MEASUREMENTS OF THE NUCLEAR HANLE-EFFECT ON 19F FOR COMBINED ELECTRIC AND MAGNETIC INTERACTION

(1)

HAL Id: jpa-00216835

https://hal.archives-ouvertes.fr/jpa-00216835

Submitted on 1 Jan 1976

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

MEASUREMENTS OF THE NUCLEAR

HANLE-EFFECT ON 19F FOR COMBINED

ELECTRIC AND MAGNETIC INTERACTION

W. Kreische, H. Niedrig, H. Pemsel, K. Reuter, K. Roth

To cite this version:

(2)

C7-496 JOURNAL DE PHYSIQUE Colloque C7, suppldment au no 12, Tome 37, De'cernbre 1976

MEASUREMENTS OF THE NUCLEAR HANLE-EFFECT

ON

"F

FOR COMBINED ELECTRIC AND

MAGNETIC INTERACTION

W. KREISCHE, H. NIEDRIG, H. PEMSEL, K. REUTER and K. ROTH

Physikalisches lnstitut der Universitat Erlangen-Niirnberg Erwin-Rommel-Strape l

D 8520 Erlangen, F R G

RBsumB. - Les mesures de l'effet nuclbire Hanle, i. e. de la dependance de la polarisation lineaire des rayons y par rapport A l'interaction hyperfine, ont et6 etendues ii des cas oh gradients de champ electrique statique et de champs magnktiques sont combines. Les experiences ont et6 ex&- cut& sur du BeFz et du CaFz avec une irradiation de 197 keV de l9F. Les resultats sont discutes et compares avec une theorie simple.

Abstract. - The measurements of the Nuclear Hanle-Effect (NHE), that means the dependance of the linear polarization of the y-radiation on the hyperfine interaction, were extended to cases with combined static electric field gradients and magnetic fields. The experiments were done on BeFz and CaFz with the 197 keV-radiation of l9F. The results are discussed and compared with a simple theory.

1 . Introduction.

-

First Nuclear Hanle-Effect (NHE) measurements have been performed some years ago [l, 21 with the investigation of the dependence of the linear polarization of y-radiation on the magnetic hyperfine interaction. In the absence of any perturba- tion fields, the LHC- and RHC-polarized components of the y-radiation from an aligned nuclear state inter- fere. This results in a time independent polarization distribution. If, however, a magnetic field is applied parallel to the direction of observation and perpendicular to the alignment axis (which was the beam axis in the above mentioned experiments), the frequencies of the LHC- and RHC-polarized components are no longer equal, resulting in a time dependent relative phase and polarization distribution, where the plane of polarization rotates around the direction of the magnetic field with a frequency, which is proportional to the energy difference of the interfering components. In a time integral measurement, the polarization is averaged over the time, weighted with the decay probability. For increasing rotation frequency, that means for increasing hyperfine splitting, the interference pattern tends to wash out in a time integral measurement and the polarization will vanish.

In this paper the theory of the NHE is extended to

such cases, where the static magnetic field is combined with an axial symmetric time independent electric field gradient parallel to the direction of the magnetic field. 2. Theory.

-

We consider a pure y-transition from an excited nuclear level ] 3,, b

>

to a level

J J,, c

>.

where the ensemble of the excited nuclei is described relative to a z-axis (in our case this will be the axis of the accelerator beam) by the population parameters P(b) of the magnetic sublevels

I

b

>.

If such a state

I

b

>

interacts with a static external magnetic field or a static axial symmetric electric field gradient, it is useful to choose the axis of quantiza- tion (2'-axis) parallel to the field direction, as in the 2'-system the interaction Hamiltonian is diagonal. In the general case the ensemble of the excited nuclei must be transformed from the z- to the .?-system and the radiation field from the 2'- to the z"-system, if the

direction of observation (z"-axis) does not coincide with the Y-axis.

