IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 60, NO. 1, FEBRUARY 2013 3

Large-Area Crystalline Microcolumnar LaBr :Cefor High-Resolution Gamma Ray Imaging

Harish B. Bhandari, Vladimir Gelfandbein, Stuart R. Miller, Akash Agarwal, Brian W. Miller,H. Bradford Barber, Member, IEEE, and Vivek V. Nagarkar, Member, IEEE

Abstract—Novel fabrication methods for cost-effective andlarge-volume production of important lanthanide halide scintilla-tors are currently being explored.Here we report on the growth of LaBr :Ce scintillator films

in a novel light conserving morphology known as CrystallineMicrocolumnar Structure™ (CMS™), using Hot Wall Evapora-tion (HWE) technique. This method produces specimens whichpreserve the response uniformity over the area of the film, and lowattenuation of light throughout its thickness. Using this approach,we have produced LaBr :Ce film samples measuring 3–7 cm indiameter and approaching 2 cm in thickness, with densely packedmicrocolumns averaging m in diameter. Some of thesefilms show bright light emissions compared to their crystallinecounterparts, demonstrating energy resolution of % at 122keV ( Co emission) and uniformity in light response across thearea of the scintillator. Imaging data acquired using the Univer-sity of Arizona Bazooka SPECT detector incorporating our CMSLaBr :Ce film demonstrated m spatial resolution at 122keV in single-photon counting imaging mode. This technique per-mits fabrication of thick films that can simultaneously provide thehigh absorption efficiency and high spatial resolution required forsmall-animal SPECT imaging and other medical and non-medicalapplications.

Index Terms—Gamma ray detector, hot wall evaporation, scin-tillator, SPECT.

I. INTRODUCTION

A MONG the various functional imaging techniques,SPECT and PET maintain important and growing roles

in the study of disease models in small animals as well asin patient care [1], [2]. Since these well-established nuclearmedicine imaging modalities are also applicable in the plantand environmental sciences, these techniques are expectedto play a dominant role in probing plants, microbes, and theenvironment. These applications require high spatial resolution,not only because of the small scale of the details to be imaged,but also for demanding quantification tasks. In addition to reso-lution requirements, enhanced sensitivity is critically important

Manuscript received December 06, 2011; revised April 27, 2012; acceptedJuly 10, 2012. Date of publication September 20, 2012; date of current versionFebruary 06, 2013. This work was supported in part by DTRA under GrantHDTRA1-10-C-0073 and by DOE under Grant DE FG02-06ER84434.H. Bhandari, V. Gelfandbein, S. R. Miller, A. Agarwal, and V. V. Na-

garkar are with Radiation Monitoring Devices, Inc. (RMD), Watertown, MA02472 USA (e-mail: hbhandari@rmdinc.com; vgelfandbein@rmdinc.com;smiller@rmdinc.com; aagarwal@rmdinc.com; vnagarkar@rmdinc.com).B.W.Miller and H. B. Barber are with the University of Arizona, Tucson, AZ

85724 USA (e-mail: molinero@email.arizona.edu; bradb@radiology.arizona.edu).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TNS.2012.2213612

for reducing image acquisition time, improving temporal reso-lution for certain dynamic phenomena, increasing throughputfor studies, and imaging structures with low intrinsic uptake.It is clear that an advanced scintillation detector that can

simultaneously provide the required resolution and sensi-tivity would therefore be of significant value. Such detectorscan now be realized using new high-performance materialssuch as SrI :Eu [3], LuI :Ce [4] and lanthanum halides such asLaBr :Ce, LaCl :Ce, provided that these materials are econom-ically synthesized in the required thicknesses and large-areaformats.In this report, we discuss the fabrication of cerium doped

lanthanum bromide (LaBr :Ce) in a Crystalline MicrocolumnarStructure™ (CMS™) using Hot Wall Evaporation (HWE) tech-nique for SPECT imaging application. For most SPECT ap-plications a 1 cm thick LaBr :Ce detector provides the suffi-cient stopping power. This paper addresses the prospects of theHWE method to achieve the required thickness of CMS LaBrover large active areas and focuses on efforts to develop bettercolumnar structured scintillators.

