Perturbed angular correlation: Difference between revisions

Revision as of 16:54, 24 November 2019

Revision as of 17:00, 24 November 2019

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PAC goes back to a theoretical work by Donald R. Hamilton <ref>Donald R. Hamilton: On Directional Correlation of Successive Quanta. In: Physical Review. Band 58, Nr. 2, 15. Juli 1940, S. 122–131, doi:10.1103/PhysRev.58.122</ref> from 1940. The first successful experiment was carried out by Brady and Deutsch <ref>Edward L. Brady, Martin Deutsch: Angular Correlation of Successive Gamma-Ray Quanta. In: Physical Review. Band 72, Nr. 9, 1. November 1947, S. 870–871, doi:10.1103/PhysRev.72.870</ref> in 1947. Essentially spin and parity of nuclear spins were investigated in these first PAC experiments. However, it was recognized early on that electric and magnetic fields interact with the nuclear moment, providing the basis for a new form of material investigation: nuclear solid-state spectroscopy.

After Abragam and Pound <ref>A. Abragam, R. V. Pound: Influence of Electric and Magnetic Fields on Angular Correlations. In: Physical Review. Band 92, Nr. 4, 15. November 1953, S. 943–962, doi:10.1103/PhysRev.92.943</ref> published their work on the theory of PAC in 1953, many studies with PAC were carried out afterwards. In the 1960s and 1970s, interest in PAC experiments sharply increased, focusing mainly on magnetic and electric fields in crystals into which the probe nuclei were introduced. In the mid-1960s, ion implantation was discovered, providing new opportunities for sample preparation. The rapid electronic development of the 1970s brought significant improvements in signal processing. From the 1980s to the present, PAC has emerged as an important method for the study and characterization of materials .<ref>Th. Wichert, E. Recknagel: Perturbed Angular Correlation. In: Ulrich Gonser (Hrsg.): Microscopic Methods in Metals (= Topics in Current Physics. Band 40). Springer, Berlin/Heidelberg 1986, {{ISBN|978-3-642-46571-0}}, S. 317–364, doi:10.1007/978-3-642-46571-0_11</ref><ref>Gary S. Collins, Steven L. Shropshire, Jiawen Fan: Perturbed γ−γ angular correlations: A spectroscopy for point defects in metals and alloys. In: Hyperfine Interactions. Band 62, Nr. 1, 1. August 1990, S. 1–34, doi:10.1007/BF02407659</ref><ref>Th. Wichert, N. Achziger, H. Metzner, R. Sielemann: Perturbed angular correlation. In: G. Langouche (Hrsg.): Hyperfine Interactions of Defects in Semiconductors. Elsevier, Amsterdam 1992, {{ISBN|0-444-89134-X}}, S. 77</ref><ref>Jens Röder, Klaus-dieter Becker: Perturbed γ–γ Angular Correlation. In: Methods in Physical Chemistry. John Wiley & Sons, Ltd, 2012, {{ISBN|978-3-527-32745-4}}, S. 325–349, doi:10.1002/9783527636839.ch10</ref><ref>Günter Schatz, Alois Weidinger, Manfred Deicher: Nukleare Festkörperphysik: Kernphysikalische Messmethoden und ihre Anwendungen. 4. Auflage. Vieweg+Teubner Verlag, 2010, {{ISBN|978-3-8351-0228-6}}</ref>. B. for the study of semiconductor materials, intermetallic compounds, surfaces and interfaces. Lars Hemmingsen et al. Recently, PAC also applied in biological systems. <ref>Lars Hemmingsen, Klára Nárcisz Sas, Eva Danielsen: Biological Applications of Perturbed Angular Correlations of γ-Ray Spectroscopy. In: Chemical Reviews. Band 104, Nr. 9, 1. September 2004, S. 4027–4062, doi:10.1021/cr030030v</ref>

