1. Applications of gamma ray spectrometry A) Study of nuclear structure, nuclear transitions and nuclear reactions 1) Properties and advantages of nuclear electromagnetic radiation studies 2) Facets of basic research by means of gamma spectroscopy 3) Basic methods: a) Determination of level energies and decay scheme b) Measurement of level spins and parities, transition multipolarities... c) Measurement of transition probabilities (from level life time, Coulomb excitation...) 4) Some interesting examples: a) Study of states with very high spins ( very fast nuclear rotation) b) Superdeformed states c) Giant resonances 5) High energy „nuclear“ spectrometry – example: Study of neutral meson production in heavy ion collisions B) Applications 1) Activation analysis 2) Material research by PIGE and PIXE methods 3) Usage of diffraction method at crystallography

2. Study of nuclear properties, transitions and reactions Unique properties of electromagnetic interactions: 1) Simple well known description of interaction H EM Transition matrix element is: where ψ i and ψ f are wave functions of initial and final state Transition probability → matrix element → direct information ψ i and ψ f Main goal is to understand properties of system consists of finite number of strongly interacting particles (nucleons) Properties of electromagnetic interactions and emission of photons during different nuclear processes are used. Observed gamma rays make possible to study nuclear structure → understanding of strong interaction

3. 2) Interaction energy of elmg interaction at nucleus is given by hadron electric charges and their electric currents (given by charged hadron motion and magnetic momenta of all hadrons): whereis four-vector of potential andfour-vector of charge current Assumption: nucleus – system of point like nucleons: Charge density: Current density: Interaction of nucleon Magnetic momenta, where - nuclear magneton Motion of charged nucleons whereis isospin projection (convention is t z proton = +1/2 and neutron -1/2), v i velocity and s i spin gyromagnetic ratios: g 0 = g p + g n a g 1 = g n – g p proton g p = 5,58 neutron g n = - 3,82 Study of elmg interaction – direct test, charge distribution, velocities of nucleons, nuclear spins and izospins

4. 3) Weak interaction constant – α = 1/137, application of perturbative methods, mostly first order is sufficient, higher orders are necessary only in the case of suppression of first order transition by conservation laws or selection rule Clean radiation field at vacuum (φ = 0): Maxwell equations are fulfilled → Common vector field is possible express by arbitrary complete set of ortoghonal solutions of these equations. We will use: where Maxwel equations are equivalent to: Intensities of electric and magnetic field: 4) Simple multiple expansion and selection rules: This equation is satisfied (J and M are integer numbers) by: and We can resolve arbitrary to set of these solutions (P = E or M): Reminder: = 0 where j J (kr) – spherical Bessel function and - normalized spherical harmonic function

5. Approximation: 1) Nucleon motion is nonrelativistic 2) Radiation wave length is long against nuclear radius A E γ << [MeV] 50 45 100 35 200 28 Selection rules: Quantum field → E γ = ħω, component z of momentum M·ħ q*q – operator with eigenvalue of photon number Long wave approximation Photon has spin I and parity π : EJ → I = min J, π = (-1) I MJ → I = min J, π = (-1) I+1 → members with the lowest J value ( ) Transition between levels with spins I i and I f and parities π i and π f : I = |I i – I f | for I i ≠ I f I = 1 for I i = I f > 0 π = (-1) I+K = π i ·π f K=0 for E and K=1 for M Electromagnetic transition with photon emission between states I i = 0 and I f = 0 don´t exist

6. Studies using gamma ray and electron spectrometry 1) Basic properties of nuclei – quantum system of strongly interacting nucleons new nuclear shapes, highly excited particle and hole states, electromagnetic response (spin, izospin...), different collective states 2) Nucleon motion in extreme conditions – high excitation, high spins (rotation), superdeformed states, giant dipole resonances 3) Study of fundamental symmetries of elementary particles inside hadron system, new degree of freedoms at nuclear field, resonance and strangeness production, parton degrees of freedom Spectrometer EXOGAM on beam of radioactive beam at GANIL (France) Photon spectrometer TAPS during its first stay at GANIL

7. Determination level energies and decay scheme construction 1) As accurate determination of transition energy as possible 2) Coincidence measurements – determination of transition placement at cascade (intrinsic geometry of anticompton spectrometer and multidetector set-ups) Spectrum and decay scheme from 166m Ho decay study performed by means of anticompton Spectrometer of NPI of ASCR – focused on weak transition with high energy deexcitating rotational bands on vibrational states 3) Level energies from reactions

