Band 25, Heft 12

In dem orthokomplementären, quasimodularen Verband der Teilräume des Hilbert-Raumes lassen sich die Relationen der Implikation und Kommensurabilität als Operationen definieren. Dadurch wird es möglich, diesen Verband als einen quantenlogischen Aussagenkalkül zu interpretieren. Die Begriffe Implikation und Kommensurabilität stimmen dabei überein mit den im Rahmen der Logik operativ definierten entsprechenden Begriffen.

The Mößbauer effect of the 129 keV transition in 195Pt has been observed. By use of a Ge(Li) detector any contribution from the strong 99 keV Mößbauer line could be eliminated. The width of the resonance absorption line corresponds to the natural line width. We derived from the magnitude of the observed Mößbauer effect the branching ratio in the decay of the 129 keV level as I (129)/I (31) = ( 5.7 ± 1.6)% .

The derivation of a general formula for the coefficient of dielectric recombination is reviewed, and approximate formulae known in the literature are discussed. With the aid of Burgess' simplified formula calculations of the coefficient of dielectronic recombination for the elements C, O , Ne, Mg, Si, S and Fe in the temperature range 108 - 4 x 106 °K are performed. The results are presented in figures and in tabular form. Taking into account dielectronic and radiative recombination, the ionization equilibrium for the various stages of these elements is determined and compared with recent results of other authors.

The rate coefficients for electron collisional-radiative ionization and recombination have been calculated on the basis of a simplified level scheme for hydrogenic ions in a homogeneous and fully contained plasma with self-absorption for (Doppler broadened) Lyman a radiation. The energy distribution of the electrons is assumed to be Maxwellian. Photoionization is neglected. The cal-culation have been done for a range of electron temperature of Z 2 to 10 Z 2 eV and electron density of 10 14 Z 7 to 10 24 Z 7 m -3 , where Z is the charge number of the bare nucleus.

The compression temperature of a theta pinch is calculated as a function of the circuit para-meters and the final /?-value of the plasma. One of the results is that the temperature, T, at the peak magnetic field, B, scales of (B B) t/s , where B is the initial rate of rise of the magnetic field. A possibility of combining two capacitor banks to increase the implosion heating rate is discussed. Abstract The compression temperature of a theta pinch is calculated as a function of the circuit parameters and the final β-value of the plasma. One of the results is that the temperature, T̂, at the peak magnetic field, B, scales of (Ḃ, ̂B̂) t/s , where Ḃ is the initial rate of rise of the magnetic field. A possibility of combining two capacitor banks to increase the implosion heating rate is discussed.

A hydrodynamic model for the heating of a plasma generated by the interaction of an intense giant laser pulse with a plane, solid target is developed. It is shown that in the case of nanosecond light pulses and a finite focal spot diameter, the plasma production may be considered as a steady state problem. Expressions for the electron temperature, the expansion energy of the ions, and the total particle number in the plasma as a function of the incoming light intensity are derived. An estimate of the ion temperature is discussed.

Experiments on laser produced plasmas with light intensities between 2·10 11 and 5·10 12 W/cm 2 are reported. Measurements of the electron temperature and the expansion energy were performed. In the case of LiD targets the highest temperature observed was 200 eV. Using carbon targets a maximum temperature of 330 eV was measured. The corresponding expansion energies reach values as high as 13 keV. The experimental results are in good agreement with a stationary, hydrodynamic theory. We conclude from our data that in our LiD and C plasmas ions and electrons have the same temperature.

Ion-slip coefficients in Demetriades and Argyropoulos' generalized Ohm's law are studied quan-titatively in the first approximation for partially ionized Ar and He under various non-isothermal gas conditions. The macroscopic forces due to collisions between electrons, ion, and neutral atoms are accounted by averaging the momentum transfer cross sections over the Maxwellian velocity distributions of the colliding particles. To incorporate the appropriate interpolation and extrapola-tion techniques in the low energy limit, Frost and Phelps' cross sections for electron-atom collisions and Dalgarno's value for ion-atom resonant charge-transfer cross sections were used. The weighted average momentum transfer cross sections thus obtained, which are also important in other diffusion and transport processes, are tabulated at various particle kinetic temperatures for both gases. A family of curves representing values of ion-slip coefficients calculated from these data is plotted. With the generalized Ohm's law written in its inverted form, the influence of ion-slip on the "Hall conductivity" in Kruger et al's formulation is discussed.

