Isomerism shift

The physical effect of the isomer shift manifests itself in the fact that the positions of the spectral lines in the atomic spectra of different isomers of a chemical element differ. If the spectral lines also show hyperfine structure due to the magnetic moments of the atomic nuclei , the shift relates to the centers of gravity of the lines.

The effect also occurs with gamma spectra and is then also called Mössbauer isomerism shift .

The isomer shift provides important information about the core structure and about the physical, chemical and biological environment of atoms. It was proposed to use the effect to investigate any changes in natural constants over time.

Isomeric shift of the atomic spectra

The isomeric shift of the atomic spectra is the energy or frequency shift in the atomic spectra as a result of the substitution of one core isomer by another. The effect was predicted by Weiner in 1956 ) and experimentally observed for the first time in 1959. The theory developed by Weiner also comes into play in the explanation of the Mössbauer isomer shift.

terminology

The first work on the isomer related to atomic spectra and used the term Kernisomerieverschiebung of spectral lines ( nuclear isomeric shift on spectral lines ) . After the discovery of the Mössbauer effect , the isomer shift was also detected in gamma spectra, where it is also called the Mössbauer isomer shift . For more details on the history of the discovery and the terminology used, see Weiner.

Isomerism versus isotope shift in atomic spectra

Atomic spectral lines arise when electrons transitions between different atomic energy levels , which are accompanied by photon emission . Atomic levels are a manifestation of the electromagnetic interaction between electrons and nuclei. The energy levels of two atoms whose nuclei are different isotopes of the same element differ, despite having the same atomic number , because of the different numbers of neutrons . These differences lead to the isotope shift of the spectral lines. ${\displaystyle E}$ ${\displaystyle Z}$ ${\displaystyle N}$

For nuclear isomers, the numbers of protons and neutrons are the same, but the quantum state of the nuclei is different. The electrical charge distributions in the core differ. This causes a difference in the corresponding electrostatic core potentials , which leads to a difference in the atomic energy levels. The isomer shift of the atomic spectral lines is given by ${\displaystyle \delta \varphi }$ ${\displaystyle \varphi }$ ${\displaystyle \Delta E}$

${\displaystyle \Delta E=-{\text{e}}\int \delta \varphi \left|\psi \right|^{2}{\text{d}}\tau }$

Here is the wave function of the electron involved in the transition with its electrical charge (negative elementary charge ). The integration is carried out via the electron coordinates. ${\displaystyle \psi }$ ${\displaystyle -e}$

Isotopic and isomeric shifts are both consequences of the finite dimensions of the atomic nucleus. The isotope shift was discovered experimentally and then explained theoretically. The isomer shift, however, was predicted and only demonstrated later in the experiment. With the isotope shift, the calculation of the interaction energy between electrons and nuclei is a relatively simple electromagnetic problem. It is more difficult with isomers because the isomeric excitation is caused by the strong interaction. This partly explains why the isomer shift was not discovered earlier: the adequate theory, and in particular the shell model , was not developed until the late 1940s and early 1950s. The experimental proof of this effect was only made possible by a new technique - the spectroscopy of metastable, isomeric nuclear states - which was also only developed in the 1950s.

In contrast to the isotope shift, which is (in a first approximation) independent of the structure of the nuclei, the isomer shift depends on this structure. Therefore, more extensive information is obtained from the isomerism shift than from the isotope shift. The measurement of the difference in core radii between the excited and ground state, which is possible via the isomer shift, is one of the most sensitive tests of core models. In addition, the isomer shift in combination with the Mössbauer effect represents a unique instrument that has also found applications in many other areas outside of physics.

The isomer shift and the shell model

Within the framework of the shell model, there is a class of isomers in which a single nucleon (known as "optical") causes the difference in the charge distributions of two isomeric states. This applies in particular to nuclei with odd protons and even neutron numbers in the vicinity of closed shells , for example with In-115 , for which the effect was calculated by Weimer and predicted that it should be far larger than the natural line width and therefore measurable.

The value of the shift measured three years later for Hg-197 was fairly close to that calculated for In115. In Hg-197 , however, in contrast to In-115, the optical nucleon is a neutron and not a proton, and the electron-free neutron interaction is much smaller than the electron-free proton interaction; therefore, an effect a hundred times smaller was expected. This discrepancy is explained by the fact that optical nucleons are not free but bound particles. The measurement results could be explained in the context of Weimer's theory by assigning an effective electrical charge to the optical neutron . ${\displaystyle Z/A}$

Mössbauer isomer shift

The Mössbauer isomer shift is the shift of spectral lines observed in gamma spectroscopy when comparing two different nuclear isomer states in two different physical, chemical or biological environments. It is a consequence of the combined effect of the recoil-free Mössbauer transition between two nuclear isomeric states and the transition between two atomic states in the given medium.

