Spin-dependent scattering and absorption of thermal neutrons on dynamically polarized nuclei

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Spin-dependent scattering and absorption of thermal neutrons on dynamically polarized nuclei

H. Glättli, J. Coustham

To cite this version:

H. Glättli, J. Coustham. Spin-dependent scattering and absorption of thermal neu- trons on dynamically polarized nuclei. Journal de Physique, 1983, 44 (8), pp.957-965.

�10.1051/jphys:01983004408095700�. �jpa-00209679�

Spin-dependent scattering ^and absorption ^{of thermal neutrons}

on dynamically polarized ^nuclei

H. Glättli and J. Coustham

I.R.F., Service de Physique ^{du Solide et} de Résonance Magnétique, CEN-Saclay, 91191 Gif-sur-Yvette Cedex, ^France (Reçu ^{le 10 mars} 1983, accepté le 22 avril 1983)

Résumé.

La polarisation dynamique nucléaire ainsi _que le concept ^de température ^de spin ^de réservoirs d’énergie

Zeeman sont utilisés _pour obtenir des longueurs de diffusion dépendant ^du spin bN d’isotopes différents, présents

dans la même cible. Une généralisation simple permet ^{de montrer la} possibilité ^de mesurer bN même pour des noyaux invisibles par résonance magnétique nucléaire. On montre aussi comment on peut obtenir des rapports précis de bN pour différents isotopes ^{ou des} rapports de diffusion et d’absorption pour le même isotope. ^{On donne}

des valeurs numériques ^de bN pour 13C, 35Cl, 79Br, 81Br ainsi que des limites supérieures pour 31P, ^{37Cl et 41K.}

Abstract.

Dynamic ^nuclear polarization ^{and the} spin-temperature concept of nuclear Zeeman reservoirs are

systematically ^{used to obtain} spin-dependent scattering lengths bN ^of separate isotopes ^{in the same} target ^A simple generalization shows the way ^to measure bN for nuclei invisible by ^nuclear magnetic resonance. It shows also how to obtain precise ^ratios of bN for different isotopes ^{or of} spin-dependent absorption ^and scattering ^{of the same} isotope.

Values of bN ^are given for 13C, 35Cl, 79Br, 81Br ^{as well as} upper limits for 31P, 37Cl ^{and 41K.}

Classification Physics ^Abstracts

24.70

76.60

1. Introduction.

In the past years, polarized ^{neutrons and} polarized

nuclei have been used to measure spin-dependent scattering lengths ^and absorption ^cross sections of slow (S-wave) ^{neutrons on nuclei. In order to obtain}

those scattering lengths, ^a molecular beam type experiment ^{has been set} up, where the Larmor _pre- cession angle ^{of the neutrons inside a} target ^{can be} measured as a function of nuclear polarization [1].

Such an experiment has been described in simple

terms using ^the concept ^of pseudo-magnetism. ^Since

this experiment ^{needs a} monochromatic, polarized

neutron beam, ^a straight transmission measurement on the same samples ^also gives ^a measurement of the

spin-dependent absorption ^for neutrons at the wave-

length ^used (A ^{= 1.07} A).

We briefly recall here the definitions of the relevant parameters for the interaction neutron-nucleus. A review of the different aspects ^of pseudo-magnetism

can be found in reference [2]. ^The scattering ^{of an}

S-wave neutron (spin ^{S =} 1/2) ^{on a nucleus} (spin l)

can be described by ^two scattering lengths, b+ ^{and b _,} corresponding ^{to the two} spin ^channels J,

^{I +} 1/2.

It is convenient to express the scattering length ⁱⁿ

operator ^form

where bo ^{is the} spin-independent part, ^{well known} in slow neutron scattering ^{work as} the coherent

scattering length. ^The spin-dependent part

is responsible for the so-called spin-incoherence since, ^{in most of those} experiments, the nuclei are not

polarized.

If the nuclei have a polarization ^P = I z )/I, they produce, inside the target, ^a field H * as first

proposed by Baryshevski ^and Podgoretski [4] ^which

we call pseudo-magnetic ^field

where the sum is over the different nuclei, ^{of number} density Ni. ^The pseudo-magnetic ^moments y* ^are

related to the scattering lengths by

where gn ^{= -} 1.913 is the neutron magnetic ^moment

in units of nuclear magnetons ^and ro ⁼ 2.817 ^x 10-13 cm is the classical radius of the electron. The two brackets in equation (3) being ^{close to} unity, p*

can be of the order of the Bohr magneton JlB ^and

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01983004408095700

958

hence M* comparable ^to electronic magnetizations, provided the nuclear polarization ^{is large.}

The pseudo-magnetic ^{field H * causes the neutron} spins ^to precess inside the target ^The precession angle