Frequenzen und relative Intensitäten der Hyperfeinstrukturlinien eines Rotationsübergangs eines zweiatomigen Moleküls, dessen beide Quadrupolwechselwirkungsenergien vergleichbar mit der Rota-tionsenergie sind, werden exakt berechnet. Aus den Rotationsübergängen J = 2 → 3, 14→15, 15 →16, 16→17 und 17→18 von 115 ln 127 J wurden die Dunham-Koeffizienten und Kernquadru-polkopplungskonstanten dieses Moleküls bestimmt: y 01 = 1105,246(15) MHz, Y 21 = 2,4 (6) kHz, Y 11 = -3,121 (6) MHz, Y 02 = -227 (13) Hz, e q v Q( 115 ln) = - 607,5 (5) +0,8 (8) (v+1/2) MHz, e q v Q( 127 J) = -386,4 (4) -2,3 (8) (v +1 /2) MHz.

A closed expression for the vibration-rotation hamiltonian of linear molecules is derived and discussed. By use of the commutation relations and sum rules this expression is then rearranged to a form similar to that of WATSON 1 for nonlinear molecules.

The effects of internal strains on the tunneling levels of KCl : Li are investigated quantitatively. The method, as developed in a preceding paper by TIMME, DISCHLER, and ESTLE 1 , is further improved here. A reinterpretation is presented for two experimental results reported in the literature: the resonances in the phonon spectrometer curve and the specific heat (Schottky) anomaly. The agreement with these experiments and also with paraelectric resonance is good, if isotropic strains are assumed with an average energy of 20 GHz, corresponding to a stress of 30 ± 10 kp/cm 2 . For the cube edge tunneling interaction a value of 10 GHz is derived.

The Raman spectra of the monoclinic compounds strontium Chromate, lead Chromate and of the mineral crocoite (PbCrO 4 ) have been recorded at 300 °K and 77 °K. The spectrum of the orthorhombic modification of lead Chromate has also been recorded. The spectra of the monoclinic and of the orthorhombic PbCrO 4 were found to be indistinguishable, whereas the spectra of the isomorphous monoclinic salts SrCrO 4 and PbCrO 4 are remarkably different. Inversion doubling was observed in SrCrO 4 but less distinctly in monocrystalline crocoite.

From measured intensity functions, published in a previous paper, partial interference functions, partial pair correlation functions, partial atomic distribution functions, and partial coordination numbers were calculated and discussed. According to the theory of Faber and Ziman, the electrical resistivity of molten Mg-Sn alloys was calculated from the partial interference functions and from pseudopotentials reported by Animalu and Heine. The calculated values, being normalized to the resistivity of the molten components, are in good agreement with values measured by a rotating field method. The partial interference functions are derived by the assumption of independency of concentration. This assumption is proved by discussion of the partial coordination numbers and the results of electrical resistivity determinations.

The spatial and temporal development of self-focusing of light pulses is investigated. The beam diameter in CS 2 and molten para-di-chlorobenzene decreases with increasing incident laser power to small values in good agreement with theory. The strong influence of beam divergence, non-linearity of refractive index, and absorption on self-focusing action is found to agree well with numerical calculations. It is shown that both backward stimulated Brillouin and Raman scattering terminate the self-focusing process.

In this article an apparatus is presented which gives a precisely known multiplication of the elementary effect in thermal diffusion experiments, avoiding the drawbacks of the swing-separator (Trennschaukel). This is achieved by using a different method of concentration nivellation than customary with the swing-separator, viz. thermosyphon action.

The influence of the neutron dose, the neutron spectrum and the sample preparation on Argon diffusion in neutron-irradiated KCl crystals was investigated. No effect of the concentration of the rare gas atoms nore of any other aliovalent atoms produced by nuclear reactions was observed. However radiation damage introduced by the fission neutrons seemed to influence the diffusion behavior. This radiation-damage could be annealed in the presence of thermal or slow epithermal neutrons. Lattice defects which are developed by cleaving of the crystals influenced the gas diffusion too.

The present paper presents the results of an investigation of the nucleation process during the formation of evaporated gold films on UHV cleaved rocksalt single crystals. The dependence of the nucleation rate and the sticking coefficient on the substrate temperature and deposition rate has been studied in detail. The results are interpreted in terms of a kinetic nucleation model. It is shown that this interpretation based upon atomistic considerations is successful and allows to determine the main model parameters, such as the binding energy of the single atom to the substrate or the activation energy of surface diffusion. An upper limit can be given for the jump distance of the single atom.

