Volume 103A, number 3 PHYSICS LETTERS 25 ]une 1984
HIGHER ORDER LEVEL MIXING RESONANCES ON ORIENTED NUCLEI P. PUT, R. COUSSEMENT, G. SCHEVENEELS, F. HARDEMAN
Instituut voor Kern- en Stralingsfysika, Celestijnenlaan 200 D, 3030 Leuven, Belgium and
I. BERKES, B. HLIMI, G. MAREST, J. SAU and E.H. SAYOUTY
Institut de Physique Nucl&ire, UnipersitO Claude Bernard, Lyon Iet IN2P3, 69622 Villeurbanne Cedex, France Received 15 March 1984
Higher order level mixing resonances have been measured on the 40 s half-life l°9mAg in Zn. It is shown that the line- width is tunable with the misalignment angle of the electric to magnetic axes, and enables precise quadrupole coupling deter- minations. For l°9mAgzn eQ Vzz/tS = 3.08(2) T has been established.
Introduction. In a previous paper we presented the concept o f level mixing resonances on oriented nuclei (LMR/ON), and have shown the feasibility of such an experin]ent on the 85 ns half-life excited state of 111Cd [ t ]. We predicted that the method could also be applied to states with much longer lifetimes, as long as they are shorter than the spin-lattice relax- ation time. We mentioned that for longer lifetimes, i.e. smaller natural linewidths, the experimental line- width is tunable through the misalignment angle between the magnetic field and the electric field gradient, without intensity loss. The experimental resolution is limited in this case only by the field in- homogeneities. In this publication we prove these predictions on 109mAgZn, where the 88 keV(7/2) level has a 40 s lifetime.
The alignment of 109mAg is obtained through the decay of the low-temperature oriented mother state
109Cd in the electric field gradient o f a Zn single crys- tal. At our measuring temperatures ( 5 - 7 inK) the in- equality of the 109mAg substate populations is not very large, and so the level mixing of substates with adjacent magnetic quantum numbers (Am = 1) does not change appreciably the angular distribution o f the 88 keV gamma-line, but mixings involving high- and low-m levels give measurable effects. This feature necessitated the elaboration o f the higher order level ,nixing theory.
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Higher order level mixing theory. The matrix ele- ments of the combined magnetic plus electric quadru- pole interaction, misaligned over an angle/3 are:
eQVzz
Hm,m = 4 I ( 2 I - 1) [3rn2 I ( / + 1)] - rngtlNB cos t3, (1) Hm,m+ 1 = -gllNB sin/3 <mllxlm -+ 1 >, (2) where the quantization axis is oriented along Vzz and the x-axis is in the plane defined by the z-axis and the magnetic field B. The corresponding level scheme is given by the well known B r e i t - R a b i diagram (see e.g.
fig. la). It can be seen that for some magnetic fields several pairs o f levels degenerate, or nearly degenerate, involving simultaneously various values of Am. The mixing o f Am = 1 crossing levels can be easily calcu- lated in first order perturbation. For higher Am pairs the mixing must be calculated in Amth order perturba- tion theory. Details of this calculation will be published in ref. [2] ; in that reference it is explained how such level mixings result in a resonant change of the angular distribution o f radiation. The main conclusions are the following:
(i) Resonances in the angular distribution will occur with a full width at half maximum,
P = 2Wmm,/glaNArn , (3)
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Volume 103A, number 3 PHYSICS LETTERS 25 June 1984 W
( 1 0 - 2 6 j
2 I
Am ~- 6
0 _ ~ A m = 4
I i
bm=5
-1 " - ' ~ r n = 3
_ 3 ! ,,
- 4 @ I , , '
m,.l. m' -- 1 m+m'=2 m+m'=3 m+m'=4
I I I I I Ii I I I
1.06 @
1.04
1.02
I i I I I
{- 3/2 >
&m =2
I
!
II I I I I
I - 1/2 >
~'Am ~. 2
[÷ 1/2 )
m+m'=5 ~ _ ~ 2 >
I R i ~ -"--~5/2> ~-i'--..~
[ m+m'=6
l I I
!
