S. Flügge – författare

191 Apart from numerous difficulties arising from the high pressure technique as such, there is a natural limitation to the possibility of applying a hydrostatic pressure, since liquids under pressure will solidify above a certain pressure limit. 8 2 Up to pressures of 3 X 10 kg.jm. at room temperature, a liquid like isopentane can be used. For higher pressures helium gas may be used, perhaps to about 9 2 10 kg.jm. , but BRIDGMAN already encountered enormous leakage difficulties 7 when using this gas at 7.10 kg.jm.2 at 90° K. A solution has been found by applying mechanical pressure for the range 8 9 2 between 3 X 10 and 10 kg.jm. , by using silver chloride as transmittant. In this case, however, one has to apply unknown corrections for shearing stress and deformation of the sample, a problem which BRIDGMAN solved experimentally by a determination of the resistivity in the pressure region between 2 and 8 2 5 X 10 kg.jm. , by the hydrostatic and by the mechanical pressure method as well, and applying the correction factor thus determined to the results obtained at higher pressures. Though this method seems to be right in good approximation, the data for the highest pressures are to be considered as less accurate.

Ziff. 13. 41 Wir wollen das Problem folgendermaBen formulieren: Gegeben sei eine be- liebige physikalische Eigenschaft eines Kristalls beliebiger Symmetrie. Welche Bedingungen zwingt die Symmetrie des Korpers der betreffenden physikalischen Eigenschaft auf? Man braucht sich dabei keineswegs auf die Kristallsymmetrien zu beschranken. Die Unter- suchungen konnen leicht_auf Korper ausgedehnt werden, die durch irgendeine andere Gruppe von orthogonalen Transformationen in sich iibergefiihrt werden, die die Transformationen dieser Gruppe also als Symmetrieoperationen besitzen. Fiir uns ist nur der Fall der Zylinder- symmetrie (Gruppe Coo) und der Isotropie (Gruppe Roo) wichtig. Beide lassen sich im An- schlul3 an die Symmetrieelemente der Kristalle leicht behandeln. Spezielle* Falle dieses Problems sind schon zahlreich gelost worden, s. z. B. [1], [2]. Der Losungsweg war umstandlich und miihsam, Fehler stellten sich mit- unter ein und blieben lange Zeit unentdeckt. Erst in den letzten Jahren wurde das Problem auf verschiedenen Wegen systematisch angegriffen [3], [4], auf- bauend auf einer Arbeit von HERMANN [5], die zunachst anscheinend unbeachtet geblieben war.Einige der Verfahren, die bisher entwickelt wurden, und ihre Anwendungsmoglichkeiten sollen hier zusamtnengestellt werden. Andere werden nur kurz arlgedeutet, bei diesen muB auf die Originalliteratur verwiesen werden. Physikalische Einwirkungen auf einen Kristallkorper rufen bestimmte Effekte hervor. Die Einwirkung !l kann allgemein durch ein Feld beschrieben werden (Temperatur, elektrisches Feld, mechanische Spannung oder Verzerrung usw.), auch bei dem Effekt ~ ist dies oft moglich, s. Tabelle 4a. Bei hinreichend Tabelle 4a.

71 For a given value of I the field is independent of the geometrical composition of the coil inside the winding space. The actual number of turns and the cross­ section of the conductors is entirely determined by the impedance of the power supply to which the magnet should be adapted. In the case of low impedance (high current and low voltage) few turns of thick metal should be used. In the case of high impedance (low current and high voltage) many turns of thin material are needed. High impedance coils are made of square wire or flat strip wound into layers or "pancakes" 1. A nice system for low impedance coils was deve­ loped by BITTER. The turns of his magnets consist of flat copper discs separated by thin insulating sheets and joined together at their edges. In this type of coil the current density is higher near the axis than at the exterior, resulting into a higher value for G (see above). For the details of the construction we refer to the original papers 2, 3. If the power is dissipated at a low voltage the cooling may be achieved with the help of water. Distilled water should be preferred over mains' water in order to prevent the magnet from corrosion. In the case of a high voltage coil some non-inflammable organic fluid should be used. A low viscosity and a large specific heat are advantageous.