The transformations were performed by the three dimensional rotation matrices a;;,(~) and a)if;,(~), where S and R stand for the tripe1 of the correspond-

ing Euler angles. The transition amplitude for y-quanta with the circular polarization q is given by [3] :

In this formula it is assumed, that the line width

r

is equal for all substates

I

b

>

and zero for the substates

I

c

>

(that means,

I

J,, c

>

is assumed to be the ground state of the nucleus). The observed intensities of the

(3)

MEASUREMENTS OF THE NUCLEAR HANLE EFFECT ON 19F C7-497

radiation polarized parallel (I,,) and perpendicular (I,) to the zz"-plane respectively are the absolute values of the amplitudes, weighted with the population parameters P(b) and averaged over all substates

I

c

>.

with

i

All,,(b, c) = - (AF1(b, c) T ~ " ( b , c))

.

4

With the usual definition of the linear polarization one gets :

where the following functions were used for abbreviation :

with

jmm'

Inn'

The function 8';;;; contains all informations about the concerning nuclear spins and the geometry of the problem, where the hyperfine interaction appears only in the interference terms.

If the direction of observation of the y-quanta coincides with the 2'-axis and is perpendicular to the z-axis, in eq. (1) all components of the rotation matrix 'B~,(R) with q # 4 1 vanish. For this special geometry of the NHE in eq. (3) the interference terms vanish in the denominator and the hard-coreterm in the numerator, so that the polarization can be written in the following form :

The factor P,;,; is different from zero only in the case, if

Because of the relation between the phase and the angle cp between the axis of the detector D,, and the 22"- plane

I!Jbfbj = (b;

-

b;) cp (8)

(4)

C7-498 W. KREISCHE, H. NIEDRIG, H. PEMSEL, K. REUTER AND K. ROTH

If there is a time dependent interaction which leads to a relaxation of the alignment, eq. (9) must be changed to

E,;

-

E,;

p =

C

e-'lT P,,;,; cos

A

t

( b i b ; )

where T is the relaxation time. The time integrated polarization is obtained by calculating the weighted average of eq. (10) :

This gives

-

'c*

P =

y

b; b; P,;,;

{

1 +[(E,;

-

~b;)/fi]' 2'' )-l where z* is the effective lifetime, defined by

1/2* = l/z

+

1 / T .

Considering a y-transition with 3, = 512 and 3, = 112 and a time independent interaction between the excited nucleus and a magnetic field combined with an axial symmetric electric field gradient parallel to the direction of the magnetic field, one gets for the hyperfine splitting

E,;

-

Eb! = 3(bi2 - bj2) haQ

+

(bi - b j ) haL (14) where wQ is the quadrupole frequency of the state

1

Jb, b

>,

defined by

and w, the Larmor frequency

with B being the applied magnetic field.

For the discussed geometry it turnes out, that the interferences between the substates b; = 112 and bi =

-

312 respectively b; =

-

112 and b; = 312 contribute to the polarization with the same weight and therefore one gets for the pure time independent interaction (2" = 2) :

-

2 2 - 1

Pc = p012

{

(1 +(WO

+

2 wL) 7 )

+

2 2 -1

+ ( l + ( w , - 2 w 3 ' c ) (17) where p, is a combination of population parameters obtained from ref. [l] :

eq. (17) represents a superposition of two Lorentzian shaped curves lying symmetric to B = 0, each with a maximum polarization of p,/2. For vanishing W,, that

means for pure magnetic interaction, one gets only one Lorentz curve centered at B = 0 with a maximum polarization of p, [l] :

If relaxation processes must be considered, the maximum polarization is damped by an additional factor

z * / ~ and the curve is broadened according to eq. (12) :

-

'c*

PM,R =

-

' P O / [ ~ 4- (2 OL 'c*)2]

.

