- Email: [email protected]
One-photon |Δm| = 2 nuclear magnetic resonance near level crossings
Volume 105A, number 4,5
PHYSICS LETTERS
15 October 1984
ONE-PHOTON IAm I = 2 NUCLEAR MAGNETIC RESONANCE NEAR LEVEL CROSSINGS C. BACK 1, R. DEMEURE, P. DESCHEPPER, L. GRENACS, J. LEHMANN, P. LEBRUN 2, C. LEROY a, A. MAIO 4, L, PALFFY s and A. POSSOZ 6 Institut de Physique Corpusculaire, Universit~ Catholique de Louvain, Louvain-la-Neuve, Belgium
Received 5 June 1984 Revised manuscript received 13 August 1984
The one-photon IAml = 2 nuclear magnetic resonance in 12B(/= 1) was investigated. It is found that this resonance is quasi-allowed near low-field level crossings. Some of its applications are considered.
One-photon I ~ n l = 2 nuclear magnetic resonance is made possible via admixtures in nuclear sublevels. If the energy spacing of sublevels is due to Zeeman effect, the amplitude a of these admixtures is given by the ratio B L / B z , where B L and B z are the local (off-diagonal) perturbing field and the quantizing field, respectively. In the high-field NMR (B z ~ 10 4 G) a is generally small, e.g. for rigid lattices (B L ~ 1 G) one has ~ ~ 10 - 4 [1]. For such small admixtures this resonance is practically forbidden. This resonance, however, can be enhanced by a substantial decrease of the level spacing. One opportunity is offered by level crossing; another by a special low-field regime of NMR, i.e. when oriented nuclei (produced and oriented in nuclear reactions for example) are implanted in suitable hosts where the nuclear orientation is preserved with a very low field B z. Combining these two kinds of enhancement we have observed the onephoton IAml = 2 resonance in 12B ( I = 1) [2,3]. The oriented 12B was produced in the 11 B(d, p)12B reaction and recoil-implanted in single crystals (s.c.) of Mg and Au in presence o f a low holding field B z. NMR transitions between substates of 12 B were detected through the resonant modification of (the beta1 Now at: Ministry for Health, Grand Duchy of Luxembourg. 2 Now at: Fermilab, Batavia, IL 60510, USA. a Now at: Physics Department, McGill University, Montreal, P.Q., Canada. 4 Now at: INIC, University of Lisbon, Portugal. s F.N.R.S., Belgium. 6 Now at: CERN, Geneva, Switzerland. 0.375-9601/84/$ 03.00 ©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
ray) angular distribution in the decay 12B(fl-)12C. The distribution is essentially given by [4,5] : W(0) ~ 1 - P cos 0 ,
(1)
where P i s the 12B polarisation, and 0 is the angle between P and the beta momentum. P is related to the substate populations Pm as P = Pl - P - 1, while the alignment is ~ = 1 - 3p 0 (note that ~ has no direct relevance to this work), with ~'Pm = 1. As in earlier work [5] the deuteron energy, E d = 1.6 MeV, and the recoil angle, 0 R = (49 + 3) °, were chosen to maximize the polarisation of 12B(p ~ 9.5%) Betas from the recoil-implanted 12B were counted with two telescopes located above (n) and below (0) the reaction plane respectively (fig. 1); these telescopes consisted o f plastic scintillators interspersed with plastic absorbers. Fast coincidences from the scintillation counters traversed by the electrons were required. The timing sequence was 40 ms implantation, 2 ms waiting time, 58 ms counting (the lifetime of 12B is 30 ms). The single-crystal of Mg was oriented with its c-axis along B z (i.e. alongP). Au was oriented with its (100> axis along B z. The quadrupolar coupling lifts the degeneracy of the 0 -> -+1 Zeeman-frequencies (see insert (c) in fig. 1). It is known from Haskell et al. [6] that the implantation of 12B in Mg occurs at a single site. One of the Iml = 1 crosses the m = 0 level at B z 45 G. Off-diagonal couplings (spin-spin effects and quadrupole inhomogeneities) readily induce level mixing at B z where one thus expects a strong enhancement of the 1 ~ - 1 one-photon resonance. Further255
Volume 105A, number 4,5
PHYSICS LETTERS
15 October 1984
11B d
(
30
=49 "~=
(O)
20 10
4~'X~2B
5~XXX~v"
' ~ Host (Mg~A%..)
