Showing papers in "Physical Review in 1933"

On the Constitution of Metallic Sodium

Abstract: Previous developments in the theory of metals may be divided clearly into two parts: that based principally upon the hypothesis of free electrons and dealing with conductivity properties, and that based upon calculations of valence forces and dealing with the chemical properties. In the present article an intermediate point of view is adopted and the free-electron picture is employed in an investigation of chemical properties of metallic sodium. The assumption is made that in the metal the K and L shells of an atom are not altered from their form in the free atom. The properties of the wave functions of the electrons are discussed qualitatively, first of all, and it is concluded that the binding energy will be positive even when the Pauli principle is taken account of. This is followed by a quantitative investigation of the energy to be associated with the lowest state. First of all it is shown to what extent the present picture takes account of the interactions of electrons with both parallel and antiparallel spins, and to what extent remaining effects may be neglected. Next a Schroedinger equation is solved in order to determine the lowest energy level for various values of the lattice constant. To this a correction is made to account for the Pauli principle and from the result the lattice constant, binding energy and compressibility are calculated with favorable results.

The Positive Electron

Abstract: Out of a group of 1300 photographs of cosmic-ray tracks in a vertical Wilson chamber 15 tracks were of positive particles which could not have a mass as great as that of the proton. From an examination of the energy-loss and ionization produced it is concluded that the charge is less than twice, and is probably exactly equal to, that of the proton. If these particles carry unit positive charge the curvatures and ionizations produced require the mass to be less than twenty times the electron mass. These particles will be called positrons. Because they occur in groups associated with other tracks it is concluded that they must be secondary particles ejected from atomic nuclei.

The Evaporation of Atoms, Ions and Electrons from Caesium Films on Tungsten

Abstract: Precision methods for measuring the number of caesium atoms adsorbed on tungsten are described. With these methods for determining $\ensuremath{\theta}$ (the fraction of the tungsten surface covered with Cs), the rates of atom, ion and electron emission are measured as functions of $\ensuremath{\theta}$ and $T$, the filament temperature. The rate of atom evaporation, ${\ensuremath{ u}}_{a}$, increases rapidly with $\ensuremath{\theta}$ and with $T$. At low filament temperatures and high pressures of Cs vapor the concentration of adsorbed Cs atoms approaches a limit 3.563\ifmmode\times\else\texttimes\fi{}${10}^{14}$ atoms ${\mathrm{cm}}^{\ensuremath{-}2}$ of true filament surface (one Cs atom for four tungsten atoms). This film ($\ensuremath{\theta}=1$) exhibits all the characteristics of a true monatomic layer. The formation of a second layer begins only at filament temperatures corresponding to nearly saturated Cs vapor. A theory of the formation of a second and of polyatomic layers is given and experiments supporting it are described. The heat of evaporation (given by the Clapeyron equation) for Cs atoms from clean tungsten is 2.83 volts (65,140 calories), 1.93 volts or 44,473 calories at $\ensuremath{\theta}=0.67, \mathrm{and} 1.77$ volts or 40,757 calories at $\ensuremath{\theta}\ensuremath{\simeq}1$. The adsorbing tungsten surface after proper aging is homogeneous, except that about 0.5 percent of it (active spots) can hold Cs more firmly than the rest. The procedure in obtaining electron (${\ensuremath{ u}}_{e}$) and ion (${\ensuremath{ u}}_{p}$) emission for zero field and the large changes in the effect of external field with $\ensuremath{\theta}$ are described. From both ${\ensuremath{ u}}_{e}$ and ${\ensuremath{ u}}_{p}$ the contact potential ${V}_{c}$ is calculated, agreeing, except for very concentrated films, with ${V}_{c}$ calculated entirely from data on neutral atom evaporation. At constant temperature the electron emission increases to a maximum at $\ensuremath{\theta}=0.67$ and decreases as $\ensuremath{\theta}=1$ is approached. The positive ion emission increases rapidly to a maximum at $\ensuremath{\theta}\ensuremath{\simeq}0.01$ and then decreases. The work function (exponent in Dushman type equation) for electrons at $\ensuremath{\theta}=0.67$ is 1.70 volts (clean tungsten=4.62 volts). The work function for ions is 1.91 volts at $\ensuremath{\theta}=0, \mathrm{and} 3.93$ volts at $\ensuremath{\theta}=0.67$. It is shown by experiment that the saturated ion current from a clean hot (1200-1500\ifmmode^\circ\else\textdegree\fi{}K) tungsten filament is an accurate measure (experimental error of about 0.2 percent) of the number of atoms striking the filament per second. The condensation coefficient ($\ensuremath{\alpha}$) for atoms striking a tungsten filament is proved by experiment to be unity from $\ensuremath{\theta}=0$ to nearly 1. The important bearing of this fact and of the experimentally observed existence of surface migration or diffusion on the mechanism of evaporation and condensation in dilute and concentrated films is discussed. In addition surface migration is correlated with irregular ion evaporation rates occurring when two phases (dilute and concentrated films of Cs) exist on the tungsten surface. Transient effects in which $\ensuremath{\theta}$ changes with time are studied and entirely explained by the observed rates of evaporation and condensation. This and other facts are used to justify a surface phase postulate according to which all the properties of the adsorbed film are uniquely determined by $\ensuremath{\theta}$ and $T$.

