Gamma-ray

spectroscopy
Alison Bruce
University of Brighton

Aim is to give an overview for non-specialists but also some details that
specialists might find useful.
Contents:

• Basic gamma-ray properties, observables

• Methods of producing the nuclei of interest (not an exhaustive list)

• Gamma-ray interactions in matter

• Detector types

• Detector arrays

• Measurement techniques:
Angular correlation, angular distribution
Linear polarisation
Lifetime measurements: Doppler Shift Attenuation Method
Recoil Distance Method
Electronic timing
 What is a gamma ray?

metres

Gamma ray: high frequency / short wavelength electromagnetic radiation.

Useful as a probe of the nucleus as the electromagnetic interaction is well

understood and only weakly perturbs the nucleus.
Gamma rays carry spin 1
which leads to interesting cases where a 0+ state is the
lowest excited level:

Sum-energy spectrum in
coincidence with protons
populating the states of
interest.
3.35 MeV
0+

0 MeV
0+
40Ca

Schirmer et al., PRL 53 (1984) 1897

See also 137Ba, Pietrella et al., Nature 526 (2015) 406
What is gamma-ray spectroscopy?
We study gamma rays emitted from excited nuclei to obtain
information about:

Transition energies and coincidence relationships

Level structure

Transition rates
Lifetimes, quadrupole moment

Angular correlations and linear polarisations

Spin, Parity (also magnetic moments).

Transition branching ratios, mixing ratios

Wavefunctions, transition matrix elements, etc
Why study gamma rays ?

Gamma rays provide a superb probe for nuclear structure!

Relatively easy to detect with good efficiency and resolution.

Emitted by almost all low-lying states.

Penetrating enough to escape from target chambers to reach detectors.

Gamma rays arise from EM interactions and allow a probe of structure

without large perturbations of the nucleus.

No model dependence in the interaction (EM is well understood).

 The basics of the situation:
Ei Ji  i

El

Ef Jf f
The energy of the gamma ray is given by Ei-Ef

The angular momentum carried away is given by Ji-Jf

From conservation of angular momentum:

│Ji-Jf│ ≤  ≤ Ji+Jf

where  is the multipolarity of the transition

 The basics of the situation:
Ei 2

Ef 0

│2-0│ ≤  ≤ 2+0

Here J = 2 and  = 2
so we say this is a stretched transition
 The basics of the situation:
Ei 3

Ef 2

│3-2│ ≤  ≤ 3+2

Here J = 1 but  = 1,2,3,4,5

and the transition can be a mix of 5 multipolarities

 The basics of the situation:
Ei Ji  i

El

Ef Jf f
Electromagnetic transitions:
 electric

 magnetic+1

YES E1 M2 E3 M4

NO M1 E2 M3 E4
 The basics of the situation:
Ei 2+

Ef 0+

│2-0│ ≤  ≤ 2+0

 = 2 and no change in parity

YES E1 M2 E3 M4

NO M1 E2 M3 E4

pure (stretched) E2
The basics of the situation:
Ei 3+

Ef 2-

Here J = 1 but  = 1,2,3,4,5

YES E1 M2 E3 M4

NO M1 E2 M3 E4

Mixed E1/M2/E3/M4/E5
The basics of the situation:
Ei 3+

Ef 2+

Here J = 1 but  = 1,2,3,4,5

YES E1 M2 E3 M4

NO M1 E2 M3 E4

Mixed M1/E2/M3/E4/M5
 The basics of the situation:

3+ -> 2+: mixed M1/E2/M3/E4/M5

3+ -> 2-: mixed E1/M2/E3/M4/E5

In general only the lowest 2 multipoles compete

and (for reasons we will see later)

l+1 multipole generally only competes if it is electric so:

3+ -> 2+: mixed M1/E2

3+ -> 2-: almost pure E1 (v. little M2 admixture)

 The basics of the situation:

Amount of mixing is given by the mixing ratio 

given by 

3+ -> 2+: M1/E2 admixture

%E2 =

%M1 =
 Not quite so basic:

Transition rate T [s-1] given by:

2
→ ‼

Note the l dependence on the energy, the double factorial (what is that?)

this is the bit that has the physics in it,

∑ 2 it’s the matrix element between the initial
and final wavefunctions squared and is
related to the B() by
B() = ∑ 2
 Not quite so basic:

Typical transition rates [s-1]: Note:

T(E1) = 1.59 x 1015 (E)3 B(E1) • Electric transitions faster than magnetic

T(E2) = 1.22 x 109 (E)5 B(E2)

• Higher multipolarity => slower rate
T(M1) = 1.76 x 1013 (E)3 B(M1)

T(M2) = 1.35 x 107 (E)5 B(M2) • Transition probability proportional

to transition energy => low-energy transitions

E in MeV
are hard to observe and other processes
B(E) in e2fm2
e.g. internal conversion start to compete.
2
B(M) in fm2
 Not quite so basic:

Single particle estimates (also called Weisskopf estimates)

T(E1) = 1.02 x 1014 (E)3 A2/3

T(E2) = 7.26 x 107 (E)5 A4/3

T(M1) = 3.18 x 1013 (E)3

T(M2) = 2.26 x 107 (E)5 A2/3

Measuring level lifetimes gives us transition rates which can be interpreted

as single particle (or collective) and hence give an indication of the type of

motion
Methods of producing the nuclei of interest
Out-of-beam spectroscopy:

Nucleus is stopped
Not many gamma rays emitted (Gamma-ray multiplicity low)

e.g. decay from a fission source, from stopped radioactive ion beams
(ISOL or fragmentation), or de-excitation of isomeric states

In-beam spectroscopy:

Nucleus is moving
Lots of gamma rays emitted (Gamma-ray multiplicity high)

e.g. compound nucleus reaction, Coulomb excitation

 Out-of-beam spectroscopy

Stopper

1
RIB
2

Get first information on lifetimes, decay modes, Q-values and

scheme of excited levels
Two Reaction Processes
Beam at Relativistic Energy  Reaction Products still travelling at 
~0.5‐1 GeV/A Relativistic Energies

Target Nucleus
Projectile
fragmentation
Abrasion Ablation
Beam fissions

Target Nucleus Projectile
fission
Ion-by-ion identification with e.g the FRS:

A B

Z  FRS = Fragment Recoil Spectrometer at GSI
Cocktail of fragments
Chemically independent

H.Geissel et al., NIM B70 (1992) 286.

 Ion-by-ion identification with e.g the FRS:

TOF

20000

Time of flight
Time of Flight

10000
-> 
COUNTS

0
2000 2400 2800 3200
Time of Flight
 Ion-by-ion identification with e.g the FRS:

30000

25000

20000
Position information
counts

15000

10000 gives trajectory -> 

5000

0
-80 -40 0 40 80
S4 position (mm)
 Ion-by-ion identification with e.g.the FRS:

20000

Nb Mo
15000
Tc Z identification: Music
Zr
E  Z 2 f (  )
counts

10000
MUSIC
GAS: 90%Ar and 10%CH4
5000
Readout: 8 Anodes

0 Resolution: 0.3
800 1200 1600 2000
energy loss M.Pfützner et al. NIM B86 (1994) 213
Isotope identification
Isotope identification
Isotope identification

S. Pietri et al.,
RISING data
107Ag beam
212,214,216Pb: 8+ isomers:
A. Gottardo, J.J. Valiente Dobon, G. Benzoni et al., PRL 109 (2012) 162502 
 Energy levels well described in seniority scheme

A. Gottardo, J.J. Valiente Dobon, G. Benzoni et al., PRL 109 (2012) 162502 

 In-beam spectroscopy

Low-energy in-beam spectroscopy (up to 10 MeV per nucleon)

e.g.
Fusion evaporation.
Multi-nucleon transfer reactions
Coulomb excitation
Single nucleon transfer reactions
Intermediate-energy in-beam spectroscopy (50 -100 MeV per
nucleon)
e.g.
Coulomb excitation
Spallation
Knockout
E.g. fusion evaporation:

First particles are emitted..

p
Then gamma rays
 Gamma-gamma coincidence matrices

Usually
set a
time window
~ 500 ns

From Dave Cullen’s web page

Gamma-ray patterns reveal nuclear structure

• Collective rotation
(left) of a deformed
nucleus leads to regular
band structures

• Single-particle
generation of spin
(right) in a spherical
nucleus leads to an
irregular level structure
Suggestions for tutorial discussion:
1. How can the 0+ first excited state in 40Ca decay to the ground
state by 2 gamma rays if there are no intermediate levels?