I I I I I I I I I I I I I I
0 .2 .4 .6 .8 1. 1.2 1.4 1.6 1.8 2. 2.2 2,4 2.6 2.8B(T
Fig. 1. Breit-Rabi diagram for l°9mAgZn with # = 7 ° misalignment angle (a) and the anisotropy of the 88 keV gamma rays versus magnetic field at T = 7 mK (b). The continuous line is not a fit but a calculated curve with following parameters eQ Vzz/
h (l°gmAgZn) = 99.6(30) MHz, T 1T = 2.9 Ks and 77% substitutional fraction as deduced previously.
where 2Wmm, is the minimal distance o f two mixing levels.
(ii) The minimal approach 2 W m m , is:
2 W m m , = 2 g # N B (sin/3) Am (m + m ' ) a m -1 [ ( A m -- 1)!] 2
X ( m [ I x [ m - 1) (m - 111xlm - 2) ... ( m ' + l lIx[m').
(4)
Eq. (3) shows, that for higher order transitions the linewidth depends strongly on the misalignment angle /3: I~c~ (sin/3) Am. Thus, even for not too small misalign-
ment angles, narrow high order resonances will occur.
(iii) LMR is caused b y a resonant change o f the orientation by quantum state mixing. Since the differ- ence in direction o f the angular m o m e n t u m vector o f the mixing states is large for high Am cases, this change in orientation will also be large for mixings with a high Am. Furthermore, if the orientation o f the nuclei is established b y very low temperature orientation, the sublevel populations can be very different for high Am cases. This explains why this Am = 3 mixing is very im- p o r t a n t in this experiment.
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Volume 103A, number 3 PHYSICS LETTERS Experiments. Zn sinNe crystals were cut perpen-
dicularly to the c-axis. The orientation o f the c-axis with respect to the surface has been checked by Laue backscattering with an accuracy o f 1 o. Carrier free 109Cd has been electroplated and diffused at 220°C under H 2 atmosphere.
The Zn single crystal has been soldered to the cold finger of the dilution refrigerator of the University of Lyon at various misalignment angles ¢t. Gamma rays were detected in the magnetic field direction. In order to make sure that the t09mAg(88 keV) state is not strongly reoriented by thermal relaxation, the proce- dure outlined in ref. [3] has been followed: orientation versus temperature has been registered at low external field (Bex t = 0 . 7 - 0 . 9 T) and at high field (Bex t = 6 T).
Taking into account the hyperfine field in the frame- work of the rough two-sites model, computer-fits real- ized as in ref. [3] yield the Korringa constant, C K =
25 June 1984 T T 1 = 2 . 4 - 2 . 9 Ks for 109mAgZn and 7 0 - 7 7 % substi- tutional fraction. In the temperature range o f most o f the level mixing experiments ( t / T ~ 1 7 0 - 1 9 0 K - 1), CK/T(IO9mAgZn) ~ 500 s > T1/2(88 keV). Ernst et al.
[4] found for 109mCd in Cd a reorientation time Tr 800 s at this temperature which is o f the same order.
Though the thermal relaxation is slow, its effect on the resonances has to be taken into consideration. The master equation of the relaxing nuclei must be solved as in ref. [3]. This gives the stationary value o f the density matrix o f the relaxing nuclei, if one takes into account only the diagonal elements of this matrix, written in the eigenstates of the combined hyperfine hamiltonian. The B~ orientation parameters can then be calculated, and the angular distribution of the radi- ation versus applied magnetic field deduced.
The following results have to be pointed out:
(a) The thermal relaxation tends to erase the reso- nances.
1'07 r I J I
I I I I
1.3 1.4 1.5 1.6 1.7 B ( T )
Fig. 2. aim = 3 resonance measured at ~ = 7 ° and ~ = 4 ° at T = 7 mK. The continuous line is a fit using a lorentzian absorption line plus a linear background.