Aa is given by

where yn ^{= - 2 n.2 917} (s G)-’ ^{is the} gyromagnetic

ratio of the neutron. If there are several polarized

nuclear species ^{in the sample, the} precession angles

add algebraically. ^{Their sum can} be measured with great accuracy by ^a beam method which has been described in the past [1-3] ^and which is the extension of standard molecular beam techniques ^{to neu-}

trons [8]. ^{We remind here} only briefly ^the gist ^{of the}

method :

Inside a homogeneous magnetic ^field Ho, a ^neutron beam, initially polarized along Ho, ^{is made to} precess at its Larmor frequency COL

Yn Ho. This is achieved

by ^{a first rf coil,} which is tuned at resonance (wrf

wL) ^and produces ^{a field} Hi such that the neutron

polarization, ^on leaving ^the coil, ^is transverse to Ho (900 pulse). ^{At some distance} L, ^a second, identical, ^rf coil is then used to rotate the polarization ^{of the}

neutrons by another 900. If Ho ^is perfectly homoge-

neous, if we are exactly ^{at resonance and if there}

is no phase difference between the two rf coils, ^the

neutron polarization ^{is found} antiparallel ^to Ho

after the second coil. The neutron precession ^{due to a} pseudo-magnetic ^field acting between the coils induces

a phase ^{shift Aa and the neutron} polarization ^{is no} longer ⁱⁿ phase with the rf field in the second coil.

The 900 pulse ^is only ^{effective on the} in-phase ^com-

ponent ^{and the} resulting polarisation along Ho, Pz,

measured by ^an analyser ^after the second coil, ^is simply Pz

^{cos Aa.}

In the foregoing, ^the scattering length ^{has been}

assumed to be real. Strictly speaking ^{b is} complex.

The imaginary part ^{b" accounts for all} absorption

processes. If a’ is the absorption ^{cross section, the} optical ^theorem gives

b" b for almost all nuclei, ^{since £ = 1} A, ^{b N}

10-12 cm and ac 10-22 cm2 in the cases where a

measurement of bN by ^{our method is} possible.

We have, therefore, ^{two almost} mutually ^exclusive

cases :

1) a’ 10-22 cm 2 : it is experimentally ^{feasible to}

measure p* (no absorption) ^{and b = Re} (b) ^{to a} very

good approximation.

2) a, Z 10-22 cm2 : a transmission experiment

can give _Qpol, ^the polarization ^{cross section or} spin dependent part ^{of the neutron} transmission.

The polarization ^cross section is defined by

where _p is the neutron polarization and cO ^{the cross}

section for unpolarized ^neutrons. (Note that in this definition QT ^still depends ^{on the nuclear} polarization

of the target) Gpol is related to the measured flipping

ratio R

1+ /1- i.e. the ratio of transmitted neutron intensities with incoming polarizations ^{± p,} by

From the experimentally determined up,,, ^{one would} like to obtain J2, ^{i.e. the} capture ^cross section for thermal neutrons in the two spin ^{channels J =}

I ± 1/2. ^The problem ^{is to} distinguish ^the capture from all other _processes which take a neutron out of the transmitted beam. Inelastic scattering ^{can be} neglected

at the low temperature ^{and with the} precision ^{we are} working ^at A clearcut case is then encountered when

Bragg scattering ^{can also be} neglected. This is the

case for suitably ^oriented single crystals ^{or for neutron} wavelengths above cutoff Under these assumptions,

we have

In the opposite case, polycrystalline samples ^and

neutron wavelengths ^{far below} cutoff, ^an integration

over the Bragg scattering gives

In most cases, the flipping ratio will be close to

unity ^{and we can} expand

It is thus possible ^{to obtain in our} set-up experi- mentally ^either spin-dependent scattering length ^or absorption (or ⁱⁿ favourable cases even both) pro- vided the main experimental problems ^{have been} solved, ^{which are the} production ^{and the} measurement of the nuclear polarization. ^These problems ^{will be}

discussed in detail in section 2. Part of the ideas

presented there have already ^been applied ^{to the}

measurement of both spin-dependent capture ^and scattering ^{of 6Li} [5].

Section 3 gives ^some experimental ^{results obtained}

on KCI, KBr, Ca3(P04)2 ^and BaC03. ^These examples, although quite different from one another, ^exhibit

a certain number of characteristic features which should be common to a large ^class of substances.

Together with ^CaO [3] ^these examples ^also show, how dynamic polarization ^{can be} generally appli-

cable. In most of these samples, sufficient polarization

has been obtained, ^without lengthy optimization ^{of all}

parameters pertinent ^to dynamic polarization, ^{at the}

external conditions of - 100 mK and 2.5 tesla.

