1 / 38

EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture IV

EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture IV. Ranjan Bhowmik Inter University Accelerator Centre New Delhi -110067. ASSIGNMENT OF SPIN & PARITY. General Properties of Electromagnetic Radiation.

ellery
Télécharger la présentation

EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture IV

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYSLecture IV Ranjan Bhowmik Inter University Accelerator Centre New Delhi -110067

  2. ASSIGNMENT OF SPIN & PARITY Lecture IV SERC-6 School March 13-April 2,2006

  3. General Properties of Electromagnetic Radiation • Individual nuclear states have unique spin and parity. For decay from (Ei Ji Mi pi ) to (Ef Jf Mf pf), the electromagnetic radiation must satisfy the following relations: • Energy Eg = Ei - Ef • Multipolarity|Ji - Jf| L  (Ji + Jf) • M-state M = Mi - Mf • Parity p = pipf For time varying field, the vector potential A should satisfy the vector Helmholtz equation : The scalar Helmholtz equation has the following solution with states of good angular momentum L and parity (-1)L Lecture IV SERC-6 School March 13-April 2,2006

  4. ELECTRIC & MAGNETIC TRANSITIONS • The corresponding Vector solutions are : Parity (-1)L+1 Parity (-1)L At large distances (kr » 1), Electric and magnetic fields complimentary : E(r ; E) = H(r ; M) H(r ; E) = -E(r ; M) At short distances (kr « 1 ) |E(r ; E)| >> |H(r ; E)| |H(r ; M)| >> |E(r ; M)| This justifies the names 'Electric' and 'Magnetic' for the two types of fields. Electric field interacts with charges  Electric multipole excitation Magnetic field interacts with currents (magnets)  Magnetic multipole excitation Lecture IV SERC-6 School March 13-April 2,2006

  5. ELECTRIC DIPOLE RADIATION • The classical radiation field from an oscillating dipole is given by • P ~ E  H ~ sin2q  r2 • which is maximum in a plane  to dipole direction [ zero at 0] • The electric field is in the plane containing the dipole. • Quantum mechanically, this correspond to a dipole field with L=1 M=0 with linear polarization along q P • For an axially symmetric oscillating quadrupole field (Q20) the radiation pattern P ~ E  H ~ sin2qcos2q  r2 [ zero at 0 & 90] • Quadrupole field with L=2 M=0 with linear polarization along q Lecture IV SERC-6 School March 13-April 2,2006

  6. ANGULAR DISTRIBUTION OF MULTIPOLE RADIATION • Angular distribution Z(W) =| A(r,q,f) |2 is a function of q only • For magnetic radiation, role of E & H are interchanged • Similar angular distribution for electric and magnetic multipoles • would differ in plane of polarization • Adding all the M components incoherently would result in isotropic unpolarized radiation • Electric dipoleradiation at 90 • Polarization M = 0 || to axisM = 1  to axis • Electric Quadrupole radiation at 90 Polarization M = 1 || to axis M =2  to axis Lecture IV SERC-6 School March 13-April 2,2006

  7. ELECTROMAGNETIC TRANSITION PROBABILITY The transition probability for the nucleus decaying from a state |JiMi > to state |JfMf > by an interaction R is given by • Since we are not interested in the orientation of either the initial or the final nucleus, we sum over all Mf and average over all Mi . Angular distribution of the photon would involve contributions from different allowed values of L & M. Since kR « 1, the transition probabilityTfi decrease rapidly with L and the lowest allowed L is important. Lecture IV SERC-6 School March 13-April 2,2006

  8. MULTIPOLARITY OF TRANSITION • For a change in angular momentum DL = |Ji - Jf| the dominant multipolarities are : M1 & E2often have comparable strength Lecture IV SERC-6 School March 13-April 2,2006

