1. Spectroscopy W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 1

2. Chemical Evolution of our Universe W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 2

3. W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 3 S. Mason. Chemical Evolution (Clarendon Press, 1992), pp. 40-45. Chemical Evolution of our Universe

4. W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy Probes for Nuclear Structure To “see” an object, the wavelength of the light used must be shorter than the dimensions d of the object ( ≤ d). (DeBroglie: p=ħk=ħ2  / Rutherford’s scattering experiments d Nucleus ~ few 10 -15 m Need light of wave length < 1 fm, equivalent energy E Not easily available as light Can be made with charged particle accelerators 4 Scan energy states of nuclei. Bound systems have discrete energy states  unbound E continuum

5. What Structure? - Spectroscopic Goals W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 5 Bound systems have discrete energy states  unbound E continuum  Scan energy states of nuclei. Desired information on nuclear states (“good quantum numbers”): Energy relative to ground state (g.s.) (E i, i=0,1,…; E*) Stability, life time against various decay modes (,…) Electrostatic moments Q j  see below Magnetostatic moments M i  see below Angular momentum (nuclear spin) Parity (=spatial symmetry of quantum ) Nucleonic (neutron & proton) configuration (e.g., “isospin” quantum #) Nuclear Level Scheme +0-+0- E*

6. Particle and  Spectroscopy W. Udo Schröder, 2011 Nuclear Experiment 6 Individual or multi detector setups, spectrometers Off-line activation measurements Identify scattered/transmuted projectile & target nuclei, measure m, E, A, Z, I,.. of all ejectiles (particles and -rays).

7. How to Excite Nuclei: Inelastic Nuclear Reactions Coulomb excitation of rotational motion for deformed targets or vibrations. W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 7 p, n,..transfer rxns, e.g., (d, n), ( 3 He,d). Final state is excited Target Projectile Fusion/compound nucleus reactions, Final state is highly excited, thermally metastable Scan the bound nuclear energy level scheme 

8. Coulomb Excitation (Semi-Classical) spherical deformed Excitation probability in perturbation theory: For small energy losses (weak excitations: t t(R 0 ) V coul (t)  coll 180 0 - Torque exerted on deformed target  excitation of collective nuclear rotations Transfer of angular momentum from relative motion: Angular dependence of excitation probability: Adiabaticity Condition: Fast “kick” will excite nucleus Otherwise adiabatic reorientation of deformed nucleus to minimize energy !

9. W. Udo Schröder, 2012 Mean Field 9 Observation of Collective Nuclear Rotations z b a  := quadrupole deformation parameter Quadrupole moment ( Deviation from spherical nucleus ) Wood et al.,Heyde Deexcitation-Gamma Spectra Measured energies (keV)

10. Method: Particle Spectroscopy W. Udo Schröder, 2011 Nuclear Experiment 10 (A+a) Excited states Energy Spectrum of Products b Particle Energy E b  Counts   Excited States g.s.  Particle a Beam Quadrupole Magnet Faraday Cup Populate (excite) the spectrum of nuclear states. Measure probabilities for excitation and de-excitation Reconstruct energy states {E i,I i, i } from energy, linear and angular momentum balance. Obtain structure information from probabilities. Bound systems have discrete energy states  unbound E continuum Reaction A(a,b)B* E

11. Method: Simultaneous Absorption & Emission Spectroscopy W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 11 Reaction 64 Ni(p,p’) 64 Ni* :inelastic proton scattering, absorb E from beam 64 Ni gs + 1 + 2 + 3 +…  pDpD pCpC pBpB pApA Scattered Proton Spectrum  p-energy loss Deexcitation  Spectrum

12. Example: Inelastic Particle Scattering W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 12 238 U+d  238 U*+d’ Scattered deuteron kinetic energy spectrum E’ d = E’ d ( d, E d ) Beam HPGe Deexcitation- Spectrum Coincident cascades Coincident cascades indicate nuclear band structure (rotational, vibrational,...)

