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EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture VI

EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture VI. Ranjan Bhowmik Inter University Accelerator Centre New Delhi -110067. Measurement of Nuclear Moments. g-Factor. Current loop produces a magnetic dipole moment m = iA/c Moving charge loop has a moment

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EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture VI

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

  2. Measurement of Nuclear Moments Lecture VI SERC-6 School March 13 - April 2,2006

  3. g-Factor • Current loop produces a magnetic dipole moment m = iA/c • Moving charge loop has a moment • m = (e/T)* pr2/c= evr/2c = (e/2mc) ħ • There is a similar equation for the internal charges in a proton due to its intrinsic spin • Total magnetic moment contribution due to protons in a nucleus m =gl + gss • Neutrons can only contribute due to the spin T We have gl = mN gs = 5.5857 mN for proton gl = 0 gs = -3.8256 mN for neutron Lecture VI SERC-6 School March 13 - April 2,2006

  4. Schmidt Values • The magnetic moment of a nucleus is defined as the expectation value of m along the spin direction J • For a single independent nucleon this is calculated to be • Substituting j =   s and s =1/2 we get • for j= l + 1/2 • for j = l - 1/2 Lecture VI SERC-6 School March 13 - April 2,2006

  5. Schmidt values Odd N Odd Z Lecture VI SERC-6 School March 13 - April 2,2006

  6. Deviations for Schmidt Values • For near closed-shell nuclei deviations arise due to motion of the odd nucleon affecting the charge distribution in the core • Intrinsic moments affected by nuclear medium • velocity dependent spin-orbit term introduces a correction • Excitation of the core : coupling to vibrational states • Truncated model space in shell-model calculations • The 'empirical' g-factors that reproduce the observed g-factors in s-d and f-p shell nuclei are : • gs = 0.75 gsbare glπ= 1.1 µN glν = − 0.1 µN NPA694(2000)157 Lecture VI SERC-6 School March 13 - April 2,2006

  7. Deformed Nuclei • For deformed nuclei, [NnZLW] orbitals are not pure single particle wave functions but admixtures of different -values • Measurement of g-factor is a sensitive test of the wave function • g-factor of the levels in a band is given by : • Intrinsic g-factor is given in terms of the single particle configurations • Rotational g-factor Lecture VI SERC-6 School March 13 - April 2,2006

  8. Magnetic Rotation in Pb Band 1 Strong M1 & weak E2 transition Interpreted to be due to orthogonal p (particle-type)& n (hole-type) quasiparticle angular momentum Lecture VI SERC-6 School March 13 - April 2,2006

  9. Shears Mechanism Low spin : p and n j values othogonal ; large m High spin : p and n j values parallel ; reduced m Comparison with Tilted Axis Cranking Confirmation by g-factor measurement of band-head Lecture VI SERC-6 School March 13 - April 2,2006

  10. Measurement of g-factor • A nucleus with magnetic moment m will precess in an external magnetic field B with the Larmor frequency wL In fusion reaction, the nuclear spin is preferentially oriented perpendicular to the beam direction, leading to an anisotropy in angular distribution The effect of precession of the spin in the external field is to rotate the angular distribution in time t by an angle Dq = wLt Level with mean life time t will rotate by wLt Lecture VI SERC-6 School March 13 - April 2,2006

  11. Larmor Frequency • Larmor frequency in an external magnetic field wL=gmNB/ħ • Corresponds to a time period T=p/w = 60 ns(g/B) • g in Nuclear Magneton, B in Tesla • External magnetic field varies over wide range • 1-2 Tesla  iron-core electromagnet • 5-12 Tesla  superconducting solenoid • 10-100 Tesla  static field in ferromagnet • 103-104 Tesla  transient magnetic field for fast moving ions in a magnetized material • Depending on the lifetime t different types of field employed Lecture VI SERC-6 School March 13 - April 2,2006

  12. Techniques for measuring g-factor • Depending on the life time of the state, various methods can be employed : • Life times 1 ns - 1ms • Time Differential Perturbed Angular Distribution (TDPAD) • Lifetimes 1ps – 1ns • Implantation & Perturbed Angular Correlation (IMPAC) • Transient Field method • Transient field with Plunger • Long Lived Isomers ( ~ ms) • Stroboscopy • NMR Lecture VI SERC-6 School March 13 - April 2,2006

  13. TDPAD Technique • Stop the recoiling nuclei in a diamagnetic cubic lattice • Apply external magnetic field ~ Tesla perp. To beam dir. • Decay curve of the isomer by delayed coincidence or pulsed beam • Put detectors at q in the reaction plane • Compare the ratio of counts in +q and -q detectors • Decay curve in the presence of external field • where Lecture VI SERC-6 School March 13 - April 2,2006

  14. TDPAD measurement in 214Fr • produced in 208Pb(11B,5n) • g-g delayedcoincidence with 1068 keV line of 214Fr • Mean lifefor 11+ isomer t =148 ns • External field 2.4 T • Plotted ratio R(t) • R ~ ¾ a2sin(2wLt) sin(2q) • Maximum sensitivity at q=45 NPA567(1994)445 g = 0.511

  15. Pulsed beam technique • Experiment done at IUAC using TDPAD Setup • 12C + 165Ho with Ta recoils stopped in Holmium • Pulsed beam 2.5 ns width 1ms repetition frequency • NaI detectors at q= ±45 for off-beam g-detection • 0.7 T magnetic field • Fields 5T - 12T can be produced by superconducting solenoids

  16. g-Factor measurement in 193Pb Lecture VI SERC-6 School March 13 - April 2,2006