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Volume 103A, number 3 PHYSICS LETTERS 25 June 1984 (b) The time o f reorientation T r o f the nucleus de-
pends on B, T and C K. In the high temperature limit T r ~ CK/T, at low temperature T r < CK/T. In our case, for instance at T = 7 m K T r ~ 0.7 CK/T. This point will be developed in a forthcoming paper.
During the level mixing experiments the magnetic field was swept continuously during 1 0 - 1 6 h. The W(0 °) versus magnetic field plots have been corrected for the small (-+10%) temperature variations. Fig. lb shows a run taken with/3 -- 7 °. The mean value for several runs o f the Am = 3 peak centres o f gravity, corrected for the tilting angle, is B = 1.540(1 2) T. The background above the peaks, due to different super- positions o f mixings, has been taken into account with a second order polynomial. This yields for the ratio o f the electric quadrupole coupling to the magnetic mo- ment for 109mAgZn: eQVzz/la = 3.08(2) T. With /l(109mAg) = 4.27(13)/~N, eQ Vz z /h( l Ogm Ag z n ) = 99.6(30) MHz. The Knight shift is estimated from the Korringa dipole-dipole relaxation to be of the order of 0.15% and can be neglected.
In a recent paper Vzz(AgZn) = +1.7(1) X 1017 V/cm 2 has been deduced from an integral nuclear orientation experiment [6]. Using this value we would obtain Q(109mAg) = 2.4 b, which is too high for a nearly spherical nucleus. We suppose that the authors o f ref. [6] have underestimated the electric field gra- dient, by using a reference quadrupole m o m e n t uncor- rected for the antishielding and assuming 100% substi- tutional fraction in their sample.
The first and third resonances on fig. lb are Am = 2 mixings. The measurement shows that the linewidth increases with magnetic field as predicted in eq. (3).
The second resonance is 2xrn = 3, and is, as expected obviously narrower than the two others. The linewidths at this resonance are P(13 = 7 °) = 120(20) mT and lP(13 = 4 °) = 35(6) mT. These values show clearly the tunability o f the linewidth and their ratio agrees with- in the quoted errors on/3 and P with the (sin 13)am re- lation.
Conclusion.
(i) This experiment, combined with that o f ref.
[1 ] shows that LMR/ON can be performed on levels in a lifetime-range o f 10 - 7 s - 6 0 s, the upper limit be- ing about the spin-lattice reorientation time. The ob- servation o f LMR/ON at this long lifetime shows that the method is not sensitive to spin-spin relaxation, as it can be expected from the fact that LMR/ON does not depend on any phase relation.
(ii) High order mixings produce for high spin inter- mediate states strong and narrow resonances. This feature opens the possibility of quadrupole interaction determination on high spin isomeric states oriented by nuclear reactions.
(iii) The precision o f the method is only limited by the inhomogeneities o f the crystal and the magnetic field. In the measurement at 13 = 4 ° the experimental linewidth corresponds to 4.7 X 10 - 9 eV. If the resolu- tion is defined as P/Bre s, it can be compared to the 57Fe M6ssbauer resolution P/A in which A is the qua- drupole splitting. In this experiment we obtained for /3 = 4 °, r/Bre s = 0.023(4) which is already considerably better than the 57Fe M6ssbauer resolution E/A ~ 1.
As the magnetic moment of 109mAg is known only to 3%, no effort has been done in this case to attain the limit of the method. As LMR/ON is a resonant meth- od, the substitutional fraction does not effect its pre- cision.
References
[1] R. Coussement et al., Phys. Lett. 97A (1983) 301.
[2] R. Coussement, P. Put, G. Scheveneels and F. Hardeman, Hyp. Int., to be published.
[3] I. Berkes et al., Hyp. Int. 15/16 (1983) 233.
[4] H. Ernst, E. Hagn and E. Zech, Phys. Lett. 93A (1983) 357.
[5] G.M. Stinsow, A.R. Pierce, J.C. Waddington and R.G.
Summers-Gill, Can. J. Phys. 49 (1971) 906.
[61 E. van Walle, D. Vandeplassche, C. Nuytten, J. Wouters and L. Vanneste, Phys. Rev. B28 (1983) 1109.
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