8. Determination of level spins and transition multipolarities 1)Usage of electromagnetic transition selection rules – usage of selection rules and knowledge about spin of some level, which transition connects 2) Usage of ratios between probabilities of gamma transition and emission of conversion electron“ 3) Usage of angular distribution of gamma rays against nuclear spin 4) Angular correlation of two photons emitted in sequence at cascade: 5) Information about spins from reactions: analysis of different reaction histories – different reactions excite levels with different spins Determination of transition conversion coefficient Conversion coefficients for separate shells α K, α L, α M, α N... Properties: 1) Conversion coefficients increase with increasing of transition multipolarity 2) α(M) > α(E) 3) fast decreasing with transition energy Dependency of total conversion coefficients on transition energy, sketchy picture (values taken from ADNDT 21(1978)4-5) Oriented nuclei – study of angular distribution Orientation by magnetic field, preferred direction of beam in reaction Legendre polynomials Spin orientation intensity

9. Determination of transition probabilities using life time of levels 1) Electronic methods – measurement of decay curve Resolution of BaF 2 - ~ 100 ps Resolution of reaction time (often from accelerator RF) ~ 1 ns Total resolution in the order from units up to parts of ns Time spectrum – gauss (prompt) + exponential curve (isomer) Available the lowest limit: τ ~ ns = 10 -9 s Isomere state measurement Off beam measurement (after irradiation): τ ~ min - ∞ Transport system and measurement during irradiation: τ > ~ s On beam measurements: Modification of time spectrum for τ comparable with FWHM

10. 2) Usage of Doppler shift Velocity of compound nucleus: A)We use study of ratio of Doppler shifted and not shifted lines intensities as function of distance, in which reflected nuclei are stopped Compound nucleus is created during reaction a(A,C): Velocity of reflected nucleus depends on reaction kinematics in the case of Coulomb excitation and direct reaction Energy of photon emitted by moving nucleus: where θ – angle between directions of nucleus motion and photon emission Dependency of ratio E γ /E γ0 = f(θ) Resolution: HPGE ~ 0,003 and scintillator ~ 0,05 for θ = 0 o and 180 o is energy difference maximal: Dependency of compound nucleus velocity on beam energy Ratio of intensities emitted by reflected nuclei in motion and stopped : where d = v·t 0 is distance between target and foil which is stopping reflected nuclei v << c → omission of member with (v/c) 2

11. Measurable life time range: τ ~ 10 -12 – 10 -15 s B) Doppler shift attenuation method Production of reflected nuclei → deceleration and scattering inside target or thin plate → emitted photon has different Doppler shift of energy → complicated shape of line Measurable life time range: τ ~ 10 -10 – 10 -12 s Line shape analysis → determination of level life time Distances d in the range 1 – 10 -2 mm (distance is measured electrically) Example of measurement of gamma lines from levels with different life time Relation of ionization losses and path: Δx = (dE/dx) -1 ΔE Path for measurable change of velocity or stopping depends on Z of reflected nucleus and target material, but x < 10 -2 mm Problems: 1) Description of deceleration and multiple scattering of reflected nucleus 2) Life time of previous transition in the cascade Target 0.7 – 1.5 μm, foil 5- 10 μm Au, Ta, Bi Example of Doppler shift attenuation measurement (taken from D. Poenaru, W Greiner: Experimental Techniques in Nuclear Physics)

12. Determination of transition probabilities using Coulomb excitation Heavy ion beams are used → high charge → excitation of states with high spin Energy can not be higher then Coulomb barrier energy where Z 1, Z 2, A 1 a A 2 are parameters of beam and target nuclei Advantageous: 1) Clean electromagnetic process 2) Minimal background – without nuclear reactions on target or surrounding material 3) Dominant excitation by E2 transitions (v/c relatively small → B(M) >B(EI+1) for I > 1) → excitation of rotational bands with E2 transitions 4) Possibility of choice of case with excitation to spin state ↔ large projectile scattering angle – common detection of scattered projectile, reflected nucleus and gamma quantas Connection of Coulomb excitation, life time measurements and magnetic momenta determination Further methods: Nuclear resonance fluorescence– usage of Mőssbauer phenomena τ = 10 -17 -10 -14 s, proton resonance τ < 10 -16 s Measurable life times τ = 10 -13 -10 -9 s

13. Studies of states with very high spin Excitation of high spin states by heavy ion collisions (Spins Iħ ≥ 40ħ) Study is possible by 4PI multi detector spectrometers Compound nucleus creation (τ > 10 -20 s) – 1) nuclei with big proton excess 2) radioactive nuclei beam – also nuclei with neutron excess Usage of Coulomb excitation Excitation energy: E EX = E CM + Q Maximal achievable spin μ – reduced mass of colliding nuclei R – the biggest distance which can be possible for compound nucleus creation Approximation: partial wave only up to l MAX Maximal spin of stable rotating nucleus (classical estimates) Superdefor- med states Projectile energy in CM Reaction energy

