here n is the dimension of the μth irreducible repreentation, g the order of the group and Xi the character the ith class. C; is the sum over all representaon matrices of the class i. For μ-6 we find that (k|e6|k>=1 for 2 k=±1, ±5, ±7, and all other lements are zero. The general result is that any three airs of linear combinations of these 6 basic functions ill transform like г. The remaining two basic func

[1] Lewiner, J., and Meijer, P. H. E., J. of Res. Nat. Bur. Stand. (U.S.), 73A (Phys. and Chem.), No. 2, 241-247 (Mar.-Apr. 1969).

[2] Hutchings, M. T., Solid State Physics 16, 227 (1964). [3] Wybourne, B. G., Phys. Rev. 148,317 (1966).

[4] Geschwind, S., and Remeika, J. P., Phys. Rev. 122, 757 (1961). [5] Stevens, K. W. H., Proc. Phys. Soc. (London) A65, 209 (1952). [6] Bethe, H., Ann. der Phys. 3, 133 (1929).

[7] Opechowski, W., Physica 7,552 (1940).

[8] Luttinger, J. M., and Kittel, C., Phys. Rev. 73, 162 (1948). See also J. de Boer and R. Van Lieshout, Physica 15, 569, 1949. R. Lacroix, Helv. Phys. Acta 30, 374 (1957). (All references are for cubic field only.)

[9] Heine, V., Group Theory in Quantum Mechanics (Pergamon Press).

[10] Meijer, P. H. E., and Bauer, E., Group Theory, Amsterdam, North Holland Publishing Co., 1962.

(Paper 75A5-683)

hearn, A. J., Quantitative analysis of solids by spark source lass spectrometry (Proc. Intern. Conf. on Mass Spectroscopy, yoto, Japan, Sept. 6-13, 1969), Chapter in Recent Development in ass Spectroscopy, K. Ogata and T. Hayakawa, Eds., pp. 150-157 Iniversity of Tokyo, Press, Tokyo, Japan, 1970).

ey words: Fluctuations; homogeneity; ion sensitive emulsion; ass spectrometry; precision; quantitative analysis; solids; spark urce; trace elements.

spark source mass spectrometry, the ion sample generally mispresents the solid sample. Consequently, standard reference aterials are needed for direct comparison with the unknown or r the determination of correction factors. The precision in measureent of matrix element ions, trace element ions and their ratio is pendent on the homogeneity of the ion sensitive emulsion used. ethods for testing emulsion uniformity and results on Q2 plates e presented. In some the nonuniformity is less than 5%; in others > to a 60% change in 8 cm has been detected. Under optimum nditions, matrix ions are measured with an RSD ≤ 5% but with ace ions this precision is usually poorer. This means that the ace element contents of the recorded ion sample fluctuate. The ace ions in a spark source ion sample from NBS SRM Platinum 1 fluctuate but not independently. Ion microprobe and other sts should indicate whether the observed fluctuations arise in lid sample inhomogeneities or in fluctuations in the production d/or transmission of trace ions in SSMS.

mer, H. E., Methods of calibrating weights for piston gages, t. Bur. Stand. (U.S.), Tech. Note 577, 54 pages (May 1971) 55 nts, SD Catalog No. C13.46:577.

ey words: Balance; buoyancy; calibration; standards; substitution eighing; transposition weighing; true mass; uncertainty; value. enerally weights for piston gages have odd denominations that e often not readily calibrated by intercomparison methods. Theree, these weights are frequently calibrated by direct comparison ethods. This paper presents direct comparison methods for caliating piston gage weights for use with both equal-arm balances d single-pan balances. Methods of estimating the uncertainty of e values obtained are given. Also included are methods of checking blunders or gross errors.

sloss, P., Rebbert, R. E., Sieck, L. W., Ion-molecule reactions the radiolysis of ethane, J. Chem. Phys. 54, No. 6, 2612-2618 arch 15, 1971).

ywords: Charge transfer; deactivation; ethane; ion-molecule; ctions: mass spectrometry; radiolysis.