13. Measuring Energy Transfer: The Q Value Equation Cross Section, Kinematics & Q Values W. Udo Schröder, 2008 13 Measure kinetic energy E 3 vs. angle  3 to determine reaction Q value. Predict energies of particles at different angles as functions of Q. How to interpret energies of scattered particles:

14. Transmutation in Compound Nucleus Reactions W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 14 Q Decay of CN populates states of the “evaporation residue” nucleus Use mass tables to calculate Q g.s. E ER * Excited levels of ER

15. Technology: Typical Setups Particle Experiments W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 15 Modified, after K.S. Krane, Introduction to Nuclear Physics, Wiley&Sons, 1988 Simultaneous measurement of time of flight, specific energy loss and residual energy of particles  E, Z, A Simultaneous measurement of specific energy loss E and residual energy E of particles  E, Z, (A) Particle E-E/TOF Setup E-E Setup = Total Energy Residual Energy E = ToF Time of Flight Total Energy

16. W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy Particle ID (Z, A, E) Specific energy loss, spatial ionization density, TOF Particle ID with Detector Telescopes Si Telescope Massive Reaction Products SiSiCsI Telescope (Light Particles) He Li Be Na Ne F O N C B 20 Ne + 12 C @ 20.5 MeV/u -  lab = 12° EE E-E E-E Telescope 16

17. W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy THE CHIMERA DETECTOR Chimera mechanical structure 1m 1° 30° REVERSE EXPERIMENTAL APPARATUS TARGET BEAM Experimental Method  E-E  Charge  E-E E-TOF  Velocity, Mass Pulse shape Method  LCP Basic elementSi (300  m) + CsI(Tl) telescope Primary experimental observables TOF  t  1 ns Kinetic energy, velocity  E/E Light charged particles  2% Heavy ions  1% Total solid angle  /4  94% Granularity1192 modules Angular range1°<  < 176° Detection threshold <0.5 MeV/A for H.I.  1 MeV/A for LCP CHIMERA characteristic features 688 telescopes Laboratori del Sud, Catania/Italy 17

18. W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 18 GRETA Detector Configuration ƒTwo types of irregular hexagons, 60 each, 3 crystals/cryostat= Œ 40 modules Detector – target distance = 15 cm $750k  GRETINA Technology in  spectroscopy Greta HPGe Array Realistic coverage: Ω/4=0.8 Spatial resolution: ∆x=2 mm

19. W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 19 I.-Y. Lee, LBNL, 2011 Use Compton scattering laws to identify & track interactions of all ’s. Conventional method requires many detectors to retain high resolution and avoid summing. -Ray Tracking with HPGe Detector Array

20. Characteristic Examples of Level Schemes W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 20 Single-particle spectra: Irregular sequence, half- integer spins, various parities. Collective vibrations: O + g.s., even spins & parity, regular sequence with bunching of (0 +,2 +,4 + ) triplet Collective rotations: Regular quadratic sequence 0 +,2 +,4 +,…. Only even or only odd spins, I=2, uniform parity.

21. W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 21 Characteristic Level Schemes-Light Nuclei Different densities of states. Similarities in energies, spin, parity sequence for mirror nuclei: (N, Z)=(a, b)=(b,a) mirror

22. W. Udo Schröder, 2011 Gamma Decay 22 Gamma Decay of Isobaric Analog States For same T, wfs for protons and neutrons are similar  “Mirror Nuclei” 19 Ne and 19 F W.u.

