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Muon spin rotation (μSR) detected electron spin echo envelope modulation (ESEEM)
Volume 157, number 6,7
PHYSICS LETTERS A
5 August 1991
Muon spin rotation (p.SR) detected electron spin echo envelope modulation (ESEEM) A. Henstra, T.-S. Lin’ and W.Th. Wenckebach Huygens Laboratory, University ofLeiden, P.O. Box 9504, 2300 RA Leiden, The Netherlands Received 18 January 1991; revised manuscript received 7 June 1991; accepted for publication 13 June 1991 Communicated by J.I. Budnick
The recently developed method of NOVEL, in which very rapid cross polarization between electron spins and nuclear spins is induced, is proposed to be extended to the field of 1sSR. This would provide a method to unravel the ESR and ESEEM spectra of muonated radicals. The proposal is backed up by an experiment in a molecular crystal, where the ESEEM spectrum of an excited triplet state is observed indirectly via NMR.
A typical problem studied by muon spin rotation (~xSR)[1] concerns the case that a positive muon is implanted in a silicon crystal. In order to compensate for the added positive charge an extra electron is bound close to the muon site. Thus, a deep donor, equivalent to a hydrogen impurity, is created. Two major questions arise, the position of the muon and the wave function of the unpaired electron. The obvious way to determine the wave function of an unpaired electron is to measure its hyperfine interactions with all neighbouring nuclear spins. In the past decade the method of level crossing resonance (LCR) [2,31 has been successfully introduced for this purpose. In this method the nuclear hyperfine interactions are obtained from the intensities of the magnetic field where the level splitting of the muon spin matches the level splittings of the nuclear spins and, as a result, the IISR signal decays more rapidly. Thus, e.g., the position of the muon in silicon could be unraveled [41. This paper concerns a new alternative technique we propose to use to determine the latter wave function ofthe unpaired electron [51.We believe it to be particularly useful in cases where LCR cannot be observed because of unsuitable values of the hyperfine interactions or where the hyperfine interactions are On sabbatical leave from Chemistry Department, Washington University, St. Louis, MO, USA. Elsevier Science Publishers B.V. (North-Holland)
very complicated, so measurements at various intensities of the magnetic field are necessary. As our new technique is not restricted to the above described case of ~ in silicon, it may be useful in many cases where an unpaired electron spin is created near the implanted positive muon. The wave function of an unpaired electron is most easily obtained using electron nuclear double resonance (ENDOR) [6] to determine its hyperfine interactions with all neighbouring nuclear spins. Pulsed techniques like electron spin echo envelope modulation (ESEEM) [7] have proven to be the most sensitive. Then two microwave pulses are given at the resonance frequency of the electron spins: a 900 pulse followed after a time t by a 1800 pulse. After another delay r the electron spin echo (ESE) signal is recorded. The intensity of this ESE signal decays as a function of i because of transverse relaxation processes. However, on top of this decay, it also shows oscillations as a function of time: electron spin echo envelope modulation (ESEEM). This modulation is due to interference of signals from electron spins experiencing different hyperfine fields, i.e., where surrounding nuclei are oriented differently. As a result, the Fourier transform of the ESEEM signal directly yields the hyperfine interactions of the electron spin with its neighbouring nuclei. Unfortunately, for such pulsed ESR techniques at least 1 0’° electron spins are necessary, and therefore they lack 431
Volume 157, number 6,7
9~=O
PHYSICS LETTERS A
______
______ T
_______
_______
the hyperfine its ESEEM signal interactions. of the unpaired electron and hence ~O
Fig. I. The microwave pulse sequence accomplishing iiSR detected ESEEM. During the first and last pulse rapid cross polarization between the electron spin and the muon spin takes place, and during the free precession period the hyperfine interactions are active, resulting in a modulation of the echo signal as a function oft. 0 is the phase ofthe microwaves,
sufficient sensitivity for the problem described above. The essential idea in our proposed method is to transfer the precessing electron spin polarization which gives rise to the ESEEM signal to the muon spins. Subsequently, the transferred polarization is detected by the much more sensitive method of j~iSR. For the polarization transfer we intend to use a recently developed method, nuclear spin orientation via electron spin locking (NOVEL) [8]. The proposed experiment, detecting ESR and ESEEM via IISR, is performed as follows. We consider a conventional Lt~SRexperiment where muons are implanted in the sample with their spin parallel to the external magnetic field B0. We consider the case that upon implantation of a muon an unpaired electron spin is created. The latter may be unpolarized. Directly after implanting the muon, we apply the microwave pulse sequence shown in fig. 1. It consists of three pulses at the resonance frequency of the electron spin separated by a time r which may be varied. The first and the last pulse are identical, the middle pulse is more intense and phase shifted by 900. Directly after the last pulse the ~.tSRsignal is detected. As we will see below, by plotting the intensity of this signal as a function of ~we will obtain
