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On detecting the recoilless emission of internal conversion electrons, auger electrons, and β - particles
Volume 29A, number 8
ON
PHYSICS
DETECTING THE ELECTRONS,
US Amy
LETTERS
RECOILLESS EMISSION AUGER ELECTRONS,
30 June 1969
OF INTERNAL CONVERSION AND P-PARTICLES
D. E. CARLSON Nuclear Defense Laboratory, Edgewood Arsenal,
Maryland,
USA
Received 13 May 1969
It is shown that the recoilless emission of low-energy internal conversion electrons, Auger electrons, and &particles could be detected as temperature dependent effects in spectra obtained with high resolution @-spectrometers.
The recoilless emission and absorption of low-energy gamma rays by the nuclei of atoms in a crystal is commonly known as the Mbssbauer effect [l]. In this phenomenon, the recoil momentum of a certain fraction of the nuclei emitting or absorbing gamma rays is transmitted to the entire crystal. However, the possibility of recoilless emission is not limited to lowenergy gamma rays but may also occur for any emission process in which the recoil energy of the emitting atom is small compared with the interactomic binding energy. In fact, recoiless emission of the neutrinos emitted during electron capture was suggested by Visscher [2] in 1959. While low-energy CY -particles from ff -decaying nuclei are so energetic that the probability of recoilles emission is vanishingly small, the same is not true for low-energy electrons. Electrons are emitted from atoms by internal conversion and Auger processes, and from nuclei by P-decay. In general, the recoil energy of a free atom that emits an electron is given by
R=$
*[l+(--)+(s)y,
(1)
where m. is the rest mass of the electron, M is the mass of the recoiling atom, v is the velocity of the electron and E is the kinetic energy of the electron. The fraction of recoilless electrons at low temperature should be given by the same expression as derived from the Debye Model for recoilless y-rays 131. That is, f M exp(-f R/k0) where 0 is the Debye tamperature of the crystal and where R is given by eq. (1). The recoilless emission of internal conversion electrons should be evident as a temperaturedependent shift of the centroid of the conversion
lines. The natural line widths of low-energy conversion electrons are much larger than the recoil energies of the emitting atoms since the line widths are determined by the lifetimes of the excited states [4]. If a certain fraction, f, of the conversion electrons are emitted recoillessly, then the centroid of the conversion line will be increased in energy by - fR when compared with the centroid for no recoilless emissions (at a temperature >>0). For the Kconversion electron in 73Ge (E = 2.4 keV, R = N 1.8 x 10-2 eV, f = 0.43 at - OoK), a resolution of - f R/E = 3.2 X 10-6 is need to observe the shift in the centroid of the line. The situation is very similar for Auger electrons that may be ejected from the outer electronic shells of an atom when a vacancy is created in the inner shells [5]. For example, in Si the K$LI &So) Auger electron (a K vacancy filled by an LI electron, resulting in the ejection of an LI electron, leaving the atom in the lS, state) should have a relative line shift of -8.1 X 10e6 (E N 16.6 keV, R = 3.1 X 10_2eV, f N 0.42 at - OOK). The recoilless emission of low-energy 6 -particles should be evident as a temperature-dependent tall at the upper end of the /%spectrum. There should also be a contribution to this tail from some of the emission events involving recoil. This can be seen by first considering B-particles that are emitted from free atomic nuclei. The maximum P-particle energy will be equal to Q -R where Q is the disintegration energy and R is the recoil energy of the free atoms. If the atoms are placed in a lattice, then the interactions with the lattice vibrations will cause the maximum B -particle energy to be -Q -R + kT. However, if a fraction of the p-de449
Volume
29A, number 8
PHYSICS
LETTERS
cays are recoilless, the msximum energy for the recoilless events will be equal to Q. Therefore, the intensity of the tail should depend on both the phonon spectrum and the recoilless fraction f. For the 40-keV B-particle emitted by lo6Ru, the relative extent of the tail should be - R/Q = 5.5 X 10-6 (R = 0.22 eV, f M 0.0017 at N O°K). It should be pointed out that this effeet will be extremely difficult to detect, mainly because of the low counting rates for j3-particles near the maximum energy. Since relative line positions can be measured with a resolution of approximately 1 part in 105 with present 6-spectrometers [S], it may be possible to detect the effects of recoilless electron emission in the near future. However, it seems
30 June 1969
unlikely that these effects will have much influence in the general field of spectroscopy, apart from the possibility of obtaining some information about the phonon spectrum from determination of the recoilless fraction.
References R. L.
