- Email: [email protected]
Spin relaxation of polarized positive muons in paramagnetic solutions
Volume
32A.
number
PHYSICS
1
SPIN
RELAXATION
LETTERS
1 June
OF POLARIZED POSITIVE MUONS PARAMAGNETIC SOLUTIONS *
1970
IN
A. SCHENCK** Department
of Physics.
Uniwrsity
qf Washington.
Received
6 April
Seattle.
Washington
98105.
1iSA
1970
Muon depolarization was found to depend on paramagnetic ion concentration in Fe(N0 )3 solutions and can be described by muonium lattice interactions. In addition the direct muon spin re31axation due to the same type of interactions as in NMR experiments was observed.
Since the first experiments on depolarization of positive muons [l] in matter, it was pointed out that only muonium formation can explain the large depolarization in times < 10-9 set observed in insulators and the dependence of polarization on applied external magnetic fields. This theory was supported by the observations that polarized muons stopped in metals showed no depolarization due to the fact that the hyperfine coupling in muonium ground state is entirely broken by fast electron exchange rate. A fully developed theory of muon depolarization by muonium formation taking into account the muonium electron interaction with the environment was given by Ivanter and Smilga [2] including formulas for residual polarization both in parallel and transverse magnetic fields with respect to the direction of polarization. Two important parameters are involved in their theory: 1. lifetime of muonium T, (the lifetime is terminated by chemical reactions); 2. muonium electron-spin-flip frequency u, due to electron lattice interactions. In the present experiment, of which first results are presented here, it was the aim to measure the residual polarization as a function of V. The idea was to use a water target with various amounts of paramagnetic ions in order to change v by virtue of the dipole-dipole interaction between muonium electron and paramagnetic ion. Further more one might observe in highly concentrated solutions a direct relaxation of the muon spin after the muon has become part of a chemical compound. This would
* Supportedin part by NSF and AEC. **On leave from I. Physikalisches Institut, of Heidelberg.
University
1.0
_/---
i
I
0.6 0.6 %50.4 0.2
--,
1
V-N, /’
_cx-,
.---
7
..--.’
I-r
2_“._,,,2
II,,
Fig.
1.
be due to the same kind of mechanism leading
to proton spin relaxation as observed in NMR experiments. The experimental setup was the same as used in the recent high precision measurement of the magnetic moment of the muon [3] at the 184 inch Synchrocyclotron at the Lawrence Radiation Laboratory, Berkeley. The external magnetic field (11 K Gauss) was perpendicular to the direc, tion of polarization. Larmor precession of muonspin leads to the following distribution of 1 - e decay events. N = No exP (-t/TC1 )[1 + 2 A, exp (- t/7,,lax) X X cos (Wt + @)I. Here t is the actual lifetime of a stopped ~1,rp = 2.198 (Isec = mean lifetime of p’s, A, = maximum available asymmetry due to beam polarization and target and counter geometry; 5 = depolarization factor due to muonium formation, Trelax = T2 = transverse muon spin relaxation time, when the muon has become part of a chemical compound, and o = muon precession frequency. 19
Volume 32A. number 1
PHYSICS
LETTERS
1 June 1970
for both models which represent the best fits. The v ccN2 model is a better fit to the data leading to a lifetime for the muonium of T = 6X10-11 set and the relation v N 2X low31 N2. It is assumed that the observed depolarization in pure water is entirely due to the hyperfine mixing in the muonium ground state. The results for rrelax =f(N) fig. 2, shows that l/~,,l~ is proportional to N as known from relevant proton relaxation times in NMR. Further, when comparing proton relaxation measurements in Fe(N03)3 solutions [4] with our results we get in accordance with spin relaxation theories T2(proton) T2(muon)
N
pmuon 2 ( c1proton 1 = 10
where p muon and ~1proton are the respective magnetic moments. The following concentrations of Fe(N03)3 solutions were used in the target: O.OOlM, O.OlM, O.lM, 0.5M, lM, 2M, 3M. Fig. 1 and fig. 2 present the preliminary results of the measurements. Fig. 1 shows the dependence of 5 on the paramagnetic ion concentration. In order to fit the formula given by Ivanter and Smilga to the data, one has to make an assumption as to how the muonium electron spin flip frequency depends on the ion concentration N. Two models were assumed: 1. Translational diffusion induced relaxation, this leads to v m N; 2. Relaxation induced by spin flips of the paramagnetic ions, while the average distance to the next neighbor ions is of the order of the distance between the ions themselves. This leads to v mN2. Fig. 1 shows, also, the curves
*****
20
The generous support by Professor K. M. Crowe, Lawrence Radiation Laboratory, Berkeley and many stimulating discussions with Professor R. W. Williams, University of ‘Washington, Seattle are gratefully acknowledged. References (11 A rather complete bibliography
can be found in A. 0. Weissenberg, Muons, (North Holland, Amsterdam, 1967) [2] I. G. Ivanter and V. P. Smilga, Soviet Phys. JETP 27 (1968) 301. [3] J. F. Hague, J. E. Rothberg, A. Schenck, D. L. Williams, R. W. Williams, K. K. Young and K. M. Crowe, to be published. [4] M. Bloembergen, Thesis, Leiden, 1948. E. L. Hahn, Phys. Rev. 80 (1950) 580.