v. Formation of negative ions by processes other than attachment in the gaseous phase at low X/po 17. Introduction. As early as 1912, J. J. THOMSON [32J in his first mass spectro­ graph observed negative ions of 0-, Cl-, H- and what he believed to be N-. He at first ascribed these to possible dissociation of polar gaseous compounds by electron impact but control studies using ionization at low energies in glow discharges indicated that this was not the origin. O. W. RICHARDSON [33J in his book on emission of electricity from hot bodies reported negative ions to come from hot salts. From there on many experimental studies over the years indicated that negative ions could be formed by various processes. By the middle nineteen hundred and thirties the data fairly clearly identified several processes as being active and MASSEY and SMITH [34J developed the theory underlying some of them. More data are summarized in MASSEY'S excellent little monograph on Negative Ions and in )L\SSEY and BURHOP'S recent book [35]. Since that period, stimulated by various investigations and certain industrial problems, very careful studies of the appearance of such ions by mass spectrograph have been carried out in the laboratory of K. G. EMELEUS in Belfast by SLOANE and his co-workers [3J that haw clarified the questions and indicated what ions have been observed and something of the processes at work.

Sect. 23. 325 transitions have been drawn for which L1~=0 (n-components). Moreover it is assumed that the hfs splitting of the 3 s 2 Pal, level is negligibly small compared with that of the 3 s 25,/, level. BACK and GOUDSMIT succeeded in resolving the structure of the components of the Bi I line A 4722 A. In each transition they found 10 components, so that in this case 21 + 1 = 10, and the nuclear spin of 209 Bi becomes 1 = 9/ , Later on their results for a group of components were 2 reproduced and published by ZEEMAN, BACK and GOUDSMITI. There are only a few examples where the influence of a magnetic field on the hfs of spectral lines has been shown experimentally in weak, intermediate and strong fields. One of them is the beautiful experiment by JACKSON and 2 KUHN on the Zeeman effect of the hfs of the Na D line A 5890 A. These authors used an atomic beam light source and photographed the lines in absorption.They showed that for the components of this line there was a real Zeeman effect in magnetic fields up to a magnetic field strength of about 1600 oersted, whereas there is a transition to the Back Goudsmit effect in stronger fields, the latter being completed at a field strength of about 3000 oersted. VI. The use of the Zeeman effect in the analysis of atomic spectra.

243 number n and orbital angular momentum 1, but also a total angular momentum 1 f = 1 ± !. This modification lead to striking successes for the model. Almost without exception, the ground state spins of odd nuclei were found to be cor­ rectly predicted. Furthermore several other features of nuclei such as the occur­ rence of isomeric states and the values of magnetic dipole moments were explained, at least qualitatively. However the model completely failed to explain the large values of observed electric quadrupole moments and certain regularities in nuclear spectra, especially of rare earth nuclei. 4. 1950-1953. The emphatic success of the shell-model modified by a spin­ orbit force gave the necessary confidence and incentive to physicists to apply the model in detail to individual nuclei. Guided by parallel calculations in atomic spectroscopy, considerable effort was devoted to computing spectra of levels of nuclear systems with the so-called "Intermediate Coupling Model" in which the independent particle motion is considered to be perturbed by central particle­ particle interactions and spin-orbit forces. Computational labour restricts such calculations to nuclei near closed shells, say within four particles or holes of closed shells. This explains why only light nuclei (A < 20) and isolated groups of nuclei higher in the Periodic Table were thus treated. Usually such calculations were rewarded by agreement with experiment especially those for light nuclei 2 and 20S nuclei near the double closed shell at Pb 3.