14. Yrast line – connects states with the highest spin for given energy After compound nucleus creation evaporation of some Nucleons (especially neutrons) → fast energy decrease ~ 8 MeV/n only small decrease of angular momenta ~ 1ħ/n Excitation energy is lower than separation energy → 10 -15 s deexcitation by gamma quants: 1) Statistical (starting at high state density) E1 transitions from the highest excitated states 2) E2 transitions near to Yrast line – not only inside rotational bands (because of crossing) → high number of transitions with small intensity – „quasicontinuum“ 3) Regular structure of rotational bands ~ 1MeV above Yrast line → sufficient intensity → observation of single transitions Deexcitation of compound Nucleus with very high spin (rotation) (taken from D. Poenaru, W Greiner: Experimental Techniques in Nuclear Physics] Total deexcitation time ~ 10 -9 s, number of emitted photons ~ 30 competitive high energy gamma depopulating giant dipole resonances Two type of rotation: 1) Collective rotation – region of deformed nuclei – collective motion of many nucleons 2) Noncollective rotation – spherical and weakly deformed nuclei – high spin given by motion of a few nucleons

15. Superdeformed states States with very high deformation (axis ratio 2:1 and more) High spins - transitions between single types of rotation with drastic changes of nucleus shape Hamiltonian for rotation of axially symmetrical nucleus: Adiabatic condition – rotation is slow against singleparticle motion and vibrations → H intr and H vib Are separated High spins – fast rotation → strong Coriolis interaction between particle and rotational motion Band crossing – strong Coriolis interaction decrease energy of excited singleparticle state above which rotational band develops → crossing with band above ground state Long rotational bands deexcitated by long cascades of E2 transitions with very near energies High spins ~ 40 - 70 first nucleus 152 Dy (1984) Example of rotational bands in situation of adiabatic approximation Predicted by shell model – spacing between shells for deformed potential Only small probability of such state population ~ 1 %

16. Giant resonances Different types of giant resonances (taken from WWW pages of GANIL) Relative correlated motion of different Nucleon types: 1)with different spin orientation 2)with different isospin orientation (proton liquid against neutron) Deexcitation of single and double giant dipole resonance populated by coulomb excitation on 208 Pb. Energy 13 MeV and 26 MeV, width is given by natural width described by Lorentz curve – studied by spectrometer TAPS at GSI Darmstadt (J. Ritman: Phys. Rev Lett.70(1993)533) High energy transitions Giant resonances are nicely populated by Coulomb excitation

17. Production of neutral mesons during heavy ion collisions π 0  γ+γ (98.8 %) η  γ+γ (39.4 %) Decays: M 2 γγ = 2E 1 E 2 (1-cosΘ 12 ) Simulation of combinatorial background Study of π 0 and η meson production during heavy ion collisions by means of spectrometer TAPS Number of produced particles per one participant nucleon as dependency on collision energy (TAPS review)

18. Application of gamma spectrometry 1) Activation analysis - A)Neutron – sample is irradiated by neutrons from reactor → production of radioactive nuclei → study of characteristic radiation B) Fluorescence – sample is irradiated by X-rays → striking of electrons from atomic shell → characteristic X-rays C) Determination of neutron flow from foil activation – similar to neutron activation analysis, we know amount of irradiated material and we determine neutron flow – usage by reactor physics. It is possible to use for determination of other particle beam flow Sensitivity limit is given by accuracy of gamma intensity determination ~ 1% known neutron flux → activity is proportional to amount of studied element very sensitive – search of trace amounts of elements Sensitivity depends on element (range up to 8 orders) → up to pg (10 -12 g) studied object is not damaged – possibility „scanning“ Reactor LVR-15 of NRI One of archeological artifacts studied at NPI ASCR

19. 2) On ion beam: A)PIXE – (Particle Induced X-ray Emission) charged ions (mostly protons) with energy ~ 2 – 4 MeV → ionization of atoms → production of characteristic X-rays Van de Graffův accelerator at NPI ASCR is used for material research using also PIGE and PIXE methods Example of aerosol measurement at NPI – Department of neutron physics Composition of samples for ecology, archeology,... Sensitivity up to 1 ppm (10 -6 ) at μg material amount) Principle of PIXE method © C2RMF, T. Calligaro Study of historical artifacts by PIXE and PIGE methods (C2RMF laboratory)

20. 3) X-ray diffraction crystallography Determination of crystal structure, biological objects and substances, materials … by means of X-ray diffraction Usage of synchrotron radiation: B) PIGE – Particle-Induced Gamma ray Emission) reactions of light nuclei with production of characteristic gamma rays reactions (p,γ), (p,p´γ) and (p,Xγ) Surface composition for material research Method PIGE © C2RMF, T. Calligaro Tandetrom at NPI ASCR is used for PIGE and PIXE studies Also possibility of X-ray laser Based on free electrons: Synchrotron laboratory at Grenoble Undulator