23. W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 23 Examples of Level Schemes: SM vs. Collective

24. W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 24

25. W. Udo Schröder, 2012 Principles Meas 25 Example 159 103 76 60 33 0 241 Am 237 Np 5.378 MeV 5.433 MeV 5.476 MeV 5.503 MeV 5.546 MeV 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 30 40 50 60 70 80 90 100 110 120  Energy (keV) - 5 MeV  Energy (keV)  -Decay of 241 Am, subsequent  emission from daughter Find coincidences (E , E  ) 9  -rays, 5 

26. W. Udo Schröder, 2012 Principles Meas 26 Example 159 103 76 60 33 0 241 Am 237 Np 5.378 MeV 5.433 MeV 5.476 MeV 5.503 MeV 5.546 MeV 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 30 40 50 60 70 80 90 100 110 120  Energy (keV) - 5 MeV  Energy (keV)  -Decay of 241 Am, subsequent  emission from daughter Find coincidences (E , E  ) 9  -rays, 5 

27. W. Udo Schröder, 2012 Principles Meas 27 Example 159 103 76 60 33 0 241 Am 237 Np 5.378 MeV 5.433 MeV 5.476 MeV 5.503 MeV 5.546 MeV 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 30 40 50 60 70 80 90 100 110 120  Energy (keV) - 5 MeV  Energy (keV)

28. W. Udo Schröder, 2012 Principles Meas 28 Example 159 103 76 60 33 0 241 Am 237 Np 5.378 MeV 5.433 MeV 5.476 MeV 5.503 MeV 5.546 MeV 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 30 40 50 60 70 80 90 100 110 120  Energy (keV) - 5 MeV  Energy (keV)

29. W. Udo Schröder, 2012 Principles Meas 29 Example 159 103 76 60 33 0 241 Am 237 Np 5.378 MeV 5.433 MeV 5.476 MeV 5.503 MeV 5.546 MeV 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 30 40 50 60 70 80 90 100 110 120  Energy (keV) - 5 MeV  Energy (keV)

30. W. Udo Schröder, 2012 Principles Meas 30 Example 159 103 76 60 33 0 241 Am 237 Np 5.378 MeV 5.433 MeV 5.476 MeV 5.503 MeV 5.546 MeV 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 30 40 50 60 70 80 90 100 110 120  Energy (keV) - 5 MeV  Energy (keV)

31. W. Udo Schröder, 2012 Principles Meas 31 Example 159 103 76 60 33 0 241 Am 237 Np 5.378 MeV 5.433 MeV 5.476 MeV 5.503 MeV 5.546 MeV 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 30 40 50 60 70 80 90 100 110 120  Energy (keV) - 5 MeV  Energy (keV) No  coincidences !  must be g.s. transition

32. W. Udo Schröder, 2012 Principles Meas 32 Example 159 103 76 60 33 0 241 Am 237 Np 5.378 MeV 5.433 MeV 5.476 MeV 5.503 MeV 5.546 MeV 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 30 40 50 60 70 80 90 100 110 120  Energy (keV) - 5 MeV  Energy (keV)

33. W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 33

34. Exercises: Nuclear Electrostatic Moments Consider a nucleus with a homogeneous, axially symmetric charge distribution 1.Show that its electric dipole moment Q 0 is zero. 2.Assume for the charge distribution a homogenously charged rotational ellipsoid with semi axes a and b, given by. Show that 3. From the measured 242 Pu and 244 Pu  spectra determine the deformation parameters  of these two isotopes. W. Udo Schröder, 2007 Nuclear Deformations 34

35. Alpha-Gamma Spectroscopy 251Fm  247Cf W. Udo Schröder, 2012 Nuclear Deformations 35

36. W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 36

37. Spectroscopic vs. Intrinsic Quadrupole Moment W. Udo Schröder, 2010 Gamma Decay 37 m I =I z  I≠0: Transformation body-fixed to lab system Any orientation quadratic dependence of Q z on m I “The” quadrupole moment

38. Electromagnetic Radiation Gamma-Gamma Correlations 38 Protons in nuclei = moving charges  emits electromagnetic radiation, except if nucleus is in its ground state! Heinrich Hertz E. Segré: Nuclei and Particles, Benjamin&Cummins, 2 nd ed. 1977 Point Charges Nuclear Charge Distribution Monopole ℓ = 0 Dipole ℓ = 1 Quadrupole ℓ =2 Propagating Electric Dipole Field

