Transcript Bez tytułu slajdu - Mössbauer Spectroscopy Division

Mössbauer spectroscopy
A. Błachowski and K. Ruebenbauer
Mössbauer Spectroscopy Division, Institute of Physics
Faculty of Mathematics, Physics and Technology
Pedagogical University
PL-30-084 Kraków, ul. Podchorążych 2, POLAND
Tel.: +(48-12) 662-6317, +(48-12) 662-6319
Fax: +(48-12) 637-2243
Electronic address: [email protected]
World Wide Web Page: www.elektron.ap.krakow.pl
A contribution to “INŻYNIERIA I EDUKACJA”
Białka Tatrzańska, 15-17 November 2006
Copyright © 2006 Artur Błachowski and Krzysztof Ruebenbauer
Mössbauer spectroscopy
•
One has to make suitable radioactive
precursor having sufficiently long
lifetime albeit not too long. Such
precursors are made applying various
nuclear reactions, i.e., either accelerated
beam of charged strongly interacting
particles or neutrons in conjunction with
the suitable nuclear target.
•
Precursors decay and populate nuclear
level in question. All meta-stable
nuclear states are characterised by the
following good quantum numbers: spin
I and parity p. Decay schemes suitable
for the Mössbauer spectroscopy are
shown at the side. Other decays could
be used sometimes as well. Sometimes
α decays or isomeric transitions are used
to populate the resonant level. In some
cases a population due to the nuclear
reaction is used.
• The beam emitted from the
source could be strongly
absorbed in the resonant
absorber containing the same
nuclei in the ground state.
Subsequent decay occurs in
random directions and/or it
follows via the electron capture.
Hence one can expect strong
beam
attenuation
under
resonant conditions. However
there is serious problem of the
nuclear recoil occurring in the
source and absorber.
Are any hopes to see resonant absorption?
Let us assume that the resonant atom is confined to some restricted space. For the
sake of simplicity let us consider one-dimensional problem with the probability
density along the x-direction described by the normalised density function ρ(x)
having the average value equal null. One can calculate corresponding
characteristic function φ(q) as the Fourier transform of the density function. The
symbol ћq stands for the momentum transfer to the system during emission or
absorption, respectively. Furthermore one can expand characteristic function into
semi-invariants according to the equation:

 l

(q)   dx exp[ iqx ] ρ( x) ; κ l  (i)l  l ln (q) .
 q
q 0

Those semi-invariants could be used to calculate the recoilless fraction along the
x-direction as:
 L 1

f (q)  exp     κ l q l  .
 l 2  l ! 

The fraction of events 0 < f(q) < 1 proceeds without recoil preserving natural
width of the line. Example of such behaviour is shown at the side for the ground
state of the surface atom. A density function has been calculated solving the
Schrödinger equation for the surface potential well. Note the forward/backward
asymmetry of the recoilless fraction.
Hyperfine interactions – the most important feature
For the sake of simplicity we are going to consider hyperfine interactions in the
semi-classical approximation. Mössbauer spectroscopy is capable to see the
following lowest order terms:
1. Electric monopole interaction due to the involvement of two nuclear states additional second order Doppler shift is seen as well.
2. Electric quadrupole interaction in the point-like nucleus limit.
3. Magnetic dipole interaction including eventual hyperfine anomaly.
A hyperfine Hamiltonian in the main axes of the electric field gradient tensor
takes on the following form for a particular nuclear state (usually total shift is
added to the excited state Hamiltonian):
H   α 0  I z cos β  sin β  I x cos   I y sin    AQ  3I 2z  I 2  η  I 2x  I 2y    S 1 .
Levels for some simple selected case are shown below.
Transition intensities could be calculated in terms of the electromagnetic transition
operators acting on the particular nuclear hyperfine sub-states:
 I e me | TkM e
( Lp p g )
(q | ε) | I g mg  .
Spectrum shape
Doppler scans are used to obtain spectrum shape versus applied first
order Doppler shift along the beam. One can either move the source
or absorber applying some predefined periodic motion.
Generally spectrum shape is described by the so-called transmission integral
formalism:



1
 f s   s f s 


P(v)  B0  1     
exp

t
L
(

)
  d
.
A
2
2

2

(

/
2
)

(


v)





s


Basic principle of the spectrometer is shown below.
Real life spectrometer MsAa-3 produced by RENON
•
Bench for the room temperature
measurements. One can see the laser
powered Michelson - Morley
interferometer used to calibrate the
velocity scale, velocity transducer
with the collimator hiding source
(absorber is attached to the exit
window of the collimator) and the
proportional detector with the high
voltage supply and pre-amplifier.
Power supply for the spectrometer,
and power supply for the laser are in
the background.
Details of the resonant beam path are shown below. One can see the front end of the
transducer, collimator mounted in the safety ring, proportional detector with the beryllium
window and the detector high voltage supply integrated with the charge sensitive preamplifier.
Front end of the collimator is shown with the attached absorber. A detector is seen from the
top.
• General
view
of
the
electronics is shown at the
side. One can see the
spectrometer central unit,
rechargeable battery used as
the power supply buffer, and
the digital oscilloscope used
for the diagnostic purposes.
Central unit of the spectrometer is shown with two universal temperature controllers. This
unit has two TCP/IP ports 100Base-Tx connecting spectrometer to the Internet.
Vacuum oven for transmission geometry measurements on the absorbers. The oven is able to
reach 800 °C. See the beam entrance beryllium window.
• High
temperature
oven
designed for the emission
Mössbauer spectroscopy on insitu oriented single crystal
sources
maintained
under
controlled atmosphere and
temperature up to
1200 °C.
See the bottom part of the
transducer with the light frame
used to move the reference
absorber. The frame surrounds a
detector holder. The gas inlet
valve and the micrometer screw
used to set up internal
goniometer are seen at the base
of the oven.
Something special – gravitational shift of the light
frequency measured directly in the laboratory
ΔE / E  ( gH ) / c 2 .
One of the most important transitions
Examples of some spectra
| AQ |  0.3333 mm/s, S   1.4 mm/s and B  16.0 T .
Positive quadrupole coupling constant corresponds here to the positive principal
component of the electric field gradient. Positive shift means that the electron
density within the nucleus is lower than corresponding density within the source
nucleus. Note that it is impossible here to determine sign of the principal
component of the electric field gradient for the magic angle β = 54.7 deg. Nonscalar part of the excited state Hamiltonian has the following form for the example
considered:
H e   α 0  I z cos β  I x sin β   AQ  3I 2z  I 2
.
Thank you very much for your
attention.