'c (20)

Using a solid target for the NHE experiments, there may occur the case, that only a fraction X of excited nuclei sit on lattice sites with an electric field gradient and the rest will only see the external magnetic field. In this case the polarization should be written in the form

In all below described experiments there was used a usual Compton polarimeter [4] for the measurement of the linear polarization of the y-radiation. The ratio

computed with the numbers N , and NI, of the scattered

quanta detected in the detectors D, and Dll respectively is connected with the polarization of the radiation by

where R is the polarization sensitivity of the polarimeter.

3. Experiments.

-

The measurements were performed with the 197 keV radiation from the second excited state in 19F (J" = 5/2', 'c = 128.8 $- 1.5 ns,

(5)

MEASUREMENTS O F THE NUCLEAR HANLE EFFECT ON 19F C7-499

512'-level obtained from a Legendre-fit the linear polarization of the y-radiation could be determined according to eq. (18). This procedure was done with the measurement cited in [l], but in general it is useful to take p, as a fit parameter. One cause is, that the polarization sensitivity R of the used Compton polarimeter could not be determined exactly. Measu- rements of R at other energies than 197 keV for the same polarimeter [4] suggest a R = 10. The experimental setup was the same as described in ref. [2], where the external magnetic field was produced by an electromagnet with an axial hole in one pole cap, which performed simultaneously the entrance colli- mator for the polarimeter. A schematic drawing of the setup is given in figure 1.

FIG. 1. - Schematic drawing of the experimental set up. The angle was chosen to be v, = 0 for all measurements. The

magnetic field was applied perpendicular to the beam axis.

3.1 AQUEOUS B e F 2 - s 0 ~ u ~ 1 o ~ . - In order to avoid static electric field gradients at the ''F nuclei and relaxation of the alignment due to lattice vibrations, an aqueous solution of beryllium fluorine with a viscosity y = 0.035 poise was used as a target, which was separated from the accelerator vacuum by two Havar foils. The average target current of the 5.0 MeV proton beam was about 100 nA. As the viscosity of the target arose with the irradiation time, the solution was changed after each 30 minutes at the end of one measurement. The res,ult for the ratio r together with a X2-fit according to eq. (20) is shown in figure 2. We got a r , = 0.299 for the maximum asymmetry and an effective lifetime z * = 122.1 ns, which is only about 5

%

smaller than the lifetime of the 512'-level. From this values, together with R = 10 one gets for the maximum polarization following eq. (23) :

3.2 y-BeF,. - The measurements of the Nuclear Hanle-Effect with combined magnetic and electric interaction were performed at room temperature with a solid y-BeF, powder target and a proton beam of

FIG.. 2. - NHE-spectrum of the 197 keV radiation of l9F

obtained with a target, consisting of an aqueous BeFz-solution a t room temperature.

E, = 5.5 MeV. The average target current was about 30 nA. The result is shown in figure 3, where the theo- retical curve is a fit of the measurements according to eq. (21) with

X

= 0.79 and an electric field gradient due to eq. (15) of

V,, = (0.78

+

0.06) 10" V/cm2

.

(25)

FIG. 3.

-

NHE-spectrum of the 197 keV radiation of the probe nucleus 19F implanted in a lattice of y-BeF, via a (p, p')-reaction

with E, = 5.5 MeV.

(6)

C7-500 W. KREISCHE, H. NIEDRIG, H. PEMSEL. K. REUTER AND K. ROTH on interstitial sites in the lattice, which was determined

to have a hexagonal low quartz structure with the parameters

a, = 4.72

+

0.02

A

by diffuse X-ray scattering. From this analysis it was obtained, that after the irradiation of the target mate- rial the intensity of the (013)-peak was increased by a factor of three, whereas the other peaks have not been changed. This (013)-plane contains interstitial lattice sites, which should have a vanishing EFG.

3.3 CaF,. - For the measurements at a natural CaF,-crystal, this was mounted on a cool-finger, which was held at 77 K during the measurements. The total number of protons collected at the target was about 3 X 1016, obtained with a target current of

FIG. 4. - NHE-spectrum of 19F in a natural CaFz-crystal

at 77 K.

about 300 nA of the 5.5 MeV beam. The result is shown in figure 4 together with a fit due to eq. (21) with

X

= 0.21 and an EFG

V,, = (1.19

+

0.06) 101* V/cm2

.