II. MATERIAL SYNTHESIS

RMD’s HWE technique was used to fabricate CMSLaBr :Cescintillators. HWE is a vacuum deposition process that is de-rived from epitaxial growth techniques, whose characteristic isthe growth of robust, uniform homoepitaxial layers under condi-tions of thermodynamic equilibrium, yet with aminimum loss ofmaterial. In its simplest form, the growth apparatus consists of acylindrical quartz crucible positioned upright in a vacuum andwrapped with a tantalum strip heater. The evaporation source“boat” is placed at one end, typically the bottom, and a cooledsubstrate at the other end. The heated cylinder wall serves toenclose, deflect and effectively direct the vapor from the sourceto the substrate, where molecules are deposited with a shallowimpinging angle. With the substrate being the coldest part (rela-tively) in the system, molecules condense on the substrate aloneand do not accumulate on the hot walls, making an efficient useof the source material to form a film on the substrate.Fabrication of large-area thick scintillators is possible using

an HWE system (up to 50 50 cm , limited only by the equip-ment size and up to 2.5 cm thick). The microcolumnar texturingof the film’s cross-section offers some degree of relaxation tothe film and is thus less prone to structural instabilities arisingfrom intrinsic stresses. The HWE fabrication is characterized byhigh growth rates, 25 to 100 m/min, hence a typical scintillatorfabrication can be accomplished in only a few hours. Overall,HWE can be an economical process for rapid experimentationand production of important scintillators.

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4 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 60, NO. 1, FEBRUARY 2013

For HWE fabrication of LaBr :Ce, commercially availableanhydrous beads of LaBr (CAS# 13536-79-3) and CeBr(CAS# 14457-87-5) are mixed in pre-calculated proportionsand loaded in to the source boat for evaporation. Since the vaporpressures and molecular weights of LaBr (1.0 mTorr at 716 C,378.6 gm/mol) [5] and CeBr (3.1 mTorr at 716 C, 379.8gm/mol) [6] are similar, the resulting dopant concentration(mole %) in a deposited LaBr :Ce film is close to the loadingconcentration (weight %) of pre-mixed charge. For instance,40 gm of LaBr and 2 gm of CeBr , pre-mixed charge yieldsa LaBr :Ce specimen whose Ce concentration is mol%, asconfirmed by inductively coupled plasma mass spectrometer(ICP-MS) analysis. A similar observation was made during fab-rication of LaBr :Pr from a mixture of LaBr and PrBr , owingto their similarities in vapor pressure and molecular weights.While the concentration profile of the dopant is fairly uniformalong the thickness of the specimen, no compositional analysishas been conducted to verify point-to-point dopant distributionon the specimen surface. Under circumstances where a systemof materials has widely dissimilar vapor pressures for a giventemperature, the HWE setup can be modified to evaporateprecursors simultaneously at desired rates from separate boats.This approach enables reliable control of dopant distributions inthe HWE-fabricated scintillator film. For instance, RMD’s Con-tinuous Phoswich™ scintillators [7] have been fabricated usinga dual-boat configuration to establish a dopant concentrationgradient in the scintillator by gradually increasing/decreasingthe dopant evaporation rate, which otherwise is challenging toaccomplish via melt-grown processes.Past research on vapor-deposited scintillators shows that

properties critical to their superior performance are stronglydependent on their microstructure [8]–[10]. Some of the keyfactors that influence columnar growth during evaporation areadatom surface mobility, rate of evaporation, substrate rough-ness, angle of incidence of evaporant molecules, and mostimportantly, the temperature of the surface where depositionoccurs, all of which reside in the parameter space that canbe controlled to optimize the properties of thick films. TheStructure-Zone (SZ) model, first proposed by Movchan andDemchishin [11], describes the evolution of film microstruc-ture during growth and its strong dependence on temperature.According to the SZ model, high substrate temperatures (

is the melting point) lead to highly crystalline mi-crocolumns, whereas low temperatures ( ) result inamorphous microcolumns.Just as substrate temperature plays a critical role in the HWE

process, the substrate’s physical properties, such as surfaceroughness, thickness, and coefficient of thermal expansion(CTE), also affect the outcome of HWE fabrication of LaBrscintillators. It is our observation that during the deposition ofLaBr :Ce film onto a quartz substrate, the deposited materialdevelops extrinsic stresses due to the large differences inCTE values between film and substrate, which leads to pooradhesion, cracking and delamination. Quartz, whose CTE is

/ C, has a large CTE mismatch with LaBr whosehexagonal close packing (HCP) structure has a CTE value of

/ C along its c-axis and / C along its a-axis.This mismatch of CTEs translates to large stresses and subse-quent delamination of films from their substrates, especially for

Fig. 1. (Top) LaBr :Ce film deposited at 300 C, cm in thickness andcm in diameter. (Bottom) CMS™ LaBr :Ce film deposited at C,cm in thickness and cm in diameter deposited using hot wall evaporation(HWE).