39. Gamma-Gamma Correlations 39 Nuclear Electromagnetic Transitions Conserved: Total energy (E), total angular momentum (I) and total parity (): I2+I2+ 1-1- 0+0+ EiEi Consider often only electric multipole transitions. Neglect weaker magnetic transitions due to changes in current distributions. I2+I2+ 1-1- 0+0+ EfEf  Initial N i spatial symmetry  retained in overall combination N f + Illustration conserved spatial symmetry

40. Gamma-Gamma Correlations 40 Selection Rules for Electromagnetic Transitions Conserved: Total energy (E), total angular momentum (I, I z ), total parity (): z mimi mfmf mm Coupling of Angular Momenta Quantization axis : z direction. Physical alignment of I possible (B field, angular correlation)

41. W. Udo Schröder, 2011 Gamma Decay 41 Transition Probabilities: Weisskopf’s s.p. Estimates Consider single nucleon in circular orbit (extreme SM) Weisskopf Estimates

42. W. Udo Schröder, 2011 Gamma Decay 42 Weisskopf’s Eℓ Estimates T 1/2 for solid lines have been corrected for internal conversion. Experimental E1: Factor 10 3 -10 7 slower than s.p. WE  Configurations more complicated than s.p. model, time required for rearrangement Experimental E2: Factor 10 2 faster than s.p. WE  Collective states, more than 1 nucleon. Experimental Eℓ (ℓ>2): App. correctly predicted.

43. W. Udo Schröder, 2011 Gamma Decay 43 Weisskopf’s Mℓ Estimates T 1/2 for solid lines have been corrected for internal conversion. Experimental Mℓ: Several orders of magnitude weaker than Eℓ transitions.

44. W. Udo Schröder, 2011 Gamma Decay 44 Isospin Selection Rules Reason: n/p rearrangements  multipole charge distributions photon interacts only with 1 nucleon ( = 1/2)  T = 0, 1 Example E1 transitions: Enhanced (collective) E2, E3 transitions T = 0 Collective (rot or vib) WF does not change in transition.

45. W. Udo Schröder, 2011 Gamma Decay 45 Gamma Decay of Isobaric Analog States For same T, wfs for protons and neutrons are similar  “Mirror Nuclei” 19 Ne and 19 F W.u.

46. W. Udo Schröder, 2012 Nuclear Deformations 46 Electrostatic Multipole (Coulomb) Interaction Monopole ℓ = 0 Dipole ℓ = 1 Quadrupole ℓ =2 Point Charges Nuclear charge distribution |e|Z e  z symmetry axis Quadrupole Q ≠0, indicates deviation from spherical shape Different multipole shapes/ distributions have different spatial symmetries

47. W. Udo Schröder, 2012 Nuclear Spins 47 Magnetization: Magnetic Dipole Moments Moving charge e  current density j  vector potential, influences particles at via magnetic field e,m  Loop = I x A= current x Area(inside) current loop: =0

48. W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 48

49. Lecture Plan Intro to Nuclear Structure W. Udo Schröder, NCSS 2012 Nuclear Spectroscopy 49 DayTimeTopic Monday 6/25 09:00-10:00 10:30-11:30 How do we know about NS? Nuclear Spectroscopy. Nucleon-Nucleon forces and 2-body Systems Tuesday 6/26 09:00-10:00 10:30-11:30 Mean Field and its Symmetries, Spin and Isospin Fermi Gas Model Wednesday 6/27 09:00-10:00 10:30-11:30 Spherical Shell Model Simple Predictions and Comparisons Thursday 6/28 09:00-10:00 10:30-11:30 Residual Interactions/ Pairing Deformed Nuclei and their Spectroscopy Friday 6/29 09:00-11:30Final Exam