NX~.. /
0i " " x ,
,
,
,
10~ , ~
50-
~10
-2C
43
-30
I//////////////A
(c)
42
K/////////////A 7"7"3
• '1~1Bz
~
,, / / I . t ..................
B
• _Host
12cml
V~Vm
.v/l,
~1 vl
~//Au
v~Au
i//11//i/////~/5/
(b)
-'~.6
Fig. 1. (a) Top-view of the target arrangement, I l B (~150 ug/cm 2) on inox backing. (b) Schematic side-view of the apparatus (a simplified version of that in ref. [5] ), 1 .... 6, plastic scintillator electron counters. Coincidences: 123(n) and 456(0). B z is perpendicular to the reaction plane (coaxial with the nuclear polarization). Oscillating field B x (not indicated) is coaxial with the recoil di. rection of 12B. (c) and (d) show the frequencies of magnetic substrates of 12B implanted into a s.c. of Mg(clIBzlIP) and into Au [same scale on (c) and (d)]. The quadrupolar frequency of 12B in Mg (e'~qQ/h = 46.5 kHz) and the Zeeman frequency of 12B (vZ = 765 Hz/G) are from ref. [6].
more, since the two Iml = 1 levels are shifted together, this resonance is expected to be much narrower than the allowed I A m l = 1 resonance where only one o f the levels is affected. In Au, which is cubic and hence has no quadrupole coupling, an analogous mixing occurs at B z = 0. Fig. 2 is a plot o f the normalized beta decay asymmetry A (Bz) defined as A = [N(Tr)/N(O)] Bz / [N(~r)/N(O)] 0 - 1 ,
(2)
where N O ) are counting rates. The denominator in eq. (2), measured with B z = 0, normalizes for counter efficiencies. Using eq. ( 1 ) , A ~ 2P. The polarization 256
o f 12B implanted in Au is well preserved above B z 20 G. The asymmetry observed with Mg is expected to be small because the diagonal quadrupolar coupling acts as a "holding" field in the absence o f B z. The " d i p " around B z is due to a partial depolarization o f 12B as a result o f the level mixing near B z . One can show, from the depth o f the dip, that the polarization o f 12B in Mg is fairly preserved. A resonant oscillatory field ( B x ) tends to equalize the populations o f the sublevels involved, i.e. it decreases the beta asymmetry. In our measurements the frequency v o f B x was kept fixed and B z was varied. Fig. 3 is a plot o f the transition frequencies v versus
Volume 105A, number 4,5
PHYSICS LETTERS
B z observed in Mg. A t these frequencies the change in
A (%)
~5
~Au
{
f++÷{+*"g
.+ + .,..~+.~,. o
15 October 1984
5
p÷
~5
/*s ;o
7'5
~;o 8z(Gauss)
F~. 2. The up/down beta decay asymmet[y A in the decay of polarised 12B recoil implanted in Au and in a s.c. of Mg versus the "holding" field B z. The dip (Mg) us due to level mixing at the level crossing.
a s y m m e t r y 5A exhibits resonant m a x i m a , as illustrated b y the insert in t h a t figure ( o b t a i n e d at v = 94 kHz). Three kinds o f resonances are observed: IAml = 1 onep h o t o n allowed resonances (squares), the I A m I = 2 o n e - p h o t o n resonance (full circles) and I A m I = 1 resonances due to t w o - p h o t o n transitions (open circles). The latter will n o t be discussed here. The e n h a n c e m e n t o f the IA m I = 2 o n e - p h o t o n resonance near B z = 45 G (Mg) and near the zero field ( A u ) is s h o w n in fig. 4. The main properties o f this resonance can be s u m m a r i z e d as: (1) This resonance is quasi-allowed near low-field level crossings. (2) It is a n a r r o w resonance. Its w i d t h , F ( B x 2 ) , was measured (with s.c. Mg) versus B ~ By e x t r a p o l a t i o n to B x = 0, we o b t a i n e d F ( 0 ) < 90 Hz. (3) The resonance signal is e n h a n c e d b y a misalignm e n t o f the c-axis w i t h respect to B z . This is because
6A(%)
(75)
4 120 V(kHz) ::~6A
,o0
002L_j
,<
80
o' .¢~/
12~in s.c.Mg
70 6C
J /
~ =
301-~ |
I/
0V
•
I 10
/" ,o
v=9~kHz /
I
'
(55)
/• /
(85} (95)
I
(45)
(125)
.JJ'S I-.
