the measurement of the incoherent neutron scattering length of the deuteron

4
The measurement of the incoherent neutron scattering length of the deuteron B. van den Brandt a , H. Gl¨ attli b , P. Hautle a, , J.A. Konter a , F.M. Piegsa a,c , O. Zimmer c,d a Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland b SPEC and LLB, CEA Saclay, F-91191 Gif-sur-Yvette Cedex, France c Technische Universit¨ at M¨ unchen, James-Franck Strasse DE-85748, Germany d Institut Laue-Langevin, Avenue des Martyrs, F-38042 Grenoble, France article info Available online 6 August 2009 Keywords: Few-body physics Spin-dependent scattering length Neutron–deuteron Dynamic nuclear polarisation NMR abstract The project has the goal to directly determine the bound spin-dependent neutron–deuteron scattering length b i;d by measuring the pseudomagnetic precession of polarised cold neutrons passing through a target with polarised nuclei. A precise measurement of b i;d can be used to increase the accuracy of the only poorly known doublet neutron–deuteron scattering length b 2;d which is a crucial input parameter for novel effective field theories. We briefly report on the first measurements performed, discuss the systematics and consequent strategies to improve the accuracy of the experiment. & 2009 Elsevier B.V. All rights reserved. 1. Introduction An accurate direct determination of the spin-dependent (incoherent) neutron scattering length of the deuteron b i;d is of great importance. Combining the value with the well known coherent neutron deuteron scattering length b c;d [1] will provide a new value of the doublet neutron–deuteron scattering length b 2;d , which represents a crucial input for modern effective field theories of low-energy interactions among nucleons [2]. Presently b 2;d is known only with 6% accuracy from an indirect determina- tion dating back to the seventies [3]. An experiment currently running at the cold, polarised neutron beam line FUNSPIN at SINQ at the Paul Scherrer Institute in Switzerland has the aim to determine b i;d directly using the phenomenon of pseudomagnetic precession [4,5]: owing to the spin-dependent refractive index, the spin of neutrons passing through a polarised target precesses around the axis of nuclear polarisation with the precession angle being proportional to the bound incoherent scattering length b i of the nuclear species present in the sample. The pseudomagnetic precession angle j can be measured very accurately using Ramsey’s well-known atomic beam technique [6], adapted to neutrons [7] and is given for a sample consisting of various nuclear species k j ½rad¼ 2ld X k ffiffiffiffiffiffiffiffiffiffiffiffi I k I k þ 1 s P k N k b i;k ð1Þ where l is the neutron de Broglie wavelength, d is the thickness of the polarised sample and I is the spin of the nuclear species present with number density N and polarisation P . The precisely known value of the proton incoherent scattering length b i;p allows us to adopt a method proposed in Ref. [8], which relies on a relative measurement employing a sample containing both protons and deuterons. This way we avoid the experimental difficulties associated with absolute measurements of number density and nuclear polarisation, which would limit considerably the final accuracy. This brief report describes the status of the project and discusses, starting from the most recent data, the further improvements necessary to measure the spin-dependent nd scattering length with better accuracy than the present literature value. 2. Principle of the measurement We shortly recall the procedure for the determination of b i;d , which in practice differs slightly from the one given in Ref. [8]. Several measurements of precession angles j in combination with the corresponding NMR signal integrals, which are proportional to P k N k , have to be performed. First both isotopes are polarised simultaneously via dynamic nuclear polarisation DNP [7]. When the microwaves are switched off, the sample temperature decreases to about 100 mK where the nuclear polarisation remains essentially frozen (the relaxation times at 2.5 T are in the order of several hundred hours) and the ‘‘total’’ precession angle can be determined. Using rf-saturation the protons are then selectively depolarised without significantly affecting the ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/nima Nuclear Instruments and Methods in Physics Research A 0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.07.053 Corresponding author. E-mail address: [email protected] (P. Hautle). Nuclear Instruments and Methods in Physics Research A 611 (2009) 231–234