Fig. 2. An SEM micrograph of the film cross section, showing highly orientedgrowth of CMS LaBr :Ce, measuring 1.5 mm in thickness, with microcolumnsmeasuring m diameter.

films whose thickness is mm. Hence, there is a need foran alternative substrate material, which in our case is sapphire,whose CTE is /deg. C. Sapphire is a good choice asa substrate for HWE deposition of LaBr in general, because itnot only has a suitable CTE, but it is chemically inert and canwithstand the high temperatures utilized in the HWE process.This unique approach of HWE fabrication has been used

to produce a thick LaBr :Ce scintillator sample measuringup to cm in thickness and 7 cm in diameter, as shownin Fig. 1(top). This sample was deposited at a relatively lowsubstrate temperature of 300 C, whose resulting growth ratewas m/min. Although the film scintillates under gammaradiation, a well-defined photopeak was not registered withthe 2 cm thick sample. We suspect the sample had low trans-parency to its scintillation light. CMS samples deposited athigher substrate temperatures ( C), as in the case for the

mm thick LaBr :Ce film shown in Fig. 1(bottom) showedexcellent scintillation properties. The growth rate for CMS

BHANDARI et al.: LARGE-AREA CRYSTALLINE MICROCOLUMNAR LABR :CE FOR HIGH-RESOLUTION GAMMA RAY IMAGING 5

Fig. 3. X-ray excited emission spectra for LaBr doped with (left) cerium (Ce) and (right) praseodymium (Pr). Ce-doped films emit in the blue region (360–380nm) and are due to transition of Ce . Pr-doped films show multiple sharp emissions in the green and red regions (489, 532, 621, 646, 682, 735 nm)and are a result of transitions in Pr , mainly from and levels.

films tend to be slower owing to lower condensation efficiencyat higher substrate temperature but nevertheless CMS sampleshave good scintillation performance in terms of resolution andtransparency. The characterization results described below arefocused on thin CMS films i.e., 0.6, 1 and 2 mm thick films.

III. CMS SCINTILLATOR CHARACTERIZATION

A. Morphology

The scanning electron micrograph (SEM) of a cross sectionfor LaBr :Ce film is shown in Fig. 2 and shows that anisotropiccolumnar growth is possible in a hexagonally closed packedsystem like LaBr . The microcolumns measure 15–20 m indiameter in a free standing film whose thickness measures 1.5mm. The columns although highly-oriented, are not orientednormal to film edge; this is a result of angular deposition and canbe easily rectified with sample rotation. The columnar growthstrongly suggests that these films exhibit similar anisotropy inoptical properties as well. LaBr , which has an HCP structure,shows a strong tendency to grow along the c-axis normal to thesubstrate surface, which coincides with the columnar axis. Thisresults in a larger refractive index in the columnar axis directionin the film [12]. A direct consequence of this anisotropy of re-fractive index is efficient piping of the light along the columnsvia total internal reflection. In the microcolumnar structure ofLaBr , the internal surfaces that reflect the light, in principal,are the grain boundaries that separate the columns vertically.If the surface roughness of the column boundary is significantlysmaller than the emission wavelength ( nm for LaBr :Ce),scattering can be minimized to an appreciable extent. Thus, thelight-conserving nature of microcolumnar scintillator can resultin higher overall light yield than that of melt-grown crystals, aswas observed during our earlier work [7].Transparency in LaBr is an important attribute to achieve

high detection efficiency, especially for thick scintillators.LaBr films often appear opaque to the eye due to scatteringof light from the grain boundaries, however the light propa-gation through microcolumns is very efficient owing to total

internal reflection. In the CMS LaBr , the microcolumns arewell crystallized and oriented within its thickness, resulting innegligible light absorption or scattering. For light attenuationdata on CMS LaBr , please see Section D. According to theSZ growth model, CMS films grown at high temperature i.e.,

C will result in large columns whose diameter is on theorder of the film thickness. This type of growth lowers thegrain-boundary surface area per unit volume, which results inoptically transparent LaBr films. Optically transparent filmsare not discussed in this paper.