/s / J ~o-
Bx=IG
(65)
110
5C
12~-in s.c.Mg
,//
J J'J'J " /
/
12~-
(35) (/,7)
/.~
.<:o
~ ~ ,~ ~'" " I v~ll-.~4 ~ ' u I I 30 50 70
,,/=
11
(53)
i• s.c.Au 11251
I
I 90
Bz(GQuss) I I I 110
Fig. 3.12B in Mg. Resonance-mixing in the ( v - B z ) plane; squares and full circles indicate I Am I = 1 allowed and IAm I = 2 0ne-photon resonances, respectively. The open circles indicate a resonance which is presumably a two-photon transition. Measurements were taken with IBxl = 3 G and B z was modulated by IABzl = 1 G (50 Hz). Insert shows the modified asymmetry 6A (B z) for ~ = 94 kHz.
!7
0 I
I
I
I
20
40
60
80
Bz(Cxauss)
Fig. 4. The one-photon IAml = 2 resonance in 12B implanted in a s.c. of Mg and Au. The frequency v of B x (in kHz) is indicated on the top of the resonances. These data show the enhancement of this resonance near level crossings. 257
Volume 105A, number 4,5
PHYSICS LETTER S
the off-diagonal components o f the quadrupolar coupling strengthen the level mixing in the case of misalignment, (4) Let us finally note that this resonance does not affect an initial nuclear alignment ~ , while the allowed IAm I = 1 resonance does so. To conclude, let us briefly mention some applications o f the IAml = 2 one-photon resonance: The property (2) could be used to study the dipolar interactions between the implanted nucleus and its neighbours. (3) is exploited to align the c-axis by minimizing the resonance signal versus the (c, Bz) angle. This technique of c-axis alignment has already been used, namely to 12N implanted in s.c. Mg [7]. (4) was used, for calibration purposes, in an experiment [5] that measured the correlation between nuclear alignment and electron direction in the/~ decay of 12B. Note also that a similar effect has been discussed [8] relative to the observation made in experiments for 14N in polycrystalline solids [9]. We take great pleasure in acknowledging Professor V.L. Telegdi for his kind interest, critical remarks and encouragement. We thank Professor R. Coussement
258
15 October 1984
for useful discussions during the course of the experiment. We finally thank Mr. J. Van Mol for his help in data taking and operating the van de Graaff machine.
References [ 1 ] P. Slichter, Principles of magnetic resonances (Harper and Row, New York, 1965). [2] A.T. Maio, The observation of forbidden l,xml = 2 onephoton nuclear magnetic resonance transitions in 12B(I = 1) nuclei, Ph.D. thesis presented at the Katholieke Universiteit te Leuven (1980), unpublished. [3] C. Back, R.M.N. sur 12B implant~ dans un cristal de Mg; croisement de niveaux et transition interdites, M~moire, Universit~ Catholique de Louvain (1976), unpublished. [4] M. Morita, N. Nishimura, A. Shimizu, H. Ohtsubo and K. Kubodera, Prog. Theor. Phys. Suppl. 60 (1976) 1. [5] P. Lebrun, P. de Schepper, L. Grenacs, J. Lehmann, C. Leroy, L. Palffy, A. Possoz and A. Maio, Phys. Rev. Lett. 40 (1978) 302. [6] R.S. Haskell, F.D. Correll and L. Madansky, Phys. Rev. Bll (1975) 3268. [7] H. Brandle, L. Gtenacs, L.-P. Roesch, V.L. Telegdi, P. Truttmann and A. Zehnder, unpublished result, ETH Zurich (1977). [8] G. Bodenhausen, Prog. NMR Spectrosc. 14 (1981) 137. [91 R.B. Creel, E.D. yon Meerwall and R.G. Barnes, Chem. Phys. Lett. 49 (1977) 501.