  17. Electric Quadrupole Moment • Strong electric field gradient In a non-cubic lattice • Hyperfine splitting DE =[3m2-J(J+1)]eQVzz/[4J(2J-1)] • Transition frequency harmonics of ħwQ = 3eQVzz/[4J(2J-1)] • Typical field gradient Vzz ~ 1018 V/cm2 • Time period ~ 20 ns for Q = 1barn • In a polycrystalline material no preferential direction • Angular correlations attenuated due to hyperfine interaction • W(q,t) = 1 + S Gkk(t) ak Pk(cosq) • Attenuation factor Gkk(t) = S S2n cos(nwt) • Relative amplitude of the harmonics depend on spin J Lecture VI SERC-6 School March 13 - April 2,2006

  18. Measurement of Static Quadrupole Moment 16O + 159Tb with recoiling 169Ta stopping in the target Hexagonal lattice Large electric field gradient Vzz ~ 6.1017 V/cm2 NaI detectors at 0 and 90 5/2- Attenuation factor calculated from angular anisotropy: Shows periodic structure in time dependence from which w and spin I can be calculated Lecture VI SERC-6 School March 13 - April 2,2006

  19. Extension to short lifetimes • For short lifetimes, not possible to measure the entire wt cycle • Periodically switch the magnetic field 'up' and 'down' • Put detectors at q and preferably also at p  q • To measure the field up-downcounting asymmetry and systematic error, get Double ratio r where  &  are the counts in 'field up' and 'field down' position • Another ratio r4 is which corrects for beam spot change Lecture VI SERC-6 School March 13 - April 2,2006

  20. Small Precision Angle • Small rotation Dq < 100 mrad • Precession angle given by Dq • where e =(1+r)/(1-r) • S is the logarithmic derivative of angular distribution • S is maximum at q ~ 45 in fusion reaction • g-factor estimated from • g = w ħ /BmN = (Dq . ħ)/tBmN • Lifetime t must be known For Coulomb Excitation W(q) ~ Z20 = sin2q cos2q S Maximum at 22.5,67.5 Lecture VI SERC-6 School March 13 - April 2,2006

  21. IMPAC Technique • Energetic recoils implanted in a ferromagnetic host • Large internal magnetic field ~ 30 - 100T • Static field can be aligned by applying a small external magnetic field ~ 0.01 – 0.1 T perpendicular to beam direction • Rotation Dq can be measured either by angular distribution or by angular correlation • Corrections required for transient field and feeding delay • Corrections small if lifetime large compared to feeding time and stopping time Lecture VI SERC-6 School March 13 - April 2,2006

  22. g-factor measurement in 110Cd • 110Cd populated in 13C + 100Mo reaction • Target evaporated on a 4 mg/cm2 Gd foil cooled to LN2 • External field of 0.05 T to polarize internal field • Field reversed every 15 min • Lifetime of 10+ level ~ 800 ps >> stopping time (~ 2ps) • Feeding and transient field corrections neglected • Static hyperfine field in Gd ~ 30 T at 92K • From the shift in angular distribution in ‘field up’ & ‘field down’ conditions, precession angle calculated • 7- level ( t ~ 1ns) fed from 10+ level, large feeding correction Lecture VI SERC-6 School March 13 - April 2,2006

  23. Rotation of Angular Distribution • 10+ state of 110Cd stopping in a ferromagnetic host 10+ 8+ 7- 6+ NPA591(1995)533 Lecture VI SERC-6 School March 13 - April 2,2006

  24. Transient Field Technique Lecture VI SERC-6 School March 13 - April 2,2006

  25. Transient Field Technique • Ions moving in a ferromagnetic material subjected to large transient field • Arises due to partially filled electronic orbits • Kilo Tesla for light nuclei ( Z ~8) and Mega Tesla for Z ~ 90 • BTR= a Z(v/v0) exp(-bv/v0) where v0 Bohr velocity • Easily aligned by small external field Rotation in transient field Lecture VI SERC-6 School March 13 - April 2,2006

  26. Transient Field Method Direct feeding of low spin levels in Coulomb Excitation B field Magnetisation Target recoil Beam In Ferromagnetic layer B field direction is set Recoiling Coulex nuclear spins aligned perp. to beam Precess about B field Angular distribution of decay gamma emission rotated Coulex Recoil Nuclear spin Target Layer Ferromagnetic Layer Stopper Lecture VI SERC-6 School March 13 - April 2,2006

  27. g-factor in Inverse Kinematics Lecture VI SERC-6 School March 13 - April 2,2006

  28. Particle Detection with Coulomb Excitation Beam excited by Coulomb excitation High sensitivity due to coincident detection of recoils Lifetime can be measured simultaneously by DSAM technique Lecture VI SERC-6 School March 13 - April 2,2006

  29. Measurement of precision Angle Lecture VI SERC-6 School March 13 - April 2,2006

  30. Measurements in Ni isotopes Lecture VI SERC-6 School March 13 - April 2,2006

  31. Transient Field Plunger Method • Large feeding time for levels produced in fusion reaction • Feeding level decays in flight • No rotation of spin direction for the feeding level • Nucleus traverses the ferromagnetic layer with rotation of spin axis • Stops in non-magnetic material and emits second gamma PLUNGER Magnetisation Beam Target recoil Nuclear spin shifted B field Target Layer Ferromagnetic Layer Stopper unshifted Lecture VI SERC-6 School March 13 - April 2,2006

  32. Lecture VI SERC-6 School March 13 - April 2,2006

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