Quantum Statistics of Almost Classical Assemblies

Abstract: The sum of states of an assembly in statistical equilibrium may be transformed into an integral in phase space, which is analogous to the classical Gibbs phase integral. With the use of an equation obtained by Bloch it is possible to expand the quantum phase integral in powers of Planck's constant $h$. The present method of treating the problem supplements that of Wigner and of Uhlenbeck and Gropper by furnishing a more convenient means of obtaining the $h$-expansion.

Successive Approximations by the Rayleigh-Ritz Variation Method

Abstract: Approximate eigenvalues given by the Rayleigh-Ritz variation method for handling linear differential equations are examined and relations are established between the discrete eigenvalues obtained in successive approximations. These relations should be of use in practical computations. A method for fixing upper bounds to eigenvalues is given and a procedure previously employed by the writer to simplify determinant calculations is adapted for use in the present theory.

Transport Phenomena in Einstein-Bose and Fermi-Dirac Gases. I

Abstract: In this paper the general theory of transport phenomena in simple gases is concluded, and numerical values of the gas coefficients for heat conductivity and viscosity are obtained as a function of the temperature and density for the particular case of molecules acting as rigid elastic spheres. In the Introduction will be found a qualitative discussion of the principal results obtained and an interpretation of these results according to elementary considerations. In Section 1 the method of solution of the integral equations with which the formal theory of Part I was concluded is given together with the resulting general equations for the heat conductivity and viscosity coefficients. Since the integral equations can be solved only by a method of successive approximations, the expressions for the gas coefficients are in the form of infinite series the rapidity of convergence of which depends on a suitable choice of a complete set of auxiliary functions. In Section 2 all of the integrals appearing in the first two terms of the infinite series are evaluated. That only two terms are required is due to the fact that one is able to make an excellent choice of functions to represent the auxiliary set. In the evaluation of these integrals restriction is made in the application of the theory to small values of the degeneracy parameter $A$, since only terms in the zeroth and first power of $A$ are retained. This restriction is only slightly greater than that imposed by the fundamental postulates of the general theory which restrict its applicability to moderately rare gases. In Section 3 the final equations for the gas coefficients are applied to gases consisting of molecules which interact quantum-mechanically as rigid elastic spheres of diameters and masses associated with the gases helium and hydrogen.