→sec

e reactions of ions generated in ethane irradiated with gamma - have been studied by analyzing the neutral products formed in ctions with ethane and with other molecules. In experiments he presence of added (C,D,);CDCD, for example, it is shown that following reactions take place: C¿H; + C2H1 → (C‚H¡,)* 1, + H2; sec-CH$ + (C2D;)1⁄2CDCD; → n-CHD + CD. The inmediate (CH)* ion can be stabilized by collisions, and will then dergo an undetermined reaction (neutralization or proton transto give n-C,Ho as a product. The overall rate constant for reacof the ethyl ion with ethane is shown to be≥ 10 cm3/molee-s. Similarly, it is demonstrated that the reaction: C2H; + C2H«→ 1, leads predominantly to the formation of t-butyl ions under these

conditions: C1H$ + (C2D;)1⁄2CDCD3 · (CH3)3CD+C6D Supplementary experiments performed in a photoionization mass spectrometer demonstrate that ethyl ions undergo a "resonance H transfer" reaction with ethane: CH; +C¿Ð ̧→CD; +C2H,D2, with a rate constant of 1.1 × 10 10 cm3/molecule-s. Similarly, the ethane parent ion reacts with ethylene: CH« +C2D‡ C2H, + C2H2D. A series of experiments carried out in the presence of added CD, demonstrate that the reactions of ethylene ions, such as: CH; +C2D1 C,D,H, can be conveniently studied in an ethane system.

Becker, D. A., LaFleur, P. D., Production and certification of NBS biological standard reference materials, Proc. 4th Annual Conf. on Trace Substances in Environmental Health, June, 1970, pp. 433-435 (University of Missouri, Columbia, Mo. March 1971).

Key words: Biological standards; blood standard; botanical standards; environmental samples; standard reference material; tissue standard; trace analysis.

The use of adequate standards is important in the trace element analyses of complex biological materials comprising many environmental and biomedical samples. Available biological materials for interlaboratory comparisons are almost exclusively "round-robin" type samples, and have failed to provide a well-characterized widely distributed and easily available standard. The NBS Office of Standard Reference Materials is in the process of acquiring, analyzing and certifying a series of biological standards. These standards, when issued, will include six botanical standards, a blood standard and a tissue standard.

Bennett, H. S., Absorbing centers in laser materials, J. Appl. Phys. 42, No. 2, 619–630 (Feb. 1971).

Key words: Antimony; heat conduction; laser materials; Nd-doped glass; platinum; stress components; thermoelastic theory.

One of the severe problems encountered in high-power-solid-state laser systems is the thermal damage to laser rods and optical elements arising from metallic or dielectric inclusions; i.e., impurities with physical and optical properties which differ substantially from those of the host material. Such inclusions may absorb an appreciable amount of the incident radiation and thereby may produce major stresses within the host material. In this paper, the dependence of the maximum value of the tensile stress upon the size of the inclusion and upon the physical properties of the host is examined. The feasibility of using optical techniques to detect metallic and dielectric inclusions in laser materials before they cause damage also is studied. The computations suggest that the use of laser pulse widths of the order of microseconds or longer may be more promising for the detection of small incipient absorbing centers than the use of nanosecond pulse widths.

Bennett, H. S., F centers in ionic crystals: Semicontinuumpolaron models and polarizable-ion models, Phys. Rev. B. 3, No. 8, 2763-2777 (April 15, 1971).

Key words: CaF2; CaO; F center; internal Stark effect; KCl; optical phonons; polarizable ion model; semicontinuum polaron model.

The three lowest-lying F center states for KCl, CaO, and CaF2 are calculated within the framework of five semicontinuum polaron models and one polarizable ion model. The movement of the nearest neighbor ions to the F center and the F electrons are treated in a

self-consistent manner in these models. Exact solutions to these models for the states involved in the transitions of optical absorption and emission are obtained numerically. In addition the internal Stark effect due to noncubic phonons is estimated. The absorption, the emission energy, and the lifetime of the first excited state are evaluated for the six models. It is shown that a semicontinuum polaron model agrees best with the experimental results for KCl and that the polarizable ion model gives the best results for CaO and CaF2. In addition the semicontinuum polaron model and the internal Stark effect predict that the relaxed state in KCl consists of a strong mixing of 2p-like and 2s-like states which are spatially diffuse.

Boyne, H. S., Laser frequency stabilization techniques and applications, Proc. 24th Annual Frequency Control Symp., on Frequency Control, Atlantic City, N.J., April 27-29, 1970, pp. 233339 (U.S. Army Electronics Command, Fort Monmouth, N.J., 1970), IEEE Trans. Instr. Meas. IM-20, No. 1, 19–22 (Feb. 1971).