  9. RADIATION FROM ORIENTED NUCLEI • Random orientation of nuclei : radiation is isotropic as all Mi substates are to be added incoherently:radioactive decay • Nuclei oriented perpendicular to z-axis:fusion • Populates large spins with Mi ~ 0 by heavy ion fusion • Mi 0 nuclei decaying predominantly to Mf  0 For L=1 M = 0 • Emitted radiation maximum at q ~ 90 • Polarization || to z-axis for Electric transition For L=2 M = 0,  1 • Emitted radiation minimum at q ~ 90 • Polarization || to z-axis for Electric transition L=DJ for stretched transition • Nuclei oriented along z-axis : polarized nuclei M = LAngular distribution opposite; polarization reversed in sign Lecture IV SERC-6 School March 13-April 2,2006

  10. ALIGNMENT IN NUCLEAR REACTION • In fusion reaction between even-even nuclei, compound nucleus is populated with high spin at M=0 state. Successive particle emission would broaden the M-distribution. • Since the g-decay along the cascade is mostly stretched in nature (DJ =L) the M-distribution of the decaying state Ji would be centered around M=0 • If the spin distribution is symmetric i.e. P(-M) = P(M) NUCLEAR ALIGNMENT • Asymmetric spin distribution P(M) > P(-M) leads to NUCLEAR POLARIZATION Gaussian parameterization for oriented nuclei: P(Mi) ~ exp(-Mi2/s2)/Si exp(-Mi2/s2) with s/Ji ~ 0.3 Lecture IV SERC-6 School March 13-April 2,2006

  11. ANGULAR DISTRIBUTION IN FUSION • Angular distribution of g-transitions can be measured by moving the detector to a different q and normalising the counting rate w.r.t. a fixed detector • Shows pronounced anisotropy : • W(q) = 1 +a2P2(cosq) +a4P4(cosq) • Symmetric about 90 • W(q) = W(p - q) • Only even orders allowed with Nmax  2L • 'Beam in' & 'Beam out' directions equivalent Nucl. Phys. A95(1967)357 Lecture IV SERC-6 School March 13-April 2,2006

  12. Theoretical angular Distribution • The theoretical angular distribution from a state Ji to a state Jf by multipole radiation of order L, L' can be written as : where rK Statistical Tensor describing initial state population. Only even K allowed for symmetric M distribution Depends on the population width s Normalize to transitions with known multipolarity AK Geometrical factor depending on 3j, 6j, 9j symbols Sensitive to L-change in the high spin limit AK(JiLL'Jf) ~ AK(DJ,L) Lecture IV SERC-6 School March 13-April 2,2006

  13. ANUGULAR DISTRIBUTION FOR PURE MULTIPOLES • Angular distribution coeffs for pure multipoles in high spin limit for ideal initial M-distribution P(M) =1 for M=0 or  ½ Lecture IV SERC-6 School March 13-April 2,2006

  14. SYSTEMATICS OF L=2 TRANSITIONS • Angular distributions for DJ =2 very similar with a minimum at 90 • For most transitions • a2 = +0.30  0.09 • a4 = -0.09  0.05 • 20 transitions show large deviation due to external perturbation • Large anisotropy consistent with a narrow M-distribution s ~ 0.3 J PRL16(1966)1205 Lecture IV SERC-6 School March 13-April 2,2006

  15. SYSTEMATICS OF DIPOLE TRANSITIONS • Dipole transitions have a maximum at 90 • a2 -ve -a2 ~ 0.4 - 0.6 • If there is no change in parity, M1 can be mixed with E2 transitions • Angular distribution sensitive to the mixing ratio d • As the transitions are weak L=1 mostly seen in coincidence measurements E2 PRL16(1966)1205 M1,E2 Lecture IV SERC-6 School March 13-April 2,2006

  16. MIXING RATIO d • If for transition between states Ji Jf two multipolarities L, L' are allowed, d is the ratio of the reduced nuclear matrix elements • d a real number -     • Sign of d depends on the relative phase of the nuclear matrix elements • Angular distribution To extract d from measured W(q), rK must be estimated from a model of P(M) or extracted from pure E2 angular distribution Lecture IV SERC-6 School March 13-April 2,2006