Electronic Structures of Polyatomic Molecules and Valence. IV. Electronic States, Quantum Theory of the Double Bond

Abstract: The possible types of electronic states of polyatomic molecules (assuming fixed nuclei and neglecting spin fine structure) are discussed and tabulated (Table I) with the help of simple group theory methods, applying results of Bethe and Wigner A notation for electronic states ($\ensuremath{\psi}'\mathrm{s}$) and molecular orbitals ($\ensuremath{\varphi}'\mathrm{s}$) for molecules having any type of symmetry to be found among the 32 crystal classes, is adopted; this is essentially the same as that used by Placzek for designating the vibrational states of molecules It is shown how the possible $\ensuremath{\psi}'\mathrm{s}$ corresponding to any given electron configuration (set of $\ensuremath{\varphi}'\mathrm{s}$) can be determined for any type of symmetry; for the more complicated cases, the results are tabulated (Table V) It is shown how all the selection rules for transitions between electronic states of molecules can be easily determined Limitations resulting here from the application of the Franck-Condon principle are discussed Extending work of Bethe, tables are given (Tables II-IV) showing how the various types of electronic states of atoms and of diatomic and polyatomic molecules ($S$, $P$, ${\ensuremath{\Sigma}}^{+}$, $\ensuremath{\Delta}A$, etc) go over into various other types of states if the symmetry of the original system is decreased Examples are given showing how electronic wave functions ($\ensuremath{\psi}'\mathrm{s}$) of molecules can be constructed which conform to the possible types (Table I) allowed by the symmetry of the nuclear skeleton, and which at the same time, with Slater's method, are antisymmetrical in the electrons (cf section 2 and Eqs (9-12)) It is shown that for molecules having all their electrons in closed shells or electron-pair bonds, zeroth approximation $\ensuremath{\psi}'\mathrm{s}$ which conform to the identical representation of the molecule's symmetry group (analogous to $^{1}S$ of atoms and $^{1}\ensuremath{\Sigma}^{+}$ or ${^{1}\ensuremath{\Sigma}_{g}}^{+}$ of diatomic molecules) can be built up either by using electron-pair bonds or by using molecular orbitals The approximate construction of molecular orbitals as linear combinations of atomic orbitals, in such a way that they conform to the types allowed by the symmetry of the molecule, is discussed and illustrated (cf Eqs (3, 8)) Several statements made in a previous paper (III) of this series, on the quantum theory of the double bond, are here justified by the methods mentioned above, thereby also providing examples of the application of the latter Some additional details concerning the nature of the double bond are given Finally, it is shown that the model of the double bond given in III should according to the theory be altered somewhat for the perp form of the molecule, in a way which offers the possibility of improved agreement with experiment

Theory of the energy distribution of photoelectrons

Abstract: Because of the thermal energies of the electrons in a metal there can be no sharply defined maximum emission energy of photoelectrons, as was once supposed. On the basis of the Sommerfeld theory and the Fermi-Dirac statistics, expressions are derived for the form of the energy distribution and current voltage curves in the vicinity of the apparent maximum energy. The method used is similar to that used by Fowler in computing the total emission current. In Part I the energies normal to the emitting surface are considered. At 0°K the theoretical current-voltage curve is a parabola tangent to the energy axis at Vmax, while for higher temperatures it approaches the axis asymptotically. In Part II the treatment is extended to the total energy of emission and in this case the current-voltage curve at 0°K is a parabola concave toward the voltage axis and cutting it at a large angle. At higher temperatures there is an asymptotic approach. Even at room temperature there is an uncertainty of several hundredths of a volt in Vmax, though the theory yields a method of determining the maximum energy which would be observed at 0°K. Both parts of the theory are found to be in agreement with new experiments on molybdenum. The bearing of the theory on the photoelectric determination of h is discussed.