39 2 2 Here B = hJ8:!t Ib and A = hJ8:!t Ia where Ia and Ib are the moments of inertia parallel and perpendicular respectively to the symmetry axis. ~ V I(J + 1) is 2n the total angular momentum of the molecule and K ~ its projection on the 2n symmetry axis. If the molecule possesses a permanent electric dipole moment it can absorb a quantum of microwave energy hv and make a transition to a higher rotational' state governed by the selection rules L1 I = + 1, L1 K = O. The pure rotational absorption frequency is then given by v=2BI (1. 2) where I is the angular momentum quantum number for the upper state of the transition. If an isotopic substitution is made for an atom lying along the sym- metry axis of the molecule, thus changing its moment of inertia and hence its B value, the rotational absorption frequency will shift. The program of mass determination from microwave spectra is to correlate this frequency shift with the change in mass of the substituted isotope. These shifts can range from a few Mc to several thousands of Mc for a change of one mass unit, being larger generally for the lighter atoms.Typical isotopic shifts in the middle mass region (A =60 to 130) are 100 Mc per mass unit. As mentioned above, frequency shifts in the 24000 Mc region can be measured to at least an accuracy of 0.

Sect. 13. 203 and the geometric elements for the large orbit are re-computed. From the analysis it cannot be decided whether the third body is close to the visual primary or secondary component; this can only be decided by measuring the orbital motion on an astrometric background of other stars (Chap. IV). In accurate long-term problems the perspective change in the apparent orbit due to motion of the center of mass in the line of sight, must be taken into account. In the future this feature of orbital analysis will undoubtedly become more and more important. An example of the required reduction is the orbital analysis of the 61 Cygni system by A. FLETCHER!. 1890 90 1960 0 Fig. 11. Relative orbit of the visual binary Kruger 60. * visual observations. 0 photographic observations. IV. Analysis of orbit referred to external reference system. 13. Introduction. In the preceding Chap. III we dealt with the analysis of the relative orbit of the two components of a binary star. We now extend the analysis to the measurements and orbits of the individual components referred to a system of, presumably distant, reference stars.Both micrometer measure- ments and, particularly, meridian circle positions have been successfully employed in the past; the current observing technique is primarily long-focus photographic astrometry. The problems studied include those of mass-ratio and parallax, and of perturbations. Long-focus technique and analysis are in the first place suitable for the so-called resolved binaries, whose components are clearly separated.

177 Die statistische Mechanik ist ursprunglich von BOLTZMANN und GIBBS auf der Grundlage der Hamiltonschen Mechanik entwickelt worden. Da wir jedoch den Ausgangspunkt als ein Problem der Atom-Mechanik formullert haben, muB eine streng logische Darstellung des Gebietes notwendig an die Quantenmechanik anknupfen. Trotzdem werden wir im folgenden aus zwei Griinden die Theorie zuerst auf klassischer Grundlage entwickeln. Einmal ist das Begriffssystem der Quantenstatistik (abnlich wie das der Quantenmechanik) in moglichst weit- gehender Analogie zur klassischen Theorie aufgebaut worden. Die Vorwegnahme der letzteren bringt daher eine wesentliche Vereinfachung der Darstellung und eine Erleichterung des Verstandnisses. Zum anderen bleibt fUr die uberwiegende Mehrzahl der Anwendungen von der Quantenstatistik nur eine geringfUgige Korrektur an den Resultaten der klassischen Theorie ubrig, die sich bereits im Rahmen der letzteren plausibel machen (wenn auch nicht beweisen) laBt. Prak- tisch benutzt man daher in den meisten Fillen die Methoden der klassischen statistischen Mechanik, deren Kenntnis somit ohnehin unentbehrlich ist.Die axiomatische Basis der statistischen Mechanik wird naturgemaB zunachst durch die Axiome der Wahrscheinlichkeitsrechnung und der Mechanik gebildet. Auf dieser Grundlage lassen sich allgemeine Satze uber statistische Gesamtheiten , ableiten, die fur den Aufbau der Theorie von auBerordentlicher Bedeutung sind, aber im wesentlichen formalen Charakter besitzen. Bei dem Versuch, die statisti- sche Mechanik zu einer physikalischen Theorie auszugestalten, stoBt man auf eine Lucke, die sich trotz vielen Bemuhungen bisher auf deduktivem Wege nicht hat schlie Ben lassen.