The adsorption of CO on a clean Pd(lll) surface has been studied by means of low energy electron diffraction (LEED), contact potential measurements and flash desorption. At coverages ㊀ between 1/3 and 1/2 ordered adsorption phases are observed for which structure models are derived. The maximum increase of the work function Δϕ is about 1 eV; Δϕ is proportional to ㊀. Adsorption isotherms have been measured between 100 and 300 °C and the isosteric heat of adsorption E ad has been determined as a function of ㊀. E ad is constant (34 kcal/mole) up to ㊀ = 1/3 and then decreases owing to structural influences and intermolecular interactions.

An approximation method for determination of vibrational resonance parameters, based upon the invariance of anharmonicity constants against phase changes, is described. Several examples, including resonances in the spectra of CO 2 , OCN - , CH 3 I, and some 1,1-disubstituted ethylenes, are given.

Zinc sulphate decomposes upon melting. Molten Li 2 SO 4 -ZnSO 4 and Na 2 SO 4 -ZnSO 4 are thermally stable with up to 80 mole% of ZnSO 4 . We have measured the density and electrical conductivity of these melts. By extrapolation we have calculated the density (ϱ) and molar electrical conductivity (Λ) of pure molten zinc sulphate and we have obtained (t in °C) ϱZnSO 4 = 3.463 - 0.470 x 10 -3 t(g/cm 3 ), ΛZnSO 4 = 0.0950 t-35.4 (cm 2 /ohm, mole).

The phase diagram and electrical conductivity of cubic lithium sulphate with small quantities of thulium sulphate and aluminium sulphate have been measured. We have also measured the tracer diffusion coefficients of Tm 3+ and Al 3+ in pure cubic lithium sulphate. The diffusion coefficients of the trivalent ions are much lower than those of the univalent and divalent cations. The results indicate that the trivalent ions are trapped in the lattice.

Iwata, Tanaka and Nagakura, and Hayashi, Iwata and Nagakura have observed in ethylether-isopentane solutions (1 : 1) at 77 °K, in the case of the complexes of tetracyanobenzene (TCNB) as the electron acceptor with the electron donors mesitylene (Me), durene (Du) and hexamethyl-benzene (HMB), an unstructured long-lived, long-wave emission band by exciting the complexes in the charge transfer (CT) band. They interpreted the 11, lw band as a CT-phosphorescence of a t t charge transfer triplet excited state | D + A" | . This would be of considerable theoretical interest and significance also for an interpretation of photochemical processes. In the present communication, we report results which lead us to a different interpretation of the 11, lw emission band under discussion. The emission spectra of the complexes of tetracyanobenzene (TCNB) with the electron donors toluene (To), p-xylene (Xy), mesitylene (Me), durene (Du) and hexamethylbenzene (HMB) were studied in glassy solutions in propylether at 100 °K. In the case of TCNB-To, -Xy, -Me and -Du, when the complexes were irradiated in the CT-band so that the complex components were not excited, we observed either the structured phosporescence band of TCNB which originates from a locally excited triplet state of complexed TCNB or, at large donor concentrations, the unstructured long-lived, long-wave emission band within the green spectral range. In the case of TCNB-HMB, only the 11, lw emission may be observed. The 11, lw unstructured emission superimposed on the structured TCNB phosphorescence may also be observed when TCNB, singly soluted in glassy solvents or crystallized, is irradiated in the 31,600 cm -1 (St S0) peak. Obviously, the 11, lw emission band may not be characteristic of the complexes of TCNB. Simultaneously with the 11, lw emission, a new molecular species X can be identified by a new absorption spectrum after irradiating either TCNB itself within the S0 —St 31,600 cm -1 peak or the TCNB-complexes within the CT-absorption band. X is formed by a reaction of the triplet ex-cited TCNB. The excitation in the long-wave absorption peak of X at about 21,000 — 22,000 cm -1 gives rise to an emission with a maximum in the same spectral range as the 11, lw emission band. Accordingly, we interpret the 11, lw emission as a delayed emission of X due to an energy transfer from the triplet excited TCNB. Abstract Iwata, Tanaka and Nagakura, and Hayashi, Iwata and Nagakura have observed in ethyletherisopentane solutions (1 : 1) at 77 °K, in the case of the complexes of tetracyanobenzene (TCNB) as the electron acceptor with the electron donors mesitylene (Me), durene (Du) and hexamethylbenzene (HMB), an unstructured long-lived, long-wave emission band by exciting the complexes in the charge transfer (CT) band. They interpreted the 11, lw band as a CT-phosphorescence of a charge transfer triplet excited state . This would be of considerable theoretical interest and significance also for an interpretation of photochemical processes. In the present communication, we report results which lead us to a different interpretation of the 11, lw emission band under discussion. The emission spectra of the complexes of tetracyanobenzene (TCNB) with the electron donors toluene (To), p-xylene (Xy), mesitylene (Me), durene (Du) and hexamethylbenzene (HMB) were studied in glassy solutions in propylether at 100 °K. In the case of TCNB-To, -Xy, -Me and -Du, when the complexes were irradiated in the CT-band so that the complex components were not excited, we observed either the structured phosporescence band of TCNB which originates from a locally excited triplet state of complexed TCNB or, at large donor concentrations, the unstructured long-lived, long-wave emission band within the green spectral range. In the case of TCNB-HMB, only the 11, lw emission may be observed. The 11, lw unstructured emission superimposed on the structured TCNB phosphorescence may also be observed when TCNB, singly soluted in glassy solvents or crystallized, is irradiated in the 31,600 cm -1 (S 1 ← S 0 ) peak. Obviously, the 11, lw emission band may not be characteristic of the complexes of TCNB. Simultaneously with the 11, lw emission, a new molecular species X can be identified by a new absorption spectrum after irradiating either TCNB itself within the S0 -St 31,600 cm -1 peak or the TCNB-complexes within the CT-absorption band. X is formed by a reaction of the triplet excited TCNB. The excitation in the long-wave absorption peak of X at about 21,000 - 22,000 cm -1 gives rise to an emission with a maximum in the same spectral range as the 11, lw emission band. Accordingly, we interpret the 11, lw emission as a delayed emission of X due to an energy transfer from the triplet excited TCNB.