2. Dynamic ^nuclear polarization : production ^and

measurement

2.1 PRODUCTION.

Measurements of p* ^{on metallic} samples containing ^one single isotope ^{with non-zero} spin ^are straightforward by ^use of « brute force »

polarization ^{at low} temperature. Results have been

reported ^{for most feasible cases} [1]. ^{Here we are} only

concerned with dynamic ^nuclear polarization (DNP).

This method works quite generally in insulators ’

containing ^{a small amount} (= ¹⁰¹⁹ cm-3) ^of para-

magnetic impurities like transition metal ions, ^lattice

defects or free radicals. Details can be found in refe-

rence [6]. ^The principle of the method is to « cool » the

spin-spin interaction reservoir of the impurities ^desi- gnated ^{in the} following by its Hamiltonian operator JeNz. This is achieved by microwave irradiation close to the paramagnetic ^resonance (EPR) line. It has been shown that there is an efficient thermal contact

between HNZ and the nuclear Zeeman reservoirs

3Cz, ^{in the} sample. ^{As a} consequence, the spin tempe-,

rature of the nuclei _may become much lower than the lattice temperature. This leads to high ^nuclear pola-

rization of positive ^or negative sign, dependent ^on

whether the microwave irradiation takes place ^below

or above the EPR line. The scheme works best with

strongly polarized impurities and when the frequency spectrum ^of JeNz ^{is not too} different from 3Czl. ^This implies ^{the use of low} temperatures ( ¹ K) ^and high

fields (Z 2.5 T). Quantitative predictions ^{of the}

attainable polarizations ^{in a} given sample ^{are in} general impossible ^{due to the} basically ill-controlled and badly ^known paramagnetic impurity system.

We have found, however, that, ^under the external conditions used in our set-up, (i.e. T ^{0.2 K and} H ⁼ 2.5 T) ^{DNP works} always ^{unless one of the} following adverse conditions occurs :

-

Width of the EPR line > 100 MHz (e.g. ^F-

centres in KI).

-

Spin-lattice relaxation of the nuclei bypassed by ^{a mechanism} independent ^{of the} paramagnetic impurities (e.g. H2, CH4).

In the samples reported here, much lower spin

temperatures have been reached than those feasible

by ^« brute force » cooling. ^{As in the latter,} all the nuclei present ^{in the} sample ^{will be} polarized after micro-

wave irradiation. They may, however, ^not necessarily

have the same spin temperature, ^{since the} coupling

between JeZI ^and XNZ may be different for different

species.

Once the dynamic polarization achieved, ^{the micro-}

waves are shut off. Around 0.1 K, the thermal contacts of the different HZI amongst ^them (mixing) ^{or with the}

lattice (relaxation) ^{are then} very small and it is possible

to saturate selectively ^a single ^nuclear species ⁱ by radiofrequency irradiation at the NMR frequency

and thus to reduce its polarization ^{to zero in a time}

short compared ^to relaxation (T1) ^and mixing ^times (’tmix). ^{If both are also} long compared ^{to the time}

needed to measure a(0) ^the precession angle ^{of the}

neutrons after saturation is then

where a(Px) ^{is the} precession angle before saturation.

Equation (10) yields pi through equation (4).

The procedure ^{can be} repeated for each nuclear

species ^{in the} sample. ^The only condition, ^besides

,

long im;x, is sufficient separation ^{of the NMR fre-} quencies for the different isotopes. ^{In our} field of 2.5 T this is generally ^{the case with one} possible exception,

i.e. 47 Ti and 49Ti. This possibility ^to separate ^the pseudo-magnetic fields from different nuclei gives ^the DNP, besides its higher polarization, ^{two distinct} advantages ^over the « brute force » method : it obviates the need for costly isotope separation ^{and it is}

insensitive to the everpresent hydrogen ^contamina-

tion.

The difficult problem ^{is then not to obtain} high enough ^nuclear polarization, ^{nor to measure the}

different precession angles selectively. ^In most cases, the crucial problem ^{will be the} knowledge ^{of the}

nuclear polarization.

2.2 MEASUREMIENT. - In general, ^nuclear polariza-

tions can be measured by ^{standard NMR} absorption techniques. ^The integrated ^NMR absorption signal, Sx, is related to the nuclear polarization Px by

V ⁼ al is the volume of the cylindrical sample ^of

section a and length ^l. Ca ^{is an} experimental ^constant, dependent ^on geometry (filling factors) ^and Q-factor

of the NMR coil, rf level and frequency, gain ^{of the} amplifiers ^{as well as} integration ^{time constant} (for analog integration) ^or step (in ^{case of} digital integra- tion). ^{It is difficult to know} C. a priori, but it is _easy to keep ^{it constant} throughout ^a given experiment.