PHYSICS LETTERS
15 October 1984
ONE-PHOTON IAm I = 2 NUCLEAR MAGNETIC RESONANCE NEAR LEVEL CROSSINGS C. BACK 1, R. DEMEURE, P. DESCHEPPER, L. GRENACS, J. LEHMANN, P. LEBRUN 2, C. LEROY a, A. MAIO 4, L, PALFFY s and A. POSSOZ 6 Institut de Physique Corpusculaire, Universit~ Catholique de Louvain, Louvain-la-Neuve, Belgium
Received 5 June 1984 Revised manuscript received 13 August 1984
The one-photon IAml = 2 nuclear magnetic resonance in 12B(/= 1) was investigated. It is found that this resonance is quasi-allowed near low-field level crossings. Some of its applications are considered.
One-photon I ~ n l = 2 nuclear magnetic resonance is made possible via admixtures in nuclear sublevels. If the energy spacing of sublevels is due to Zeeman effect, the amplitude a of these admixtures is given by the ratio B L / B z , where B L and B z are the local (off-diagonal) perturbing field and the quantizing field, respectively. In the high-field NMR (B z ~ 10 4 G) a is generally small, e.g. for rigid lattices (B L ~ 1 G) one has ~ ~ 10 - 4 [1]. For such small admixtures this resonance is practically forbidden. This resonance, however, can be enhanced by a substantial decrease of the level spacing. One opportunity is offered by level crossing; another by a special low-field regime of NMR, i.e. when oriented nuclei (produced and oriented in nuclear reactions for example) are implanted in suitable hosts where the nuclear orientation is preserved with a very low field B z. Combining these two kinds of enhancement we have observed the onephoton IAml = 2 resonance in 12B ( I = 1) [2,3]. The oriented 12B was produced in the 11 B(d, p)12B reaction and recoil-implanted in single crystals (s.c.) of Mg and Au in presence o f a low holding field B z. NMR transitions between substates of 12 B were detected through the resonant modification of (the beta1 Now at: Ministry for Health, Grand Duchy of Luxembourg. 2 Now at: Fermilab, Batavia, IL 60510, USA. a Now at: Physics Department, McGill University, Montreal, P.Q., Canada. 4 Now at: INIC, University of Lisbon, Portugal. s F.N.R.S., Belgium. 6 Now at: CERN, Geneva, Switzerland. 0.375-9601/84/$ 03.00 ©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
ray) angular distribution in the decay 12B(fl-)12C. The distribution is essentially given by [4,5] : W(0) ~ 1 - P cos 0 ,
(1)
where P i s the 12B polarisation, and 0 is the angle between P and the beta momentum. P is related to the substate populations Pm as P = Pl - P - 1, while the alignment is ~ = 1 - 3p 0 (note that ~ has no direct relevance to this work), with ~'Pm = 1. As in earlier work [5] the deuteron energy, E d = 1.6 MeV, and the recoil angle, 0 R = (49 + 3) °, were chosen to maximize the polarisation of 12B(p ~ 9.5%) Betas from the recoil-implanted 12B were counted with two telescopes located above (n) and below (0) the reaction plane respectively (fig. 1); these telescopes consisted o f plastic scintillators interspersed with plastic absorbers. Fast coincidences from the scintillation counters traversed by the electrons were required. The timing sequence was 40 ms implantation, 2 ms waiting time, 58 ms counting (the lifetime of 12B is 30 ms). The single-crystal of Mg was oriented with its c-axis along B z (i.e. alongP). Au was oriented with its (100> axis along B z. The quadrupolar coupling lifts the degeneracy of the 0 -> -+1 Zeeman-frequencies (see insert (c) in fig. 1). It is known from Haskell et al. [6] that the implantation of 12B in Mg occurs at a single site. One of the Iml = 1 crosses the m = 0 level at B z 45 G. Off-diagonal couplings (spin-spin effects and quadrupole inhomogeneities) readily induce level mixing at B z where one thus expects a strong enhancement of the 1 ~ - 1 one-photon resonance. Further255
Volume 105A, number 4,5
PHYSICS LETTERS
15 October 1984
11B d
(
30
=49 "~=
(O)
20 10
4~'X~2B
5~XXX~v"
' ~ Host (Mg~A%..)