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ARTICLE IN PRESS

Nuclear Instruments and Methods in Physics Research A 611 (2009) 231–234

Contents lists available at ScienceDirect

Nuclear Instruments and Methods inPhysics Research A

0168-90

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/nima

The measurement of the incoherent neutron scattering lengthof the deuteron

B. van den Brandt a, H. Glattli b, P. Hautle a,�, J.A. Konter a, F.M. Piegsa a,c, O. Zimmer c,d

a Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerlandb SPEC and LLB, CEA Saclay, F-91191 Gif-sur-Yvette Cedex, Francec Technische Universitat Munchen, James-Franck Strasse DE-85748, Germanyd Institut Laue-Langevin, Avenue des Martyrs, F-38042 Grenoble, France

a r t i c l e i n f o

Available online 6 August 2009

Keywords:

Few-body physics

Spin-dependent scattering length

Neutron–deuteron

Dynamic nuclear polarisation

NMR

02/$ - see front matter & 2009 Elsevier B.V. A

016/j.nima.2009.07.053

esponding author.

ail address: [email protected] (P. Hautle).

a b s t r a c t

The project has the goal to directly determine the bound spin-dependent neutron–deuteron scattering

length bi;d by measuring the pseudomagnetic precession of polarised cold neutrons passing through a

target with polarised nuclei. A precise measurement of bi;d can be used to increase the accuracy of the

only poorly known doublet neutron–deuteron scattering length b2;d which is a crucial input parameter

for novel effective field theories. We briefly report on the first measurements performed, discuss the

systematics and consequent strategies to improve the accuracy of the experiment.

& 2009 Elsevier B.V. All rights reserved.

1. Introduction

An accurate direct determination of the spin-dependent(incoherent) neutron scattering length of the deuteron bi;d isof great importance. Combining the value with the well knowncoherent neutron deuteron scattering length bc;d [1] will provide anew value of the doublet neutron–deuteron scattering length b2;d,which represents a crucial input for modern effective fieldtheories of low-energy interactions among nucleons [2]. Presentlyb2;d is known only with 6% accuracy from an indirect determina-tion dating back to the seventies [3].

An experiment currently running at the cold, polarised neutronbeam line FUNSPIN at SINQ at the Paul Scherrer Institutein Switzerland has the aim to determine bi;d directly using thephenomenon of pseudomagnetic precession [4,5]: owing to thespin-dependent refractive index, the spin of neutrons passingthrough a polarised target precesses around the axis of nuclearpolarisation with the precession angle being proportional to thebound incoherent scattering length bi of the nuclear speciespresent in the sample. The pseudomagnetic precession angle j�can be measured very accurately using Ramsey’s well-knownatomic beam technique [6], adapted to neutrons [7] and is givenfor a sample consisting of various nuclear species k

j� ½rad� ¼ 2ldX

k

ffiffiffiffiffiffiffiffiffiffiffiffiffiIk

Ik þ 1

sPkNkbi;k ð1Þ

ll rights reserved.

where l is the neutron de Broglie wavelength, d is the thickness ofthe polarised sample and I is the spin of the nuclear speciespresent with number density N and polarisation P. The preciselyknown value of the proton incoherent scattering length bi;p allowsus to adopt a method proposed in Ref. [8], which relies on arelative measurement employing a sample containing bothprotons and deuterons. This way we avoid the experimentaldifficulties associated with absolute measurements of numberdensity and nuclear polarisation, which would limit considerablythe final accuracy.

This brief report describes the status of the project anddiscusses, starting from the most recent data, the furtherimprovements necessary to measure the spin-dependent ndscattering length with better accuracy than the present literaturevalue.

2. Principle of the measurement

We shortly recall the procedure for the determination of bi;d,which in practice differs slightly from the one given in Ref. [8].Several measurements of precession angles j in combination withthe corresponding NMR signal integrals, which are proportional toPkNk, have to be performed. First both isotopes are polarisedsimultaneously via dynamic nuclear polarisation DNP [7]. Whenthe microwaves are switched off, the sample temperaturedecreases to about 100 mK where the nuclear polarisationremains essentially frozen (the relaxation times at 2.5 T are inthe order of several hundred hours) and the ‘‘total’’ precessionangle can be determined. Using rf-saturation the protons arethen selectively depolarised without significantly affecting the