Mdssbauer,
Z. Phys. 151 (1958) 124. Phys. Rev. 116 (1959) 158. H. S. Lipkin, Ann. Phys. 9 (1960) 332. K. Siegbahn, Alpha-beta and gamma-ray spectroscopy, Vol 2(North Holland Publishing Co., Amsterdam, 1966) p. 951. Ibid, p. 1523. K. Siegbalm and K. Edvarson, Nucl. Phys. 1 (1956) 137.
;: W. M. Visscher, 3. 4.
5. 6.
*****
EFFECT
OF PRESSURE ON T, AND BAND STRUCTURE TRANSITION METAL ALLOYS
IN
W. GEY and D. KGIINLEIN Physikalisches
Institut der Universitltt Received
Karlsruhe,
75 Karlsruhe,
Germany
9 May 1969
Measurements on ten alloys of the series Zr-Nb-Mo show a close correlation of dT,/dp with the d-band structure of these alloys and suggest that the d-band is virtually rigid with respect to pressure.
In an attempt to detect some unifying principle for the complex reaction of superconductivity of transition metals and their alloys to application of hydrostatic pressure, the alloy series Zr-NbMO was chosen on the following grounds : 1) The series is homologous in structure [l]. 2) Data on the electronic specific heat coefficient y and BD exist [2]. 3) Presumably no effects of electronmagnon interactions complicate the situation. The main result is that for all 10 alloys the variation of Tc with pressure is strongly influenced by the shape of the d-band. Pressure up to 75 kbar was generated in a piston-cylinder type cell [3]. At first sight, the results are rather complex. For Nh and Nb-rich alloys a pronounced kink near 20 kbar occurs in the otherwise T,(p) behaviour. For Nb-Zr alloys with 20, 40 and 60 at. % Zr and for Nb73Mo27 no kink is observed; Tc(#) is nearly linear for all pressures. The results on alloys are collected in fig.l., to450
gether with other relevant parameters. The occurence of the kink in T,(P)for the Nb-rich alloys is represented by splitting of d In T,/dP into two branches forp < 20 kbar and p > 25 kbar, respectively. We discuss here the results for p > 25 kbar where the slope d In T,/dP decreases monotonically with increasing number n of valence electrons per atom at zero pressure *. One notes that d lnT,/dP changes sign at a concentration near that at which T (n) has a maximum. Since in these alloys T, tn) is closely related to the d-band structure, this suggests that T,(p) is likewise connected with the d-band. Analyzing the data in this respect it is found that a best data fit is obtained by the simple relation
* n is thus defined by the chemical composition. It is not to be confused with the actual electron concentration which may be pressure dependent.
ON
PHYSICS
DETECTING THE ELECTRONS,
US Amy
LETTERS
RECOILLESS EMISSION AUGER ELECTRONS,
30 June 1969
OF INTERNAL CONVERSION AND P-PARTICLES
D. E. CARLSON Nuclear Defense Laboratory, Edgewood Arsenal,
Maryland,
USA
Received 13 May 1969
It is shown that the recoilless emission of low-energy internal conversion electrons, Auger electrons, and &particles could be detected as temperature dependent effects in spectra obtained with high resolution @-spectrometers.
The recoilless emission and absorption of low-energy gamma rays by the nuclei of atoms in a crystal is commonly known as the Mbssbauer effect [l]. In this phenomenon, the recoil momentum of a certain fraction of the nuclei emitting or absorbing gamma rays is transmitted to the entire crystal. However, the possibility of recoilless emission is not limited to lowenergy gamma rays but may also occur for any emission process in which the recoil energy of the emitting atom is small compared with the interactomic binding energy. In fact, recoiless emission of the neutrinos emitted during electron capture was suggested by Visscher [2] in 1959. While low-energy CY -particles from ff -decaying nuclei are so energetic that the probability of recoilles emission is vanishingly small, the same is not true for low-energy electrons. Electrons are emitted from atoms by internal conversion and Auger processes, and from nuclei by P-decay. In general, the recoil energy of a free atom that emits an electron is given by
R=$
*[l+(--)+(s)y,
(1)
where m. is the rest mass of the electron, M is the mass of the recoiling atom, v is the velocity of the electron and E is the kinetic energy of the electron. The fraction of recoilless electrons at low temperature should be given by the same expression as derived from the Debye Model for recoilless y-rays 131. That is, f M exp(-f R/k0) where 0 is the Debye tamperature of the crystal and where R is given by eq. (1). The recoilless emission of internal conversion electrons should be evident as a temperaturedependent shift of the centroid of the conversion