Key words: Frequency; laser; laser frequency measurement; stabilization; techniques; time standard.

A review of progress in laser stabilization techniques and laser frequency measurement is given. Methods for relating laser frequencies to the time standard and methods for absolute laser frequency stabilization are described. Experimental information on reproducibility and noise characteristics is reported. Application to frequency and wavelength standards is discussed.

Boyne, H. S., Hall, J. L., Barger, R. L., Bender, P. L., Ward, J., Levine, J., Faller, J., Absolute strain measurements with a 30 meter vacuum interferometer, Proc. Conf. Laser Applica tions in the Geoscience, Huntington Beach, Calif., June 1969, pp. 215-225 (1970),

Key words: Earth strain; earth tide; geophysics; laser strainmeter; seismograph.

We present details on the design and performance of a 30 meter interferometric strain gauge. We also discuss a practical method for recording absolute earth strain measurements by comparing length changes in the interferometer with an absolute wavelength standard.

Cezairliyan, A., A high speed method of measuring thermal expansion of electrical conductors, Rev. Sci. Instr. 42, No. 4, 540 541 (April 1971).

Key words: High-speed measurements; high temperature; platinum; thermal expansion.

A transient method for the measurement of thermal expansion of electrical conductors is described. The method is based on detecting the change in radiance coming from a constant radiation source as a result of the expansion of the specimen placed between the radiation source and a radiation detecting system. The specimen can be pulse heated from room temperature to near its melting point in less than one second and pertinent experimental quantities can be measured with a time resolution of 0.4 ms and a full-scale signal resolution of one part in 8000. To check the method, preliminary experiments were performed on platinum in the temperature range 300 to 700 K. The estimated inaccuracy of the results is within 5 percent. The agreement of the results with those in the literature is within 3 percent.

Chappell, S. E., Humphreys, J. C., Silicon detector measurements of energy deposition in aluminum by monoenergetic electrons (Proc. Annual Conf. Nuclear Space Radiation, La Jolla, Calif., July 1970), IEEE Trans. Nuclear Science NS-17, No. 6, 272-277 (Dec. 1970).

Key words: Absorbed energy vs depth; absorbed-energy distributions; incident monoenergetic electrons; Monte Carlo calculations; simi-infinite aluminum medium; silicon detector.

The energy deposited at various depths in aluminum by incident monoenergetic electrons has been measured with a silicon semi conductor, transmission detector. Beams of monoenergetic electrons with incident energies of 0.50, 0.75, and 1.0 MeV were directed normally on a semi-infinite slab of aluminum in which a 0.196-mm silicon detector was positioned at various depths. The pulse-height distributions recorded with the detector were converted to absorbed energy distributions from which the probability of energy absorption per incident electron in the specific layer, as well as the absorbed energy as a function of depth in the material, could be determined The curves of absorbed energy as a function of depth obtained for aluminum at each energy were compared to those calculated by Berger and Seltzer, employing a Monte Carlo method. Good agreement is shown between calculations and measurements.

Collin, G. J., Ausloos, P., Ion-molecule reactions in the condensed-phase radiolysis of hydrocarbon mixtures. III. Reactions of i-CH¡ and tert-CH; ions originating from neopentane, J. Am. Chem. Soc. 93, No. 6, 1336-1340 (March 24, 1971).

Key words: Ion-molecule reactions; neopentane; neutralization; radiolysis; unimolecular/fragmentation.

The liquid phase radiolysis of neopentane has been investigated in the presence of various hydrocarbons and electron scavengers. It is found that the neopentane parent ion dissociates to vied t-C4H and iso-CH ions with optimum yields of ~2.4 and ~0.9. respectively. The iso-CH ion reacts with various added alkanes by the H transfer mechanism: CH+RH2 →iso-C‚H1R The relative rates of reaction with different RH2 additives have been determined, and show the same trends as those observed for these reactions in the gas phase. That is, the rate is seen to increase with an increase in the exothermicity of the reaction (as calculated from gas phase thermodynamic data). The effect of the AH of reacta is, however, more pronounced in the liquid than in the gas phase. The t-butyl ion reacts more slowly with alkane additive than does the isobutene ion, but reacts effectively with isobutene and combines with a negative ion from CCl, to form t-C,HCl. Neutralizat of the t-butyl ion leads to the formation of isobutene and propviete Danos, M., Gibson, B. F., Very high-momentum components in nuclei and far "subthreshold" production of quarks, Phi Rev. Letters 26, No. 8, 473–476 (Feb. 22, 1971).