  17. DETERMINATION OF MIXING RATIO d • Angular distribution of g-rays sensitive to DJ and mixing ratio • Solid curve : pure L=2 • Dotted curve : pure L=1 • Dashed & dot-dashed curve: • mixed transition d = -1 & +1 • Large interference effects for DJ =1 • Knowledge of both a2 & a4 important to identify the spin change DJ Lecture IV SERC-6 School March 13-April 2,2006

  18. ANGULAR CORRELATION • Weak transitions in a g-cascade can only be identified in g-g coincidence measurements • Angular correlation W(q1, q2, f) can be calculated theoretically if M-state population is known with sum over all variables K, K1, K2, q1, q2 For decay from symmetric M-distribution all K are even Lecture IV SERC-6 School March 13-April 2,2006

  19. ANGULAR CORRELATION • As a special case, we consider radioactive decay of a cascade of g-transitions. Because of the random orientation of the 4+ state populated by b-decay, all rK zero. By summing over all other indices the angular correlation is obtained as : where AK(1), AK(2) are the coefficients characterising the two transitions and q is the angle between the detectors. Lecture IV SERC-6 School March 13-April 2,2006

  20. ANGLAR CORRELATION : SYMMETRY PROPERTIES • Symmetric M distribution, 'beam in' & 'beam out' equivalent • W(q1,q2, f) = W( p - q1, p - q2, f) • Additional symmetries involving f p - f and f p +f • NIMA313(1992)421 • Integration over out-of-plane angle f product of angular distributions NPA563(1993)301 • Integration over angle of one detector Integration over all detectors gives the angular distribution Angular distribution from angular correlations using large array Lecture IV SERC-6 School March 13-April 2,2006

  21. Similarity between angular distribution & angular correlation Lecture IV SERC-6 School March 13-April 2,2006

  22. Anisotropy in angular distribution PRC53(1996)2682 • 'Gated angular distribution' extracted from the angular correlation W(q1,q2) by summing over all q2 • Anisotropy defined as E2 E1 M1/E2 E2/M1 where qA ~ 0 or 180 qB ~ 90 • Sensitive to DJ & d • Gating with unknown L possible Mixing Angle Three possible solutions !! need linear polarization data Lecture IV SERC-6 School March 13-April 2,2006

  23. Directional Correlation from Oriented Nuclei • Useful information about DJ can be obtained by measuringcoincidences between two detectors, one near 90 and the other near 0 with respect to beam direction • If the detectors are sensitive to both radiations g1 & g2 we can distinguish between • (i) g1 in detector 1 • g2 in detector 2 • (ii) g2 in detector 1 • g1 in detector 2 DCO = W(g1,q1; g2,q2)/W(g1,q2; g2,q1) Lecture IV SERC-6 School March 13-April 2,2006

  24. DCO Ratio • Ignoring f dependence we get • DCO ratio ~ [W(g1;q1)*W(g2; q2)] / [W(g1; q2)*W(g2; q1)] • = [W(g1; q1)/ W(g1; q2)] * [W(g2; q2)/W(g2; q1)] • If both radiations g1 and g2 have the same multipolarity, they have similar angular distribution and DCO ratio =1 • If they have different multipolarity i.e. L=1 for g1 and L=2 for g2 both terms greater than 1 and DCO ~ 2 • Exchange of angles or exchange of gating multipolarity would invert the ratio • Generalization valid only for Stretched transitions ! • Some papers have inverted definition i.e. NIMA275(1989)333 Lecture IV SERC-6 School March 13-April 2,2006

  25. EXPERIMENTAL DCO RATIO • Gate on E2 transition • 607 keV transition E2 • 484, 506, 516, 568, 617 keV transitions dipole 93Tc E2 gate PRC47(1993)87 Lecture IV SERC-6 School March 13-April 2,2006

