Mössbauer spectroscopy

A. Błachowski and K. Ruebenbauer

Mössbauer Spectroscopy Division, Institute of PhysicsFaculty of Mathematics, Physics and Technology

Pedagogical UniversityPL-30-084 Kraków, ul. Podchorążych 2, POLAND

Tel.: +(48-12) 662-6317, +(48-12) 662-6319Fax: +(48-12) 637-2243

Electronic address: sfrueben@cyf-kr.edu.plWorld 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 thesake of simplicity let us consider one-dimensional problem with the probabilitydensity along the x-direction described by the normalised density function ρ( x)having the average value equal null. One can calculate correspondingcharacteristic function φ( q) as the Fourier transform of the density function. Thesymbol ћq stands for the momentum transfer to the system during emission orabsorption, respectively. Furthermore one can expand characteristic function intosemi-invariants according to the equation:

. )(ln )( κ; )ρ( ]exp[ )(0

q

l

ll

l qq

ixiqxdxq

Those semi-invariants could be used to calculate the recoilless fraction along thex-direction as:

. κ!

1 exp )(

2

L

l

l

l ql

qf

The fraction of events 0 < f(q) < 1 proceeds without recoil preserving naturalwidth of the line. Example of such behaviour is shown at the side for the groundstate of the surface atom. A density function has been calculated solving theSchrödinger equation for the surface potential well. Note the forward/backwardasymmetry of the recoilless fraction.

Hyperfine interactions – the most important feature

For the sake of simplicity we are going to consider hyperfine interactions in thesemi-classical approximation. Mössbauer spectroscopy is capable to see thefollowing 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 tensortakes on the following form for a particular nuclear state (usually total shift isadded to the excited state Hamiltonian):

. η 3 sin cos βsin β cos α 2222

0 1IIIIIIIH SA yxzQyxz

Levels for some simple selected case are shown below.

Transition intensities could be calculated in terms of the electromagnetic transitionoperators acting on the particular nuclear hyperfine sub-states:

. )()( gg

pLp

kMee mI|||mI ge εqT

Spectrum shape

Doppler scans are used to obtain spectrum shape versus applied firstorder 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 integralformalism:

. )( exp v)( )2(

1

2 1 (v)

220

Lt/

dff

BP A

s

sss

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 pre-amplifier.

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 in-situ 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 lightfrequency measured directly in the laboratory

. )( Δ 2c/gHE/E

One of the most important transitions

Examples of some spectra

. T 016 and mm/s 41 mm/s, 33330 .B.S.|A| Q

Positive quadrupole coupling constant corresponds here to the positive principalcomponent of the electric field gradient. Positive shift means that the electrondensity within the nucleus is lower than corresponding density within the sourcenucleus. Note that it is impossible here to determine sign of the principalcomponent of the electric field gradient for the magic angle β = 54.7 deg. Non-scalar part of the excited state Hamiltonian has the following form for the exampleconsidered:

. 3 βsin β cos α 22

0 IIIIH zQxze A

Thank you very much for your attention.