Nuclear Spectroscopy 1 Spectroscopy W Udo Schrder NCSS

Nuclear Spectroscopy 1 Spectroscopy W. Udo Schröder, NCSS 2012

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

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

4 Probes for Nuclear Structure To “see” an object, the wavelength l of the light used must be shorter than the dimensions d of the object (l ≤ d). (De. Broglie: p=ħk=ħ 2 /l) Rutherford’s scattering experiments d. Nucleus~ few 10 -15 m Need light of wave length l < 1 fm, equivalent energy E Nuclear Spectroscopy Not easily available as light Can be made with charged particle accelerators Scan energy states of nuclei. Bound systems have discrete energy states unbound E continuum W. Udo Schröder, NCSS 2012

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

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

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

Coulomb Excitation (Semi-Classical) 1800 -q Torque exerted on deformed target excitation of collective nuclear rotations Transfer of angular momentum from relative motion: Angular dependence of excitation probability: spherical Adiabaticity Condition: Fast “kick” will excite nucleus For small energy losses (weak excitations: deformed Vcoul(t) Otherwise adiabatic reorientation of deformed nucleus to minimize energy tcoll t(R 0) ! t Excitation probability in perturbation theory:

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

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

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

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

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

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

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

Particle ID with Detector Telescopes Particle ID (Z , A, E) Specific energy loss, spatial ionization density, TOF Si. Cs. I Telescope (Light Particles) Si Telescope Massive Reaction Products DE-E Telescope 16 DE Nuclear Spectroscopy E-DE 20 Ne + 12 C @ 20. 5 Me. V/u - lab = 12° Na Ne F O N C B Be Li He W. Udo Schröder, NCSS 2012

THE CHIMERA DETECTOR Laboratori del Sud, Catania/Italy CHIMERA characteristic features E-E Charge E-E E-TOF Velocity, Mass Pulse shape Method LCP Basic element Si (300 m) + Cs. I(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% Granularity 1192 modules Angular range 1°< < 176° Detection threshold <0. 5 Me. V/A for H. I. 1 Me. V/A for LCP 17 Experimental Method Nuclear Spectroscopy REVERSE EXPERIMENTAL APPARATUS 688 telescopes TARGET 30° 1° Chimera mechanical structure 1 m W. Udo Schröder, NCSS 2012 BEAM

18 Technology in g spectroscopy Greta HPGe Array Nuclear Spectroscopy Realistic coverage: Ω/4 p=0. 8 Spatial resolution: ∆x=2 mm W. Udo Schröder, NCSS 2012 GRETA Detector Configuration �Two types of irregular hexagons, 60 each, 3 crystals/cryostat= � 40 modules Detector – target distance = 15 cm $750 k GRETINA

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

Characteristic Examples of Level Schemes Nuclear Spectroscopy 20 Single-particle spectra: Irregular sequence, halfinteger spins, various parities. W. Udo Schröder, NCSS 2012 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, DI=2, uniform parity.

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

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

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

24 Nuclear Spectroscopy W. Udo Schröder, NCSS 2012 Example of g –particle Spectroscopy

241 Am 159 Principles Meas 0 5. 237 Np Find coincidences (Ea, Eg) 9 g-rays, 5 a g Energy 25 103 76 60 33 50 5. 47 3 6 5. 5 46 Me Me. V Me V V (ke. V) e. V M 78 e. V 5. 3 M 3 43 5. Example a-Decay of 241 Am, subsequent g emission from daughter 120 110 100 90 80 70 60 50 40 30 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 a Energy (ke. V) - 5 Me. V W. Udo Schröder, 2012

241 Am 159 Principles Meas 0 5. 237 Np Find coincidences (Ea, Eg) 9 g-rays, 5 a g Energy 26 103 76 60 33 50 5. 47 3 6 5. 5 46 Me Me. V Me V V (ke. V) e. V M 78 e. V 5. 3 M 3 43 5. Example a-Decay of 241 Am, subsequent g emission from daughter 120 110 100 90 80 70 60 50 40 30 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 a Energy (ke. V) - 5 Me. V W. Udo Schröder, 2012

241 Am 159 5. 237 Np g Energy 0 120 110 100 90 80 70 60 50 40 Principles Meas 27 103 76 60 33 50 5. 47 3 6 5. 5 46 Me Me. V Me V V (ke. V) e. V M 78 e. V 5. 3 M 3 43 5. Example 30 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 a Energy (ke. V) - 5 Me. V W. Udo Schröder, 2012