Key words: Coherent production; cosmic rays; high momentum components; many-body clusters; nuclei; quarks.

An estimate, valid for inelastic processes, of the probabilities the high-momentum components in nuclei resulting from mary body correlations, together with data from Serpukhov, is used ha derive upper limits for the quark-production cross section near the threshold.

Danos, M., Spicer, B. M., Quartet structure in light nuclei. Z. Physik 237, 320–326 (1970).

Key words: Collective correlations; four particle-four hole states. light nuclei; quartets; rotational states; vibrational states.

The nature of the low-lying even parity, even spin states of b nuclei are discussed in terms of the quartet scheme, and many e their properties can be given by it. These states are also the lying states important in the collective correlations model of the cam dipole resonance, and the quartet scheme thus provides a descripti) * of them.

DeVoe, J. R., Spijkerman, J. J., Mössbauer spectrometry, dr. Chem. Annual Reviews 42, No. 5, 366R-388R (April_1471)

Key words: Chemical applications; literature; Mössbauer spect copy; review.

A review of the literature on chemical applications of Mosstat Spectrometry for 1968 and 1969 are presented. This is done pr marily with a table of pertinent information on compour ↑ techniques. New developments in the field are also presented

Dibeler. V. H., Photoionization studies and thermodynamic properties of some halogen molecules, (Proc. Intern. Conf. on Mass Spectroscopy, Kyoto, Japan, Sept. 8-13, 1969), Chapter in Recent Development in Mass Spectroscopy, K. Ogata and T. Hayakawa, Eds., pp. 781-790 (University of Tokyo Press, Tokyo, Japan, 1970).

Key words: Chlorine monofluoride; dissociative ionization; fluorine; heats of formation; hot bands; hydrogen fluoride; ion pairs; mass spectrometry; molecular ionization; photoionization; vacuum ultraviolet.

Mass spectra and ion yield curves for molecular and dissociative ionization processes are measured for fluorine, hydrogen fluoride, chlorine, and chlorine monofluoride by means of a combined vacuum av monochromator and mass spectrometer. Ionization and dissociation energies and heats of formation of the molecules are obtained and compared with values derived from thermochemical and spectroscopic studies.

Fatiadi. A. J., Determination of inososes with an alkaline solution of copper(II) oxalate-tartrate complex (the Somogyi reagent) and reaction mechanisms involved, Carbohy drate Res. 17,419-430 (March 1971).

Key words: Determination; electron-transfer; inosose; oxidation; quantitative; radical; reagent.

Four inososes have been analyzed with the Somogyi reagent and mpirical equations for their quantitative determination were derived because reaction of the Somogyi reagent with inososes afords nonstoichiometric quantities of cuprous oxide, and each nosose has a different reducing power.

Results from spectrophotometric and e.s.r. studies of the mechaism of oxidation of inososes with the Somogyi reagent at 25 to 55° re in agreement with a one-electron transfer process; however, at 10 to 100°, extensive degradation of inososes by the Somogyi reagent ccurs, doubtless caused by generation of transient radicals during he oxidation, as evidenced by results of a radical-scavenging xperiment.

Pickett, F. R., Resistivity of polycrystalline aluminum and copper in high magnetic fields: The effect of temperature and urity, Appl. Phys. Letters 17, No. 12, 525-527 (Dec. 15, 1970). ey words: Aluminum; copper; magnetoresistance.

ata are presented on the resistivity of polycrystalline aluminum nd copper at 40 kOe and at temperatures from 4 K to 30 K. Specien purity varies over three decades of residual resistance ratio. For ther metal, the actual resistivity measured in the field at a given mperature decreases with increasing specimen purity. This result important for proposed high magnetic field applications of these etals.

rcolow, W. H., Technical Standards Coordinator, Clinical therometers (Maximum-self-registering, mercury-in-glass), t. Bur. Stand. (U.S.), Prod. Stand. 39–70, 12 pages (May 1971) cents, SD Catalog No. C13.20/2:39–70.