dissociation, E, of a dimer into two monomers and that, E', of a trimer into a dimer and a monomer. The observed velocity distribution for a beam of sodium iodide is shown in Fig. 23. The monomer and dimer distributions, which are each of the form of Eq. (9. 2), are separately shown. The sum of the two assumed distributions is seen to agree with the experimental data. The data for lithium bromide are shown in Fig. 24. The separate distributions for the monomer, dimer, and trimer required to fit the data are shown as is the sum of these distributions. An attempt to describe the observed distribution in terms of a monomer and a dimer only is shown by the dotted line, where the relative amounts of these species have been adjusted to give a fit on the low velocity side of the spectrum. Table 2. Summary oj data on the degree of association oj diatomic molecules. The data on the fluorides are from unpublished results of M. EISENSTADT, G. ROTHBERG and P. KUSCH. Uncertainties in E and E' are given in parentheses. E E' Temperature OK I ----- ----" Species at which a2 a, kcaljmole p~10-2mmHg RbCl 866 0. 063 48. 0 (0. 5) I KCI 0. 083 897 45·8 (0. 7) I KI 823 0. 046 , 45·3 (0·9) NaC] 920 0. 259 44. 6 (0·9) i NaI 817 0. 235 38. 6 (3-4) LiC] 2.

449 one finds that for y = Fo (e) C= :n; V3 [Po (2'Yj) 3 -kjF(i) + (2'Yj)! Fd (2'Yj) 3 -ijF (*m, } 1 ( 14.17) C2 = :n; [ - (2'Yj)! Fd (2'Yj) 3 -ijF(i) + Fo (2'Yj) 3 -~;r(i)J, and if y is to be Go(e), C and Chave the same form with Go (2'Yj) replacing Po (2'Yj) 1 2 and G~(2'Yj) replacing Fd(2'Yj). The values of the functions at eo =2'Yj may be ob- tained from (14.8). 1 J. K. TYSON has employed the modified Hankel functions of order one- third 2 as solutions of (13.4) to obtain expressions for the Coulomb functions for L =0 which converge near e =2'Yj. His results appear as linear combinations of the real and imaginary parts of n ~(x) = (12)!e-;/6 [A;{- x) - iB;(-x)J, (14.18) and its derivatives multiplying power series in x = (e - 2'Yj)j(2'Yj)1. For values 1 away from the turning point for L =0, TYSON has obtained forms for Po{e) and Go(e) which are similar to (13.1) to (13.3). The JWKB approximation is again the leading term, and some higher order corrections are given. Expressions similar to Eqs. (14.11) and (14.12) have been obtained by T.D. 3 NEWTON employing the integral representation of (4.4).His results give re- presentations of FL(e), Gde) in the vicinity of e=2'Yj [whereas (14.11), (14.12) converge near e=eLJ when L

will be "asymptotically integrable", that is to say, if we displace a vector parallel to itself along a closed curve whose total length is proportional to r, then, as we remove the curve to infinity, the change of the vector that results from the circuit about the curve will tend to zero. In the presence of gravitational radiation the total energy will not be con­ served, because the waves carry some energy with them; analogous statements apply to the linear momentum, etc. But that is not all; if there is no coordinate 2 system in which the field strengths drop off as 1/r , then there is no possibility to generate out of one vector" at infinity" a whole field of parallel vectors" at infinity". Thus we are unable in the presence of radiation to define, even at infinity, a "rigid displacement", the type of coordinate transformation that is presumably generated by the energy integral. Under these circumstances it is very difficult to see how one can define the "free vector" energy -linear momen­ tum in a convincing manner. These ambiguities of course do not imply that general relativity lacks quan­ tities that obey equations of continuity; rather, general relativity suffers in this respect from an embarras de richesse. There is an infinity of such quantities, and our difficulty is to single out a subset and to present these as the "natural" l expressions for energy, linear momentum, etc.