The Effect of Exchange on the Scattering of Slow Electrons from Atoms

Abstract: Reasons are given why the Born approximation is incapable of dealing with the scattering of slow electrons. Since this approximation assumes that the sine of the phase angle $\ensuremath{\delta}$ equals $\ensuremath{\delta}$, the results computed by the Born method become completely unreliable when $\ensuremath{\delta}$ is greater than $\frac{\ensuremath{\pi}}{2}$. Exact solutions then must be obtained. Equations are set up, including exchange effects, for the best possible wave function for an electron scattered from hydrogen or helium when the complete wave function is of the separable type usually used in atomic theory. These equations are solved on the differential analyzer to find the best possible curves for the $\ensuremath{\delta}'\mathrm{s}$, for the angle distribution of scattering and for the total cross section, for this type of wave function. The check with experiment for helium is good, the maximum discrepancy in any of the $\ensuremath{\delta}'\mathrm{s}$ being only ten degrees. No data for atomic hydrogen are available. The small error introduced by the use of separable wave functions (neglect of polarization) is discussed. The conclusions are that exchange effects are not important for electron energies greater than 30 volts, and below this energy have an appreciable effect only on the angle distribution curves, and not on the cross section curves. An analytic solution of the equations, valid for any atom having closed electronic shells, is obtained for a simplified form of atomic wave function and potential. The results confirm the above conclusions, and also show that exchange is less important in scattering from heavy atoms than from light ones.

On Compton's Latitude Effect of Cosmic Radiation

Abstract: By considering the influence of the earth's magnetic field on the motion of charged particles (electrons, protons, etc.) coming to the earth from all directions in space, it is shown that the experimental variation of cosmic-ray intensity with magnetic latitude, as found by Compton and his collaborators, is fully accounted for. The cosmic radiation must contain charged particles of energy between limits given in the paper. The experimental curve may be represented by a suitable mixture of rays of these energies, but it is not at all excluded that a part of the radiation may consist of photons or neutrons. For predominantly negative particles there must be in the region of rapidly varying intensity a predominant amount of rays coming from the east, and conversely for positive rays. Because of the fact that in regions near the magnetic equator there is a predominance of rays coming nearly horizontally, the absorption by the atmosphere may be increased. Finally the fact that Compton's result definitely shows that the cosmic rays contain charged particles gives some support to the theory of super-radioactive origin of these rays advanced by one of the present authors.

A Geographic Study of Cosmic Rays

Abstract: Data are given from measurements of the intensity of cosmic rays by 8 different expeditions at 69 stations distributed at representative points over the earth's surface. Each set of apparatus consisted of a 10 cm spherical steel ionization chamber filled with argon at 30 atmospheres, connected to a Lindemann electrometer, and shielded with 2.5 cm of bronze plus 5.0 cm of lead. Measurements were made by comparing the ionization current due to the cosmic rays with that due to a capsule of radium at a measured distance, the radium standards used with the several sets of apparatus having been intercompared. The method of detecting and correcting for the following disturbing effect is discussed: insulation leak and absorption, local gamma-radiation, radioactive contamination of the ionization chamber, and shielding from cosmic rays by roof and horizon. Intensity vs. barometer (altitude) curves are given for various latitudes. These show not only the rapid increase with altitude noted by previous observers, but also the fact that at each altitude the intensity is greater for high latitudes than near the equator. At sea level the intensity at high latitudes is 14\ifmmode\pm\else\textpm\fi{}0.6 percent greater than at the equator; at 2000 m elevation, 22 percent greater; and at 4360 m, 33 percent greater. This variation follows the geomagnetic latitude more closely than the geographic or the local magnetic latitude, and is most rapid between geomagnetic latitudes 25 and 40 degrees. Consideration of the conditions necessary for deflection of high-speed electrified particles by the earth's magnetic field indicates that if the cosmic rays are electrons, they must originate not less than several hundred kilometers above the earth. The data can be quantitatively explained on the basis of Lemaitre and Vallarta's theory of electrons approaching the earth from remote space. Acknowledgment is made of the cooperation of more than 60 physicists in this program, 25 of whom are named.

Relative Intensity Tables for Spectrum Lines

Abstract: Relative intensities for a large number of multiplets have been calculated from well-known theoretical formulas. These intensities have been tabulated for future reference in making analyses of spectra. The tables are grouped under each resultant spin, from singlets $S=0$, to octets $S=\frac{7}{2}$ and include all probable values of $L$ and $J$. It is shown how the same tables apply to $\mathrm{jj}$-coupling, to hyperfine structure, and to related multiplets.