y words: Clinical thermometers; glass thermometers, clinical; rcury-in-glass thermometers; thermometers, self-registering, nical.

is Voluntary Product Standard covers the requirements and thods of testing maximum-self-registering, mercury-in-glass rmometers of the types commonly used for measuring body tem atures, such as oral and rectal types in both regular and basal perature scales. It is intended to serve as a nationally recog ed basis for certification of compliance by manufacturers and procurement purposes by consumers. The standard includes uirements for bulb and stem glasses, mercury, dimensions, perature scale ranges, and graduations, and performance criteria thermometer aging, hard shaking determination, and accuracy scale reading.

Garner, E. L., Machlan, L. A., Shields, W. R., Standard Reference Materials: Uranium isotopic standard reference materials, (Certification of uranium isotopic standard reference materials), Nat. Bur. Stand. (U.S.), Spec. Publ. 260-27, 162 pages (April 1971) $1.25, SD Catalog No. C13.10:260-27.

Key words: Absolute isotopic abundance; ignition procedure; isotopic standards; mass spectrometry; stoichiometry; uranium.

An ignition procedure has been developed that will yield reproducible stoichiometry for U3Os. The effects of temperature, length of ignition, rate of cooling, pressure and type of atmosphere were investigated. This ignition procedure has been used for the blending of high purity 235U and 238U separated isotopes to prepare calibration standards for the determination of bias effects in the thermal emission mass spectrometry of uranium. Weight aliquoting was used to prepare calibration mixes with 235U/238U ratios of more than 10 and less than 0.1 and to add a 233U spike for the determination of minor isotope abundances in the uranium isotopic standards by the isotope dilution technique.

A description of the unique features of the mass spectrometer instrumentation including the source, NBS collector and expanded scale recorder are given. Two specific analytical procedures were used for the isotopic analysis of uranium and are adaptable, within a general framework, to fit the particular ion current intensity requirements of a wide range of isotopic distributions. Mass discrimination due to evaporation and ionization on the filaments, and other parameters such as temperature, time, sample size, sample mounting, total sample composition, acidity, filament material, pressure, nonohmic response, R-C response and source memory were studied as part of the development effort to establish sound analytical procedures.

The absolute isotopic abundances of 18 uranium SRMs were determined by thermal emission mass spectrometry. The general approach was to determine absolute 235U/238U ratios by using calibration mixes to correct for filament bias. Then the absolute 234U and 236U were determined by 233U isotope dilution. For SRM U-0002, isotope dilution was the only practical means of determining the low abundance of 235 as well as the 234U. The limits given for the isotopic composition of the uranium SRMS are at least as large as the 95 percent confidence limits for a single determination and include terms for inhomogeneities of the material as well as analytical

errors.

Geltman, S., Burke, P. G., Electron scattering by atomic hydrogen using a pseudo-state expansion II. Excitation of 2s and 2p states near threshold, J. Phys. B: Atom. Molec. Phys. 3, No. 8, 1062–1072 (Aug. 1970).

Key words: Close coupling calculation; electron scattering; pseudostate expansion.

The pseudo-state modification of the close-coupling expansion is applied to the 2s and 2p excitation of atomic hydrogen by electron impact. Pseudo-states are used which assure the implicit inclusion of all important excited state polarizabilities. A detailed comparison is made with results obtained from other modifications of the closecoupling expansion and the eigenphase minimum principle is used to determine the best result for each partial cross section. Comparison of the theory and experiment in the first electron volt above the n = 2 threshold shows very good agreement in the ratio Q(1s-2s)/ Q(1s-2p), but a 20% discrepancy exists between the individual cross section magnitudes when experiment is normalized to the Born approximation at higher energies.

Green, M. S., Cooper, M. J., Sengers, J. M. H. L., Extended theromodynamic scaling from a generalized parametric form, Phys. Rev. Letters 26, No. 9, 492–495 (March 1, 1971).

Key words: Coexistence curve; critical point; liquid-gas phase transition; parametric form; scaling; thermodynamic properties. The Josephson-Schofield parametric representation for lowest order thermodynamic scaling is generalized, introducing an additional critical exponent. Expansions around the critical point are deduced for the various thermodynamic properties of fluids and to lowest order, the asymptotic power law forms are recovered. Ex