NX~.. /
0i " " x ,
,
,
,
10~ , ~
50-
~10
-2C
43
-30
I//////////////A
(c)
42
K/////////////A 7"7"3
• '1~1Bz
~
,, / / I . t ..................
B
• _Host
12cml
V~Vm
.v/l,
~1 vl
~//Au
v~Au
i//11//i/////~/5/
(b)
-'~.6
Fig. 1. (a) Top-view of the target arrangement, I l B (~150 ug/cm 2) on inox backing. (b) Schematic side-view of the apparatus (a simplified version of that in ref. [5] ), 1 .... 6, plastic scintillator electron counters. Coincidences: 123(n) and 456(0). B z is perpendicular to the reaction plane (coaxial with the nuclear polarization). Oscillating field B x (not indicated) is coaxial with the recoil di. rection of 12B. (c) and (d) show the frequencies of magnetic substrates of 12B implanted into a s.c. of Mg(clIBzlIP) and into Au [same scale on (c) and (d)]. The quadrupolar frequency of 12B in Mg (e'~qQ/h = 46.5 kHz) and the Zeeman frequency of 12B (vZ = 765 Hz/G) are from ref. [6].
more, since the two Iml = 1 levels are shifted together, this resonance is expected to be much narrower than the allowed I A m l = 1 resonance where only one o f the levels is affected. In Au, which is cubic and hence has no quadrupole coupling, an analogous mixing occurs at B z = 0. Fig. 2 is a plot o f the normalized beta decay asymmetry A (Bz) defined as A = [N(Tr)/N(O)] Bz / [N(~r)/N(O)] 0 - 1 ,
(2)
where N O ) are counting rates. The denominator in eq. (2), measured with B z = 0, normalizes for counter efficiencies. Using eq. ( 1 ) , A ~ 2P. The polarization 256
o f 12B implanted in Au is well preserved above B z 20 G. The asymmetry observed with Mg is expected to be small because the diagonal quadrupolar coupling acts as a "holding" field in the absence o f B z. The " d i p " around B z is due to a partial depolarization o f 12B as a result o f the level mixing near B z . One can show, from the depth o f the dip, that the polarization o f 12B in Mg is fairly preserved. A resonant oscillatory field ( B x ) tends to equalize the populations o f the sublevels involved, i.e. it decreases the beta asymmetry. In our measurements the frequency v o f B x was kept fixed and B z was varied. Fig. 3 is a plot o f the transition frequencies v versus
Volume 105A, number 4,5
PHYSICS LETTERS
B z observed in Mg. A t these frequencies the change in
A (%)
~5
~Au
{
f++÷{+*"g
.+ + .,..~+.~,. o
15 October 1984
5
p÷
~5
/*s ;o
7'5
~;o 8z(Gauss)
F~. 2. The up/down beta decay asymmet[y A in the decay of polarised 12B recoil implanted in Au and in a s.c. of Mg versus the "holding" field B z. The dip (Mg) us due to level mixing at the level crossing.
a s y m m e t r y 5A exhibits resonant m a x i m a , as illustrated b y the insert in t h a t figure ( o b t a i n e d at v = 94 kHz). Three kinds o f resonances are observed: IAml = 1 onep h o t o n allowed resonances (squares), the I A m I = 2 o n e - p h o t o n resonance (full circles) and I A m I = 1 resonances due to t w o - p h o t o n transitions (open circles). The latter will n o t be discussed here. The e n h a n c e m e n t o f the IA m I = 2 o n e - p h o t o n resonance near B z = 45 G (Mg) and near the zero field ( A u ) is s h o w n in fig. 4. The main properties o f this resonance can be s u m m a r i z e d as: (1) This resonance is quasi-allowed near low-field level crossings. (2) It is a n a r r o w resonance. Its w i d t h , F ( B x 2 ) , was measured (with s.c. Mg) versus B ~ By e x t r a p o l a t i o n to B x = 0, we o b t a i n e d F ( 0 ) < 90 Hz. (3) The resonance signal is e n h a n c e d b y a misalignm e n t o f the c-axis w i t h respect to B z . This is because
6A(%)
(75)
4 120 V(kHz) ::~6A
,o0
002L_j
,<
80
o' .¢~/
12~in s.c.Mg
70 6C
J /
~ =
301-~ |
I/
0V
•
I 10
/" ,o
v=9~kHz /
I
'
(55)
/• /
(85} (95)
I
(45)
(125)
.JJ'S I-.