x
5 August 1991
The evolution of the effective fields experienced by the electron spin and its polarization are shown in fig. 2. In this figure, we use a frame of reference rotating with the microwave frequency co about the z-axis, which is the direction of the external magnetic field B0 Then, because the microwave field is at the resonance frequency of the electron spin, the effective field in the z-direction is equal to B0 I W/Ys = 0, where Ys is the gyromagnetic ratio of the electron spin. Furthermore, during the first and last pulse, the microwave field is oriented along the x-direction and has a constant value B~.In the middle more intensevalue pulse, the phase shifted by 900, so it has a larger B~ while it isisoriented along the y—
direction. The gist of our method is that we choose the intensity of the first and last microwave pulse such that y~B~ is equal to the ~SR resonance frequency. E.g., for a small hyperfine interactionwe choose y~B~ equal to y,. 11301 where y~is the gyromagnetic ratio of the muon spin. This condition is easily achieved using loop gap resonators [8]. Then, as we have shown previously for electron spins and nuclear spins, rapid cross polarization on a submicrosecond time scale between the muon spin and the electron spin is induced by their mutual dipolar interaction [8]. As a result, after the first pulse, the electron spins are polarized along the x-axis of the rotating frame at the expense of the muon spin polarization. We note that the ESR spectrum is directly obtained by measuring the significant decrease of the IXSR signal after the first pulse as a function of the microwave frequency. After the first pulse, the electron spin polarization dephases just as it would do after a 90°pulse: because of internal fields in the crystal its orientation
X
Fig. 2. The different effectivefields experienced by the electron spin and the evolution ofits polarization vector.
432
Volume 157, number 6.7
PHYSICS LETTERS A
slowly drifts away from the x-direction. Also because of transverse relaxation its amplitude diminishes. After a first delay t we apply the second pulse, which is a standard 180°pulse. Its amplitude is chosen very large, so polarization transfer between the electron spin and the muon spin is impossible. Because of the second pulse, after a second delay ‘r the electron spin polarization is rephased and oriented along the x-direction again. It should give rise to an ESE signal. However, it cannot be observed directly because its intensity is too small. To observe it, we apply the third pulse, which like the first one, induces rapid cross polarization between the muon spin and the electron spin. Thus, the electron spin polarization that would have given rise to an ESE signal is transferred back to the muon spin. So it can subsequently be measured by observing the i.tSR signal. More interestingly, by measuring the intensity of the thus obtamed jtSR signal as a function oft, one obtains the ESEEM signal and hence the hyperfine interactions of the electron spin, To test the above described procedure experimentally without needing to refer to an actual j.tSR experiment, we performed an experiment on a model system in which the muon spins were replaced by proton spins. It consists of a single crystal of naphthalene containing a small amount of pentacene. By irradiating the crystal with a pulsed nitrogen laser, the pentacene molecules are photoexcited into their triplet states. These triplet states provide highly polarized electron spins (S= 1) with a lifetime of 20 Jis. We now use the experimental procedure described above to transfer the ESEEM signal of these electron spins to the proton spins in the crystal, so we can detect it via their nuclear magnetic resonance (NMR) signal. Our test experiment is performed at room temperature and in a magnetic field of 0.291 T. In contrast to the proposed 1.tSR experiment, now we start with highly polarized electron spins and unpolarized nuclear spins. Therefore the first microwave pulse in the pulse sequence is modified, and we use the sequence shown in fig. 3 instead. Just as in the previous experiment, the first pulse yields electron spin polarization in the x-direction. But, when the electron spins are created by the laser pulse, they are already polarized along the z-direction. So, this first pulse is now simply a 90°pulse. From this point on-
5 August 1991
‘T
T
=0
=
~
2
Fig. 3. The microwave pulse sequence used in naphthalene doped with pentacene. A standard two-pulse echo is generated, and the refocused magnetization is aligned to the microwave field generated by the third, it/2 phase shifted pulse. During this pulse, polarization transfer from the electron spin to the surrounding proton spins takes place.