Remarkable Optical Properties of the Alkali Metals

Abstract: Thin films of alkali metals opaque to visible light are highly transparent in the ultraviolet region. The point in the spectrum at which transparency commences moves toward shorter wave-lengths with decreasing atomic number as follows: Cs 4400; Rb 3600; K 3150; Na 2100; Li 2050A. The transparency continues as far down the spectrum as the investigations have gone (1860A). In this region the phenomenon of plane polarization by reflection is observed. The reflecting powers of these metals for different wave-lengths have been measured. From these measurements and also from the Brewsterian angles for plane polarization, the refractive index of a potassium film has been calculated. The values range from 0.90 at 2147A to 0.50 at 3100A. Since the refractive index is less than unity total reflection takes place, although the critical angle is not sharply defined. Interference maxima and minima in the spectrum of light reflected from a metal film permit a rough determination of the film thickness.

On the Plasticity of Crystals

Abstract: A. Smekal(1) recently in a letter to The Physical Review is still advocating the idea that microscopic crevices are the essential cause of the peculiar mechanical and plastic behavior of rocksalt and crystals in general. Although conclusive evidence has repeatedly been brought forth by myself and other writers that Smekal's "imperfection" theory does not account for some of the most essential physical properties of crystals, his remarks in the mentioned letter require some comment.

The Continuous Absorption of Oxygen Between 1750 and 1300A and Its Bearing Upon the Dispersion

Abstract: In connection with recent measurements of the dispersion of oxygen down to 1920A, the continuous absorption of oxygen between 1750 and 1300A has been investigated quantitatively with a small fluorite spectrograph by the photographic-photometric method. The results are given in a graph, which shows that the absorption co-efficient $\ensuremath{\alpha}$ as function of the wave number $\ensuremath{ u}$ has a relatively sharp maximum at 6.8\ifmmode\times\else\texttimes\fi{}${10}^{4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ ($\ensuremath{\lambda}=1450\mathrm{A}$) and falls off rather symmetrically on both sides. The maximum absorption coefficient reduced to N.P.T. is about 490 ${\mathrm{cm}}^{\ensuremath{-}1}$. The absorption in this region of the spectrum is so strong that during a few minutes exposure a great part of the oxygen disappears, being dissociated and probably absorbed by the metal walls of the tube. By integration of the absorption curve one gets the corresponding $f$-value according to the equation $\ensuremath{\int}\ensuremath{\alpha}(\ensuremath{ u})d\ensuremath{ u}=\frac{\ensuremath{\pi}\mathrm{Nf}{e}^{2}}{m{c}^{2}}=(2.38\ifmmode\times\else\texttimes\fi{}{10}^{7})f$. The $f$-value calculated from this expression is 0.193 compared with 0.202 calculated from the dispersion measurements. The corresponding resonance wave-length from the dispersion measurements is 1468 in fairly good agreement with the observed position of the maximum of absorption. A dispersion formula which takes into account the distribution of absorption in a continuous band is given, and is applied to the dispersion of oxygen.