Taking into account the universal correlation of the force constants of halide bonds with their respective dissociation energies (excluding the fluorides), an internuclear potential energy function of the type V(r) = D e (1-e -α(r-re) ) 2 + β (1-δ F,X ) (r - r e ) 2 e- γ(r-re) has been proposed for the diatomic halides. α und β, in the latter are constants for a specific series, γ is determined from the rotational-vibrational constant α e , and the function reduces to the ordinary Morse potential function in the case of the fluorides. It, moreover, performs as well as the Hulburt-Hirschfelder 5-parameter function, and, unlike the latter, utilizes the anharmoni-city constant ω e X e as an internal check.

Our previously proposed modification of Hoffmann's extended Hückel method is discussed, and its use in the determination of the dissociation energies of H 3 M-H type molecules where the H 3 M moiety is taken as a unit examined. The proposed technique is also used to study the angular dependence of the total potential energy of the previously studied molecules, as a consequence of which it is suggested that the proportionality constants (in this case the F e 's) are atom-atom parameters, transferable from molecule to molecule. The latter concept is used in the theoretical determination of the geometries and energetics of CH 3 , SiH 3 , NH 3 , PH 3 ,_as well as some of their ionic forms. Finally, as a result of our calculations, we suggest that CH 3 is planar with a much flatter potential minimum than CH 3 .

After a discussion of former publications on the problem of the existence of promethium in nature, studies o f our own on this problem are reported. In these researches, 200 kg of gadolinite were separated with regard to Pm by using one- and two-stage cation-exchange separations and nitrilotri-aceticacid for elution and Cu 2+ as barrier-ion. The experiments yielded a beta-activity in the mixture-fractions between Sm and Nd. Because of its chemical behaviour and its half-thickness of 4.4 mg/cm 2 that corresponds with a β-maximum energy of 230 keV ( 147 Pm: 223 keV), this beta activity could be identified as 147 Pm. For the lanthanide oxides of gadolinite a 147 Pm content of 7.3 · 10 - 17% could be deduced, which agrees well with the value of 4.5 · 10 - 17% found by Erämetsä in 20 t lanthanide oxides of 6000 t apatite. The possible origin o f the 147 Pm-isotope we found in gadolinite is discussed (fallout, actinium anomaly, spontaneous fission of 238 U, and others), and the reaction 11,Id 2,6a 14 6Nd (n, y) is supposed to be the cause of the relatively short-lived isotope. The difference between the neutron flux (36 n/cm 2 · min) that was deduced from the saturation activity of 147 Pm, and the values of the neutron flux at the earth's surface or crust (0.001-0.24 n/cm 2 · min) that up to now have been looked upon as probable by other authors, is also mentioned. Moreover, the question of the possible existence of a long-lived isomer of one of the known Pm-isotopes is rised.