wards the experiment is the same as described above. The intensity of the third pulse is chosen to obey y5B~=y,B0, where y~is the gyromagnetic ratio of the proton spins, so now the electron spin polarization in the x-direction, i.e., the intensity of the ESE or ESEEM signal, is transferred to the proton spins. Also in contrast to the proposed j.tSR experiment, the resulting NMR signal is difficult to observe. Therefore the experiment is repeated 50000 times before this signal is measured by CW NMR. The intensity ofthe NMR signal as a function of the delay time t between the pulses is shown in fig. 4b. The scatter in the points obtained by NMR is mainly caused by inaccuracy in tuning the microwave frequency to the centre of the ESR line. It has been checked that delaying the third pulse after the echo drastically reduces the NMR signal. To check whether the result obtained in fig. 4b really represents the ESEEM signal, we also performed a standard ESEEM experiment. For this purpose we skip the third pulse in fig. 3 and record the echo itself at a time ‘rafter the second pulse. We note that such an ESEEM study of the triplet state of pentacene at room temperature was earlier performed in ref. [9]. In fig. 4a a part ofthe time-domain ESEEM spectrum is shown, in which the proton Zeeman frequency of 12.4 MHz dominates. The window marks the region where the complete pulse sequence displayed in fig. 3 is used. The ESEEM signal and the NMR signal as a function of the delay time ‘rcoincide. So, the observed effect is indeed due to polarization transfer of the precessing electron spin p0larization to the nuclear spins. Our test experiment also allows us to study the dynamics of the cross polarization during the last microwave pulse. The following experiment shows that 433
Volume 157, number 6,7
PHYSICS LETTERS A
a
5 August 1991
-
>-
tJ~)
-I /
~
Lu
0 Lu Lu
0
___________________________ 0’
0
-
J
0.6
1
I 1.5
1.0
0.8
(~1\
7k
~\ ~\f j
-
b
I ~/ +
N’
I
0.45
0.50
0.55
Fig. 4. (a) Directly recorded ESEEM. The part in the window is enlarged in (b). The points (b) are the NMR results, showing the possibility of NMR detected ESEEM.
this transfer is very fast. At a constant value oft where the resulting NMR signal is large, the length ‘rL of the third pulse is varied. We measure the resulting intensity of the NMR signal as a function of ‘rL~The result is plotted in fig. 5. We see that the shape of the curve is not exponential but that transfer takes place in a time as short as 200 ns. In ref. [10] a full theoretical analysis of the polarization transfer is given. It is found to be given by the Fourier transform of the term of the dipolar Hamiltonian responsible for polarization transfer. A numerical evaluation of this term fits perfectly with the observed curve. This treatment is easily extended to the present case. In the extreme case of one pair of an electron spin and a nuclear or muon spin, fig. ~ should even have displayed a perfect sinusoidal behaviour, and a specific value of ‘rL would exist where the complete muon spin polarization is transferred to the electron spin or vice versa. Furthermore the transfer time in the proposed i.tSR experiment is in—
Fig. 5. The growth rate ofthe nuclear spin polarization as a function of the length of the locking pulse tL. The solid line is a guide to the eye.