Cx depends ^{on the} way the absorption line is recorded.

A frequency sweep gives Cx

y2x Ix ^{while for a field}

sweep Cx = Yx Ix.

In order to treat the three different cases below, ^we only ^need equation (11) ^and equation (4), ^{rewritten as}

where d, = (4 Tcyj (1/v) depends only ^{on the neutron} velocity.

1) ^The simplest ^{case occurs when a thermal} equili-

brium signal 82 ^{for the} given ^{nucleus can be obtained}

From the measured lattice temperature TL, ^{we know} Pfl. TL ^is usually between 0.5 K and 4 K, ^a compro- mise between short enough T1 ^{and a} strong enough signal. ^{In this} case, the polarization ^is simply given by

where E is the so-called enhancement of the NMR

signal ^{due to the} dynamic polarization. ^{For small}

polarizations (constant ^{NMR line} shape) ^{E can be}

960

obtained more conveniently ^from absorption ^or absorption derivative amplitudes. ^The pseudo-ma- gnetic ^{moment is then}

2) It may happen that the thermal equilibrium signal S ° is invisible (long T, ^weak signal). However, ^one

may often see the much stronger polarized signal Sx.

jMj* ^{can then be obtained if, in the same} sample, ^there happens ^to be another nuclear species y ^{with known} polarization Py ^{and a signal} Sy ^{visible at the same} frequency ^as Sx.

a) Py ^{may be known as in 1), via} the thermal equi-

librium signal Syo, ^i.e. Py

Ey Pyo. ^From the measured ratio

one obtains

Through ^{the ratio} (Sy/S,J at constant frequency, ^we

have here replaced ^the knowledge ^of Nx Px by ^the

measurement of Ny Py ^{on a} different nucleus in the

sample.

b) ^There may ^not be any thermal equilibrium signal

visible in the sample. ^A possible way ^out is then to infer Py from its measured contribution to the neutron

precession, å(XY’ ^provided pg ^{is known.} Equation (11)

and equation (12) yield ^then

Equation (17) ^{shows a} way ^{to measure} ratios of _pseu-

do-magnetic ^moments by measuring ^two phase ^shifts

and two polarized ^NMR absorption lines. Such measurements can be more precise than those des- cribed in 1) ^and 2a) ^{since neither a} generally ^{weak and}

thus noisy ^thermal equilibrium signal, ^{nor a know-} ledge ^of sample length, density, isotopic ^{abundance or}

neutron wavelength ^{is needed}

3) ^{Just for} completeness. ^{and even if it has not} yet been applied ⁱⁿ practice, ^a last scheme _may be _pro-

posed Suppose ^{there is no NMR} signal Sx visible,

not even the polarized, but there is a measurable

phase ^shift Aa.,. Suppose again ^{that we have in the} sample ^{a second nuclear} species ^with phase ^shift åcxy.

It must then be ascertained that there exists a spin

temperature ^{common to the x} and y species. ^This

can in principle ^{be done} by measuring ^the mixing

time by ^means of the time dependence ^{of the neutron} precession. If there is a common spin temperature

for not too high polarizations (high temperature

approximation) ^and

It can be seen from (18) ^{that a} knowledge ^{of the} pola-

rization Py ^{is in this case} useless. The ratios (Nx/Ny)

and (Aa.x/Aa.y) ^at equal spin temperatures give ^the

ratio of the pseudo-magnetic ^{moments. This is} again ^a

relative measurement, which is intrinsically precise.

A common spin temperature ^{needs short} mixing

times while separate measurements of Aoc need long

Lmix. The ^two requirements ^are contradictory only

in appearance, since -rmi. during polarization ^is usually much shorter than the mixing ^{time in the}

absence of microwave irradiation.

It might ^be pointed ^{out here that the} proposed

measurements use simply the fact that there is, ^besides

the NMR signal, ^a second linear relation between an

observable (the ^neutron precession angle) ^{and the}

nuclear polarization. ^From equation (9b) it is clear that the transmission flipping ^{ratio R} is another _pos- sible measurement. Many ^{of the above} experiments

can then be generalized by replacing essentially pi by aip., ^{and Aa; by ARi. In} particular, if Aa and AR

are measured on the same isotope, ^{where there obvious-} ly ^{cannot be} any problem ^about spin temperature, ^a precise ^{ratio of} pseudo-magnetic ^{moment and} polari-

zation cross section can be obtained However, ^as already stated, ^{this is} only possible ^{for a limited} range, where O’pol ^is large enough ^to be measured and small

enough ^{not to} preclude ^the precession measurement.

3. Results,

Cl.