  26. DCO Ratio : advantages • Can be used for weak transitions • More sensitive to angular distribution i.e. W(q)2 • Ideal for small arrays with limited number of angle combinations • Not overly sensitive to choice of angles • 75 < q1 < 105 • q2 < 30 or q2 >150 • DCO similar for both M1 & E2 transitions if DJ =1 • Large interference effect for mixed transitions • DCO ambiguity for DJ=0, 1 gate on L=2 q1=90 f =0 Lecture IV SERC-6 School March 13-April 2,2006

  27. Sensitivity of DCO Ratio to mixing parameter EPJA17(2003)153 Two solutions, need polarization data !! Lecture IV SERC-6 School March 13-April 2,2006

  28. POLARIZATION MEASUREMENTS • Angular distribution for both E1 and M1 similar; maximum at 90 • Can be distinguished by polarization measurement • Stretched E1 transition has polarization vector in-plane • stretched M1 transition has polarization vector perpendicular to plane • Maximum polarization at q = 90 • Can be studied in • (i) singles • (ii) in coincidence with another detector (PDCO) • (iii) measuring polarization of both detectors (PPCO) RMP31(1959)711 NIM163(1979)377 NIMA362(1995)556 NIMA378(1996)516 NIMA430(1999)260 Lecture IV SERC-6 School March 13-April 2,2006

  29. POLARIZATION FORMALISM • Polarization in a nuclear reaction : • where J0 , J90 are the average intensities of the Electric vector in plane with the beam direction & perp. to the plane. • Angular distribution : • Polarization : • Maximum at 90 with a value • for pure E1, M1 or E2: • P = +1 (E1,E2) ; -1 (M1) Lecture IV SERC-6 School March 13-April 2,2006

  30. Measurement of Polarization • Compton Scattering is sensitive to the polarization direction • Vertically polarized photons would be preferentially scattered in the horizontal plane • Klein-Nishina formula • Maximum sensitivity at q ~ 90 Lecture IV SERC-6 School March 13-April 2,2006

  31. Detection of Compton-scattered radiation • Two Ge detectors : one as scatterer and other as detector of scattered radiation • Need large efficiency for coincident detection • Identified as Eg = E1 + E2 • Experimental Asymmetry a(Eg) corrects for any instrumental effect between horizontal & vertical plane Lecture IV SERC-6 School March 13-April 2,2006

  32. Different Designs of Polarimeter CLOVER GAMMASPHERE Lecture IV SERC-6 School March 13-April 2,2006

  33. CLOVER as a Polarimeter • Polarization sensitivity • Q = A/P where P is polarization of the incident radiation • Large polarization sensitivity • Q ~ 13% at 1 MeV • Large Compton detection efficiency ~ 40% at 1 MeV • Measurement in singles or in coincidence NIMA362(1995)556 Lecture IV SERC-6 School March 13-April 2,2006

  34. Measurement of Polarization Electric Magnetic Lecture IV SERC-6 School March 13-April 2,2006

  35. Polarization Measurement in 163Lu PRL86(2001)5866 NPA703(2002)3 Lecture IV SERC-6 School March 13-April 2,2006

  36. Polarization measurement in 163Lu Confirmation of the wobbling mode in 163Lu through combined angular distribution and linear polarization measurement Lecture IV SERC-6 School March 13-April 2,2006

  37. Polarization-Direction Correlation PDCO Polarization-Polarization Correlation PPCO • With the availability of a large array of Clover detectors, we can measure the polarization of one or both g-rays in coincidence. This results in additional information in the form of PDCO (where one polarization is measured) or PPCO where both polarizations are measured. Combined with DCO this provides a powerful tool for spin assignment. I 4+ 2+ NIMA430(1999)260 Lecture IV SERC-6 School March 13-April 2,2006

  38. Lecture IV SERC-6 School March 13-April 2,2006

More Related