Hyperfine Structure in Intermediate Coupling

Abstract: The theory is extended to intermediate coupling and to cosine laws of force between nucleus and electron varying with different powers of their distance apart. In addition to Goudsmit's constants ${a}^{\ensuremath{'}}$, ${a}^{\ensuremath{'}\ensuremath{'}}$, there appears a third coupling constant ${a}^{\ensuremath{'}\ensuremath{'}\ensuremath{'}}$ for each electron, which gives energy matrix elements for the same $l$ and different $j$. The theory is in approximate agreement with observation. The gross structure is used to determine the parameters of the theory of intermediate coupling and hence $\stackrel{-}{(\frac{1}{{r}^{3}})}$. This together with ${a}^{\ensuremath{'}\ensuremath{'}}$ gives nuclear magnetic moments having roughly the same value for different configurations and stages of ionization. The variation of $\frac{1}{{r}^{3}}$ as determined from gross structure shows changes in screening agreeing with those supposed to exist for ${(6s)}^{2}$ of Pb I, Tl I in order to explain the isotope shift as due to differences in nuclear radii. The discrepancies between gross structure and theory are shown to be connected with similar discrepancies in hfs and the discrepancies of the ratios $\frac{{a}^{\ensuremath{'}\ensuremath{'}}}{{a}^{\ensuremath{'}}}$ are reasonably explained by perturbations due to other configurations.

On the Mass Defect of Helium

Abstract: If one assumes that the potential energy between protons and neutrons has the shape of a simple potential hole, it is possible from the experimental value of the mass defect of the ${\mathrm{H}}^{2}$, to derive a connection between the mean width and the depth of this curve. This connection proves to be, to a large extent, independent of the finer details of the potential curve. By assuming a certain probable value, obtained from scattering experiments, for the width of the potential hole, it is possible to make calculations on the mass defects of other nuclei. Such computations were carried out for He and yield values which are greater than the mass defect of ${\mathrm{H}}^{2}$ by a rather large factor. This agrees with experiment. For the higher elements, the Pauli principle has to be taken into account and the structure of higher nuclei is discussed on this basis.

A Mechanism of Acquirement of Cosmic-Ray Energies by Electrons

Abstract: Publisher Summary The growth of stellar magnetic fields as occurring in sunspots can give rise, according to Faraday's law of electromagnetic induction, to electric fields capable of giving electrons energies corresponding to 1010 volts. Because of the repulsion of the current responsible for the magnetic field, the electron is hurled away from the spot as it acquires its energy. It is usually considered that the assumption of the existence of electronic energies of the order 1010 volts is attended with considerable theoretical difficulties. This chapter presents the possibility of the production of cosmic-ray energies in stellar spots, analogous to sunspots on the Sun. The sunspots possess considerable magnetic fields that grow in comparatively short intervals of time. A consideration of the existing magnitudes will show that line integrals of the electric field of the order 1010 volts may readily arise through the Faraday law as a result of the growth of such magnetic fields. However, the detailed working out of the matter involves certain considerations that require careful attention.

The Electrostatic Production of High Voltage for Nuclear Investigations

Abstract: The developments in nuclear physics emphasize the need of a new technique adapted to deliver enormous energies in concentrated form in order to penetrate or disrupt atomic nuclei. This may be achieved by a generator of current at very high voltage. Economy, freedom from the inherent defects of an impulsive, alternating or rippling source and the logic of simplicity point to an electrostatic generator as a suitable tool for this technique. Any such generator needs a conducting terminal, its insulating support and a means for conveying electricity to the terminal. These needs are naturally met by a hollow metal sphere supported on an insulator and charged by a belt conveying electricity from earth potential and depositing it within the interior of the sphere. Four models of such a generator are described, three being successive developments of generators operating in air, and designed respectively for 80,000, 1,500,000 and 10,000,000 volts, and the fourth being an essentially similar generator operating in a highly evacuated tank. Methods are described for depositing electric charge on the belts either by external or by self-excitation. The upper limit to the attainable voltage is set by the breakdown strength of the insulating medium surrounding the sphere, and by its size. The upper limit to the current is set by the rate at which belt area enters the sphere, carrying a surface density of charge whose upper limit is that which causes a breakdown field in the surrounding medium, e.g., 30,000 volts per cm if the medium is air at atmospheric pressure. The voltage and the current each vary as the breakdown strength of the surrounding medium and the power output as its square. Also the voltage, current and power vary respectively as the 1st, 2nd and 3rd powers of the linear dimensions.