^KCI has been chosen as the host material for measurements on the Cl isotopes since it combines several advantages :

a) ^{it has a cubic} crystal structure. This is important

for isotopes ^with spin ^I > 1/2 ^{since an} electric field

gradient splits ^{the NMR line in 2 1 + 1} components.

The splitting ^is dependent ^on the direction of the

crystal ^{axes with} respect ^{to the} magnetic ^{held This} splitting presents ^an unnecessary complication ^for single crystals ^{and even} precludes ^the observation of the NMR line for polycrystalline samples ^{in most}

cases. Even for a cubic crystal, ^lattice imperfections

result in noncubic crystal fields for a non negligible part of the nuclei and care has to be taken to account for these ^« abnormal » nuclei which are invisible by

NMR but perfectly ^seen by ^neutrons.

b) ^{KCI is} readily ^{available as} single crystals. ^{Due to}

its cubic structure, single crystals ^{are no} necessity ^for

the observation ^of the NMR line. It makes it conve-

nient, however, ^to obtain bulk samples of well known

dimension and density.

c) ^The production ^and properties ^of paramagnetic

colour centres in KCI are well known. In particular,

isolated F-centres, ^created by ^additive colouring ⁱⁿ

pure KCI, ^are weakly coupled ^to the lattice. Their

spin-lattice relaxation time is _very long ^and they ^are, therefore, ^not very efficient for dynamic polarization.

As a consequence, rather than additive colouring,

we used the next easiest method to obtain the _para-

magnetic centres, i.e. y-irradiation ^{at 77 K} using ^a 6oCo _y-source. The EPR spectrum observed ^{at 9 GHz} and 77 K, shows, ^{besides a} _strong ^F-centre signal,

a great ^number (> 20) ^{of narrow lines} spreading

over 800 G. Three samples have been used in our

measurements, with irradiation doses of 20, ^{38 and}

57 Mrad. No systematic study ^{of EPR} signal, polariza-

tion or relaxation times as a function of radiation doses have been made. All three samples ^{seemed to} polarize equally ^well (10-15 % ^for 3SCI) ^{and there are indica-}

tions that the characteristic times are not propor- tional to the radiation doses.

KCI contains four different isotopes, 3sCI, 3’Cl,

39K and 41K. It turned out that the pseudo-magnetic

field was almost entirely ^{due to 35CL This} opened interesting possibilities for the simultaneous study ^of

different nuclear magnetizations, e.g. 3sCI vs. 37Cl or

« abnormal » versus « normal » 35 CL

After saturating ^{all nuclear} species, ^{the neutron} precession angle ^{did not} get ^{back to} the initial value before polarizing. This indicated ^a remaining pseu-

do-magnetic ^{field arising from} incompletely ^saturated

« abnormal» 35Cl. A similar effect has already ^been

observed on 170 in CaO [3]. Care had thus to be taken to saturate by sweeping ^{the rf} frequency ^far beyond the visible absorption ^{line to} obtain the full

phase shift due to the total 35Cl magnetization.

Simultaneous observation of the 3sCI NMR and of the neutron precession ^then gave ^{a measure} of the

spectral diffusion time id;ff for the nuclear magneti-

zation from the « abnormal » to the « normal » nuclei. id;ff ^was several hours at 1 K in the absence of microwave irradiation. During polarization, ^{and with}

the He-bath at - 200 mK, Tdiff shortened to - 30 min.

This is short compared ^{to the} polarization ^times,

which were of the order of one day. This fact is impor-

tant, ^{since it assures that the «} abnormal » nuclei have the same polarization ^as that measured by ^NMR

on the « normal » 3sCI and hence to the total pola-

rization seen by the neutrons, ^at least after _many hours of microwave irradiation.

Monitoring ^{the 37CI NMR} signal ^{and the neutron} precession proved ^{to be a} convenient means of follow-

ing simultaneously ^{the 35CI and the 37CI} magnetiza-

tion during dynamic polarization. ^{The ratio} P(3sCI)j P(3’Cl) ^{was seen to be a} function of time, indicating

that there is no common spin temperature ^{in these} samples. ^The mixing time between the 35Cl and 3’Cl Zeeman reservoirs ^was found to be 10 hours during polarization, ^i.e. comparable ^{to the} polarization time,

and of the order of T1 (50 ^{h at 1} K) without microwave

irradiation. ^Similar mixing times have been measured between 35Cl and 39K. It is thus not surprising ^{that no}

common spin temperature has been achieved.