2. Calculate E1, E2, M1, M2 transition rates for a single particle,

500 keV transition in an A=100 nucleus. What would the
corresponding level lifetimes be?

3. What is the meaning of the phrase ‘Energy levels well described in

seniority scheme’ when describing the Pb isomers? What particles
are involved and in what orbits? (Pb, Z=82)

4. Estimate the angular momentum (in units hbar) brought into the
compound nucleus 156Dy from the fusion of a 48Ca beam on a 108Pd
target at a beam energy of Ebeam = 206 MeV.
 Gamma-ray interactions in matter
Gamma rays interact with
matter via three main reaction
mechanisms:

Photoelectric absorption

Compton scattering

Pair production

Pictures from University of Liverpool website

 Photoelectric absorption
Einstein won the Nobel Prize for
Physics for the discovery of the
photoelectric effect.

In this mechanism a γ-ray interacts

with a bound atomic electron.

The photon completely disappears and is replaced by an energetic

photoelectron. The energy of the photoelectron can be written

Ee = E – EB.
The energy of the incident gamma-ray photon minus that of the binding energy
of the electron (EB = 12eV in germanium).
 Compton scattering
Compton won the Nobel Prize for
Physics for the discovery of the
Compton effect.

In this mechanism a γ-ray interacts

with a loosely bound atomic electron.

The incoming γ-ray is scattered through an angle θ with respect to its original
direction.

The photon transfers a proportion of its energy to a recoil electron. The

expression that relates the energy of the scattered photon to the energy of
the incident photon is

1 1
 Pair production
Nobody won the Nobel Prize for Physics for
the discovery of the pair production effect
(as far as I know).

If the energy of the -ray exceeds twice the

rest mass energy of an electron (1.022 MeV),
then the process of pair production is
possible.

The incoming γ-ray disappears in the Coulomb field of the nucleus and is
replaced by an electron-positron pair which has kinetic energy

E - 1.022 MeV.

The positron is slowed down and eventually annihilates in the medium. Two
annihilation photons are emitted back to back and these may or may not
escape from the detector. Hence three peaks can be observed.
Other interactions in a real detector

Thomson Scattering
Low-energy coherent scattering off free electrons. Not
important in the energy range concerned with most nuclear
structure studies.

Nuclear Thomson Scattering

Low energy coherent scattering off nucleus.
Small effect.

Dellbrück Scattering
Scattering in the Coulomb field of the nucleus.
Important at Eγ > 3 MeV.
Pictures from University of Liverpool website
 Interactions in a small detector

A small detector is one in which only one interaction can take place.
Only the photoelectric effect will produce full energy absorption.
Compton scattering events will produce the Compton continuum. Pair
production will give rise to the double escape peak due to both
gamma-rays escaping.

Pictures from University of Liverpool website

 Interactions in a large detector

A large detector is one in which there will be complete absorption of

the gamma ray and a single gamma-ray peak, referred to as the full
energy peak will be observed.

Pictures from University of Liverpool website

 Interactions in a real detector

Within a real detector, the interaction outcome is not as simple to

predict as e.g.
one Compton scattering could be followed by another before the
gamma-ray photon escapes from the detector.
in the case of pair production, both, one or neither of the
annihilation photons could escape from the detector. Hence all
three peaks may be observed.

Pictures from University of Liverpool website

Energy dependence of the interactions

Typically we are
interested in
transitions of energy
60 keV < E < 10 MeV.
 Detector types
Two main types of material are used:

Solid state semiconductor detectors e.g. Ge, CZT

Electron-hole pairs are collected as charge

knock-on effect => an avalanche arrives at the electrode

lots of electrons => good energy resolution

cooled to liquid N2 temperature (77K) to reduce noise

Advantage: good energy resolution (~0.15 % (FWHM) at 1.3 MeV)

Disadvantages: relatively low efficiency

cryogenic operation

limit to the size of crystal/detector

Z dependence of interaction probablities
Escape suppressed HP Ge detector
 Large Gamma Arrays based on Tracking Arrays based on
Compton Suppressed Spectrometers Position Sensitive Ge Detectors

EUROBALL GAMMASPHERE AGATA GRETINA/GRETA

  10 — 5 %   40 — 20 %
( M=1 — M=30) ( M=1 — M=30)
 Compton suppression increases peak to total

Bare detector: P/T ~20% at ~ 1 MeV i.e only 20% of single events have the
full energy measured
for  only 4% of events are full energy,  0.16%

Compton suppression: P/T ~ 60%

 Detector types
Two main types of material are used:

Scintillation detectors e.g. NaI, BGO, LaBr3(Ce)

Recoiling electrons excite atoms, which then de-excite by emitting visible

light.