versely proportional to the gyromagnetic ratio of the muon [10]. So, this transfer time will be even considerably tio of the shorter, muon. due to the larger gyromagnetic ra-
~
I
434
I ~s)
I
0.4
-
I 0.5
—
This work is part of the research program of the “Stichting voor Fundamenteel Onderzoek der Materie” (FOM) and has been made possible by the financial support from the “Nederlandse Organisatie voor Wetenschappelijk Onderzoek” (NWO). T.-S. Lin also wishes to acknowledge the partial support from the PRF administered by the American Chemical Society and by the Missouri Higher Education Research Fund. References [1] S.F.J. Cox, J. Phys. C 20 (1987) 3187. [2] A. Abragam, C.R. Acad. Sci. 299 (1984) 95. [3] S.R. Kreitzman, J.H. Brewer, D.R. Harshman, R. Keitel, D.L. Williams, K.M. Crowe and E.J. Ansaldo, Phys. Rev. Lett.56(l986) 181. [4] R.F. Kiefi, M. Celio, T.L Estle, S.R. Kreitzman, G.M. Luke, TM. Riseman and E.J. Ansaldo, Phys. Rev. Lett. 60 (1988) 224. [5] ~tSRconference, Oxford (1990). [6] W.B. Mims, Proc. R. Soc. 283(1965) 542. [7] L.G. Rowan, (1965) Aol. E.L. Hahn and W.B. Mims, Phys. Rev. 137 [8] A. Henstra, P. Dirksen, J. Schmidt and W.Th. Wenckebach, J. Magn. Res. 77 (1988) 389. [9] D.J. Sloop, H.L. Yu, T.S. Lin and S.I. Weissman, J. Chem. Phys. 75 (1981) 3746. [10] A. Henstra and W.Th. Wenckebach, to be pusblished; A. Henstra, Thesis, University of Leiden (1990).
PHYSICS LETTERS A
5 August 1991
Muon spin rotation (p.SR) detected electron spin echo envelope modulation (ESEEM) A. Henstra, T.-S. Lin’ and W.Th. Wenckebach Huygens Laboratory, University ofLeiden, P.O. Box 9504, 2300 RA Leiden, The Netherlands Received 18 January 1991; revised manuscript received 7 June 1991; accepted for publication 13 June 1991 Communicated by J.I. Budnick
The recently developed method of NOVEL, in which very rapid cross polarization between electron spins and nuclear spins is induced, is proposed to be extended to the field of 1sSR. This would provide a method to unravel the ESR and ESEEM spectra of muonated radicals. The proposal is backed up by an experiment in a molecular crystal, where the ESEEM spectrum of an excited triplet state is observed indirectly via NMR.
