A new model for the ground-state spin determination in ferromagnetics: The influence of many-electron exchange effects on the ground-state total spin in titanium and nickel

A new approximate exchange interaction operator, derived from the exact atomic second quantization formalism, has been applied to the study of the magnetic properties of atoms with spin $\text{S =}\text{1}\text{2}$ and S = 1 which obey Hund's rule. The new operator involves the effects of one-pair and two-pair electron exchanges. The one-pair exchange effects are compared with the Heisenberg model. It is shown that our model comprises the symmetry properties of the atomic wavefunction and the interaction of all electrons in the unfilled shells of two atoms, which are not considered in the Heisenberg theory. The conditions under which the new one-pair exchange effect may be used to improve the old one are pointed out. The significance of the two-pair exchange effects is discussed. It is demonstrated that, owing to the simultaneous exchange of two electron pairs, the total ground-state spin of two atoms may have intermediate values in addition to those predicted by the Heisenberg model. The importance of the interrelation between the first- and second-order effects, with respect to both sign and magnitude, is pointed out. The existence of the intermediate values, even in the case where the first order exchange integral is negative, is taken as a conjecture by which one may explain the fact that the mean magnetic moment per atom in magnetic 3d metals is not equal to the spin magnetic moment of an individual atom and accounts for the existence of magnetic ordering when the first order exchange integral is negative.     

Der Einfluß der Art der Solentstehung auf die Anwendung der Regel von Schulze-Hardy und Burton-Bishop bei der Koagulation positiver Aluminiumhydroxydsole

Zusammenfassung Um den p_H-Bereich zu bestimmen, in welchem kolloides positives Aluminiumhydroxyd und in welchem Aluminat entsteht, überprüfen wir die Flockungskurve des Systems Al(NO₃)₃/KOH unter gleichzeitiger Beobachtung der p_H-Werte und des Vorzeichens der Teilchenladung. Danach wurden die Bedingungen der Entstehung einer festen Phase zwischen dreiwertigem Aluminium-Ion und dem Anion untersucht, welches als Koagulator verwendet wird. Für Aluminiumhydroxydsol in statu nascendi verschiedener Konzentrationen wurden die Koagulationswerte verschiedenwertiger Anionen wie Nitrat, Sulfat, Ferricyanid und Ferrocyanid bestimmt, welche in Torrn ihrer Kaliumsalze vorliegen. Ein Vergleich zwischen diesen Werten und denen für vollst?ndige Sole zeigt den Einflu? der Art der Solentstehung auf die Koagulationswerte dieser Elektrolyte. DieSchulze-Hardy-Regel wird best?tigt. Die Anwendung derBurton-Bishop-Regel ist begrenzt. Bei Kaliumferricyanid und Kaliumferrocyanid k?nnen wir den Dissoziationsgrad dieser Anionen aus ihren Koagulationswerten ersehen.     

Dependence of ultrasonic attenuation in semi-conductors on electric field strength

The dependence of the ultrasonic attenuation, or amplification, in semi-conductors on the electric field strength is derived. It is shown that the ultrasonic amplification does not increase linearly with the field, but, after reaching a maximum, it again decreases.     

On peripheral pion-nucleon interactions at 7 GeV

It is shown by analyzing the ^–1-nucleon interactions at 7 GeV that it is possible to select events which could be described by the one-pion exchange model. Among the 169 stars with identified recoil proton which were examined, there are approximately 17 events corresponding to the scheme having a nucleon in the lower vertex only, while the maximum number of cases having a pion-nucleon system there is 84, For the second group the distribution of the mass of particles emitted in the lower vertex has its maximum in the region of the nucleon isobar mass (T=3/2). The distribution of mass of particles emitted in the upper vertex is not in contradiction with the production of and mesons. The values of the square of the transferred four-momentum are distributed predominantly in the region of small values in agreement with the Salzman model.The authors express their sincere thanks to E. Fenyves, K. Lanius and K. D. Tolstov for permission to use their experimental data and to J. Pernegr and V. imák for valuable discussions.     

Über die binären quadratischen Formen

Ohne Zusammenfassung