EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture IV Ranjan Bhowmik Inter University Accelerator...
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Transcript of EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture IV Ranjan Bhowmik Inter University Accelerator...
EXPERIMENTS WITH LARGE EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYSGAMMA DETECTOR ARRAYS
Lecture IVLecture IV
Ranjan Bhowmik
Inter University Accelerator Centre
New Delhi -110067
Lecture IV SERC-6 School March 13-April 2,2006 2
ASSIGNMENT OF SPIN & PARITYASSIGNMENT OF SPIN & PARITY
Lecture IV SERC-6 School March 13-April 2,2006 3
General Properties of General Properties of Electromagnetic RadiationElectromagnetic Radiation
Individual nuclear states have unique spin and parity. For decay from (Ei Ji Mi i ) to (Ef Jf Mf f), the electromagnetic radiation must satisfy the following relations:
Energy E = Ei - Ef
Multipolarity |Ji - Jf| L (Ji + Jf)
M-state M = Mi - Mf
Parity = if
For time varying field, the vector potential A should satisfy the vector Helmholtz equation : 022 Ak
),()(),,( LMl Ykrjr 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 TRANSITIONSELECTRIC & 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 RADIATIONELECTRIC DIPOLE RADIATION
The classical radiation field from an oscillating dipole is given by
P ~ E H ~ sin2 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
P
For an axially symmetric oscillating quadrupole field (Q20) the radiation
pattern P ~ E H ~ sin2cos2 r2 [ zero at 0 & 90] Quadrupole field with L=2 M=0 with linear polarization along
Lecture IV SERC-6 School March 13-April 2,2006 6
ANGULAR DISTRIBUTION OF ANGULAR DISTRIBUTION OF MULTIPOLE RADIATIONMULTIPOLE RADIATION
Angular distribution Z() =| A(r,,) |2 is a function of 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 dipole radiation at 90 Polarization M = 0 || to axis M = 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 ELECTROMAGNETIC TRANSITION PROBABILITYPROBABILITY
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.
The transition probability for the nucleus decaying from a state |JiMi > to state |JfMf > by an interaction R is given by
2
12
2!)!12(
)1(8)(
iilff
l
fi MJRMJk
ll
lRlT
Lecture IV SERC-6 School March 13-April 2,2006 8
MULTIPOLARITY OF TRANSITIONMULTIPOLARITY OF TRANSITION
For a change in angular momentum L = |Ji - Jf| the dominant multipolarities are :
J Same Parityi = f
Opposite parityi f
0 M1,E2mixed radiation
E1
1 M1,E2mixed radiation
E1
2 E2 (M2,E3)M1 & E2 often have comparable strength
Lecture IV SERC-6 School March 13-April 2,2006 9
RADIATION FROM ORIENTED NUCLEIRADIATION 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 fusionMi 0 nuclei decaying predominantly to Mf 0
For L=1 M = 0 Emitted radiation maximum at ~ 90 Polarization || to z-axis for Electric transition
For L=2 M = 0, 1 Emitted radiation minimum at ~ 90 Polarization || to z-axis for Electric transition
L=J for stretched transition
Nuclei oriented along z-axis : polarized nuclei
M = L Angular distribution opposite; polarization reversed in sign
Lecture IV SERC-6 School March 13-April 2,2006 10
ALIGNMENT IN NUCLEAR REACTIONALIGNMENT 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 -decay along the cascade is mostly stretched in nature (J =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(-Mi2/2)/i exp(-Mi
2/2) with Ji ~ 0.3
Lecture IV SERC-6 School March 13-April 2,2006 11
ANGULAR DISTRIBUTION IN FUSIONANGULAR DISTRIBUTION IN FUSION
Angular distribution of -transitions can be measured by moving the detector to a different and normalising the counting rate w.r.t. a fixed detector
Shows pronounced anisotropy :
W() = 1 +a2P2(cos) +a4P4(cos) Symmetric about 90
W() = W() Only even orders allowed with
Nmax 2L 'Beam in' & 'Beam out'
directions equivalentNucl. Phys. A95(1967)357
Lecture IV SERC-6 School March 13-April 2,2006 12
Theoretical angular DistributionTheoretical 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 :
)(cos)()(1
)(cos1)(
KfiKievenK
K
KKevenK
PJLLJAJ
PaW
where K Statistical Tensor describing initial state population.