Light is collected in photomultiplier tubes (PMT) where it generates a

pulse proportional to the light collected.

Advantage: good timing resolution

can be made relatively large e.g. NaI detectors 14” x 10”
no need for cryogenics

Disadvantages: poor energy resolution

 Scintillation detectors
LaBr3(Ce)

 LaBr3(Ce) timing properties:

◦ ~ 25 ns decay time
◦ Timing Resolution FWHM of 130-150
ps with 60Co for a Ø1”x1” crystal.

 High energy resolution, 3 % FWHM at

662 keV.

 Peak Emission wavelength in Blue/UV

part of EM spectrum (380 nm),
compatible with PMTs.
Detector Characterisation

β-decay

0‐255 keV
788‐1000 keV 1.5‐3 MeV
EC α

Activity: ~0.7 counts/sec./cm3 ~0.1 counts/sec/cm3

J. McIntyre et al., NIM A 652, 1, 2011, 201‐204
 Timing resolution of cylindrical crystals

ø1”x1”
FWHM  200 ps ø1.5”x1.5”
360 ps ø2”x2”
FWHM  150 ps 180 ps 450 ps at 511 keV 
300 ps at 1332 keV
 Timing resolution of cylindrical crystals

ø1”x1”
FWHM  200 ps ø1.5”x1.5”
360 ps ø2”x2”
FWHM  150 ps 180 ps 450 ps at 511 keV 
300 ps at 1332 keV
Trade off between resolution and efficiency
Timing Precision

Trade off between good timing resolution (small detectors)

lots of statistics (large detectors)

Timing precision defined as:

TP=

TP formula Ref: H Mach private communication

 Detector requirements for in-beam
spectroscopy

Gamma rays emitted by moving reaction product:

Good energy resolution (as lots of gamma rays emitted)

High granularity (to uniquely define the -ray angle and because
lots of gamma rays are emitted – high multiplicity)

High photopeak detection efficiency (to see the weakest channels)

Good peak to total ratio (so that coincidence gates can be clean)
 Energy resolution
The major factors affecting the final energy resolution (FWHM) at a
particular energy are as follows:

ΔEInt - The intrinsic resolution of the detector system.

This includes contributions from the detector itself and the
electronic components used to process the signal.

ΔθD - The Doppler broadening arising from the opening angle of the
detectors.

ΔθN - The Doppler broadening arising from the angular spread of

recoils in the target.

ΔV - The Doppler broadening arising from the velocity (energy)

variation of the recoils across the target.
 Doppler broadening

Broadening of detected γ-ray energy arises

from:
•Spread in recoil velocity ΔV
•Distribution in the direction of recoil ΔθN
•Detector opening angle ΔθD
 Minimising Doppler broadening

There are two ways in which gamma-ray spectroscopists can mitigate

the effects of Doppler broadening.

•Reduce the detector opening angle (lower ΔθD)

- Detector granularity

•Minimise the target thickness (lower spread in recoil velocity ΔV)

Experimentalists often choose to use two or three stacked targets

rather than a single thick target e.g. 2 x 0.5 mg/cm2 rather than a
single 1 mg/cm2.

This works for normal kinematics where the spread in velocities ΔV

arises from the slowing of the recoil and not the beam.
Minimising Doppler broadening
Successful Compton suppression arrays:

Total Escape Suppressed

Spectrometer Array
Spectroscopy of 158Er

~1980 yrast states to spin ~30, naked Ge arrays

~1980-1982 TESSA
Escape suppressed array at NBI

Non-yrast bands to spins in mid 20’s

Intensity few %
Efficiency ~0.2%
Band crossing systematics,
blocking, pairing reduction
Quasi-particle configurations
Cranked shell model

J.Simpson et al., J.Phys. G10 (1984) 383

158Er expt. Daresbury –Sharpey-Schafer, Riley, Simpson et al. mid 1980’s

The 12 valence particles move in

equatorial orbits, driving the
nucleus to an oblate shape!