/s / J ~o-
Bx=IG
(65)
110
5C
12~-in s.c.Mg
,//
J J'J'J " /
/
12~-
(35) (/,7)
/.~
.<:o
~ ~ ,~ ~'" " I v~ll-.~4 ~ ' u I I 30 50 70
,,/=
11
(53)
i• s.c.Au 11251
I
I 90
Bz(GQuss) I I I 110
Fig. 3.12B in Mg. Resonance-mixing in the ( v - B z ) plane; squares and full circles indicate I Am I = 1 allowed and IAm I = 2 0ne-photon resonances, respectively. The open circles indicate a resonance which is presumably a two-photon transition. Measurements were taken with IBxl = 3 G and B z was modulated by IABzl = 1 G (50 Hz). Insert shows the modified asymmetry 6A (B z) for ~ = 94 kHz.
!7
0 I
I
I
I
20
40
60
80
Bz(Cxauss)
Fig. 4. The one-photon IAml = 2 resonance in 12B implanted in a s.c. of Mg and Au. The frequency v of B x (in kHz) is indicated on the top of the resonances. These data show the enhancement of this resonance near level crossings. 257
Volume 105A, number 4,5
PHYSICS LETTER S
the off-diagonal components o f the quadrupolar coupling strengthen the level mixing in the case of misalignment, (4) Let us finally note that this resonance does not affect an initial nuclear alignment ~ , while the allowed IAm I = 1 resonance does so. To conclude, let us briefly mention some applications o f the IAml = 2 one-photon resonance: The property (2) could be used to study the dipolar interactions between the implanted nucleus and its neighbours. (3) is exploited to align the c-axis by minimizing the resonance signal versus the (c, Bz) angle. This technique of c-axis alignment has already been used, namely to 12N implanted in s.c. Mg [7]. (4) was used, for calibration purposes, in an experiment [5] that measured the correlation between nuclear alignment and electron direction in the/~ decay of 12B. Note also that a similar effect has been discussed [8] relative to the observation made in experiments for 14N in polycrystalline solids [9]. We take great pleasure in acknowledging Professor V.L. Telegdi for his kind interest, critical remarks and encouragement. We thank Professor R. Coussement
258
15 October 1984
for useful discussions during the course of the experiment. We finally thank Mr. J. Van Mol for his help in data taking and operating the van de Graaff machine.
References [ 1 ] P. Slichter, Principles of magnetic resonances (Harper and Row, New York, 1965). [2] A.T. Maio, The observation of forbidden l,xml = 2 onephoton nuclear magnetic resonance transitions in 12B(I = 1) nuclei, Ph.D. thesis presented at the Katholieke Universiteit te Leuven (1980), unpublished. [3] C. Back, R.M.N. sur 12B implant~ dans un cristal de Mg; croisement de niveaux et transition interdites, M~moire, Universit~ Catholique de Louvain (1976), unpublished. [4] M. Morita, N. Nishimura, A. Shimizu, H. Ohtsubo and K. Kubodera, Prog. Theor. Phys. Suppl. 60 (1976) 1. [5] P. Lebrun, P. de Schepper, L. Grenacs, J. Lehmann, C. Leroy, L. Palffy, A. Possoz and A. Maio, Phys. Rev. Lett. 40 (1978) 302. [6] R.S. Haskell, F.D. Correll and L. Madansky, Phys. Rev. Bll (1975) 3268. [7] H. Brandle, L. Gtenacs, L.-P. Roesch, V.L. Telegdi, P. Truttmann and A. Zehnder, unpublished result, ETH Zurich (1977). [8] G. Bodenhausen, Prog. NMR Spectrosc. 14 (1981) 137. [91 R.B. Creel, E.D. yon Meerwall and R.G. Barnes, Chem. Phys. Lett. 49 (1977) 501.