EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture VI

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EXPERIMENTS WITH LARGE GAMMA DETECTOR
ARRAYSLecture VI
Ranjan Bhowmik Inter University Accelerator
Centre New Delhi -110067
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Measurement of Nuclear Moments
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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) ?h
• 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

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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

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Schmidt values
Odd N
Odd Z
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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 glp 1.1 µN gl? - 0.1 µN

NPA694(2000)157
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Deformed Nuclei

• For deformed nuclei, NnZ LW 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

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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
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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
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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
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Larmor Frequency

• Larmor frequency in an external magnetic field
  wLgmNB/h
• Corresponds to a time period Tp/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

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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

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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

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TDPAD measurement in 214Fr

• produced in 208Pb(11B,5n)
• g-g delayed coincidence with 1068 keV line of
  214Fr
• Mean life for 11 isomer t 148 ns
• External field 2.4 T
• Plotted ratio R(t)
• R ¾ a2 sin(2wLt) sin(2q)
• Maximum sensitivity at q45?

NPA567(1994)445
g 0.511
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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

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g-Factor measurement in 193Pb

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Electric Quadrupole Moment

• Strong electric field gradient In a non-cubic
  lattice
• Hyperfine splitting DE 3m2-J(J1)eQVzz/4J(2J-1
  )
• Transition frequency harmonics of hwQ
  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

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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
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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-down counting 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

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Small Precision Angle

• Small rotation Dq lt 100 mrad
• Precession angle given by Dq
• where e (1r)/(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 h /BmN (Dq . h)/tBmN
• Lifetime t must be known

For Coulomb Excitation W(q) Z20 sin2q cos2q S
Maximum at 22.5?,67.5?
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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

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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 gtgt 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

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Rotation of Angular Distribution

• 10 state of 110Cd stopping in a ferromagnetic
  host

10 ? 8
7- ? 6
NPA591(1995)533
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Transient Field Technique
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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
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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
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g-factor in Inverse Kinematics
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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
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Measurement of precision Angle
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Measurements in Ni isotopes
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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
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