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A line-shape analysis for spin-1 NMR signals

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A line-shape analysis for spin-1 NMR signals
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  Nuclear Instruments and Methods in Physics Research A 398 (1997) 109-125 NUCLEAR INSTRUMENTS &nflmwDS iN PHYSICS T Ef Y A line-shape analysis for spin-l NMR signals The Spin Muon collaboration (SMC) C DulyaÓ? b$ , D. AdamsÓ, B, Adevad, E. ArikÓ, A. Arvidsonf, B. Badelekfqs, M.K. Ballintij& Õ , D. Bardin *, G. Bardinh, G. BaumÕ, P. Berglund, L. Betevk, I G BirdÓ? 3, R. BirsaÕ, P. Bj~r~olmf, B.E. BannerÕ, N. de Bottonh, M. Boutemeurm, 4, * F BradamanteÕ, 5, A. J. Cranshawcy Ô, T. Bressan I, 6, S. Biiltmann iv 7, E. Burtinh, C. Cavatah, D. CrabbÓ, Cuhada?, S. Dalla TorreÕ, R. van Dantzigb, B. Derroa, A. Deshpandem, S. Dhawanm, A, Dyringf, S. EichblattÓ> 9, J.C. Faivreh, D. FaschingÕl lo, F. Feinsteinh, C. Fernandez?p, B. Frois qa , A. Gallasd, J.A. Garzon d*p, T. GaussiranÕ, R. GehringÕ, M. GiorgiÕ, E. von Goelef, St. GoertzÕ, F. Gomezd, G. Graciad, N, de Grootb* Ò, M. Grosse Perdekampa7 i2, E. GiilmezÓ, J. HarmsenÕ, D. von HarrachÕ, T. HasegawaÓ* 13, P. Hautleqy 14, N. HayashiÓs 15, C A. HeuschQ i6, N. HorikawaÓ, V.W. HughesÓ. G. Igoa, S. IshimotoÕ, i7, T. IwataÓ, EM. Kabu@, T. KageyaÓ, L. Kalinovskayaw, I*, A. Karevw, H.J. KesslerX, T.J. Ketelb, A. KishiÓ, Yu. KisselevW, L. Klostermannb,Ò, D. KramerÕ, V. ~ivo~~jinew, W. Kroger s> I6 V M. LamannaÕ, U. Landgrap, J.M. Le boff K~tinw, K. Kureks, J. K~n~r~inenq~j, Ô.q, F. Leharh, A. de Lesquen h, J. Lichtenstadty, T. Lindqvistf, M. Litmaathb,5, M. LoweÕ. lo, A. Magnonh, G.K. MahotÕ, F. Marieh, A. MartinÕ, J. Martinoh, T. MatsudaÓ, 13, B. Mayesp, J.S. McCarthyh, K. MedvedÓ, W. MeyerÕ, G. van Middelkoopb, D. MillerÓ, K. MoriÓ, J. Moromisatos, A. Nagaitsevw, * Corresponding author. E-mail: ch~s.du~ya~ciemat.es. Õ Now at Pure Atria, Hoofddorp, The Netherlands. ? Pe~aneut address: lnstitut fir Ho~henergi~hysik, Platanena?lee 6 D-15738 Zeuthen, Germany. 3 Now at Institut de Physique Nuclbaire, Universite de Lausanne, 1015 Lansanne, Switzerland. 4 Now at University of Montreal, PQ, H3C 357, Montreal, Canada. 5 Now at CERN, 1211 Geneva 23, Switzerland. 6 Now at DPhNC, University of Geneva, Geneva, Switzerland. Õ Now at University of Virginia, Department of Physics, Charlottesville, 22901 VA, USA3Õ. a Now at INFN Trieste, 34127 Trieste, Italy. Õ Now at Fermi National Accelerator Laboratory, Batavia, 60510 IL, USA. Ó Now at University of Wi~onsin, USA Ó Now at SLAC, Stanford, 94309 CA, USA. I2 Now at Yale University, Department of Physics, New Haven, 06511 CT, USA3Õ. t3 Permanent address: Miyazaki University, Faculty of Engineering, 889-21 Mjy~aki-Shi, Japan. I4 Permanent address: Paul Scherrer Institut, 5232 Villigen, Switzerland. Ó Permanent address: The Institute of Physical and Chemical Research (RIKEN), wako 3.51-01, Japan. Ó Permanent address: University of California, Institnte of Particle Physics, Santa Crnz, 95064 CA, USA. Ó Permanent address: KEK, Tsukuba-Shi, 305 Ibaraki-Ken, Japan. Ô* Permanent address: Bogoliubov Laboratory for Theoretical Physics, JINR, ui. Johot-Curie 6 RU-141980 Dubna, Russia 016%9002197/$17.00 Copyright @ 1997 Elsevier Science B.V. All rights reserved PII SO1 68-9002( 97 )003 17-3  11 C. Dulyu et al. INucl. Instr. and Meth. in Phys. Res. A 398 (1997) 109-125 J. Nassalskis, L. Naumannq* 20, T.O. Niinikoskiq, J.E.J. Oberskib, A. OgawaÓ, C. OzbenÓ, D.P. Park@, F. Perrot-Kunneh, D. Peshekhonovw, R. PiegaiaÓ, 21, L. Pinskyr, S. Platc~ovh, M. Plod, D. Posew, H. Postmab, J. PretzÕ, T. Pussieuxh, J. Pyrlikp, G. ReicherzÕ, I. Reyhancane, A. Rijllartq, J.B. Robei%?, S. Rockq,22, M. Rodriguezd>23, E. Rondiog, A. Rosadok, I. SaboÓ, J. Saboridod, A. Sandaczs, I. SavinÓ, P. SchiavonÕ, K.P. SchiilerÓ, 24, R. SegelO, R. SeitzÕ, 