B. Spectral Emission

Emission spectra of LaBr films under continuous X-ray ex-citation were measured using the Cu target X-ray generator (8keV Cu K line) operated at 40 kVp with 20 mA current. Theresulting scintillation light was passed through a McPhersonmodel 234/302-0.2 m monochromator and measured at eachwavelength with an RCA model C31034 photomultiplier tube(PMT). The operation of the whole instrument, including theX-ray trigger, the rotation of the monochromator to selectthe wavelength, data acquisition and analysis were computerdriven.Fig. 3 shows the resulting emission spectra for two LaBr

samples, one doped with 5% cerium (Ce) and the other dopedwith 1% praseodymium (Pr). In the LaBr :Ce sample, arelatively broad peak in the blue region (360–380 nm) wasobserved, due to the transition of Ce . The Pr-dopedLaBr had the effect of shifting the emission from the UV (withCe ) to green and red regions. This red-shift in LaBr :Prscintillation offers higher sensitivity for photodetectors suchas solid-state photomultipliers (SSPMs), CCDs and CMOSsensors. As shown in the Fig. 5, Pr doping produced a rathercomplex spectrum with emission peaks at 489, 532, 621, 646,682, and 735 nm. These emissions are a result oftransitions in Pr , mainly from and levels. For boththe dopants Ce and Pr, the emission spectra of the resultingLaBr films fabricated via the HWE process resembled resultspublished for the melt-grown process [13], [14].

6 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 60, NO. 1, FEBRUARY 2013

Fig. 4. Co (122 keV) Photopeak spectra obtained using the 600 m thickCMS LaBr :Ce film. Spectra were acquired by scanning the collimated sourcealong the diameter of the sample with 10 mm steps. Key observations include1) the variation in peak position is % and 2) spectra demonstrate %energy resolution at 122 keV, and also show the presence of the 136 keV gammaray line of the Co source. Further, the two peaks at the lower energy are anescape peak arising from the escape of La K X-rays from the 600 m-thickLaBr :Ce film, and K X-rays from a tungsten collimator ( keV).

C. Response Uniformity, Energy Resolution, and Brightness

To measure the response uniformity across the large area ofthe CMS LaBr :Ce scintillator, a specimen measuring 6 cm indiameter and 600 m in thickness was coupled to an R6233SBAPMT operated at 900 V. The detector areas were scanned at10 mm intervals using a collimated Co 122 keV gamma raysource (1 mm beam diameter). The resulting energy spectrawere recorded using an MCA, and are plotted in Fig. 4. Thegeneral features in each of these spectra are relatively consis-tent with each other and exhibit only % variation at the 122keV peak position, indicating very uniform light output acrossthe film. The energy resolution across the film was also uniform,measuring % at 122 keV. It is important to note thatthese spectra also show the presence of the 136 keV gamma-rayline of the Co source. All of these measurements indicate theuniformity of scintillation properties across a 6 cmwide sample.The two peaks seen at the lower energies are an escape peakarising from the escape of La K X-rays from the 600 m thickLaBr :Ce film and a peak from K X-rays from a tungsten col-limator ( keV). The energy resolution demonstrated by thisCMS sample is slightly worse than the typical energy resolutionof 7.2% at 122 keV typical of commercial LaBr crystals, how-ever it is significantly better than the energy resolution of 11%at 122 keV for NaI:Tl standard.The relative light yield was measured for the 2 mm thick

sample, shown in Fig. 1(bottom), in reference to a calibratedcommercial LaBr crystal. The PMT setup for the light yieldmeasurement was same as described previously for the lightuniformity measurements. The comparison of the resulting 122keV photopeak spectra is shown in Fig. 5. Based on their rel-ative peak positions, the light yield for the CMS LaBr filmmeasuring 35 mm in diameter and 2 mm in thickness appearsto be 59 000 Ph/MeV, given that the calibrated LaBr commer-cial crystal (15 mm right cylinder) has a light yield of 55 000Ph/Mev. Although the photopeak for the 2mm thick film sampleis characterized with pulse pile-up and escape peak of La K