While until about 2008 PAC instruments used conventional high-frequency electronics of the 1970s, in 2008 Christian Herden and Jens Röder et al. developed the first fully-digitized PAC instrument that enables extensive data analysis and parallel use of multiple probes. <ref>C. Herden, J. Röder, J. A. Gardner, K. D. Becker: Fully digital time differential perturbed angular correlation (TDPAC) spectrometer. In: Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. Band 594, Nr. 2, 1. September 2008, S. 155–161, doi:10.1016/j.nima.2008.05.001</ref> Replicas and further developments followed. <ref>Matthias Nagl, Ulrich Vetter, Michael Uhrmacher, Hans Hofsäss: A new all-digital time differential γ-γ angular correlation spectrometer. In: Review of Scientific Instruments. Band 81, Nr. 7, 1. Juli 2010, S. 073501, doi:10.1063/1.3455186</ref><ref>M. Jäger, K. Iwig, T. Butz: A user-friendly fully digital TDPAC-spectrometer. In: Hyperfine Interactions. Band 198, Nr. 1, 1. Juni 2010, S. 167–172, doi:10.1007/s10751-010-0201-8</ref>

==Measuring principle ==

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== Sample preparation ==

The amount of suitable PAC isotopes required for a measurement is between about 10 to 1000 billion atoms (10¹⁰-10¹²). The right amount depends on the particular properties of the isotope. 10 billion atoms are a very small amount of substance. For comparison, one mol contains about 6.22x10²³ particles. 10¹² atoms in one cubic centimeter of beryllium give a concentration of about 8 nmol/L (nanomol=10^-9−9 mol). The radioactive samples each have an activity of 0.1-5 MBq, which is in the order of the exemption limit for the respective isotope.

How the PAC isotopes are brought into the sample to be examined is up to the experimenter and the technical possibilities. The following methods are usual:

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=== Added during synthesis ===

PAC probes may also be added during the synthesis of sample materials to achieve the most uniform distribution in the sample. This method is particularly well suited if, for example, the PAC probe diffuses only poorly in the material and a higher concentration in grain boundaries is to be expected. Since only very small samples are necessary with PAC (about 5 &nbsp;mm), micro-reactors can be used. Ideally, the probe is added to the liquid phase of the sol-gel process or one of the later precursor phases.

=== Neutron activation ===

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</math>

For a <math>\gamma</math>-<math>\gamma</math>-cascade, <math>k</math> is due to the preservation of [[parity_parity (physics)|parity]]:

For a <math>\gamma</math>-<math>\gamma</math>-cascade, <math>k</math> is due to the preservation of [[parity_(physics)|parity]]:

:<math>0<k<\textrm{min}(2I_S, I_i+I'_i)

</math>

Where <math>I_S</math> is the spin of the intermediate state and <math>I_i</math> with <math>i=1;2</math> the [[polarity_polarity (physics)|multipolarity]] of the two transitions. For pure multipole transitions, is <math>I_i=I'_i</ math>.

<math>A_ {kk}</math> is the anisotropy coefficient that depends on the [[angular momentum]] of the intermediate state and the multipolarities of the transition.

The radioactive nucleus is built into the sample material and emits two <math>\gamma</math>-quanta upon decay. During the lifetime of the intermediate state, iei.e. the time between <math>\gamma_1</math> and <math>\gamma_2</math>, the core experiences a disturbance due to the [[hyperfine interaction]] through its electrical and magnetic environment. This disturbance changes the angular correlation to:

:<math>W(\Theta)=\sum^{k_{max}}_{k}A_{kk}G_{kk}

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</math>

<math>g</math> is the [[Landé_gLandé g-factor]] und <math>u_N</math> is the [[nuclear magneton]].

With <math>N=M-M'</math> follows:

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In cubic crystals, the axis parameters of the unit cell x, y, z are of the same length. Therefore:

:<math>V_{zz}=V_{yy}=V_{xx}</math> and <math>\eta=0</math>

In axisymmetric systems is <math>\eta=0</math> math>.

For axially symmetric electric field gradients, the energy of the substates has the values:

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For half integer spins applies:

:<math>\omega_0=6\cdot\omega_Q</math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; und &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <math>n=\frac{1}{2}|M^2-M'^2|</math>

The perturbation factor is given by:

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</math>

==References==

[[de:Gestörte_Gamma-Gamma-Winkelkorrelation]]

{{Reflist}}

[[de:Gestörte_GammaGestörte Gamma-Gamma-Winkelkorrelation]]