Only even K allowed for symmetric M distribution Depends on the population width
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(J,L)
Lecture IV SERC-6 School March 13-April 2,2006 13
ANUGULAR DISTRIBUTION FOR PURE ANUGULAR DISTRIBUTION FOR PURE MULTIPOLESMULTIPOLES
Angular distribution coeffs for pure multipoles in high spin limit for ideal initial M-distribution P(M) =1 for M=0 or ½
J L a2 a4
0 1 0.500 0
0 2 -0.357 -.542
1 1 -0.250 0
1 2 -0.179 0.429
2 2 0.357 -0.107
Lecture IV SERC-6 School March 13-April 2,2006 14
SYSTEMATICS OF L=2 TRANSITIONSSYSTEMATICS OF L=2 TRANSITIONS
Angular distributions for J =2 very similar with a minimum at 90
For most transitions
a2 = +0.30 0.09a4 = -0.09 0.05
20 transitions show large deviation due to external perturbation
Large anisotropy consistent with a narrow M-distribution ~ 0.3 J
PRL16(1966)1205
Lecture IV SERC-6 School March 13-April 2,2006 15
SYSTEMATICS OF DIPOLE SYSTEMATICS OF DIPOLE TRANSITIONSTRANSITIONS
Dipole transitions have a maximum at 90a2 -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
As the transitions are weak L=1 mostly seen in coincidence measurements
E2
M1,E2
PRL16(1966)1205
Lecture IV SERC-6 School March 13-April 2,2006 16
MIXING RATIO MIXING RATIO
If for transition between states Ji Jf two multipolarities L, L' are allowed, is the ratio of the reduced nuclear matrix elements
a real number - Sign of depends on the relative phase of the nuclear matrix elements
Angular distribution
if
if
JLJ
JLJ
)(cos)()(1)( KfiKievenK
K PJLLJAJW )()(2)(
11
)( 22 ifKifKifKfiK JLLJFJLLJFLLJJFJLLJA
To extract from measured W(), K 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 DETERMINATION OF MIXING RATIO
Angular distribution of -rays sensitive to J and mixing ratio
Solid curve : pure L=2 Dotted curve : pure L=1 Dashed & dot-dashed curve:
mixed transition = -1 & +1 Large interference effects for J =1
Knowledge of both a2 & a4 important to identify the spin change J
Lecture IV SERC-6 School March 13-April 2,2006 18
ANGULAR CORRELATIONANGULAR CORRELATION Weak transitions in a -cascade can only be
identified in coincidence measurements Angular correlation W(1, 2, ) can be
calculated theoretically if M-state population is known
with sum over all variables K, K1, K2, q1, q2For decay from symmetric M-distribution all K are even
Lecture IV SERC-6 School March 13-April 2,2006 19
ANGULAR CORRELATIONANGULAR CORRELATION
As a special case, we consider radioactive decay of a cascade of -transitions. Because of the random orientation of the 4+ state populated by -decay, all K zero. By summing over all other indices the angular correlation is obtained as :
evenK
KKK PAAW )(cos)2()1(1)(
where AK(1), AK(2) are the coefficients characterising the two transitions and is the angle between the detectors.