The enormous precession angle ^{due to the 3sCI}

nuclei (up ^{to 500} deg.) leaves the polarization ^measure-

ment as the only limiting factor for the _accuracy of

our results on p,*. ^The average value, obtained from the three samples, ^is

or

The sizeable absorption cross-section ar’o ^{of 35CI} encouraged ^{us to measure the} flipping ^{ratio as a}

function of polarization ^{in a} transmission experiment

A typical ^run is shown in figure ^{1. The} slope ^{of the} straight ^line gives _6pol according ^to equation (7). ^The straight ^{line in} figure ^{1 does not} go through ^{zero. We}

do not have a satisfactory explanation ^{for this} peculiar fact 37Cl and 39K did not give any measurable contri- bution to R, ^{even at the} highest polarizations, ^indicat- ing ^that _O’pol ^is entirely ^{due to 35Cl.}

The _average value of the three samples ^was

the precision being again ^limited by ^the polarization

measurement. The relative value of scattering length

and absorption ^has been measured at a constant

polarization, leading ^{to the ratio}

Since for our wavelength (A ^{= 1.07} A) and the KCI oriented along (001), ^{we are} very close to a number of intense Bragg reflections, ^{we can not use} equa-

Fig. ^1.

Flipping ratio of transmitted neutron beam

through ^{KCI as a} function of 35CI polarization.

962

tion (6) to extract information on u: - Jy ^{from the} measured apol*

In fact, equation (6) ^would give a’ - a-

^{58.2 b.}

It follows that the absorption cross-section for _unpo- larized nuclei

This is in disagreement with the measured value

co ^{= 24 b. The} opposite assumption, ^an average ^over all Bragg reflections in a powder, gives through equation (7)

and with Jf ^{= 24 b ;}

All one can say, then, ^{from our} result is that

a’ / a,,- > ^{3. A} measurement at a different wavelength

is planned ^{to obtain more} information. No detectable neutron precession ^{due to} the "Cl has been observed

knowing ^the polarization ^{of 37CI} (by comparing ^its

NMR signal at constant frequency with that of 35CI)

and taking ^{into account the} sensitivity ^{of our} apparatus

to measure the neutron phase shift, ^an upper limit can

be given ^{for the} pseudomagnetic ^{moment It is}

or

Note that the spin-dependent scattering ^{of 35CI is}

very strong, while that of 37CI is weak. In neutron diffraction experiments, ^{this fact can} give ^the possibi- lity ^to adjust the « incoherent » scattering through isotopic enrichment Such a procedure is often used in substances containing hydrogen (H ^versus D).

Similarly, ^no precession ^{due to 41 K has been}

observed. Its polarization ^{has not been} measured, ^but

if we make the reasonable assumption ^{that the} spin temperature ^of 41 K after a long polarizing ^{time is}

close to that of 37 CI, ^{we can still} give ^an upper limit

or

It is then possible ^to confirm the value of /.t* given

for 39K in reference [1], which has been measured in the metal with natural isotopic abundance. Including

the possible ^{error due to} 41 K, ^{we obtain}

and

A separate measurement of Jl*(39K) in KCI has been

made. It is consistent with the more precise ^value

obtained in the metal.

Br.

^{Many of the} problems regarding ^the produc-

tion and the measurement of the polarization ^{for 79Br}

and 81 Br are expected ^to be similar to Cl. This lead

us to the choice of KBr as a substance similar to KCI.

Irradiation of KBr by y-rays ^at 77 K (dose ³⁵ Mrad.) produced enough ^{colour centres for} dynamic pola-

rization. Considerably ^lower polarizations ^were

obtained than for KCI, of the order of 2 % ^{after one} day ^{of microwave} irradiation. This _may be due to the

larger width of the F-centre resonance. Since the

polarization ^was large enough ^{to measure} p* ^{for both} isotopes, ^no attempt ^{was made to} improve ^its

The T 1 of 81 Br ^{was found to be 10 h at 1.8 K. The} mixing time "Br -+ 79Br has not been measured. It is very long, ^even during microwave irradiation. This has been observed in a particular experiment : halfway through ^the polarization, ^{we started to} monitor the

’9Br signal ^{with an rf level} high enough ^to partially

saturate the ’9Br resonance. The ’9Br polarization

decreased to half of its initial value in 12 h, ^{while the} 81 Br polarization ^{continued to} increase, seemingly unperturbed Here, ^{the neutron} precession ^{cannot be}

used as in KCI to monitor the polarization. ^{The total} phase ^{shift is} very small since the two Br isotopes ^have pseudo-magnetic ^{moments of} comparably ^small magnitude ^and opposite signs ^{the small} difference being

almost exactly ^cancelled by ^{the 39K} phase ^shift during polarization. ^A typical ^run of selective satura- tion is shown in figure 2, ^{and the} phase ^{shift as a}

function of polarization for different runs is shown in

figure ^{3 for 79Br and in} figure ^{4 for 8’Br. The} resulting

Fig. ^2.