Quantum Mechanics and Objective Reality A Schrödinger function (or a density matrix) can he ascribed only to an object whose isolation time is larger than its time of revolution. This condition can never be satisfied for macroscopic bodies. Consequently, the "cut" between object and observer must not separate a macroscopic body (measuring apparatus) from the rest of the universe. Hence in an analysis of the measuring process, the state vector of the universe must be introduced. An interpretation of this state vector is given which provides an objective description of nature.

NMR emission and enhanced absorption of products of radical reactions (CIDNP) is explained by nuclear spin dependent adiabatic transitions between singlet and triplet states of transient radical pairs. In magnetic fields larger than about 1 kG only S - T o -transitions contribute to nuclear polarization. From a kinetic formulation of the pair mechanism equations for quantitative calculations of CIDNP patterns are derived.

Alkyl radicals are generated by reactions of phenyl radicals in binary mixtures of substituted alkanes. CIDNP-NMR spectra of their reaction products are explained by S - T 0 -transitions in radical pairs formed in free radical encounters. From comparisons of calculated and observed CIDNP spectra the (g-factor and the proton hyperfine coupling constant of · CHCl 2 are determined [g = 2.0080 ± 0.0003, a = (- 17.0 ± 1.0) G]. The inclusion of nuclear relaxation in free radicals in quantitative CIDNP treatments is discussed, and evidence for the radical pair mechanism causing CIDNP of phenyl derivatives during dibenzoylperoxide decompositions is presented.

Mit einem 1968 beschriebenen Ionisierungsquerschnittsdetektor mit Kr 85 -β-Strahlenquelle wurden die relativen Werte der Ionisierungsquerschnitte von Stickstoff-und Halogen-Kohlen-wasserstoffderivaten bestimmt. Führt man empirisch bestimmte "Bindungsquerschnitte" analog zu der früheren Arbeit 1 ein, so stimmen die aus „Bindungsquerschnitten“ berechneten Ionisie-rungsquerschnitte innerhalb des Meßfehlers von 2% mit den gemessenen überein. Ein Vergleich der experimentell ermittelten Werte mit den nach den Verfahren von OTVOS und STEVENSON 2 (1956), LAMPE, FRANKLIN und FIELD 3 (1957) und STEVENSON und SCHISSLER 4 (1961) berech-neten Daten zeigt, daß die Methode von OTVOS und STEVENSON zwar die günstigste Übereinstim-mung für eine Reihe von Verbindungen ergibt, die maximale Abweichung bezüglich des experi-mentellen Ionisierungsquerschnittes bei stickstoff-und halogenhaltigen Kohlenwasserstoffderiva-ten jedoch 11,5% bzw. 14,7% beträgt. Die Ursache dieser Abweichungen im Gegensatz zu den aus „Bindungsquerschnitten“ erhaltenen Ionisierungsquerschnitten ist auf die Vernachlässigung des Einflusses der chemischen Bindung auf die Größe des Ionisierungsquerschnittes zurück-zuführen. Die Größe der „Bindungsquerschnitte“ und ihre Anwendungsgesetze können mit Hilfe der Ultraviolett-Absorptionsspektren erklärt werden.

The systematics of cross sections for (n,p) and (n,a) re-actions induced by 14 - 15 MeV neutrons have been reinvesti-gated. No clear evidence for the existence of any proton shell effects in these two reactions was found. The existence of shell effects in nuclear reactions induced by 14 - 15 MeV neutrons has been postulated by several workers 1-4 , but the evidence presented has been rather weak. With the availability of more and better experimental data in recent years, a fresh look at this postulate seemed highly desirable. In case of (n,p) and (n,2n) reactions, the claim for the occurence of shell effects has already been recently repudiated 5,6 ; but for (n,α) reactions there seems to exist no evidence against the original claims 1,2 that the cross section shows a minimum when the atomic number of the re-sidual nucleus is a magic number. The present article describes briefly a reinvestigation of the systematics of the (n,p) and (n,α) reaction cross sections in the light of the latest experimental data. At 14 MeV neutron energy there appears to be no conclusive evidence for any significant proton shell effects in these two re-actions.