(keV)
Simpson et al., Phys. Rev. Lett. (1984) – prolate-oblate shape change
P.O.Tjom et al., PRL 55 (1985) 2405 –lifetime measurements
T.Bengtsson and I. Ragnarsson, Physica Scripta T5 (1983) 165
J. Dudek, W. Nazarewicz Phys. Rev C32 (1985) 298
Ragnarsson, Xing, Bengtsson and Riley, Phys. Scripta 34 (1986) 651
Successful Compton suppression arrays:
What about 158Er above 46+?
No wonder we could not see it before!

46+ = 1% of 2+ 0+
Gate in coinc with 44+

42+

Low intensity feeders!

{au; PRL 98 (2007) 
= 9.5%
Paul PRL 98 (2007) 012501
Evolution of Gamma-Ray Spectroscopy
New Detector Systems New Physics
 Mixed arrays

More recently, LaBr3(Ce) detectors have been added to arrays of Compton

suppressed detectors because of their good timing properties.

E.G. ROSPHERE at Bucharest

 15 HPGe detectors (A/C):

 10 x HPGe detectors @ 37o
 1 x HPGe detector @ 64o
 4 x HPGe detectors @ 90o

 11 LaBr3(Ce):
 ø2”x2” @ 90 and 64o (three)
(Cylindrical)
 ø1.5”x1.5” @ 90 (six) (Cylindrical)
 ø1”x1.5” @ 64o (two) (Conical)
Next generation : tracking

Detectors are segmented

longitudinally and radially.

Pinpoint the position of the first

interaction to get the angle of the

incident gamma ray (very important

if have a high v/c).

 Idea of -ray tracking
Large Gamma Arrays based on Tracking Arrays based on
Compton Suppressed Spectrometers Position Sensitive Ge Detectors

EUROBALL GAMMASPHERE AGATA GRETINA/GRETA

  10 — 5 %   40 — 20 %
( M=1 — M=30) ( M=1 — M=30)

Huge increase in sensitivity

Pulse Shape Analysis concept

A3 A4 A5

(10,10,46)
B3 B4 B5

(10,30,46)
C3 C4 C5
y

C4 B4
CORE
measured
D4
A4 x

E4 F4
791 keV deposited in segment B4
z = 46 mm
Pulse Shape Analysis concept

A3 A4 A5

B3 B4 B5

(10,10,46)
C3 C4 C5
y

C4 B4
CORE
measured
calculated D4
A4 x

E4 F4
791 keV deposited in segment B4
z = 46 mm
Pulse Shape Analysis concept

A3 A4 A5

B3 B4 B5

(10,15,46)
C3 C4 C5
y

C4 B4
CORE
measured
calculated D4
A4 x

E4 F4

791 keV deposited in segment B4 z = 46 mm

Pulse Shape Analysis concept

A3 A4 A5

B3 B4 B5

(10,20,46)
C3 C4 C5
y

C4 B4
CORE
measured
calculated D4
A4 x

E4 F4
791 keV deposited in segment B4
z = 46 mm
Pulse Shape Analysis concept

A3 A4 A5

B3 B4 B5

(10,25,46)
C3 C4 C5
y

C4 B4
CORE
measured
calculated D4
A4 x

E4 F4
791 keV deposited in segment B4
z = 46 mm
Pulse Shape Analysis concept

A3 A4 A5

B3 B4 B5

(10,30,46)
C3 C4 C5
y

C4 B4
CORE
measured
calculated D4
A4 x

E4 F4
791 keV deposited in segment B4
z = 46 mm
Pulse Shape Analysis concept

A3 A4 A5
Result of 
Grid Search
B3 B4 B5 algorithm

(10,25,46)
C3 C4 C5
y

C4 B4
CORE
measured
calculated D4
A4 x

E4 F4
791 keV deposited in segment B4
z = 46 mm
 AGATA
(Advanced GAmma Tracking Array)
v/c = 50%

Conventional 
array

Segmented 
detectors

‐ray tracking
The innovative use of detectors (pulse shape
analysis, -ray tracking, digital DAQ) will result
in high efficiency (~40%) and excellent energy
resolution, making AGATA the ideal instrument Energy (keV)

for spectroscopic studies of weak channels. The effective energy

resolution is maintained also
at “extreme” v/c values
Detector requirements for out-of-beam
spectroscopy

Gamma rays emitted by a stopped source:

Doppler broadening is not an issue..detectors can be very close but

if you do this you lose angle definition which is required for angular
measurements.