A typical problem studied by muon spin rotation (~xSR)[1] concerns the case that a positive muon is implanted in a silicon crystal. In order to compensate for the added positive charge an extra electron is bound close to the muon site. Thus, a deep donor, equivalent to a hydrogen impurity, is created. Two major questions arise, the position of the muon and the wave function of the unpaired electron. The obvious way to determine the wave function of an unpaired electron is to measure its hyperfine interactions with all neighbouring nuclear spins. In the past decade the method of level crossing resonance (LCR) [2,31 has been successfully introduced for this purpose. In this method the nuclear hyperfine interactions are obtained from the intensities of the magnetic field where the level splitting of the muon spin matches the level splittings of the nuclear spins and, as a result, the IISR signal decays more rapidly. Thus, e.g., the position of the muon in silicon could be unraveled [41. This paper concerns a new alternative technique we propose to use to determine the latter wave function ofthe unpaired electron [51.We believe it to be particularly useful in cases where LCR cannot be observed because of unsuitable values of the hyperfine interactions or where the hyperfine interactions are On sabbatical leave from Chemistry Department, Washington University, St. Louis, MO, USA. Elsevier Science Publishers B.V. (North-Holland)
very complicated, so measurements at various intensities of the magnetic field are necessary. As our new technique is not restricted to the above described case of ~ in silicon, it may be useful in many cases where an unpaired electron spin is created near the implanted positive muon. The wave function of an unpaired electron is most easily obtained using electron nuclear double resonance (ENDOR) [6] to determine its hyperfine interactions with all neighbouring nuclear spins. Pulsed techniques like electron spin echo envelope modulation (ESEEM) [7] have proven to be the most sensitive. Then two microwave pulses are given at the resonance frequency of the electron spins: a 900 pulse followed after a time t by a 1800 pulse. After another delay r the electron spin echo (ESE) signal is recorded. The intensity of this ESE signal decays as a function of i because of transverse relaxation processes. However, on top of this decay, it also shows oscillations as a function of time: electron spin echo envelope modulation (ESEEM). This modulation is due to interference of signals from electron spins experiencing different hyperfine fields, i.e., where surrounding nuclei are oriented differently. As a result, the Fourier transform of the ESEEM signal directly yields the hyperfine interactions of the electron spin with its neighbouring nuclei. Unfortunately, for such pulsed ESR techniques at least 1 0’° electron spins are necessary, and therefore they lack 431
Volume 157, number 6,7
9~=O
PHYSICS LETTERS A
______
______ T
_______
_______
the hyperfine its ESEEM signal interactions. of the unpaired electron and hence ~O
Fig. I. The microwave pulse sequence accomplishing iiSR detected ESEEM. During the first and last pulse rapid cross polarization between the electron spin and the muon spin takes place, and during the free precession period the hyperfine interactions are active, resulting in a modulation of the echo signal as a function oft. 0 is the phase ofthe microwaves,
sufficient sensitivity for the problem described above. The essential idea in our proposed method is to transfer the precessing electron spin polarization which gives rise to the ESEEM signal to the muon spins. Subsequently, the transferred polarization is detected by the much more sensitive method of j~iSR. For the polarization transfer we intend to use a recently developed method, nuclear spin orientation via electron spin locking (NOVEL) [8]. The proposed experiment, detecting ESR and ESEEM via IISR, is performed as follows. We consider a conventional Lt~SRexperiment where muons are implanted in the sample with their spin parallel to the external magnetic field B0. We consider the case that upon implantation of a muon an unpaired electron spin is created. The latter may be unpolarized. Directly after implanting the muon, we apply the microwave pulse sequence shown in fig. 1. It consists of three pulses at the resonance frequency of the electron spin separated by a time r which may be varied. The first and the last pulse are identical, the middle pulse is more intense and phase shifted by 900. Directly after the last pulse the ~.tSRsignal is detected. As we will see below, by plotting the intensity of this signal as a function of ~we will obtain
x
5 August 1991
The evolution of the effective fields experienced by the electron spin and its polarization are shown in fig. 2. In this figure, we use a frame of reference rotating with the microwave frequency co about the z-axis, which is the direction of the external magnetic field B0 Then, because the microwave field is at the resonance frequency of the electron spin, the effective field in the z-direction is equal to B0 I W/Ys = 0, where Ys is the gyromagnetic ratio of the electron spin. Furthermore, during the first and last pulse, the microwave field is oriented along the x-direction and has a constant value B~.In the middle more intensevalue pulse, the phase shifted by 900, so it has a larger B~ while it isisoriented along the y—
direction. The gist of our method is that we choose the intensity of the first and last microwave pulse such that y~B~ is equal to the ~SR resonance frequency. E.g., for a small hyperfine interactionwe choose y~B~ equal to y,. 11301 where y~is the gyromagnetic ratio of the muon spin. This condition is easily achieved using loop gap resonators [8]. Then, as we have shown previously for electron spins and nuclear spins, rapid cross polarization on a submicrosecond time scale between the muon spin and the electron spin is induced by their mutual dipolar interaction [8]. As a result, after the first pulse, the electron spins are polarized along the x-axis of the rotating frame at the expense of the muon spin polarization. We note that the ESR spectrum is directly obtained by measuring the significant decrease of the IXSR signal after the first pulse as a function of the microwave frequency. After the first pulse, the electron spin polarization dephases just as it would do after a 90°pulse: because of internal fields in the crystal its orientation
X
Fig. 2. The different effectivefields experienced by the electron spin and the evolution ofits polarization vector.
