EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture VI

EXPERIMENTS WITH LARGE EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYSGAMMA DETECTOR ARRAYS

Lecture VILecture VI

Ranjan Bhowmik

Inter University Accelerator Centre

New Delhi -110067

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

Measurement of Nuclear MomentsMeasurement of Nuclear Moments


g-Factorg-Factor Current loop produces a magnetic dipole

moment = iA/c Moving charge loop has a moment

= (e/T)* r2/c = evr/2ce/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 =glgss Neutrons can only contribute due to the spin

We have gl = N gs = 5.5857 N for proton

gl = gs = -3.8256 N for neutron

cMeMagnetonNuclear

pN 2

T


Schmidt ValuesSchmidt 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

jmj jmjm


Schmidt valuesSchmidt values

Odd Z

Odd N


Deviations for Schmidt ValuesDeviations 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 gl

π= 1.1 µN glν = − 0.1 µN

NPA694(2000)157


Deformed NucleiDeformed Nuclei

For deformed nuclei, [NnZ ] 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

RKRI ggIK

Igg

1

2 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

i

igg iK

AZgR ~


Magnetic Rotation in PbMagnetic Rotation in PbBand 1

Strong M1 & weak E2 transitionInterpreted to be due to orthogonal (particle-type)& (hole-type)

quasiparticle angular momentum


Shears MechanismShears 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


Measurement of g-factorMeasurement of g-factorA 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 = Lt

Level with mean life time will rotate by L


Larmor FrequencyLarmor Frequency

Larmor frequency in an external magnetic field L=gNB/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 103-104 Tesla transient magnetic field for fast moving

ions in a magnetized material Depending on the lifetime different types of field employed


Techniques for measuring g-factorTechniques for measuring g-factor

Depending on the life time of the state, various methods can be employed :

Life times 1 ns - 1s

Time Differential Perturbed Angular Distribution (TDPAD)

Lifetimes 1ps – 1nsImplantation & Perturbed Angular Correlation (IMPAC)

Transient Field method

Transient field with Plunger

Long Lived Isomers ( ~ ms)

StroboscopyNMR


TDPAD TechniqueTDPAD 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

TDPAD measurement in TDPAD measurement in 214214FrFr

produced in 208Pb(11B,5n) delayedcoincidence

with 1068 keV line of 214Fr Mean lifefor 11+

isomer =148 ns External field 2.4 T Plotted ratio R(t)

R ~ ¾ a2 sin(2Lt) sin(2 Maximum sensitivity at

=45

NPA567(1994)445

g = 0.511

Pulsed beam techniquePulsed beam technique

Experiment done at IUAC using TDPAD Setup

12C + 165Ho with Ta recoils stopped in Holmium

Pulsed beam 2.5 ns width 1s repetition frequency

NaI detectors at = ±45 for off-beam -detection

0.7 T magnetic field Fields 5T - 12T can be

produced by superconducting solenoids


g-Factor measurement in g-Factor measurement in 193193PbPb


Electric Quadrupole MomentElectric Quadrupole Moment

Strong electric field gradient In a non-cubic lattice Hyperfine splitting E =[3m2-J(J+1)]eQVzz/[4J(2J-1)] Transition frequency harmonics of ħQ = 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(t) = 1 + Gkk(t) ak Pk(cos) Attenuation factor Gkk(t) = S2n cos(nt) Relative amplitude of the harmonics depend on spin J


Measurement of Static Quadrupole MomentMeasurement of Static Quadrupole Moment

Attenuation factor calculated from angular anisotropy:

Shows periodic structure in time dependence from which and spin I can be calculated

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-


Extension to short lifetimesExtension 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-downcounting 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

41

4 )()()()()()()()(

NNNNNNNN


Small Precision AngleSmall 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

għħ

Lifetime must be known

For Coulomb Excitation W() ~ Z20 = sin2 cos2

S Maximum at 22.5,67.5


IMPAC TechniqueIMPAC 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


g-factor measurement in g-factor measurement in 110110CdCd

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 ( ~ 1ns) fed from 10+ level, large feeding

correction


Rotation of Angular DistributionRotation of Angular Distribution

10+ state of 110Cd stopping in a ferromagnetic host

10+ 8+ 7- 6+

NPA591(1995)533


Transient Field TechniqueTransient Field Technique


Transient Field TechniqueTransient 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= Z(v/v0) exp(-v/v0) where v0 Bohr velocity

Easily aligned by small external field

Rotation in transient field


Transient Field MethodTransient 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


g-factor in Inverse Kinematicsg-factor in Inverse Kinematics


Particle Detection with Coulomb Particle Detection with Coulomb ExcitationExcitation

Beam excited by Coulomb excitation

High sensitivity due to coincident detection of recoils

Lifetime can be measured simultaneously by DSAM technique


Measurement of precision AngleMeasurement of precision Angle


Measurements in Ni isotopesMeasurements in Ni isotopes


Transient Field Plunger MethodTransient 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

EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture VI

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