^Neutron precession angle change ^{due to 79Br and} 81 Br polarization ^{in KBr.}

Fig. ^3.

^Neutron phase ^{shift as a} function of 79Br polari-

zation.

Fig. ^4.

^Neutron phase ^{shift as a function} of 81 Br polari.

zation.

pseudo-magnetic moments, including ^an estimate of the possible systematic errors, ^are

and

This gives

Due to the smallness of both the absorption ^{and the}

achieved polarization, ^no spin-dependent transmission could be observed.

The 31 P has a spin 1/2, ^{is 100} % abundant and has a

large magnetic ^{moment There is,} therefore, ^no pro- blem to observe a thermal equilibrium signal ⁱⁿ any

compound. ^{We chose} Ca3(P04)2 ^{because it does not}

contain _any other nuclear spins (except ^{for the} very small concentrations of 43Ca and "0) ^{and because it}

is readily available and _easy to handle.

In molecular solids, y-irradiation produces ^free

radicals which are often stable at 78 K. This holds true for Ca3(P04)2. An irradiation dose of 20 Mrad.

(60CO y-rays) gives ^two strong ^{EPR lines} (as ^observed

at 9 GHz and 78 K). One, at g

2, ^{resembles an} imperfectly split doublet of 15 G width and 20 G

separation. The other looks like the powder pattern

arising ^{from an} axially inhomogeneous g-tensor. ^{It is} 90 G below, i.e. g > - ^2.06 (Fig. 5a).

It is not easy ^to get ^bulk samples of Ca3(P04)2. ^We, therefore, used circular cylinders ^of compressed powder, with known weight ^and cross-section, ^to determine Nl. The density ^{achieved was} of the order of 60 % of the bulk.

For such powder samples, cooling ^{is much more} efficient, but, ^{on the other} hand, most neutrons are

absorbed due to the penetration ^{of 3He. For a} typical sample, ^{of 1 cm} length, the dilute phase penetrating

into the powder corresponds ^{to 0.24 mm of} pure 3 He,

even at the lowest temperatures, absorbing ^{73 % of}

the neutrons. If the microwave _power exceeds a certain

threshold, ^the sample suddenly ^heats up far above 1 K.

It becomes transparent to neutrons indicating ^{a loss}

JOURNAL DE PHYSIQUE.

T. 44, No 8, AOUT 1983

Fig. ^5.

^EPR spectrum ⁱⁿ y-irradiated samples ^{at 9 GHz}

and 78 K : a) Ca3(P04)2 ; b) Ba 13 C03-

of coolant inside the powder. ^This happens ^much

before the heat load on the dilution refrigerator

becomes noticeable.

A 31 P polarization ^of only ^1.6 % ^was obtained. This value _may be due to the high impurity ^{content of the} Ca3(PO4)2. ^{A non} irradiated sample ^{from the same}

batch of powder ^{had a} T1 ^{of a} few minutes only ^at

1 K. It _may be pointed ^{out that a} polarization ^{of 1.6} %,

achieved under these unfavourable circumstances, still corresponds ^{to a} spin temperature ^{of 60 mK.}

No neutron phase ^shift dependent ^{on 31 P} polarization

was observed. An _upper limit for the pseudomagnetic

moment of 31 P can then be given

or

It _may be noted here that our sample ^of Ca3(PO4)2

is an interesting illustration of the insensitivity ^{of our}

method to hydrogen contamination. In fact, ^{a measu-} rable phase shift has been detected due to hydrogen impurities ^{in our} compound (Fig. 6a). ^{The two cha-}

racteristic EPR lines, split by ⁵⁰⁰ gauss (Fig. 5a),

show that _presence also. But despite ^these impurities,

the neutron phase ^{shift due to 31P} would have been

seen as a step, ^at the time of rf saturation, in the conti- nuous, slow evolution given by ^the relaxing hydrogen.

This will be seen clearly ^{below for 13C.}

13C, - The result of bN ^{for 13C has} already ^been published [1]. ^{A few} interesting features may justify

a more detailed description ^{than that} given in reference

[1] : ^a powder sample ^of Ba13C03, ^{enriched to 91.3} % of 13C was used. As for the phosphate, y-irradiation

63

964

Fig. ^6.

^Neutron precession angle ^{as a} function of time after DNP : a) ⁱⁿ Ca3(PO4)2; b) Ba13C03.

(20 ^{Mrad. at 78} K) created free radicals. The EPR

spectrum ^{shows an} intense line with a hardly ^visible

doublet splitting, ^{which can be} tentatively identified as

C03 (Fig. 5b).