Few gamma rays means you can have fewer big detectors but see
note above re detector angle

High photopeak detection efficiency (to see the weakest channels)

Good peak to total ratio (so that coincidence gates can be clean)
Detector requirements for out-of-beam
spectroscopy

In recent years, experiments have still tended to be performed

with arrays e.g. the use of the RISING array of Euroball clusters
for experiments at the FRS at GSI.
Detector requirements for out-of-beam
spectroscopy

Now also using mixed arrays e.g. the use of the EURICA array of 12
Euroball clusters with 18 LaBr3(Ce) detectors at BigRIPS at RIKEN.
 Typical efficiency curve

Efficiency of the 12 EURICA Cluster detectors for singles (solid symbols)

and add back (open symbols)
Suggestions for tutorial discussion:

1. Explain the origin of the part of the spectrum labelled “multiple

Compton events” in the spectrum for the ‘real detector’

2. Why are Compton suppression shields made from scintillator

material?

3. Why is the timing resolution worse for bigger scintillator

detectors?

4. Why does the efficiency curve have this shape?

 Spins and parities

Two distinct types of measurements:

Angular correlation: can be done with a non-aligned

source but need  coincidence information.

Angular distribution: need an aligned source but can

be done with singles data.

…note that these cannot measure parity but you can

usually infer something about the transition.
 The basics of the situation:

1+ Imagine the situation of

an E1 decay between two
E1  states, the initial one has
a J value of 1+ and the
0- final one a J of 0-.
 The basics of the situation:

1+ The J = 1+ state has 3 substates

with m values of ±1 and 0.
E1 

0- The J = 0- state has only 1

substate, with m=0.

When the substates of the J = 1+

state decay, the  rays emitted
have different angular patterns.
 The basics of the situation:

1+ J = 1+, m=0 decays to

J = 0-, m=0 with a
E1  sin2 distribution.

0- J = 1+, m=±1 decays to

J = 0-, m=0 with a
½(1+cos2 distribution.
 The basics of the situation:

1+ J = 1+, m=0 decays to

J = 0+, m=0 with a
E1  sin2 distribution.

0+ J = 1+, m=±1 decays to

J = 0+, m=0 with a
½(1+cos2 distribution.

So the total distribution is ½(1+cos2+ sin2+ ½(1+cos2

= 1+cos2sin2
=2 …flat, no angular dependence
Angular correlation – non-oriented source

Let’s imagine we have two -

rays which follow
1 immediately after each
other in the level scheme.
2 If we measure 1 or 2 in
singles then the distribution
will be isotropic (same
intensity at all angles)…
there is no preferred
direction of emission.
Angular correlation – non-oriented source

Now imagine that we measure

1 or 2 in coincidence. We say
1 that measuring 1 causes the
intermediate state to be
aligned. We define the z
2 direction as the direction of 1.
The angular distribution of
the emission of 2 then
depends on the spin/parities
of the states involved and on
the multipolarity of the
transition.
 A simple example:

0+ J = 0+, m=0

1+ J = 1+, m=0, m=±1

0+ J = 0+, m=0
 A simple example:

0+ J = 0+, m=0
1
1+ J = 1+, m=0, m=±1
2
0+ J = 0+, m=0

Hence for  we only see the m = ± 1 to m=0 part of the

distribution i.e we see that the intensity measured as a
function of angle (w.r.t 1) follows a 1+cos2 distribution. 
 General formula
J1
In general, 1
The gamma-ray intensity J2
varies as:
J3 2

where
is the relative angle between the two -rays
accounts for the fact that we do not have point
detectors
depends on the details of the transition and the
spins of the levels
 General formula
J1
1
J2
2
J3

2 1 1 1
1

2 1 1 1
1
The Fk coefficients contain angular momentum coupling
information …..3j, 6j symbols.
 Legendre polynomials

1
3 1
2

1
35 30 3
8

1
231 315 105 5
16

Note the dependence on cos2.