25, Y. Semertzidisq,8, F. Severb7 26, P. ShanahanÓ,9, E.P. Sichtermannb, F. SimeoniÕ, G.I. SmirnovW, A. Staudek, A. SteinmetzÕ, U. Stieglerq, H. StuhrmannÓ, M. Szlepers, K.M. Teichertk, F. TessarottoÕ, W. Tlaczalas 27, A. Tripetk>b, G. UnelÓ, M. VelascoÓ.5, J. Vogtk, R. Vossq, R. Weinsteinp, C. WhittenÓ, R. Win~oldersab, R. Will~eitaa, W. Wislickis, A. Witzmannx, A. Yaiiezd, J. Yliistalo, A M ZanettiÕ, 28, K. Zarembaa, J. ZhaoÓÓ . a University of Calt$xnia, Department of Physics, Los Angeles, 90024 CA, USA3Õ b NIKHEF, De&t University of Technology, FOM and Free University, 1009 AJ Amsterdam, The Netherland.~34 c Rice University, Banner Laboratory, Houston, 77251-1892 TX. USA31 d University of Santiago, Department of Particle Physics, 15706 Suntiago de Cornposteiu, Spain3 e Boga~i~i ~?liversit~~ nd Cekmece Nuclear Research Center, ls~a~bui Te~hni~aI ~niversit~~, stanblll ~n~uers~t~ IstambMl~ urke~3~ f Uppsala University, Department of Radiation Sciences, 75121 Uppsala, Sweden 8 Soltun Institute for Nuclear Studies and Warsw University, 00681 Warsaw, Poland3Õ h DAPNIA. C. E. Saclay, 91191 Gif%a- Ytaefte, FranceÓÕ Õ University of Bielefeld, Physics Department, 33501 Bielefeld, GermanyÓ J Helsinki University of Technology. Low Temperature Laboratory and Institute ojÕ Particle Physics Technology, Otakaari 3A, 02150 Finland k University of Mur~i~Il, Physics Depart~lent~ 80799 Mlinieh~ Cermanyz9 Õ INFN Trieste and University of Trieste. Department of Physics, 34127 Trieste, Italy m Yale University, Department of Phywics. New Haven, 06511 CT, USA31 n U~~ivers~t~ f Virginia, department of Physics, Charlotfesville. 22901 VA, USA3Õ o Northwestern University, Department of Physics, Evanston, 60208 IL, USA3Õ.32 P University of Houston, Department of Physics, Houston, 77204-5504 TX, and Institute for Beam Particle Dynamics, Houston 77204-5506 TX, USA3Õ, 32 4 CERN, i2ll Geneva 23, Switzerland I9 Now at Ericsson Telecommunication, 5120 AA Rijen, The Netherlands. 2o Deceased. ?Õ Permanent address: University of Buenos Aires, Physics Department, I428 Buenos Aires, Argentina. 22 Permanent address: The American University, Washington D.C. 20016, USA. 2Õ Now at Uppsala University, 75121 Uppsata, Sweden. 24 Now at DESY. 25 Now at Dresden Technical University, 01062 Dresden, Germany Permanent address: Brookhaven National Laboratory, Upton, 11973 NY, USA. 26 Present address: ESFR, F-38043 Grenoble, France. *Õ Now at Institute of Physics, Warsaw University of Technology. 28 Now at Institute of Radioelectronics, Warsaw University of Technology. 29 Supported by the Bund~sm~nisterjum fur Bildung, Wissenscha~, Forschung und Technologie. 3o Partially supported by TUBITAK and the Centre for Turkish-Balkan Physics Research and Application (BogaziCi University). 3Õ Supported by the U.S. Department of Energy. 3z Supported by the U.S. National Science Foundation. j3 Supported by lshida Foundation, Monbusho Grant-in-Aid for Scientific Research (Intemational Scientific Research Program and Specially Promoted Research). 34 Supported by the National Science Foundation (NWO) of the Netherlands. 35 Supported by the Commissariat B IÕEnergie Atomique. 36 Supported by Comision Interministerial de Ciencia y Tecnologia. j7 Supported by the Israel Science Foundation. 3x Supported by KBN SPUBIP31209/94.  C. Dulya et al. INucl. Instr. and Meth. in Phys. Res. A 398 (1997) 109-125 111 r ~niuers~ty af 3ochum~ Physics Departments 44780 Buc~um, Germany*Õ s ~~~rt~leaste~n University, Department of Physics, Buston, 02115 MA, USA3Õ Õ Universit?, of Main:. Institute for Nuclear Physics, 55099 Maim, German.?Õ Õ Nagoya University. CIRSE Furo-Cho, Chikusa-Ku, 464 Nagoya, Japan33 Õ Nagoya University, Department af Plrysics, Furo-Cho, Cttikusa-Ku. 464 Nagoya, Japani w JINR, Laboratory, of Particle Physics, Dubna, Russia Õ Universit.v of Freiburg, Physics Depart~ne~lt, 79104 Freihurg. Germany29 Y Tel Aviv U~zjllersit~, Schaof of P~~~..si~,.