The Infrared Spectrum of Carbon Dioxide. Part II

Abstract: Previous work by Fermi and by Dennison has shown that the principal features of the infrared and Raman spectra of carbon dioxide may be explained by taking account of the first order perturbation terms in the potential energy expression. It was not possible to predict the positions of the levels with any high degree of accuracy, however. The present paper extends this work by introducing a second order perturbation. The formula for the second order energy correction of a general linear symmetrical triatomic molecule is initially computed. This formula is then modified in order that it may be applicable to the carbon dioxide molecule in which resonance degeneracy plays an essential r\^ole. A review is made of the experimental data which determine the positions of the carbon dioxide vibrational energy levels. These include the results of a recent investigation of absorption bands appearing in the spectrum of Venus, as well as new and as yet unpublished data found by Barker and Wu. In all, twenty levels have been found and out of these, eleven are required to determine the anharmonic constants of the molecule. The remaining nine levels may then be predicted, and their positions are found to agree very accurately with the values obtained experimentally. A table is given showing the positions of a number of C${\mathrm{O}}_{2}$ infrared bands which while accessible to observation have not as yet been reported. The recent work by Langseth and Nielsen on the Raman spectrum of C${\mathrm{O}}_{2}$ is discussed.

Variation with Temperature of the Continuous Absorption Spectrum of Diatomic Molecules: Part I. Experimental, The Absorption Spectrum of Chlorine

Abstract: A photographic method was used to investigate the continuous absorption spectrum of chlorine at 18\ifmmode^\circ\else\textdegree\fi{}, 168\ifmmode^\circ\else\textdegree\fi{}, 281\ifmmode^\circ\else\textdegree\fi{}, 426\ifmmode^\circ\else\textdegree\fi{}, 580\ifmmode^\circ\else\textdegree\fi{} and 765\ifmmode^\circ\else\textdegree\fi{}C. The effect of increasing the temperature is to decrease the absorption coefficient at the maximum, and to broaden the region of continuous absorption. The results were analyzed to obtain the contributions of individual vibrational levels to the total absorption. The absorption from the level ${v}^{\ensuremath{'}\ensuremath{'}}=0$ has a single maximum, that from the level ${v}^{\ensuremath{'}\ensuremath{'}}=1$ has two maxima, and it appears probable that the absorption from the level ${v}^{\ensuremath{'}\ensuremath{'}}=2$ has three maxima.

The Far Infrared Absorption Spectra of Ammonia and Phosphine Gases under High Resolving Power

Abstract: A spectrometer of large aperture employing a reflection grating of the echelette type ruled to concentrate radiation in the region of the 1st order of 90\ensuremath{\mu} has been applied in the spectral range from 60 to 125\ensuremath{\mu}. The resolving power was several times that hitherto obtained in this region. The pure rotation absorption spectra of water vapor and of the gases N${\mathrm{H}}_{3}$ and P${\mathrm{H}}_{3}$ have been investigated. In the case of N${\mathrm{H}}_{3}$ the absorption lines shown as single in the observations of Badger and Cartwright have been found under the higher resolution of the present work to be doublets with a doublet separation of 1.33 ${\mathrm{cm}}^{\ensuremath{-}1}$. Despite the similarity of structure of the molecules P${\mathrm{H}}_{3}$ and N${\mathrm{H}}_{3}$ the pure rotation lines of P${\mathrm{H}}_{3}$ exhibit no trace of a doubling. The frequencies of the P${\mathrm{H}}_{3}$ lines and the mid-frequencies of the N${\mathrm{H}}_{3}$ doublets have been shown to agree very accurately with formulas of the type ${{\ensuremath{ u}}_{J}}^{J\ensuremath{-}1}=BJ\ensuremath{-}D{J}^{3}$. Determinations of the moments of inertia $A$ of N${\mathrm{H}}_{3}$ and P${\mathrm{H}}_{3}$ have been made and in the case of N${\mathrm{H}}_{3}$ the measurement of the doublet separation has led to a slight revision of the values for the moment of inertia $C$ and for the molecular dimensions obtained by Dennison and Uhlenbeck.