Fig. 5. Photopeak spectra acquired using a collimated Co (122 keV) sourcefor CMS LaBr :Ce film measuring 35 mm diameter and 2 mm thickness, and areference LaBr crystal measuring 15 mm right cylinder. The light yield fromCMS LaBr film measures Ph/Mev, given that the reference crystal’slight yield is 55 000 Ph/MeV.

X-rays at lower energies, its peak position reflects a light outputthat is comparable to a commercial crystal.

D. Light Attenuation

The transparency of CMS structures, as described previously,should allow the use of much thicker films, with improved de-tection efficiency, while their columnar nature suppresses lat-eral light loss. The individual gamma-ray interactions in sucha scintillator can be located well enough to yield high spatialresolution. In order to measure the light transparency or de-gree of light attenuation, a CMS LaBr :Ce sample measuring1 mm thickness was evaluated at the University of Arizona’sCenter for Gamma Ray Imaging (CGRI). A finely collimated,50 m wide, Co source was scanned from bottom to top edgeof the sample’s thickness, with the sample facing down to aPMT detector. Gamma photopeak spectra were measured in 50m steps to record light attenuation as a function of depth. Asshown in Fig. 6, the CMS samples, represented by the red andblue plots, demonstrate a nearly constant light output as a func-tion of film thickness. This implies that the light generated atthe top of the film is equally detected by the PMT compared tothat generated at the film bottom from deep -ray interactions.The results from the CMS films exhibit remarkable transparencywithin their thicknesses, with only 1% and 8% attenuation forthe two cases. The other plots in Fig. 6 that show linear attenua-tion as a function of its thickness are from prior samples whoseprocess conditions were not completely optimized. The low at-tenuation in the CMS samples compared to non-CMS samplesas seen from Fig. 6 are a result of tight control of HWE deposi-tion parameters and process optimization over years. This rep-resents a significant accomplishment in itself, however, furtherefforts are needed to translate such a performance in (1 to 2 cm)thicker films.

E. Spatial Resolution Using X-Rays

Spatial resolution was measured by imaging standard linepair phantoms from Nuclear Associates (Model 07-538) using

BHANDARI et al.: LARGE-AREA CRYSTALLINE MICROCOLUMNAR LABR :CE FOR HIGH-RESOLUTION GAMMA RAY IMAGING 7

Fig. 6. Positions of the 122 keV photopeak as a function of the point of irra-diation along the height of LaBr :Ce and LaCl :Ce scintillator films. Constantpeak positions for CMS LaBr :Ce films (red and blue) demonstrate efficientlight transmission through the film and the transparency of the CMS structure.The violet, green, and magenta plots refer to samples that predate CMS samplesand show decreasing light intensity as a function of thickness, which impliessignificant light absorption.

CMS LaBr :Ce films. The CMS films were coupled to a Photo-metrics CCD via a 3:1 fiberoptic taper. A Gendex X-ray gener-ator was used at a source-to-detector distance of 45 cm with 70kVpX-rays and images were flat-field corrected to reduce noise.The resulting images were analyzed to measure the contrasttransfer function (CTF(f)) as a function of spatial frequency.Representative images and a line profile at 3 LP/mm measuredusing a 1 mm thick CMS LaBr :Ce film is shown in Fig. 7. Thefilm resolves 3 LP/mm at 10% modulation. Considering thatthe film is 1 mm thick, this is excellent imaging performance,showing an intrinsic resolution of m for high-contrasttargets. As a note, typically such performance is expected frommicrocolumnar CsI:Tl films nomore than 500 m thick and spe-cially designed for digital radiography.