The isomer shift of the atomic spectral lines depends on the electron wave function and the difference in the electrostatic potentials φ of the two isomeric states. For a given core isomer in two different environments (e.g. different physical phases or different chemical combinations) the corresponding electron wave functions also differ. For this reason, in addition to the isomer shift of the spectral lines, which is caused by the difference in the isomer states of the nuclei, there is a shift due to the two different environments. For experimental reasons, the latter is called a source or absorber. This combined shift is the Mössbauer isomer shift. It is described mathematically with the same formalism as the nuclear isomeric shift of the atomic spectra, except that one now has to consider two electron wave functions (from source and absorber ) and the difference between the respective shifts instead of one : ${\displaystyle \psi }$ ${\displaystyle \delta \varphi }$ ${\displaystyle \psi _{\text{Quelle}}}$ ${\displaystyle \psi _{\text{Absorber}}}$

${\displaystyle \Delta E=\Delta E_{\text{Quelle}}-\Delta E_{\text{Absorber}}=-{\text{e}}\int \delta \varphi \,\left(|\psi _{\text{Quelle}}|^{2}-|\psi _{\text{Absorber}}|^{2}\right)\,\mathrm {d} \tau }$

The first measurement of the isomer shift in gamma spectroscopy with the help of the Mössbauer effect took place in 1960. This effect provides important and extremely precise information about the states of isomerism as well as about the physical, chemical and biological environments of the atoms. With this, the isomer shift found important applications in fields as diverse as atomic physics, solid state physics, nuclear physics, chemistry, biology, metallurgy, mineralogy, geology, lunar and Mars research.

The nuclear isomer shift has also been demonstrated in muonic atoms. A muon is captured by the excited nucleus in these atoms and a transition from the excited atomic state to the ground state then takes place in a time interval that is shorter than the lifetime of the excited nuclear isomeric state.

Individual evidence

1. ↑ JC Berengut, VV Flambaum: Testing Time-Variation of Fundamental Constants using a 229th Nuclear Clock . In: Nuclear Physics News . tape 20 , no. 3 , August 31, 2010, p. 19-22 , doi : 10.1080 / 10619127.2010.506119 .
2. ↑ ^{a b c} R. Weiner: Nuclear isomeric shift on spectral lines . In: Il Nuovo Cimento . tape 4 , no. 6 December 1956, p. 1587-1589 , doi : 10.1007 / BF02746390 .
3. ↑ ^{a b} R. M. Weiner: Phys. Rev. 114 (1959) 256; Zhur. Eksptl. I theoret. Fiz. 35 (1958) 284, English translation: Soviet Phys. JETP. 35 (8) (1959) 196.
4. ^ ^{A b} Adrian C. Melissinos, Sumner P. Davis: Dipole and Quadrupole Moments of the Isomeric Ed. ¹⁹⁷ Nucleus; Isomeric Isotope Shift . In: Physical Review . tape 115 , no. 1 , June 1, 1959, p. 130-137 , doi : 10.1103 / PhysRev.115.130 .
5. ^ Richard M Weiner: Analogies in physics and life a scientific autobiography . World Scientific, New Jersey 2008, ISBN 978-981-279-082-8 .
6. ^ G. K Shenoy, F. E Wagner: Mössbauer isomer shifts . North Holland Pub. Co., Amsterdam / New York 1978, ISBN 0-444-10802-5 , pp. 1 .
7. ↑ Fizicheskii Encyclopeditskii Slovar, Sovietskaia Encyclopaedia, (Physical Encyclopaedic Dictionary, Soviet Encyclopedia) Moscow 1962, p. 144.
8. ^ DA Shirley: Nuclear Applications of Isomeric Shifts. In: DH Compton, AH Schoen (eds.): Proc. Int. Conf. on the Mössbauer Effect, Saclay 1961. John Wiley & Sons, New York 1961, p. 258.
9. ↑ DA Shirley: Application and Interpretation of Isomer Shifts . In: Reviews of Modern Physics . tape 36 , no. 1 , January 1, 1964, p. 339-351 , doi : 10.1103 / RevModPhys.36.339 .
10. ^ OC Kistner, AW Sunyar: Evidence for Quadrupole Interaction of Fe ^57m , and Influence of Chemical Binding on Nuclear Gamma-Ray Energy . In: Physical Review Letters . tape 4 , no. 8 , March 15, 1960, p. 412-415 , doi : 10.1103 / PhysRevLett.4.412 .
11. ^ G. K Shenoy, F. E Wagner: Mössbauer isomer shifts . North Holland Pub. Co., Amsterdam / New York 1978, ISBN 0-444-10802-5 .
12. ↑ see also: J. Hüfner F. Scheck, CS Wu: Muonic Atoms. In: VW Hughes, CS Wu (Ed.): Muon Physics. Volume 1, Academic Press, 1977, pp. 202-304.