 A specific case:

J
1
2+
2 =0 as this is a pure E2
0+
A γ F 2022
 = ‐ 0.5976
 A specific case:

195Pt(n,)196Pt reaction

slow-neutron capture so
definitely no alignment
brought into the system

v simple system, 2 detectors

1 moving
1 fixed

circa. 1983
A specific case : 195Pt(n,)196Pt
A specific example – extract mixing ratios

arctan  ~ -86
 = -14.3 (40)
 A specific example – assign spins
188Os(n,)189Os

Assign 679 keV level as 5/2

and measure arctan  ~ -20
 = -0.36 12% quadrupole
216 keV measured as pure E2 88% dipole
 Angular correlations with arrays

Many arrays are designed symmetrically so the

range of possible angles is reduced.

In these cases it is most common to measure a

‘DCO’ ratio. e.g. in the simplest case, if you have
an array with detectors at 350 and 900:
Gate on 900 detector, measure coincident
intensities in:
• other 900 detectors
• 350 detectors

Take the ratio and compare with calculation…can

usually separate quadrupoles from dipoles but
cannot measure mixing ratios.
Angular correlations with arrays

K.R.Pohl et al., Phys Rev C53 (1996) 2682

Angular distribution
 Angular distribution

In heavy‐ion fusion‐evaporation reactions, the compound
nuclei have their spin aligned in a plane perpendicular
to the beam axis:

Depending on the number and type of particles ‘boiled off’ 
before a  ray is emitted, transitions are emitted from oriented
nuclei and therefore their intensity shows an angular 
dependence.
 Angular distribution

1 ⋯

1 ⋯

Where Ak and Pk are as before and Bk contains information

about the alignment of the state

(in principle there should be a Qk in here too but let’s forget for now)
Angular distribution: worked example 209Bi

Measure mixing ratio of 1609 keV transition

O.J.Roberts, C.R.Nita et al., Phys Rev C93 (2016) 014309

Angular distribution: worked example 209Bi

What’s the physics?

Angular distribution: worked example 209Bi

209Bi was populated in the 208Pb(7Li,2n)209Bi

reaction at a 7Li beam energy of 32 MeV…

…it’s a sort of compound nucleus reaction but

7Li breaks up into 4He and 3H so is the 4He just a

spectator?

Anyway, the question is how much alignment is in the

initial states in 209Bi??
Angular distribution: worked example 209Bi

Answer…look at something we know the Ak values

for and ‘fit’ Bk
15/2+

9/2-
Angular distribution: worked example 209Bi

Answer…look at something we know the Ak values

for and ‘fit’ Bk
W(θ)
Angular distribution: worked example 209Bi

1609 keV transition

Angular distribution: worked example 209Bi

1609 keV transition min at arctan( =-10.54

O.J.Roberts, C.R.Nita et al., Phys Rev C93 (2016) 014309

Angular distribution: worked example 209Bi

1609 keV transition:

arctan( = - 10.54

 (E3/M2) = -0.184(13)

%E3 = = 3%

%M2 = = 97%
Angular distribution: worked example 209Bi

What’s the physics?

3% 97%

O.J.Roberts, C.R.Nita et al., Phys Rev C93 (2016) 014309

 Linear polarisation

A segmented detector can be used to measure the

linear polarisation which can be used to distinguish
between magnetic (M) and electric (E) character
of radiation of the same multipolarity.

The Compton scattering cross section is larger in

the direction perpendicular to the electric field
vector of the radiation.
 ray travelling into
the slide
 Linear polarisation

Define experimental asymmetry as:

where N90 and N0 are the intensities of

scattered photons perpendicular and parallel to
the reaction plane.
 ray travelling into
the slide The experimental linear polarisation P = A/Q
where Q is the polarisation sensitivity of the
dectector.
Linear polarisation

Plot P against the

angular distribution
information to uniquely
define the multipolarity.

Data from Eurogam

 Measuring level lifetimes

electronic timing
RDM DSAM

10-6 10-9 10-12 10-15 (seconds)

DSAM – Doppler shift attenuation method

RDM - Recoil distance method

Electronic timing – Using arrays of fast scintillation detectors

 Doppler shift attenuation method

• Measure lifetimes in the range 10-15 < τ < 10-12 s.