liff. 1. 3 Aus dem geschilderten Sachverhalt ergibt sich, daB die Aufgabenstellung der statistischen Thermodynamik kondensierter Phasen notwendig verschieden ist von der der Gastheorie. Wahrend bei der letzteren die Ermittlung der thermo- dynamischen Funktionen konkreter Systeme durchaus im Vordergrund steht, handelt es sich bei kondensierten Phasen in erster Linie urn die grundsatzliche Klarung der hier auftretenden Erscheinungen, wie etwa der Struktur der Flussig- keiten, des Schmelzens, der thermodynamischen Eigenschaften der Losungen starker Elektrolyte usw. Das schlieBt naturgemaB nicht aus, daB man auch bei kondensierten Phasen in weitem Umfange quantitative VerglEiche zwischen Theorie und Experiment durchfUhrt. Solche Vergleiche mussen aber hier unter einem anderen Aspekt als in der Gastheorie betrachtet werden, was am deut- lichsten in der Tatsache zum Ausdruck kommt, daB die Theorie fast durchweg adjustierbare Parameter einfuhrt. Man kann danach in einem etwas primitiven Sinne sagen, daB die statistische Thermodynamik kondensierter Phasen, verglichen mit der Gastheorie, nur von geringem praktischen Nutzen ist.Urn so groBer ist ihre Bedeutung fur das phy- sikalische Verstandnis der Materie im kondensierten Zustand. Indem sie an ein- fachen Beispielen zeigt, wie gewisse Erscheinungen zustandekommen, liefert sie die begriffliche Grundlage fUr die Beschreibung und Einordnung solcher Er- scheinungen auch in komplizierteren Fallen. Aus dieser Moglichkeit einer in ihren Grundlagen exakten begrifflichen Erfassung ergeben sich neue Fragestel- lungen und Anregungen, welche die experimentelle Forschung in auBerordent- lichem MaBe befruchten.

69 Eine typische Aufgabe ist die: Ein bestimmter, kreisfOrmiger Objekt-Ebenen- Ausschnitt (F eld genannt) soIl mit weiBem Licht durch ein System aus brechenden Kugel- oder Plan-Flachen abgebildet werden auf eine Bild-Ebene, in einem be- 1 stimmten MaBstab und (meistens) unter Beachtung weiterer Bedingungen . Dabei sollen die Linsenfassungen und die Blende des Systems solche Durchmesser haben, daB mindestens die Punkte der Feld-Mitte durch Strahlenbiindel bestimmter GroBe (Offnung genannt) abgebildet werden. SchlieBlich sollen die unvermeid- lichen Abweichungen von der idealen punktformigen Abbildung (Aberrationen genannt) mehr oder weniger gut vernachliissigbar sein bei der Anwendung, ffir die das System vorgesehen ist.- J e nach den zur Verfiigung stehenden Mitteln hat das System mehr oder weniger Freiheitsgrade; sollen nur Linsen mit Kugel- oder Plan-Flachen vorkommen, nicht mit aspharischen Flachen (die einen hohen Fertigungsaufwand erfordern), dann hat das System endlich viele Freiheitsgrade (Konstruktionsdaten genannt): die Radien r der brechenden Flachen (bei einer Planflache ist r = 00; bei einer Kugelflache ist r positiv oder negativ, je nachdem ob das Licht von auBen her oder von innen her auf die Kugelflache trifft), die Abstande a der Flachen voneinander (langs der Rotationsachse des Systems gemessen), die Brechungsindizes n=n(A. ) der Medien zwischen den FHichen (A. ist die Wellenlange des Lichts). In der Regel hat man als Medium Luft (n = 1 nor- miert) oder Glas, bei dem die Funktion n (A.

191 Apart from numerous difficulties arising from the high pressure technique as such, there is a natural limitation to the possibility of applying a hydrostatic pressure, since liquids under pressure will solidify above a certain pressure limit. 8 2 Up to pressures of 3 X 10 kg.jm. at room temperature, a liquid like isopentane can be used. For higher pressures helium gas may be used, perhaps to about 9 2 10 kg.jm. , but BRIDGMAN already encountered enormous leakage difficulties 7 when using this gas at 7.10 kg.jm.2 at 90° K. A solution has been found by applying mechanical pressure for the range 8 9 2 between 3 X 10 and 10 kg.jm. , by using silver chloride as transmittant. In this case, however, one has to apply unknown corrections for shearing stress and deformation of the sample, a problem which BRIDGMAN solved experimentally by a determination of the resistivity in the pressure region between 2 and 8 2 5 X 10 kg.jm. , by the hydrostatic and by the mechanical pressure method as well, and applying the correction factor thus determined to the results obtained at higher pressures. Though this method seems to be right in good approximation, the data for the highest pressures are to be considered as less accurate.