Detectors, 50x50 mm2 16+16 strip, 1000 μm  25 ΔE + DSSSD detectors MCPDetector gas target Entrance window Stopping power detectors

  26. Elasticscatteringαparticlediscrimination Background a spectrum: 8Li (β-)→ 8Be*→ 2 α Background: 8Li (β-)→8Be*→ 2 α α - particle punch through 3 H ΔE Eres α 26

  27. Comparison with literature 15.8 14.4 13.5 12B states. aparticlethreshold10.0 MeV 9Be+7Li → 2α+8Li 27 Soic N., Europhys. Lett.,63 (2003), 524

  28. Resonant particle spectroscopy: • transfer and decay into the constituents • inelastic scattering followed by break up 3-body processes Ex: 10Be+9Be->15C*+a Ex: 10Be+b->6He+a+b 28

  29. Resonant particle spectroscopy Ex: A+B->C*+a The detection of break-up products select states with large partial widths for decaying into a chosen channel thus enabling the selection of states with well-developed cluster structure. High segmentation of the detection system allows for high resolution measurement. M. Milin at al. EPJ A41(2009)335

  30. 6He+12C4He+14C*4He+4He+10Be

  31. Three bodykinematics

  32. 2 2 V1L V1B q1B q1L 1 VBL 1 3 3 E1B=½m1V1L2+m1(mPEPL)/(mP+mT)2-m1V1L(2mPEPL)1/2/(mP+mT)cosq1L a12 Three body kinematics Reaction: P+T→1+2+3 Center of mass system Sequential decay relative coordinate system VBL=(2mPEPL)1/2/(mP+mT) V1B2=V1L2+VBL2-2V1LVBLcosq1L E1B=E1L-2a1E1Lcosq1L+a12

  33. f1B=f1L f1B=f1L

  34. If we detect particle one the kinematics is completely determined by the two body (particle 1 and 23) kinematics. Ifwedetectparticle 2 and 3 wehavetoreconstruct the excitationenergyofparticle 23. Ecm Total energy available in the cener of mass system m1=mass of particle 1 m23=m2+m3= mass of particle 23 M=m1+m2+m3 We define the reduced masses: m1-23=m1m23/(m1+m23)=m1(m2+m3)/M m2-3=m2m3/m2+m3

  35. 2 V2L 23 3 c’ system V3L q2L,f2L q3L,f3L VBL q1L,f1L V1L Measured quantities are E1L,q1L,f1L – E2L,q2L,f2L- E3L,q3L,f3L of one, two or even three particles NB: we note that the velocity vectors are in the 3 dimentional space not in plane and both q and f angles are important. Eg. One wants to reconstruct excitation energy of particle 23 1

  36. Reaction p+T→1+23*→1+2+3 e.g. : a+6Li→a+6Li*→a+a+d 2 V23L V2L V23B 3 V3L q2L,f2L V1B q3L,f3L VBL q1L,f1L V1L From two body kinematics one can reconstruct the excitation energy of the intermediate 23 system. See equations for two body kinematics 1

  37. 6Li+a6Li*+aa+d+a E*(6Li)=2 MeV E*(6Li)=10 MeV

  38. Reaction p+T→1+23*→1+2+3 2 V23L V2L E2-3 V23B 3 E* V3L Q(23→2+3) q2L,f2L V1B q3L,f3L VBL q1L,f1L 23 V1L E2-3=E23*+Q(23→2+3)=1/2mvrel(2-3)2=1/2m(V2L-V3L)2 1 quantities to be measured quantity we want to extract from the experiment

  39. V3L→ V3L,q3L,f3L V2L→ V2L,q2L,f2L V2Lx= V2Lsinq2Lcosf2L V2Ly= V2Lsinq2Lsinf2L V2Lz= V2Lcosq2L V2rel=(V2L –V3L)2= V2L2+V3L2-2 V2L● V3L V3Lx= V3Lsinq3Lcosf3L V3Ly= V3Lsinq3Lsinf3L V3Lz= V3Lcosq3L V2L● V3L = V2L V3Lcosqrel= V2Lx V3Lx +V2Ly V3Ly +V2Lz V3Lz= V2Lsinq2Lcosf2L V3Lsinq3Lcosf3L +V2Lsinq2Lsinf2L V3Lsinq3Lsinf3L +V2Lcosq2L V3Lcosq3L measured quantities energies and angles

  40. Summary and conclusions Cluster structures can be measured in various way. Resonant elastic scattering gives the possibility to measure the excitation function in a single run without changing beam energy.Particularly useful in RIB experiments. With this technique only unbound states can be measured and the main limitation is the minimum resonance width that can be measured. Both single particle and cluster states can be studied with RSM. Resonant particle spectroscopy is the most commonly used technique to study cluster structure. Good energy and angular resolution is required.

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