The polarization ^{as a} function of microwave fre- quency follows ^an asymmetric pattern. ^The region ^of positive polarization is broad and flat, ^{with the} opti- mum (P+ ^{= 10} %) ^{at 350 MHz below the centre of the} EPR-line, ^{while the} negative part ^is narrow, 170 ^MHz above the centre, with ^an optimum ^{of P}

¹⁵ %).

A large (200 degrees) phase ^{shift was} observed, independent ^{on 13C} polarization. ^It originates ^from hydrogen impurities. They ^{must have been in micro-} scopically ^{close contact} with the bulk BaC03, ^since they polarized ^{at the same field as the} 13C, ^i.e. they

either used the same paramagnetic impurities ^for

DNP or they ^were coupled ^{to the 13C} polarization through ^some spin-spin process. Selective saturation

Fig. ^7.

^Neutron phase ^{shift as a} function of 13C polariza-

tion.

still allowed to measure the phase ^{shift due to 13C} separately, ^{as shown in} figure ^6b.

The result, averaged ^over many ^runs (Fig. 7), ^is

or

13C, along with 170, ^{are two} of the few nuclei, ^where reasonably reliable theoretical estimates, ^{based on} shell-model calculations, ^exist [7]. ^{In both cases, the} experimental value is in quite good agreement. ^This may indicate that more calculations along these lines should not be completely ^worthless.

4. Conclusion.

To our knowledge, all the nuclei described in this paper have been polarized for the first time, _except 13C. The substances and paramagnetic impurities

used have been the first choice from an educated _guess and not the result of a lengthy optimization ^of samples.

Moreover the results reported here and summarized in table I contain all our attempts except ^{for two} unsuccessful ones : 12’I in y-irradiated ^{KI did not} polarize ^{at all, and 29Si in} phosphorous doped ^Si polarized ^so slowly that it would have taken ^unreaso-

nably long ^{to achieve a sizeable} polarization.

Table I.

Spin-dependent scattering lengths of ^some isotopes, ^obtained by ^{DNP. The three} upper limits are

meant for the absolute values.

This surprisingly high ^{rate of success} may indicate that even better results could be obtained with some

effort in sample ^{choice. DNP} is thus shown to be a

complementary ^{method to} « brute force » polariza-

tion. The wide variety of substances and paramagnetic impurities ^used indicate that DNP is quite generally

useful to measure bN, ^{the main} advantage being ^iso- topic selectivity. However, ^{if the} objective ^{is the}

measurement of _very precise spin-dependent ^scatter- ing lengths (or absorption cross-sections) ^{it may prove}

difficult in practice ^{to know} Aa/NIP ^of equation (4) ^to high accuracy, the polarization being ^{the least} precise

in most circumstances.

The considerable effort needed for more precise

measurements could only ^be justified by ^a considerable interest, theoretically ^or experimentally, ⁱⁿ precise bN

values.

Table I should be considered as an addition to the tables published in references [1] ^and [2]. ^{In the} latter,

two obvious printing ^errors should be corrected :

Jl*(165Ho) = - ^0.57 JlB and

(b+ - b_) (209Bi) = (+ 0.044 ’± 0.009) ^{x 10-12 cm.}

In addition, ^it may be pointed ^out here that the plus sign in reference [1] ^for (b+ - b -) (2’Al) is undoub-

tedly ^correct, according to two recent remeasurements.

References

[1] ^{See e.g.} GLÄTTLI, H., BACCHELLA, ^G. L., FOURMOND, M., MALINOVSKI, A., MERIEL, P., PINOT, M., ^ROU-

BEAU, P. and ABRAGAM, A., ^J. Physique ⁴⁰ (1979)

629 and references cited therein.

[2] ABRAGAM, ^{A. and} GOLDMAN, M., ^Nuclear Magnetism :

Order and Disorder (Oxford, ^Clarendon Press) 1982, Chapter ^7.

[3] MALINOVSKI, A., COUSTHAM, ^{J. and} GLÄTTLI, H., Nucl. Phys. ^{A 365} (1981) ^103.

[4] BARYSHEVSKI, ^{V. and} PODGORETSKI, M., ^Sov. Phys.

JETP 20 (1965) ^704.

[5] GLÄTTLI, H., ABRAGAM, A., BACCHELLA, ^G. L., FOUR- MOND, M., MERIEL, P., PIESVAUX, ^{J. and} PINOT, M., Phys. Rev. Lett. 40 (1978) ^748.

[6] ABRAGAM, ^{A. and} GOLDMAN, M., Rep. Progr. Phys.

41 (1978) ^395.

[7] NORMAND, J. M., ^Nucl. Phys. ^{A 291} (1977) ^126.

[8] RAMSEY, N., Molecular Beams (Oxford ^Univ. Press,

Oxford, England) ^1956.