F. Spatial Resolution Using Bazooka SPECT

The spatial resolution of a 1mm-thick CMSLaBr :Ce samplewas tested at the CGRI at University of Arizona. The samplewas mounted in a Bazooka SPECT test system [15], in con-tact with the 25 mm diameter fiberoptic faceplate of the Prox-itronic BV 2533 image intensifier. A slit source, composed of a50 m-wide tungsten slit ( cm long) was imaged using a 10mCi Co source (122/136 keV), located about 17 cm from theslit to ensure flood illumination. The beam of the slit source in-tersected the detector crystal at normal incidence. The camera’sframe rate was 120 f/s, which ensured hit per frame. A listmode data set with approximately 70 000 hits was acquired.These data were analyzed by first convolving each frame with a3 3 median window filter to smooth the clusters (gamma rayhits) and eliminate isolated hot pixels. A threshold was then usedto identify hits, and the centroid of each hit was determined.The resulting slit images in the integrating and photon countingmodes of operation of the Bazooka SPECT detector are shownin Fig. 8(top). Fig. 8(top left) shows what results when all signalclusters from all gamma ray hits are summed; this is an inte-grated image, similar to measuring energy fluence in an X-rayimaging system. Fig. 8(top right) shows the slit image formed

Fig. 7. (Top) X-ray image of a line pair phantom and (bottom) plot of the corre-sponding line profile at 3 LP/mm. These data show the intrinsic film resolutionof 3 LP/mm ( m) CTF with % modulation.

by summing all of the centroids of the individual gamma rayhits; this corresponds to the Bazooka SPECT camera operatingas a single-photon imaging system, similar to an ultra-high-res-olution gamma camera.Not surprisingly, there is a significant spatial resolution ad-

vantage to estimating the centroid of each gamma ray hit; i.e.,operating in single-photon mode. Fig. 8(bottom) shows a pro-file across each slit image of Fig. 8(top left and right), as linespread functions (LSFs). The spatial resolution, as measured bythe FWHM of the LSF, is m in integrating mode, but itis 138 m in single-photon-detection mode. This is remarkableresolution from a -ray imaging system, and demonstrates theefficacy of high-resolution imaging using the CMS scintillatorfilms.

IV. CONCLUSION

RMD’s hot wall evaporation (HWE) method has successfullydemonstrated high growth-rate (25–50 m/min) fabrication oflarge area LaBr scintillators with microcolumnar morphology.The CMS LaBr :Ce samples measuring 0.6 to 2 mm thicknessand 3 to 7 cm in diameter were successfully fabricated. Ourwork has demonstrated significant progress in minimizing lightattenuation, with less than 10% attenuation in 1 mm thick films.The scanning electron microscopy of the cross-sections for

the CMS film reveals a crystalline microcolumnar structure,

8 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 60, NO. 1, FEBRUARY 2013

Fig. 8. A slit image acquired using LaBr :Ce in Bazooka SPECT detector. (Topleft) Standard integrated image (no event centroid determination), (top right)single-photon image (event centroid determination), and (bottom) line spreadfunctions of the images produced by the two methods.

which is highly oriented and extends top to bottom edge ofthe film’s cross-section. This morphology, which is unique toHWE-fabricated films, is responsible for high intrinsic spatialresolution of m measured in single-photon countingmode using the Bazooka SPECT detector. The scintillationlight response measured from different areas of a cm diam-eter LaBr :Ce sample has been confirmed to be very uniformin brightness and energy resolution. This demonstrates theuniformity of dopant distribution and growth rate afforded bythe HWE process. The energy resolution of % (122 keV)for CMS LaBr :Ce is better than the 11% (122 keV) resolutionfor the gold-standard NaI:Tl scintillator.To date, we have produced a LaBr sample measuring 2 cm

thick and 7 cm in diameter, demonstrating the efficacy of HWEfor large volume scintillator fabrication. Thick samples needfurther improvements in terms of attenuation and response uni-formity, and efforts are currently underway towards achievingthis goal.The emission wavelengths of the CMS LaBr films are char-

acteristic of the dopants present in the film; i.e., Ce -dopedLaBr emits at 360 to 380 nm and Pr -doped emits variouslyat 489, 532, 621, 646, 682, and 735 nm, which are similar inemission to their single-crystal equivalents.

Thus, LaBr scintillator fabrication by the HWE process istime-efficient and therefore can be cost-effective. The fabricatedLaBr scintillator films demonstrate potential to meet the needsof the next generation gamma ray imaging.

ACKNOWLEDGMENT

The authors would like to thank S. Cool (RMD, Inc.) for hisvaluable comments.

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