Applications of gamma ray spectrometry
A) Study of nuclear structure, nuclear transitions and nuclear reactions
1) Properties and advantages of nuclear electromagnetic radiation studies
2) Facets of basic research by means of gamma spectroscopy
3) Basic methods:
a) Determination of level energies and decay scheme
b) Measurement of level spins and parities, transition multipolarities ...
c) Measurement of transition probabilities (from level life time,
Coulomb excitation ...)
4) Some interesting examples:
a) Study of states with very high spins ( very fast nuclear rotation)
b) Superdeformed states
c) Giant resonances
5) High energy „nuclear“ spectrometry – example:
Study of neutral meson production in heavy ion collisions
B) Applications
1) Activation analysis
2) Material research by PIGE and PIXE methods
3) Usage of diffraction method at crystallography
Study of nuclear properties, transitions and reactions
Main goal is to understand properties of system consists of finite number of strongly
interacting particles (nucleons)
Properties of electromagnetic interactions and emission of photons during
different nuclear processes are used.
Observed gamma rays
make possible to study
nuclear structure →
understanding of
strong interaction
Unique properties of electromagnetic interactions:
1) Simple well known description of interaction HEM
Transition matrix element is:
 ( EM )   f H EM  i
where ψi and ψf are wave functions of initial and final state
Transition probability → matrix element → direct information ψi and ψf
2) Interaction energy of elmg interaction at nucleus is given by hadron electric charges
and their electric currents (given by charged hadron motion and magnetic momenta of
all hadrons):
 


1  
H EM    r , t    r , t d 3r   j r , t   Ar , t d 3r
c
where




 r , t , Ar , t 
is four-vector of potential and

 
j  
  r , t , r , t 
c


four-vector of charge current
Assumption: nucleus – system of point like nucleons:
Charge density:

i
Current density:
1
2


 
 r    e    t zi    r  ri 
Motion of charged
nucleons
Interaction of nucleon
Magnetic momenta, where
j 
e
 3.151014 MeVT1
2mN c
- nuclear magneton
 
  
  
1
1   
j r    e   t zi  vi r  ri    r  ri vi   j c g si   si r  ri 
2
2
i
i
where t zi is isospin projection (convention is tz proton = +1/2 and neutron -1/2),
vi velocity and si spin
proton gp = 5,58
1
i
i
g

g

t
g
g
=
g
+
g
a
g
=
g
–
g
s
0
z
1
0
p
n
1
n
p
gyromagnetic ratios:
2
neutron gn = - 3,82
Study of elmg interaction – direct test, charge distribution, velocities of nucleons,
nuclear spins and izospins
3) Weak interaction constant – α = 1/137, application of perturbative methods, mostly
first order is sufficient, higher orders are necessary only in the case
of suppression of first order transition by conservation laws or selection rule
4) Simple multiple expansion and selection rules:
Clean radiation field at vacuum (φ = 0):
Maxwell equations are fulfilled →
 2 1 2   
   2 2  A(r , t )  0
c t 


divAr , t   0
Intensities of electric
and magnetic field:


1 A
E
c t


H   A
Common vector field is possible express by arbitrary complete set of ortoghonal solutions
of these equations. We will use: Ar, t   q eit A r 
k
where
Reminder:
k

 




    A     A  ΔA

2 2 1
k 


c
c
 
=0
Maxwel equations are equivalent to:




Ak  k 2 Ak  0      Ak  k 2 Ak  0
This equation is satisfied (J and M are integer numbers) by:
E

i
AJM

  [ r  ( j J ( kr )YJM (,  ))]
k
and
M

AJM
 r  ( jJ (kr)YJM (, ))
where jJ(kr) – spherical Bessel function and Y
(, )
- normalized spherical harmonic
function

We can resolve arbitrary Ato set of these solutions (P = E or M):
 
P
k, r 
Ar , t     dkqkJMPeit AJM
JM
J ,M , P
Quantum field → Eγ = ħω, component z of momentum M·ħ q*q – operator with
eigenvalue of photon number
Approximation: 1) Nucleon motion is nonrelativistic
2) Radiation wave length is long against nuclear radius A
1
c
c
c
6,58 1022 MeV  s  3 108 ms1
3
R   
 E 