lines. The natural line widths of low-energy conversion electrons are much larger than the recoil energies of the emitting atoms since the line widths are determined by the lifetimes of the excited states [4]. If a certain fraction, f, of the conversion electrons are emitted recoillessly, then the centroid of the conversion line will be increased in energy by - fR when compared with the centroid for no recoilless emissions (at a temperature >>0). For the Kconversion electron in 73Ge (E = 2.4 keV, R = N 1.8 x 10-2 eV, f = 0.43 at - OoK), a resolution of - f R/E = 3.2 X 10-6 is need to observe the shift in the centroid of the line. The situation is very similar for Auger electrons that may be ejected from the outer electronic shells of an atom when a vacancy is created in the inner shells [5]. For example, in Si the K$LI &So) Auger electron (a K vacancy filled by an LI electron, resulting in the ejection of an LI electron, leaving the atom in the lS, state) should have a relative line shift of -8.1 X 10e6 (E N 16.6 keV, R = 3.1 X 10_2eV, f N 0.42 at - OOK). The recoilless emission of low-energy 6 -particles should be evident as a temperature-dependent tall at the upper end of the /%spectrum. There should also be a contribution to this tail from some of the emission events involving recoil. This can be seen by first considering B-particles that are emitted from free atomic nuclei. The maximum P-particle energy will be equal to Q -R where Q is the disintegration energy and R is the recoil energy of the free atoms. If the atoms are placed in a lattice, then the interactions with the lattice vibrations will cause the maximum B -particle energy to be -Q -R + kT. However, if a fraction of the p-de449
Volume
29A, number 8
PHYSICS
LETTERS
cays are recoilless, the msximum energy for the recoilless events will be equal to Q. Therefore, the intensity of the tail should depend on both the phonon spectrum and the recoilless fraction f. For the 40-keV B-particle emitted by lo6Ru, the relative extent of the tail should be - R/Q = 5.5 X 10-6 (R = 0.22 eV, f M 0.0017 at N O°K). It should be pointed out that this effeet will be extremely difficult to detect, mainly because of the low counting rates for j3-particles near the maximum energy. Since relative line positions can be measured with a resolution of approximately 1 part in 105 with present 6-spectrometers [S], it may be possible to detect the effects of recoilless electron emission in the near future. However, it seems
30 June 1969
unlikely that these effects will have much influence in the general field of spectroscopy, apart from the possibility of obtaining some information about the phonon spectrum from determination of the recoilless fraction.
References R. L.
Mdssbauer,
Z. Phys. 151 (1958) 124. Phys. Rev. 116 (1959) 158. H. S. Lipkin, Ann. Phys. 9 (1960) 332. K. Siegbahn, Alpha-beta and gamma-ray spectroscopy, Vol 2(North Holland Publishing Co., Amsterdam, 1966) p. 951. Ibid, p. 1523. K. Siegbalm and K. Edvarson, Nucl. Phys. 1 (1956) 137.
;: W. M. Visscher, 3. 4.
5. 6.
*****
EFFECT
OF PRESSURE ON T, AND BAND STRUCTURE TRANSITION METAL ALLOYS
IN
W. GEY and D. KGIINLEIN Physikalisches
Institut der Universitltt Received
Karlsruhe,
75 Karlsruhe,
Germany
9 May 1969
Measurements on ten alloys of the series Zr-Nb-Mo show a close correlation of dT,/dp with the d-band structure of these alloys and suggest that the d-band is virtually rigid with respect to pressure.
In an attempt to detect some unifying principle for the complex reaction of superconductivity of transition metals and their alloys to application of hydrostatic pressure, the alloy series Zr-NbMO was chosen on the following grounds : 1) The series is homologous in structure [l]. 2) Data on the electronic specific heat coefficient y and BD exist [2]. 3) Presumably no effects of electronmagnon interactions complicate the situation. The main result is that for all 10 alloys the variation of Tc with pressure is strongly influenced by the shape of the d-band. Pressure up to 75 kbar was generated in a piston-cylinder type cell [3]. At first sight, the results are rather complex. For Nh and Nb-rich alloys a pronounced kink near 20 kbar occurs in the otherwise T,(p) behaviour. For Nb-Zr alloys with 20, 40 and 60 at. % Zr and for Nb73Mo27 no kink is observed; Tc(#) is nearly linear for all pressures. The results on alloys are collected in fig.l., to450
gether with other relevant parameters. The occurence of the kink in T,(P)for the Nb-rich alloys is represented by splitting of d In T,/dP into two branches forp < 20 kbar and p > 25 kbar, respectively. We discuss here the results for p > 25 kbar where the slope d In T,/dP decreases monotonically with increasing number n of valence electrons per atom at zero pressure *. One notes that d lnT,/dP changes sign at a concentration near that at which T (n) has a maximum. Since in these alloys T, tn) is closely related to the d-band structure, this suggests that T,(p) is likewise connected with the d-band. Analyzing the data in this respect it is found that a best data fit is obtained by the simple relation
* n is thus defined by the chemical composition. It is not to be confused with the actual electron concentration which may be pressure dependent.