In der vorliegenden Arbeit wird untersucht, wie sich die Knight-Shift von kleinen Lithiumtröpfchen in LiF-Kristallen mit der Größe der Tröpfchen verändert; die Tröpfdien wur-den durch Neutronenbestrahlung erzeugt, ihre Größe konnte durch Tempern verändert werden.

Tungsten tips coated with Ni, Gd and EuS are studied in a field electron microscope. Reproducible patterns are observed. The Gd-patterns show epitaxy with the W-substrate. With tempered tips the work functions are: Ni 5.1 ± 0.3 eV, Gd 3.2 ± 0.3 e V and EuS 3.1 ± 0.3eV. For the production of polarized electrons by field emission from materials with spin polarized bandstructure 1 - 4 the field emission from Gd, Ni and EuS is of interest.

Die Messungen der Änderung der Wärmeleitfähigkeit von Ni-und Ni —Cu-Legierungen im Magnetfeld bei Temperatu-ren unterhalb Raumtemperatur ergeben bis zur magnetischen Sättigung ein völlig paralleles Verhalten von X und o. Bei Stickstofftemperaturen zeigen sowohl die AX/X-als audi die zlö/ö-Kurven oberhalb der Sättigung eine Abnahme mit wach-sendem Magnetfeld, auf die bei weiterem Anstieg von H der normale dM/dH-Effekt folgt.

DANNHÄUSER und KOCH 1 haben den Nernst-Effekt von Ni —Cu-Legierungen bei Raumtemperatur gemessen und ge-zeigt, daß er bis zu rund 30% Kupfer zunimmt, bei höheren Cu-Konzentrationen aber wieder abnimmt. Für den Hall-Effekt konnte NENTWICH 2 den gleichen Verlauf mit der Cu-Konzentration nachweisen, nur war hier der Abfall schon ober-halb 20% zu beobachten. Wir haben Hall-und Nernst-Effekt bei Temperaturen bis rund 350 °C gemessen und festgestellt, daß beide Effekte sowohl im reinen Nickel als audi bei den Ni —Cu-Legierungen anfangs mit der Temperatur zunehmen, bei einer reduzierten Temperatur T/Tc = 0,8 bis 0,9 (7c = Curie-Punkt) ein Maximum erreichen und dann rasch abneh-men.

In der vorliegenden Untersuchung werden Dämpfungskennwerte allgemein formuliert. Als Beispiele sind Kennwerte freier und erzwungener gedämpfter Schwingungen aufgeführt. Die erörterten Abweichungen der meistens benutzten Umrechnungsbeziehungen von den strengen Gleichungen erklären zwanglos einander widersprechende Angaben im Schrifttum.

If a wustite sample prepared above 1000 °C is annealed at 225 °C stoichiometric FeO occurs as a metastable decomposition intermediate, as has been demonstrated röntgenographically and by means of the Mössbauer-effect.

Es wird eine Methode zur gleichzeitigen Bestimmung des transversalen Spin-Relaxationsverhaltens mehrerer, möglicherweise sogar aller Linien eines NMR-Viellinienspektrums angegeben. Der eine Meiboom-Gill-Impulsfolge begleitende Spin-Echo-Interferenzzug wird einer Fourier-Transformation unterzogen, und zur Gewinnung der Echofolge der einzelnen NMR-Signale werden mehrere partielle Rücktransformationen durchgeführt.

Recently SUTTER et al. 1 obtained a Hamiltonian for a molecule in the presence of a constant external elec-tromagnetic field. (A similar Hamiltonian has been de-veloped 2 , but including molecular vibrations, relativis-tic corrections and allowance for the fact that the mo-lecular centre of gravity differs from the nuclear centre of gravity.) We believe that the Hamiltonian of Sutter et al. is not correct, since they make two errors of principle in performing their gauge transformation. They start with a Lagrangian expressed in terms of the particle positions, rn\ in a space-fixed coordinate system. Each particle is associated with an external vector potential,-^«' = rn', where H is the constant external magnetic field. At this stage a gauge transfor-mation may be performed: An'-+An'-VnX, (1)