~, 99 Õ Tel Aviv, fsrael37 Õ Nagoya Uniuersit~. College ofÔ Medical Technology. D~iiko~?li~lar?~i , Higashi- Ku, 461 Nagoya. Japan33 Ó GKSS, 21494 Geesthacht. GernwnyÕÓ ah University aj Mow Faculty qfÕ Science, 7000 Moons. Belgium Received 5 December 1996 Abstract An analytic model of the deuteron absorption function has been developed and is compared to experimental NMR signals of deuterated butanol obtained at the SMC experiment in order to determine the deuteron polarization. The absorption function model includes dipolar broadening and a frequency-dependent treatment of the intensity factors. The high-precision TE signal data available are used to adjust the model for Q-meter distortions and dispersion effects. Once the Q-meter adjustment is made, the enhanced polarizations determined by the asymmetry and TE-calibration methods compare well within the accuracy of each method. In analyzing the NMR signals, the quadrupolar coupling constants could be determined for both the C-D and the O-D bonds of deuterated butanol. 1. Introduction Two methods to measure deuteron polarization will be compared in this paper. The ÒareaÓ method uses the ratio of enhanced and thermal equilibrium (TE) signals to determine the polarization (labeled PAR) in a manner which is mostly insensitive to disto~ions caused by the electronics of the NMR system. However, it is noise limited due to the small size of the TE signals. The ÒasymmetryÓ method fits a theoretical model of the deuteron absorption function to NMR signal data determining the polarization (labeled PAS) from the shape of the signal. The absorption function presented in this paper assumes that the spin temperature of the system is uniform throughout the sampling range of the NMR coils. Frequency-dependent distortions caused by the NMR system influence the value of the polarization measured by the asymmetry method. However, TE-signals can be used to determine the inst~ment effects and then the pola~zation values calculated with the as~rne~ method and the thermal equilibrium method agree within the accuracies of each method. In addition, using the theoretical absorption function developed here, the values of the electric quadrupolar coupling constants in the C-D and the O-D bonds of deuterated butanol (C4DsOD) were able to be determined. Consider a system of particles with spin each having a magnetic moment ~1 in a magnetic field Ho. There will be a Zeeman energy splitting of a spin-i system into 21 + 1 levels separated in energy by 61~0 = --c . Ho/Z = g~~I&, where g is the g-factor of the particle with spin and ,u~ is the nuclear magneton. When the spin system is irradiated by radio frequency (RF) energy at the Larmor frequency the spins either absorb some energy or the RF induces the spins to emit energy. The response of a spin system to RF irradiation is described by its magnetic susceptibility x(w) = xÕ(o) - ixÓ(w) in which xÓ is the absorption function and xÕ is the dispersion function. The static susceptibility is ~0 = x(O) = xÕ(O). The deuteron absorption function whose maximum occurs at its Larmor frequency cod only extends over about a 2n x 3OOkHz range, outside of which the dispersion function can be considered to have constant value ~0. The spin polarization of the  112 C D&a ef al. lNuc/. Insir. and Meth. in Phys. Rex A 398 (1997) 109-125 Phase Cable Fig. I. A block diagram of the Q-meter circuit detecting the real part of the NMR signal. material is given by the integral of the absorption function [l] (1) where N is the number of spins. The genera1 characteristics of the absorption function for deuterated butanol can be seen in Figs. 6 and 7, and are discussed in more detail later in Section 2 of this paper. 