164

A
MeV
1
1

15
E
Rj r A 3
3
1,2 10 m  A
0
R    R 
Long wave approximation
jJ (kr) 
1
 kR  1
k
(kr) J
(2 J  1)!!
50
100
200
Eγ <<
[MeV]
45
35
28
E
E
→ members with the lowest J value ( k  c  197MeV )
Selection rules:
Photon has spin I and parity π : EJ → I = min J, π = (-1)I
MJ → I = min J, π = (-1)I+1
Transition between levels with spins Ii and If and parities πi and πf :
I = |Ii – If| for Ii ≠ If
I = 1 for Ii = If > 0
π = (-1)I+K = πi·πf
K=0 for E and K=1 for M
Electromagnetic transition with photon emission between states Ii = 0 and If = 0 don´t exist
Studies using gamma ray and electron spectrometry
1) Basic properties of nuclei – quantum system of strongly interacting nucleons
new nuclear shapes, highly excited particle and hole states,
electromagnetic response (spin, izospin ...) , different collective states
2) Nucleon motion in extreme conditions – high excitation, high spins (rotation),
superdeformed states, giant dipole resonances
3) Study of fundamental symmetries of elementary particles inside hadron system,
new degree of freedoms at nuclear field, resonance and strangeness
production, parton degrees of freedom
Spectrometer EXOGAM
on beam of radioactive
beam at GANIL (France)
Photon spectrometer
TAPS during its first
stay at GANIL
Determination level energies and decay scheme construction
1) As accurate determination of transition energy as possible
2) Coincidence measurements – determination of transition placement at cascade
(intrinsic geometry of anticompton spectrometer
and multidetector set-ups)
3) Level energies from reactions
Spectrum and decay scheme from 166mHo decay study performed by means of anticompton
Spectrometer of NPI of ASCR – focused on weak transition with high energy deexcitating
rotational bands on vibrational states
Determination of level spins and transition multipolarities
1) Usage of electromagnetic transition selection rules – usage of selection
rules and knowledge about spin of some level, which transition connects
2) Usage of ratios between probabilities of gamma transition and emission of conversion
electron“
Determination of transition conversion coefficient   Ne
N
Conversion coefficients for separate shells αK, αL, αM, αN ...
Properties: 1) Conversion coefficients increase with increasing
of transition multipolarity
2) α(M) > α(E)
3) fast decreasing with transition energy
3) Usage of angular distribution of gamma rays against
Dependency of total conversion
nuclear spin
n
Spin orientation
intensity
W ( )    ( I i ) f ( I i , I f , E ( M ) J , E ( M ) J ´)P (cos )

Legendre
polynomials
coefficients on transition energy,
sketchy picture (values taken
from ADNDT 21(1978)4-5)
Oriented nuclei – study of angular distribution
Orientation by magnetic field, preferred direction of beam in reaction
4) Angular correlation of two photons emitted in sequence at cascade:
5) Information about spins from reactions: analysis of different reaction histories –
different reactions excite levels with different spins
Determination of transition probabilities using life time of levels
1) Electronic methods – measurement of decay curve
Isomere state measurement
Off beam measurement (after irradiation): τ ~ min - ∞
Transport system and measurement
during irradiation:
τ >~ s
On beam measurements:
Resolution of BaF2 - ~ 100 ps
Resolution of reaction time (often from accelerator RF) ~ 1 ns
Total resolution in the order from units up to parts of ns
Time spectrum – gauss (prompt) + exponential
curve (isomer)
Available the lowest limit:
τ ~ ns = 10-9s
Modification of time spectrum
for τ comparable with FWHM
2) Usage of Doppler shift
A) We use study of ratio of Doppler shifted and
not shifted lines intensities as function of distance,
in which reflected nuclei are stopped
Compound nucleus is created during reaction a(A,C):
Velocity of compound nucleus:
2ma c 2 Ekina
va ma
vC
vĆ 


ma  M A
c ma  M A   c 2
Velocity of reflected nucleus depends on reaction kinematics
in the case of Coulomb excitation and direct reaction
Dependency of compound
nucleus velocity on beam
energy
Energy of photon emitted by moving nucleus:
v << c → omission of member with
(v/c)2
 v

E  E 0 1  cos 
 c

where θ – angle between directions of nucleus motion
and photon emission
 E  v
for θ = 0o and 180o is energy difference maximal: max E    c

