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

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

3. Lecture VI SERC-6 School March 13 - April 2,2006 3 g-Factor Current loop produces a magnetic dipole moment  = iA/c Moving charge loop has a moment  = (e/T)*  r 2 /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  =g l  g s s Neutrons can only contribute due to the spin We have g l =  N g s = 5.5857  N for proton g l =  g s = -3.8256  N for neutron T

4. 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  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

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

6. 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 : g s = 0.75 g s bare g l π = 1.1 µ N g l ν = − 0.1 µ N NPA694(2000)157

7. Lecture VI SERC-6 School March 13 - April 2,2006 7 Deformed Nuclei For deformed nuclei, [Nn Z  ] 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

8. 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  (particle-type)& (hole-type) quasiparticle angular momentum

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

10. Lecture VI SERC-6 School March 13 - April 2,2006 10 Measurement of g-factor A nucleus with magnetic moment  will precess in an external magnetic field B with the Larmor frequency  L 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  =  L t Level with mean life time  will rotate by  L 

11. Lecture VI SERC-6 School March 13 - April 2,2006 11 Larmor Frequency Larmor frequency in an external magnetic field  L =g  N B/ħ Corresponds to a time period T=  /  = 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 10 3 -10 4 Tesla  transient magnetic field for fast moving ions in a magnetized material Depending on the lifetime  different types of field employed

12. 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 - 1  s 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

13. Lecture VI SERC-6 School March 13 - April 2,2006 13 TDPAD Technique Compare the ratio of counts in +  and -  detectors Decay curve in the presence of external field where 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  in the reaction plane

14. TDPAD measurement in 214 Fr produced in 208 Pb( 11 B,5n)  delayed  coincidence with 1068 keV line of 214 Fr Mean life  for 11 + isomer  =148 ns External field 2.4 T Plotted ratio R(t) R ~ ¾ a 2 sin(2  L t) sin(2  Maximum sensitivity at  =45  NPA567(1994)445 g = 0.511

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

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

17. 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  E =[3m 2 -J(J+1)]eQV zz /[4J(2J-1)] Transition frequency harmonics of ħ  Q = 3eQVzz/[4J(2J-1)] Typical field gradient V zz ~ 10 18 V/cm 2 Time period ~ 20 ns for Q = 1barn In a polycrystalline material no preferential direction Angular correlations attenuated due to hyperfine interaction W(  t) = 1 +  G kk (t) a k P k (cos  ) Attenuation factor G kk (t) =  S 2n cos(n  t) Relative amplitude of the harmonics depend on spin J

18. Lecture VI SERC-6 School March 13 - April 2,2006 18 Measurement of Static Quadrupole Moment Attenuation factor calculated from angular anisotropy: Shows periodic structure in time dependence from which  and spin I can be calculated 16 O + 159 Tb with recoiling 169 Ta stopping in the target Hexagonal lattice Large electric field gradient V zz ~ 6.10 17 V/cm 2 NaI detectors at 0  and 90  5/2 -

19. Lecture VI SERC-6 School March 13 - April 2,2006 19 Extension to short lifetimes For short lifetimes, not possible to measure the entire  t cycle Periodically switch the magnetic field 'up' and 'down' Put detectors at  and preferably also at    To measure the field up-down  counting asymmetry and systematic error, get Double ratio  where  &  are the counts in 'field up' and 'field down' position  Another ratio  4 is which corrects for beam spot change

20. Lecture VI SERC-6 School March 13 - April 2,2006 20 Small Precision Angle Small rotation  < 100 mrad Precession angle given by  where  =(1+  )/(1-  ) S is the logarithmic derivative of angular distribution S is maximum at  ~ 45  in fusion reaction g-factor estimated from g  ħ    ħ   Lifetime  must be known For Coulomb Excitation W(  ) ~ Z 20 = sin 2  cos 2  S Maximum at 22.5 ,67.5 

21. 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  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

22. Lecture VI SERC-6 School March 13 - April 2,2006 22 g-factor measurement in 110 Cd 110 Cd populated in 13 C + 100 Mo reaction Target evaporated on a 4 mg/cm 2 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 (  ~ 1ns) fed from 10 + level, large feeding correction

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

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

25. 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 B TR =  Z(v/v 0 ) exp(-  v/v 0 ) where v 0 Bohr velocity Easily aligned by small external field Rotation in transient field

26. Lecture VI SERC-6 School March 13 - April 2,2006 26 Transient Field Method Beam Target Layer B field Nuclear spin Coulex Recoil Target recoil 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 Ferromagnetic Layer Stopper Magnetisation Direct feeding of low spin levels in Coulomb Excitation

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

28. 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

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

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

31. Lecture VI SERC-6 School March 13 - April 2,2006 31 Transient Field Plunger Method Beam Target Layer B field Nuclear spin Target recoil Ferromagnetic Layer Stopper Magnetisation 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 shifted unshifted PLUNGER

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