₍₂₇₎

The maximum polarization obtained from the fit was

4. Discussion. - As expected, the measurement with the liquid target leads to a Lorentzian curve with a long relaxation time and an appreciable high maximum polarization. For solid BeF, the quadrupole splitting leads to a separation of the two Lorentzian shaped curves due to eq. (17). Because of the structure of this equation, the measurements are very sensitive to those nuclei, which see no EFG, because they emit y-quanta with a polarization equal to the maximum obtainable value in a zero magnetic field. The same results as in the case of a liquid target should be obtained with cubic CaF,, because there is no EFG arising from the lattice nor from the chemical bond and further there is no perceptible relaxation, which must be deduced from a time differential measurement of the perturbed angular distribution [7]. But in spite of this, the maximum polarization in the case of CaF, is smaller than for the liquid by about 23

%,

which may be due to a perturba- tion in the solid after the recoil of the probe nucleus with a relaxation time less than a few nanoseconds or to a very strong static EFG, which cannot be detected in the experiments. This loss of alignment in in beam

experiments is well known, but not yet understood. Sugimoto [S] found, that in the case of K F the alignment of the 19F nuclei in the region of early time was about 60

%

of the theoretical value. The other point of interest in the CaF, measurements is the occurence of a static EFG at the 19F nucleus. This may arise from fluorine atoms forming V,-centers. The magnitude of the EFG due to the F-F-bond in a F;-molecule was estimated as V,, = 1.185 X 10'' V/cm2, being half of the value obtained for the F,-molecule following the empirical rule of Townes and Dailey [9], using the Barnes and Smith value [l01 of

<

r - 3

>

for the p electron. Preliminary measurements of the NHE in CaF, crystals show, that the satellites in the spectra due to quadrupole interaction are shifted to smaller magnetic fields for increasing temperatures. For more detailled investigations, measurements of the time differential Nuclear Hanle-Effect at various temperatures are in progress.

References

[l] HEUSINGER, R., KREISCHE, W., LAMPERT, W., REUTER, K., [6] RICHTER, F. W. and WIEGANDT, D., 2. Phys. 217 (1968) ROTH, K. and THOMAS, K., Phys. Rev. Lett. 31 (1973) 225.

899. _{[7] HEUBES,}_{P., JOHANN,}_{H. G., KLINGER,}_W.,_KREISCHE,_W.,

[2] HEUSINGER, R., KREISCHE, W., LAMPERT, W., REUTER, K., LAMPERT, W., LOEFFLER, W., SCHATZ, G. and WITT- Rom, K. and THOMAS, K., Phys. Lett. 49B (1974) HUHN, W., Nucl. Phys. A 188 (1972) 417.

269. _{[8] SUGIMOTO,}_{K., MIZOBUCHI,}_{A. and NAKAI}_K.,_{Phys. Rev.}

131 ROSE, H. J. and BRINK, D. M., Rev. Mod. Phys. 39 (1967) B 134 (1964) 539.

306. _{[g] DAS, T. P. and HAHN,}_{E. L., Sol.}_{Stat. Phys. Suppl. 1}₍₁₉₅₈₎

[4] KREISCHE, W., Nucl. Inst. Meth. 128 (1975) 261. 119.

(7)

W. KREISCHE, H. NIEDRIG, H. PEMSEL, K. REUTER AND K. ROTH

DISCUSSION

H. ACKERMANN. - In BeF, you concluded that before and after the experiment showed, that the (0 13)- the 20 %-part of the "F* nuclei which do not feel a peak after the irradiation was increased by a factor of quadrupole interaction are situated on a special intersti- about 3 whereas the other peaks have not been changed. tial site. By which arguments you defined this lattice _{This (0 13)-plane contains interstitial lattice sites with} position ? _{a high symmetry which should be influenced by a}