241 Am 159 5. 237 Np g Energy 0 120 110 100 90 80 70 60 50 40 Principles Meas 28 103 76 60 33 50 5. 47 3 6 5. 5 46 Me Me. V Me V V (ke. V) e. V M 78 e. V 5. 3 M 3 43 5. Example 30 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 a Energy (ke. V) - 5 Me. V W. Udo Schröder, 2012

241 Am 159 5. 237 Np g Energy 0 120 110 100 90 80 70 60 50 40 Principles Meas 29 103 76 60 33 50 5. 47 3 6 5. 5 46 Me Me. V Me V V (ke. V) e. V M 78 e. V 5. 3 M 3 43 5. Example 30 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 a Energy (ke. V) - 5 Me. V W. Udo Schröder, 2012

241 Am 159 5. 237 Np g Energy 0 120 110 100 90 80 70 60 50 40 Principles Meas 30 103 76 60 33 50 5. 47 3 6 5. 5 46 Me Me. V Me V V (ke. V) e. V M 78 e. V 5. 3 M 3 43 5. Example 30 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 a Energy (ke. V) - 5 Me. V W. Udo Schröder, 2012

241 Am 159 Principles Meas 0 5. 237 Np g Energy 31 103 76 60 33 50 5. 47 3 6 5. 5 46 Me Me. V Me V V (ke. V) e. V M 78 e. V 5. 3 M 3 43 5. Example 120 110 100 90 80 70 60 50 40 No a-g coincidences ! must be g. s. transition W. Udo Schröder, 2012 30 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 a Energy (ke. V) - 5 Me. V

241 Am 159 5. 237 Np g Energy 0 120 110 100 90 80 70 60 50 40 Principles Meas 32 103 76 60 33 50 5. 47 3 6 M 5. 5 M 46 e. V e Me V V (ke. V) e. V M 78 e. V 5. 3 M 3 43 5. Example 30 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 a Energy (ke. V) - 5 Me. V W. Udo Schröder, 2012

33 Nuclear Spectroscopy W. Udo Schröder, NCSS 2012 Exercises

Nuclear Deformations 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 g spectra determine the deformation parameters b of these two isotopes. W. Udo Schröder, 2007

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

36 Nuclear Spectroscopy g Spectroscopy Theoretical Tools W. Udo Schröder, NCSS 2012

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

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

Nuclear Electromagnetic Transitions Conserved: Total energy (E), total angular momentum (I) and total parity (p): 39 Illustration conserved spatial symmetry Ei 1 - Gamma-Gamma Correlations Ip 2+ 0+ Ef g 1 - 0+ Initial Ni spatial symmetry retained in overall combination Nf +g Consider often only electric multipole transitions. Neglect weaker magnetic transitions due to changes in current distributions.

Selection Rules for Electromagnetic Transitions Conserved: Total energy (E), total angular momentum (I, Iz), total parity (p): Quantization axis : z direction. Physical alignment of I possible (B field, angular correlation) 40 Coupling of Angular Momenta z Gamma-Gamma Correlations mg mi mf

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

Gamma Decay 42 Weisskopf’s Eℓ Estimates Experimental E 1: Factor 103 -107 slower than s. p. WE Configurations more complicated than s. p. model, time required for rearrangement Experimental E 2: Factor 102 faster than s. p. WE Collective states, more than 1 nucleon. Experimental Eℓ (ℓ>2): App. correctly predicted. W. Udo Schröder, 2011 T 1/2 for solid lines have been corrected for internal conversion.

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

Isospin Selection Rules Reason: n/p rearrangements multipole charge distributions photon interacts only with 1 nucleon (t = 1/2) DT = 0, 1 44 Example E 1 transitions: Enhanced (collective) E 2, E 3 transitions DT = 0 Gamma Decay Collective (rot or vib) WF does not change in transition. W. Udo Schröder, 2011

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

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

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

48 Nuclear Spectroscopy W. Udo Schröder, NCSS 2012

Nuclear Spectroscopy 49 Lecture Plan Intro to Nuclear Structure Day Time 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: 30 Final Exam W. Udo Schröder, NCSS 2012 Topic