Lecture IV SERC-6 School March 13-April 2,2006 20
ANGLAR CORRELATION : ANGLAR CORRELATION : SYMMETRY PROPERTIESSYMMETRY PROPERTIES
Symmetric M distribution, 'beam in' & 'beam out' equivalent
W(1,2, ) = W( - 1, - 2, )
Additional symmetries involving - and +NIMA313(1992)421
Integration over out-of-plane angle )()(),,( 2121 WWWd product of angular distributions
NPA563(1993)301
Integration over angle of one detector
)(),,( 1212 WWd 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 Similarity between angular distribution & angular correlation& angular correlation
Lecture IV SERC-6 School March 13-April 2,2006 22
Anisotropy in angular distributionAnisotropy in angular distribution 'Gated angular distribution'
extracted from the angular correlation W(1,2) by summing over all 2
Anisotropy defined as
)()(
)()(2
BA
BAA
whereA ~ 0 or 180B ~ 90
Sensitive to J & Gating with unknown L
possible
Mixing Angle
PRC53(1996)2682
E2
E1 M1/E
2
E2/M1
Three possible solutions !!need linear polarization data
Lecture IV SERC-6 School March 13-April 2,2006 23
Directional Correlation from Directional Correlation from Oriented NucleiOriented Nuclei
Useful information about J can be obtained by measuring coincidences between two detectors, one near 90 and the other near 0with respect to beam directionIf the detectors are sensitive to both radiations 1 & 2 we can distinguish between (i) 1 in detector 1
2 in detector 2 (ii) 2 in detector 1 1 in detector 2
DCO = W(1,1; 2,2)/W(1,2; 2,1)
Lecture IV SERC-6 School March 13-April 2,2006 24
DCO RatioDCO Ratio
Ignoring dependence we get
DCO ratio ~ [W(1;1)*W(2; 2)] / [W(1; 2)*W)]
= [W(1; 1)/ W(1; 2)] * [W(2; 2)/W)] If both radiations 1 and 2 have the same multipolarity, they
have similar angular distribution and DCO ratio =1 If they have different multipolarity i.e. L=1 for 1 and L=2 for 2
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 RATIOEXPERIMENTAL DCO RATIO
Gate on E2 transition
607 keV transition E2
484, 506, 516, 568, 617 keV transitions dipole
PRC47(1993)87
E2 gate
93Tc
Lecture IV SERC-6 School March 13-April 2,2006 26
DCO Ratio : advantagesDCO Ratio : advantages
Can be used for weak transitions More sensitive to angular distribution
i.e. W()2
Ideal for small arrays with limited number of angle combinations
Not overly sensitive to choice of angles
75 < < 105
2 < 30 or 2 >150 DCO similar for both M1 & E2
transitions if J =1 Large interference effect for mixed
transitions
DCO ambiguity for J=0, 1
1=90 =0
gate on L=2
Lecture IV SERC-6 School March 13-April 2,2006 27
Sensitivity of DCO Ratio to mixing Sensitivity of DCO Ratio to mixing parameterparameter
EPJA17(2003)153
Two solutions, need polarization data !!
Lecture IV SERC-6 School March 13-April 2,2006 28
POLARIZATION MEASUREMENTSPOLARIZATION 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 = 90 Can be studied in
(i) singles (ii) in coincidence with another detector (PDCO) (iii) measuring polarization of both detectors (PPCO)
RMP31(1959)711NIM163(1979)377NIMA362(1995)556NIMA378(1996)516NIMA430(1999)260
Lecture IV SERC-6 School March 13-April 2,2006 29
POLARIZATION FORMALISMPOLARIZATION 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:
= +1 (E1,E2) ; -1 (M1)
Lecture IV SERC-6 School March 13-April 2,2006 30
Measurement of PolarizationMeasurement 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 ~ 90
Lecture IV SERC-6 School March 13-April 2,2006 31
Detection of Compton-scattered Detection of Compton-scattered radiationradiation
Two Ge detectors : one as scatterer and other as detector of scattered radiation
Need large efficiency for coincident detection
Identified as E = E1 + E2
Experimental Asymmetry
||
||
)(
)()(
NNEa
NNEaEA
a(E) corrects for any instrumental effect between horizontal & vertical plane
Lecture IV SERC-6 School March 13-April 2,2006 32
Different Designs of PolarimeterDifferent Designs of PolarimeterG
AM
MA
SP
HER
E
CLO
VER
Lecture IV SERC-6 School March 13-April 2,2006 33
CLOVER as a PolarimeterCLOVER 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 PolarizationMeasurement of Polarization
Electric
Magnetic
Lecture IV SERC-6 School March 13-April 2,2006 35
Polarization Measurement in Polarization Measurement in 163163LuLu
PRL86(2001)5866NPA703(2002)3
Lecture IV SERC-6 School March 13-April 2,2006 36
Polarization measurement in Polarization measurement in 163163LuLu
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-Direction Correlation PDCO Polarization-Polarization Correlation PPCOPolarization-Polarization Correlation PPCO
With the availability of a large array of Clover detectors, we can measure the polarization of one or both -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