ARTICLE IN PRESS

B. van den Brandt et al. / Nuclear Instruments and Methods in Physics Research A 611 (2009) 231–234232

deuteron polarisation and a next precession angle measurement isperformed. At each step, before and after the measurement of aprecession angle the deuteron and proton NMR signal integralsare recorded. The measurement cycle is completed with thedetermination of the instrumental phase j0 with unpolarisedsample. This is not as trivial as it seems because the completedestruction of the deuteron polarisation is difficult to achieve andto assure. We can circumvent this problem by noting that thethermal polarisation given by the Boltzmann distribution alreadyproduces a well measurable phase shift and perform a series ofphase determinations where the sample is in thermal equilibriumat well known temperatures, and extrapolate the phase to zeropolarisation.

Additionally a so-called cross-calibration of the NMR systemsis necessary which is described in detail in Section 5.2.

3. Present status and preliminary results

In a first series of measurements several problems have beenencountered and addressed. The target sample preparation hasbeen revised to prevent polarisation and density inhomogeneities,which wash out the Ramsey pattern [9]. Second, the sample sizewas decreased to 5 mm diameter to match the size of the beam, inorder to avoid systematic errors due to neutrons and NMR probingdifferent parts of the sample. The NMR coil configuration hasbeen adapted correspondingly and an additional saddle coil forrf-saturation has been integrated as well [10]. Thus, systematicerrors could be reduced, which were caused by the fact that theneutron beam saw a different part of the sample than the NMRcoils measuring the sample polarisation. Further, the polarisedtarget cryostat has been modified to reach a lower basetemperature, which is important to ‘‘freeze’’ the nuclear polarisa-tions during the phase measurements and during the cross-calibration sequence (see Section 5.2). With a new heat exchangerusing silver sinter a base temperature of 80–90 mK is now reachedin the mixing chamber and 100–110 mK in the target cell, which isfilled with 4He in order to avoid that the neutrons pass throughthe strongly absorbing 3He [11]. The Ramsey apparatus, previouslyused in Saclay, has been considerably improved and enables usnow to measure neutron precession angles with an absoluteaccuracy of about 13 [12].

A compilation of data of nd scattering length measurementsobtained with the improved setup and a 25 mg deuterated plasticsample (about 5 mm in diameter and 1.2 mm thick) is shown inFig. 1. Compared to previous measurements, systematic problemscould be much reduced but are still present on an unsatisfactorylevel. Well understood and completely satisfactory with respect tothe accuracy requirements is the neutronic part leading to the

Fig. 1. Preliminary results for bi;d from a 25 mg target sample. The three lines give

the literature value with error bars [3] for comparison.

Ramsey signals from which the pseudomagnetic phase shifts arederived [12]. The neutron beam and the NMR system now bothprobe the same but much smaller sample, such that the residualtarget inhomogeneities (found to be in the order of a few percentby scanning the target with a smaller beam) should not play animportant role any more. However, the resulting smaller NMRsignals limit the precision of the signal integral determination andthus limit directly the accuracy of the scattering lengthmeasurement (see Ref. [8, Eq. (14)]). Especially the subtractionof the large parabolic background is delicate and most probablyleads to the systematic difference between data points withpositive and negative deuteron polarisation as seen in Fig. 1.

4. Strategies to improve the apparatus

The only way to improve the present accuracy is by increasingthe NMR signal size and as we already employ state of the art cw-NMR techniques, this can be practically only achieved byincreasing the sample size. We use two Q-meter systemsoperating at around 16 and 106 MHz, respectively, to measurethe deuteron and proton NMR signals at the nominal field of 2.5 T.The 16 MHz NMR circuit is a non-resonant cable configurationwith the tuning elements mounted inside the cryostat in closevicinity to the target. The proton NMR coil, however, is connectedvia a transmission line cable of length lrf to the tuning elementssituated at room temperature [13]. Alternative NMR techniqueshave been considered, e.g. pulse NMR, but not found advanta-geous for our purpose of measuring accurately the signal integralof the 300 kHz wide deuteron NMR line.