Ratio of intensities emitted by reflected nuclei
t0
in motion
0
R(d ) 

S S
S S  S P

t
S  S (0)  e dt
P

and stopped

0

t
S  S (0)  e dt:
S

t0
where d = v·t0 is distance between target
and foil which is stopping reflected nuclei
Dependency of ratio
Eγ/Eγ0 = f(θ)
Resolution: HPGE ~ 0,003
and scintillator ~ 0,05
Distances d in the range 1 – 10-2 mm
(distance is measured electrically)
Target 0.7 – 1.5 μm, foil 5- 10 μm Au, Ta, Bi
Example of measurement of gamma lines from
levels with different life time
Measurable life time range: τ ~ 10-10 – 10-12 s
B) Doppler shift attenuation method
Production of reflected nuclei → deceleration and scattering inside target or thin
plate → emitted photon has different Doppler shift of energy → complicated shape of line
Line shape analysis → determination of level life time
Relation of ionization losses and path: Δx = (dE/dx)-1ΔE
Path for measurable change of velocity or stopping depends on
Z of reflected nucleus and target material, but x < 10-2 mm
Problems: 1) Description of deceleration and multiple
scattering of reflected nucleus
2) Life time of previous transition in the cascade
Measurable life time range: τ ~ 10-12 – 10-15s
Example of Doppler shift
attenuation measurement (taken
from D. Poenaru, W Greiner:
Experimental Techniques
in Nuclear Physics)
Determination of transition probabilities using
Coulomb excitation
Heavy ion beams are used → high charge → excitation of states with high spin
Energy can not be higher then Coulomb barrier energy
ECB ~
Z1 Z 2
1
1
( A1 3  A2 3 )
where Z1, Z2, A1 a A2 are parameters of beam and target nuclei
Advantageous: 1) Clean electromagnetic process
2) Minimal background – without nuclear reactions on target or surrounding material
3) Dominant excitation by E2 transitions
(v/c relatively small → B(M) << B(E), E1 suppressed, B(EI)>>B(EI+1) for I > 1
→ excitation of rotational bands with E2 transitions
4) Possibility of choice of case with excitation to spin state ↔ large projectile
scattering angle – common detection of scattered projectile, reflected nucleus
and gamma quantas
Measurable life times τ = 10-13 -10-9 s
Connection of Coulomb excitation, life time measurements and magnetic momenta
determination
Further methods: Nuclear resonance fluorescence– usage of Mőssbauer phenomena
τ = 10-17 -10-14 s, proton resonance τ < 10-16 s
Studies of states with very high spin
(Spins Iħ ≥ 40ħ)
Excitation of high spin states by heavy ion collisions
Compound nucleus creation (τ > 10-20s) –
1) nuclei with big proton excess
2) radioactive nuclei beam – also nuclei with neutron excess
Superdeformed states
Projectile energy in CM
Excitation energy:
EEX = ECM + Q
Reaction energy
Approximation: partial wave only up to lMAX
Maximal achievable spin
l
2
MAX
2R 2
 2 ECM  VC 

μ – reduced mass of colliding nuclei
R – the biggest distance which can be possible
for compound nucleus creation
Usage of Coulomb excitation
Study is possible by 4PI multi detector spectrometers
Maximal spin of stable
rotating nucleus (classical
estimates)
After compound nucleus creation evaporation of some
Nucleons (especially neutrons) → fast energy decrease
~ 8 MeV/n only small decrease of angular momenta ~ 1ħ/n
competitive high energy gamma depopulating giant
dipole resonances
Excitation energy is lower than separation energy → 10-15s
deexcitation by gamma quants:
1) Statistical (starting at high state density) E1 transitions
from the highest excitated states
2) E2 transitions near to Yrast line – not only inside rotational
bands (because of crossing) → high number of transitions
with small intensity – „quasicontinuum“
3) Regular structure of rotational bands ~ 1MeV above Yrast
line → sufficient intensity → observation of single transitions
Yrast line – connects states with the highest spin for given energy
Deexcitation of compound
Nucleus with very high
spin (rotation) (taken from
D. Poenaru, W Greiner:
Experimental Techniques
in Nuclear Physics]
Total deexcitation time ~ 10-9s, number of emitted photons ~ 30
Two type of rotation: 1) Collective rotation – region of deformed nuclei – collective
motion of many nucleons
2) Noncollective rotation – spherical and weakly deformed nuclei – high
spin given by motion of a few nucleons
High spins - transitions between single types of rotation with drastic changes
of nucleus shape
Hamiltonian for rotation of axially symmetrical nucleus:


2  
H
I  J  H int r  H vib
2
Adiabatic condition – rotation is slow against
singleparticle motion and vibrations → Hintr and Hvib
Are separated
High spins – fast rotation → strong Coriolis
interaction between particle and rotational motion
Example of rotational bands in
situation of adiabatic approximation
Band crossing – strong Coriolis interaction decrease energy of excited singleparticle
state above which rotational band develops → crossing with band above ground state
Superdeformed states
States with very high deformation (axis ratio 2:1 and more)
Predicted by shell model – spacing between shells for deformed potential
High spins ~ 40 - 70
first nucleus 152Dy (1984)
Only small probability of such state population ~ 1 %
Long rotational bands deexcitated by long cascades of E2 transitions with very
near energies
Giant resonances
Relative correlated motion of different
Nucleon types:
1) with different spin orientation
2) with different isospin orientation
(proton liquid against neutron)
Different types of giant resonances
(taken from WWW pages of GANIL)
High energy transitions
Giant resonances are
nicely populated by
Coulomb excitation
Deexcitation of single and double giant dipole resonance
populated by coulomb excitation on 208Pb. Energy 13 MeV
and 26 MeV, width is given by natural width described by
Lorentz curve – studied by spectrometer TAPS
at GSI Darmstadt (J. Ritman: Phys. Rev Lett.70(1993)533)
Production of neutral mesons during heavy ion collisions
Decays:
π0  γ+γ (98.8 %)
η  γ+γ (39.4 %)
M2γγ = 2E1E2(1-cosΘ12)
Simulation of combinatorial
background
Number of produced particles per
one participant nucleon as dependency
on collision energy (TAPS review)
Study of π0 and η meson production during heavy ion
collisions by means of spectrometer TAPS
Application of gamma spectrometry
1) Activation analysis -
A) Neutron – sample is irradiated by neutrons from reactor → production of
radioactive nuclei → study of characteristic radiation
known neutron flux → activity is proportional to amount of studied element
very sensitive – search of trace amounts of elements
Sensitivity depends on element (range up to 8 orders) → up to pg (10-12g)
B) Fluorescence – sample is irradiated by X-rays → striking of electrons
from atomic shell → characteristic X-rays
studied object is not damaged – possibility „scanning“
One of archeological artifacts studied at NPI ASCR
C) Determination of neutron flow from foil activation – similar
to neutron activation analysis, we know amount of irradiated
material and we determine neutron flow – usage by reactor
physics. It is possible to use for determination of other particle
beam flow
Sensitivity limit is given by accuracy of gamma intensity
determination ~ 1%
Reactor LVR-15 of NRI
2) On ion beam:
A) PIXE – (Particle Induced X-ray Emission)
charged ions (mostly protons) with energy ~ 2 – 4 MeV → ionization
of atoms → production of characteristic X-rays
Sensitivity up to 1 ppm (10-6)
at μg material amount)
Composition of samples
for ecology, archeology, ...
Example of aerosol measurement at NPI –
Department of neutron physics
Study of historical artifacts by
PIXE and PIGE methods (C2RMF
laboratory)
Principle of PIXE method
© C2RMF, T. Calligaro
Van de Graffův accelerator at NPI
ASCR is used for material research
using also PIGE and PIXE methods
B) PIGE – Particle-Induced Gamma ray Emission)
reactions of light nuclei with production
of characteristic gamma rays
reactions (p,γ), (p,p´γ) and (p,Xγ)
Surface composition for
material research
Method PIGE © C2RMF, T. Calligaro
Tandetrom at NPI ASCR is used
for PIGE and PIXE studies
3) X-ray diffraction crystallography
Determination of crystal structure, biological objects and substances, materials …
by means of X-ray diffraction
Usage of synchrotron radiation:
Also possibility of X-ray laser
Based on free electrons:
Undulator
Synchrotron laboratory at Grenoble