• Stopping time in metal foil is comparable to lifetimes of
excited states.

 v 
E shifted  E true 1  cos  
 c 
γ γ
v/c
v0/c

γ γ
 Centroid shift method
17o
 v 
E f  E true 1  cos  f 
 c 

 v 
Eb  E true 1  cos b 
 c  90o

If θ = θforward = 180 - θbackward

_
v
E f  Eb  2E true cos  163o
c
_
v v0
F   and 
v0 c

E f  Eb
F 
2E true cos 
 Recoil distance method

Have a space between the target and the stopper.

Measuring the v/c you can work out whether the gamma-
ray is emitted before/after the stopper

Vary the target/stopper distance to get a measurement

of the lifetime of the level
 Recoil distance method
Idegraded  Ie  d / v

Ishifted  I 1  e d / v 
I degraded  d / v
e
I degraded  I shifted
The Koln Plunger Device
Lifetime of the 15/2- state in 119Te

Bucurescu NIMA 837 (2016) 1. ROSPHERE

Direct measurement using ROSPHERE
at Bucharest:

 15 HPGe detectors (A/C):

 10 x HPGe detectors @ 37o
 1 x HPGe detector @ 64o
 4 x HPGe detectors @ 90o

 11 LaBr3(Ce):
 ø2”x2” @ 90 and 64o (three)
(Cylindrical)
 ø1.5”x1.5” @ 90 (six)
(Cylindrical)
 ø1”x1.5” @ 64o (two) (Conical)
ROSPHERE at Bucharest: example of 209Bi

208Pb(7Li,2n)209Bi at beam energy of 32 MeV

Gates in Ge 
to select 209Bi

Additional gate 
on 1609 in LaBr

O.J.Roberts, C.R.Nita et al., Phys Rev C93 (2016) 014309

 ROSPHERE at Bucharest: example of 209Bi

Prompt
Red = start on 1609, stop on 992 or 1132
response

Black = start on 992 or 1132, stop on 1609

Difference in the centroids is 2 (give or take

some correction factors) O.J.Roberts, C.R.Nita et al.,
Phys Rev C93 (2016) 014309
Angular distribution: worked example 209Bi

What’s the physics?

t1/2=120ps

~5Wu <1 Wu

O.J.Roberts, C.R.Nita et al., Phys Rev C93 (2016) 014309

 From first lecture:

Typical transition rates: 1

=T (σλ)
τ
T(E1) = 1.59 x 1015 (E)3 B(E1)
If E2:
T(E2) = 1.22 x 109 (E)5 B(E2)
T(E2) = 1.22 x 109 (E)5 B(E2)
T(M1) = 1.76 x 1013 (E)3 B(M1)
The transition quadrupole moment Q0
T(M2) = 1.35 x 107 (E)5 B(M2) is obtained from:

2 16πB(E2)
Q0 =
E in MeV 2
5 Ji K20 Jf K
B(El) in e2fm2
2
So measuring a lifetime gives us a transition
B(Ml) in fm2 quadrupole moment (note that we cannot get
the sign of Q0)
Using the EURICA/FATIMA array at RIKEN

Browne et al. PLB750 (2015) 448

 Quadrupole moment relates to shape
Assuming a quadrupoloid shape and that the deformation is the same

for both states, the deformation 2 can be obtained from:

3 2 5 1
1 ⋯
5 7 14

Neutron-rich Zr nuclei

Formula:
Löbner, Vetter and Honig,
Nucl. Data Tab A7 (1970) 495.

56 60 64 68 Data:
Neutron
56  number Browne et al. PLB750 (2015) 448
Suggestions for tutorial discussion:

1. In the angular correlation formula, on what might Qk depend?

2. How does the deformation parameter 2 relate to 2 and  (which

you may see elsewhere)

3. What methods are there to measure the sign of the quadrupole

moment?
Acknowledgements
(for slides and
animations)

Dr Dave Joss

Prof John Simpson

 Useful points of reference for angular
correlation and distribution

Chapters 12,14 and 15 in ‘The electromagnetic interaction

in nuclear spectroscopy’ edited by W.D.Hamilton

Q factors: Camp and van Lehn, NIM 76 (1969) 192

Alignment in compound nuclear reactions:

Butler and Twin, NIM 190 (1981) 283

Errors on  from arctan  plots:

James, Twin and Butler, NIM 115 (1974) 105