In order to profit from a larger sample while keeping itcompletely illuminated by the neutron beam, the setup had to bemodified to accommodate a larger neutron beam. However, it isnot possible to estimate the influence of a larger beam on theRamsey signals, which probably will become less visible due tounequal magnetic field integrals along the various partial beams.Unfortunately, only neutrons can tell to what extent this will bethe case (see Section 5.3). Taking this constraint into account, wedecided to increase the total beam size (target and reference) to10� 21 mm2. This required the preparation of new spin flippercoils in a transverse flat-coil design, which will provide muchimproved rf field homogeneity compared to the longitudinalsolenoid flippers used so far. Further, the larger beam sets muchhigher requirements on the beam divergence: target andreference beam have to be kept well separated over the 2.5 mdistance up to the two detectors. With two short Soller typecollimators developed for neutron imaging purposes [14] placedin crossed geometry (one vertical, one horizontal) the largelydivergent beam present at FUNSPIN could be restricted to 0:113

(FWHM).

5. Improvements achieved and constraints

5.1. Target sample and NMR signals

The larger beam allows us to use a correspondingly largertarget sample ð8� 10� 1:3 mm3Þ which increases the number ofnuclei sampled by the NMR coils by a factor of 4. The number ofwindings of the tightly fitting NMR coils (see Fig. 2) could beincreased as well, leading to a higher Q-value of the resonances.From simple considerations the gain in NMR signal expected fromthe above modifications should amount to about a factor 4 buthad to be experimentally verified. A batch of target samples, slabsof 96% deuterated polystyrene doped with d-TEMPO free radicalsranging in concentration between 1.5 and 2:5� 1019=cm3, has

ARTICLE IN PRESS

Fig. 2. Deuterated polystyrene sample with dimensions 8� 10� 1:3 mm3

mounted in a teflon frame supporting the 4 turn 106 MHz and 10 turn 16 MHz

NMR coils. This configuration is then fitted into a holder sitting in a cell filled with

liquid 4He that is thermally anchored to the mixing chamber of a 3He–4He dilution

refrigerator [11].

Fig. 3. Comparison of the deuteron and proton NMR signals both measured with

the same 16 MHz Q-meter NMR system at magnetic fields of 2.5 and 0.4 T,

respectively. The proton signal is down-scaled by a factor 5.

Fig. 4. Example of a cross-calibration of the two Q-meter NMR systems. The linear

fits through the data points cross very precisely the origin, as should be the case.

For further explanation see text.

B. van den Brandt et al. / Nuclear Instruments and Methods in Physics Research A 611 (2009) 231–234 233

been prepared and dynamic nuclear polarisation tests performedin a laboratory setup at a temperature of 1 K and magnetic field of3.5 T. The sample with 2� 1019=cm3 TEMPO was found to be theoptimum with respect to maximum polarisation and slowrelaxation, which is of great importance for the cross-calibrationof the NMR systems (see Section 5.2). At the low field of 0.38 T wemeasured a T1 of more than 1 h at 115 mK and 20 min at 135 mK.

In fact, the NMR signals recorded are now about 5 times higherin the case of protons and 3 times higher for deuterons, comparedto the previous configuration. This larger signal sizes lead to agreat improvement in the statistical accuracy of the integral

determination of better than 1%. Typical signals of the polarisedsample are shown in Fig. 3.

5.2. Cross-calibration of the NMR systems

Recall that the NMR signals, taken as integrals over the rf-absorption lines, are proportional to ckPkNk, where ck is a factoraccounting for the sensitivity of the resonance circuit (compareEq. (1)). To make full use of the method of relative measurements,all NMR signals have to be recorded with the same NMR system sothat the instrumental factor ck cancels, which would be difficult todetermine absolutely to the required accuracy. Thus an absolutepolarisation determination reduces to a comparison of signalintegrals (see Fig. 3). This requires that the proton NMR signal hasto be recorded with the deuteron NMR system at a frequencyof 16 MHz. Due to the largely different gyromagnetic ratios thisneeds a magnetic field of about 0.4 T. To avoid sweeping the fieldwithin a precession measurement cycle (see Section 2), the twoNMR systems have to be cross-calibrated.