432
Volume 157, number 6.7
PHYSICS LETTERS A
slowly drifts away from the x-direction. Also because of transverse relaxation its amplitude diminishes. After a first delay t we apply the second pulse, which is a standard 180°pulse. Its amplitude is chosen very large, so polarization transfer between the electron spin and the muon spin is impossible. Because of the second pulse, after a second delay ‘r the electron spin polarization is rephased and oriented along the x-direction again. It should give rise to an ESE signal. However, it cannot be observed directly because its intensity is too small. To observe it, we apply the third pulse, which like the first one, induces rapid cross polarization between the muon spin and the electron spin. Thus, the electron spin polarization that would have given rise to an ESE signal is transferred back to the muon spin. So it can subsequently be measured by observing the i.tSR signal. More interestingly, by measuring the intensity of the thus obtamed jtSR signal as a function oft, one obtains the ESEEM signal and hence the hyperfine interactions of the electron spin, To test the above described procedure experimentally without needing to refer to an actual j.tSR experiment, we performed an experiment on a model system in which the muon spins were replaced by proton spins. It consists of a single crystal of naphthalene containing a small amount of pentacene. By irradiating the crystal with a pulsed nitrogen laser, the pentacene molecules are photoexcited into their triplet states. These triplet states provide highly polarized electron spins (S= 1) with a lifetime of 20 Jis. We now use the experimental procedure described above to transfer the ESEEM signal of these electron spins to the proton spins in the crystal, so we can detect it via their nuclear magnetic resonance (NMR) signal. Our test experiment is performed at room temperature and in a magnetic field of 0.291 T. In contrast to the proposed 1.tSR experiment, now we start with highly polarized electron spins and unpolarized nuclear spins. Therefore the first microwave pulse in the pulse sequence is modified, and we use the sequence shown in fig. 3 instead. Just as in the previous experiment, the first pulse yields electron spin polarization in the x-direction. But, when the electron spins are created by the laser pulse, they are already polarized along the z-direction. So, this first pulse is now simply a 90°pulse. From this point on-
5 August 1991
‘T
T
=0
=
~
2
Fig. 3. The microwave pulse sequence used in naphthalene doped with pentacene. A standard two-pulse echo is generated, and the refocused magnetization is aligned to the microwave field generated by the third, it/2 phase shifted pulse. During this pulse, polarization transfer from the electron spin to the surrounding proton spins takes place.