32A.
number
PHYSICS
1
SPIN
RELAXATION
LETTERS
1 June
OF POLARIZED POSITIVE MUONS PARAMAGNETIC SOLUTIONS *
1970
IN
A. SCHENCK** Department
of Physics.
Uniwrsity
qf Washington.
Received
6 April
Seattle.
Washington
98105.
1iSA
1970
Muon depolarization was found to depend on paramagnetic ion concentration in Fe(N0 )3 solutions and can be described by muonium lattice interactions. In addition the direct muon spin re31axation due to the same type of interactions as in NMR experiments was observed.
Since the first experiments on depolarization of positive muons [l] in matter, it was pointed out that only muonium formation can explain the large depolarization in times < 10-9 set observed in insulators and the dependence of polarization on applied external magnetic fields. This theory was supported by the observations that polarized muons stopped in metals showed no depolarization due to the fact that the hyperfine coupling in muonium ground state is entirely broken by fast electron exchange rate. A fully developed theory of muon depolarization by muonium formation taking into account the muonium electron interaction with the environment was given by Ivanter and Smilga [2] including formulas for residual polarization both in parallel and transverse magnetic fields with respect to the direction of polarization. Two important parameters are involved in their theory: 1. lifetime of muonium T, (the lifetime is terminated by chemical reactions); 2. muonium electron-spin-flip frequency u, due to electron lattice interactions. In the present experiment, of which first results are presented here, it was the aim to measure the residual polarization as a function of V. The idea was to use a water target with various amounts of paramagnetic ions in order to change v by virtue of the dipole-dipole interaction between muonium electron and paramagnetic ion. Further more one might observe in highly concentrated solutions a direct relaxation of the muon spin after the muon has become part of a chemical compound. This would
* Supportedin part by NSF and AEC. **On leave from I. Physikalisches Institut, of Heidelberg.
University
1.0
_/---
i
I
0.6 0.6 %50.4 0.2
--,
1
V-N, /’
_cx-,
.---
7
..--.’
I-r
2_“._,,,2
II,,
Fig.
1.
be due to the same kind of mechanism leading
to proton spin relaxation as observed in NMR experiments. The experimental setup was the same as used in the recent high precision measurement of the magnetic moment of the muon [3] at the 184 inch Synchrocyclotron at the Lawrence Radiation Laboratory, Berkeley. The external magnetic field (11 K Gauss) was perpendicular to the direc, tion of polarization. Larmor precession of muonspin leads to the following distribution of 1 - e decay events. N = No exP (-t/TC1 )[1 + 2 A, exp (- t/7,,lax) X X cos (Wt + @)I. Here t is the actual lifetime of a stopped ~1,rp = 2.198 (Isec = mean lifetime of p’s, A, = maximum available asymmetry due to beam polarization and target and counter geometry; 5 = depolarization factor due to muonium formation, Trelax = T2 = transverse muon spin relaxation time, when the muon has become part of a chemical compound, and o = muon precession frequency. 19
Volume 32A. number 1
PHYSICS
LETTERS
1 June 1970
for both models which represent the best fits. The v ccN2 model is a better fit to the data leading to a lifetime for the muonium of T = 6X10-11 set and the relation v N 2X low31 N2. It is assumed that the observed depolarization in pure water is entirely due to the hyperfine mixing in the muonium ground state. The results for rrelax =f(N) fig. 2, shows that l/~,,l~ is proportional to N as known from relevant proton relaxation times in NMR. Further, when comparing proton relaxation measurements in Fe(N03)3 solutions [4] with our results we get in accordance with spin relaxation theories T2(proton) T2(muon)
N
pmuon 2 ( c1proton 1 = 10
where p muon and ~1proton are the respective magnetic moments. The following concentrations of Fe(N03)3 solutions were used in the target: O.OOlM, O.OlM, O.lM, 0.5M, lM, 2M, 3M. Fig. 1 and fig. 2 present the preliminary results of the measurements. Fig. 1 shows the dependence of 5 on the paramagnetic ion concentration. In order to fit the formula given by Ivanter and Smilga to the data, one has to make an assumption as to how the muonium electron spin flip frequency depends on the ion concentration N. Two models were assumed: 1. Translational diffusion induced relaxation, this leads to v m N; 2. Relaxation induced by spin flips of the paramagnetic ions, while the average distance to the next neighbor ions is of the order of the distance between the ions themselves. This leads to v mN2. Fig. 1 shows, also, the curves
*****
20
The generous support by Professor K. M. Crowe, Lawrence Radiation Laboratory, Berkeley and many stimulating discussions with Professor R. W. Williams, University of ‘Washington, Seattle are gratefully acknowledged. References (11 A rather complete bibliography
can be found in A. 0. Weissenberg, Muons, (North Holland, Amsterdam, 1967) [2] I. G. Ivanter and V. P. Smilga, Soviet Phys. JETP 27 (1968) 301. [3] J. F. Hague, J. E. Rothberg, A. Schenck, D. L. Williams, R. W. Williams, K. K. Young and K. M. Crowe, to be published. [4] M. Bloembergen, Thesis, Leiden, 1948. E. L. Hahn, Phys. Rev. 80 (1950) 580.