1.2. Detection of the deuteron ubsorption function In order to measure the absorption function, a coil of inductance L, and resistance r, is embedded in the target material. Through the inductive coupling between the spins and the coil, the impedance of the coil will become [Z] Z, = r, + iwL,( 1 + 4nsx(o)), (2) where q is the filling factor of the coil. The change of impedance is detected by a continuous-wave constant current Q-meter [3] connected to a series LRC resonant circuit as shown in Fig. 1. Here, the LRC circuit consists of the NMR coil connected via a coaxial t~smission line to the damping resistor, R, and the tuning capacitor, C. A frequency synthesizer connected to the Q-meter sweeps the RF frequency w over values where xÓ is nonzero. A complex voltage V = V(o,x) which is a function of Z,, and hence of x, is generated if the current is constant. The voltage is a supe~osition of both the signal propo~iona1 to x and the so-called Q-curve, which is the response of the Q-meter to w in the absence of x. The last stage of the Q-meter selects the real part of the voltage by using the input RF signal as a reference. The Q-curve is made symmetric around cr)d by adjusting the capacitance C. The Q-curve is measured separately by changing HO such that c& is well outside the range of the frequency scan of the Q-meter in which case xff vanishes and XÕ is negligible. The two signals are subtracted and the result is the NMR signal S(w) = Re{ V(w, x) - V(o,O)) c( xÓ(w) . (3) In a magnetic field of 2.5 T, the deuteron Larmor frequency is 2~ x 16.35 MHz, Thus, the polarization for deuterons can be approximated by , (4) where the integration limits (sweeping range of the Q-meter) extend over a 27~ x 5OOkHz band around the Larmor frequency which is the full range where xÓ is nonzero. The constant X contains all the unknown  frequency-inde~ndent gains in the Q-meter and is determined by making a thermal equilibrium (TE) eali- bration [4] of the system. In a TE cafibration, NMR signals are taken at a tempem~re around 1 K with the spin system in thermal equil~b~um with the lattice. The pola~zation calculated from the spin-l ~~l~ou~~ function is where k is BoltzmannÕs constant and T is the temperature. For o&j = 2~ x 16.35 MHz and 7Õ = I K, the polarization is P = 0.0523 % at TE for deuterons. Thus, the TE calibration determines the constant X in the following manner: The small pola~zation of the TE signals limits resolution of measuring X by Eq. (6) because the noise on the signal is appreciable. Normally, one TE signal is the average of 2000 or so double sweeps [5] over the 500 kHz sweep range. However, the noise on a TE signa is farge even if 2000 sweeps are used. By taking many signals and measuring the temperature for each signal, an average constant SC is determined. The averaging si~i~cant~y reduces the noise as can be seen in Fig. 2, where 380 TE signals of 2000 double sweeps are averaged, resulting in a Òsuper-TE-signal.Ó After the calibration constant S has been measured, Eq. (4) can be used to determine the pol~ization of the material in the enhanced polarization state once the integral of the NMR signal is determined. Enhanced polarization is attained via the dynamic nuclear polarization (DNP) process [6] in which microwaves are used to increase the ~lar~~tion. Enhanced polarizations of P 2 150 are obtainable f4,7] for deuterans, and they produce much larger signals than TE polarizations. Thus, only 200 double sweeps are needed for sufficient noise reduction to allow an accurate area determination of an enhanced signal. Fig, 2, A TE signal and a super-TE-signal. The dots are the data points of a 2000 double sweep TE kgnal. The line is a super-T&signal which is the average of 380 TE signals, which means 760000 double sweeps in total. The averaging reduces the noise sufficiently to allow a determination of the calibration constant X, and in addition, reliable fitting.
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