wards the experiment is the same as described above. The intensity of the third pulse is chosen to obey y5B~=y,B0, where y~is the gyromagnetic ratio of the proton spins, so now the electron spin polarization in the x-direction, i.e., the intensity of the ESE or ESEEM signal, is transferred to the proton spins. Also in contrast to the proposed j.tSR experiment, the resulting NMR signal is difficult to observe. Therefore the experiment is repeated 50000 times before this signal is measured by CW NMR. The intensity ofthe NMR signal as a function of the delay time t between the pulses is shown in fig. 4b. The scatter in the points obtained by NMR is mainly caused by inaccuracy in tuning the microwave frequency to the centre of the ESR line. It has been checked that delaying the third pulse after the echo drastically reduces the NMR signal. To check whether the result obtained in fig. 4b really represents the ESEEM signal, we also performed a standard ESEEM experiment. For this purpose we skip the third pulse in fig. 3 and record the echo itself at a time ‘rafter the second pulse. We note that such an ESEEM study of the triplet state of pentacene at room temperature was earlier performed in ref. [9]. In fig. 4a a part ofthe time-domain ESEEM spectrum is shown, in which the proton Zeeman frequency of 12.4 MHz dominates. The window marks the region where the complete pulse sequence displayed in fig. 3 is used. The ESEEM signal and the NMR signal as a function of the delay time ‘rcoincide. So, the observed effect is indeed due to polarization transfer of the precessing electron spin p0larization to the nuclear spins. Our test experiment also allows us to study the dynamics of the cross polarization during the last microwave pulse. The following experiment shows that 433
Volume 157, number 6,7
PHYSICS LETTERS A
a
5 August 1991
-
>-
tJ~)
-I /
~
Lu
0 Lu Lu
0
___________________________ 0’
0
-
J
0.6
1
I 1.5
1.0
0.8
(~1\
7k
~\ ~\f j
-
b
I ~/ +
N’
I
0.45
0.50
0.55
Fig. 4. (a) Directly recorded ESEEM. The part in the window is enlarged in (b). The points (b) are the NMR results, showing the possibility of NMR detected ESEEM.
this transfer is very fast. At a constant value oft where the resulting NMR signal is large, the length ‘rL of the third pulse is varied. We measure the resulting intensity of the NMR signal as a function of ‘rL~The result is plotted in fig. 5. We see that the shape of the curve is not exponential but that transfer takes place in a time as short as 200 ns. In ref. [10] a full theoretical analysis of the polarization transfer is given. It is found to be given by the Fourier transform of the term of the dipolar Hamiltonian responsible for polarization transfer. A numerical evaluation of this term fits perfectly with the observed curve. This treatment is easily extended to the present case. In the extreme case of one pair of an electron spin and a nuclear or muon spin, fig. ~ should even have displayed a perfect sinusoidal behaviour, and a specific value of ‘rL would exist where the complete muon spin polarization is transferred to the electron spin or vice versa. Furthermore the transfer time in the proposed i.tSR experiment is in—
Fig. 5. The growth rate ofthe nuclear spin polarization as a function of the length of the locking pulse tL. The solid line is a guide to the eye.
versely proportional to the gyromagnetic ratio of the muon [10]. So, this transfer time will be even considerably tio of the shorter, muon. due to the larger gyromagnetic ra-
~
I
434
I ~s)
I
0.4
-
I 0.5
—
This work is part of the research program of the “Stichting voor Fundamenteel Onderzoek der Materie” (FOM) and has been made possible by the financial support from the “Nederlandse Organisatie voor Wetenschappelijk Onderzoek” (NWO). T.-S. Lin also wishes to acknowledge the partial support from the PRF administered by the American Chemical Society and by the Missouri Higher Education Research Fund. References [1] S.F.J. Cox, J. Phys. C 20 (1987) 3187. [2] A. Abragam, C.R. Acad. Sci. 299 (1984) 95. [3] S.R. Kreitzman, J.H. Brewer, D.R. Harshman, R. Keitel, D.L. Williams, K.M. Crowe and E.J. Ansaldo, Phys. Rev. Lett.56(l986) 181. [4] R.F. Kiefi, M. Celio, T.L Estle, S.R. Kreitzman, G.M. Luke, TM. Riseman and E.J. Ansaldo, Phys. Rev. Lett. 60 (1988) 224. [5] ~tSRconference, Oxford (1990). [6] W.B. Mims, Proc. R. Soc. 283(1965) 542. [7] L.G. Rowan, (1965) Aol. E.L. Hahn and W.B. Mims, Phys. Rev. 137 [8] A. Henstra, P. Dirksen, J. Schmidt and W.Th. Wenckebach, J. Magn. Res. 77 (1988) 389. [9] D.J. Sloop, H.L. Yu, T.S. Lin and S.I. Weissman, J. Chem. Phys. 75 (1981) 3746. [10] A. Henstra and W.Th. Wenckebach, to be pusblished; A. Henstra, Thesis, University of Leiden (1990).