Comparing systematically the proton signal integral values atlow and high fields for many different polarisations, an exact ratioc106=c16 between the NMR systems can be established (Fig. 4).Ideally the polarisation stays frozen during this procedure,however, the induced currents due to the magnetic field sweepheat the target cell from 115 mK up to about 150 mK, which leadsto increased relaxation. Due to better cooling power and bettersample properties we could reduce these polarisation losses frompreviously 15% to about 4% per cycle. Nevertheless, the systematicuncertainty of the calibration measurement is hard to quantifywithout assumptions about the rate of polarisation loss as afunction of time. Obviously the calibration coefficient turnsout to be different if the low field value is combined with thehigh field value before or after the field ramp. This is illustrated inFig. 4 for a calibration sequence with about 8% loss. Of course thetwo slopes indicate the worst case and could be taken as ameasure for the maximum uncertainty of the procedure, whichwould amount to half of the loss of the sequence. This lossis difficult to decrease as the cooling power of the cryostat is inour case mainly limited by the heat transfer by the superfluidhelium [11].

We try to further restrict the error band with systematicstudies. In order to be able to vary the conditions of the sweep(such as the speed of the field sweep and the target tempe-rature) and the timing of the NMR signal measurement, a full

ARTICLE IN PRESS

180

90

0

-90

-180

Fig. 5. Neutron spin phase map over the beam cross-section of 10� 21 mm2,

measured with a CCD camera [16].

Fig. 6. Phase gradient across the beam diameter. With correction coils the gradient

could be reduced from about 293=mm to 143=mm.

B. van den Brandt et al. / Nuclear Instruments and Methods in Physics Research A 611 (2009) 231–234234

automatisation of the whole cross-calibration process has beenimplemented.

5.3. Neutron beam and phase determination

The now excellent collimation of the neutron beam allows toemploy the newly developed neutron spin phase imagingtechnique [15] to measure a phase map over the whole beamcross-section. As is immediately seen from Fig. 5, we suffer fromlarge phase differences, more than 3001 across the beamdiameter, which stem from the inhomogeneity of the magneticfield. These conditions completely exclude the use of efficient 3Heneutron counters as the Ramsey pattern will be completely lostwhen averaging over the beam. Shimming the field of the 2.5 Telectromagnet is a tedious if not impossible task. However, very

promising first results have been obtained with a pair of gradientcoils mounted on the pole pieces of the magnet. A first test withlimited current showed that the initial field gradient can bereduced (see Fig. 6) with corresponding considerableimprovement of the visibility of the Ramsey oscillations. Themechanical stability and the efficiency of such coils still need to besubstantially improved and means to precisely stabilise their fieldhave to be developed.

Another remedy to the problem could be the employment of afast position sensitive 2-D detector. State of the art CCD cameras,as we have used for imaging the phase map, still do not reach therequired accuracy within reasonable measuring time.

6. Conclusions

With all the improvements implemented we seem to touch the‘‘fundamental limits’’ of our approach. The accurate determinationof relative phases with the Ramsey apparatus that poses noproblem on a small beam diameter of 3 mm [12] gets spoiled bythe inhomogeneity of the magnetic field, when averaging over theincreased beam cross-section. We are presently working on asolution and once this is established, the precise determination ofthe NMR signal integrals and moreover the quantification of theerror from the cross-calibration will most probably set theaccuracy limit for the determination of bi;d. We estimate to reachan accuracy slightly beyond the present literature value andprovide a value for b2;d which is an important independent inputto modern effective field theory of nuclear interactions.

References

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[2] H. Grießhammer, Talk on the International Workshop on Particle Physics withSlow Neutrons, Grenoble, May 2008.

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[10] B. van den Brandt, H. Glattli, H. Grießhammer, P. Hautle, J. Kohlbrecher, J.A.Konter, F.M. Piegsa, J.P. Urrego-Blanco, O. Zimmer, in: Proceedings of the 17thInternational Spin Physics Symposium SPIN 2006, Kyoto, Japan, 2–7 October2006, AIP Conf. Proc. 915 (2007) 769.

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