Linked-Diagram Expansions for Quantum Statistical Mechanics

Abstract

A general method of calculation is described for quantum statistical mechanics. It is based on a simplification of the Laplace transform of the density matrix which follows from a theorem due to Hugenholtz. The basic result is that an element of the density matrix can be written as a sum over graphs, with the contribution of each graph factored into contributions from connected or linked graphs. Applied to the grand partition function, the exponential formula of Bloch and deDominicis is obtained in a simple way. A similar formula is then derived for the canonical ensemble and the case of a nondegenerate gas.In this way the familiar result of Uhlenbeck and Beth is obtained for the second virial coefficient. Techniques are also introduced for evaluating ensemble averages of operators. In this connection, some care must be exercised in the case of diagonal operators. Finally, these methods are used to calculate the pair-correlation function for a system of fermions interacting through shortrange forces.

Some interesting aspects of total disintegration of heavy emulsion nuclei at high energies

“…Glassgold et al (5) have proposed a model for explaining the mechanism of nucleon production through the excitation of shock waves in the target nucleus, induced by a very high energy impinging hadron. This model predicts that the peak of the angular distribution of the nucleons emitted through the excitation of the shock waves must be at an angle, 80, considerably distant from the forward direction.…”

“…Finally, it may be concluded that the cascade-evaporation mechanism of nucleon production is involved in disintegrations having Nh < 28 in high-energy hadron-nucleus interactions, whereas for the events with Nh 2 28, the nucleon production is envisaged to take place through the excitation of nuclear shock waves in the target nucleus by very energetic incident particles. The mean normalized multiplicity, RA, is defined as grey particles produced in high-energy hadron-nucleus interactions (5). This discrepancy in the observed distributions of grey particles in both the usual hadron-nucleus interactions Can.…”

“…Here i stands for the shower, s, or grey, g, particles and j represents the projectile, p, or target, T. The values of the parameter a0 occurring in [5] have been obtained by the hitand-miss trial method and are listed in Table 3 of grey and charged shower particles produced in p-AgBr collisions in the energy range -(7-400) GeV. However, (N,)P2 and (Ns)P2 represent the average numbers of grey and charged shower particles appearing in the final state of " c -~g~r interactions at 4.2GeV/nucleon.…”

“…The reason for growing interest in this problem is the idea that study of catastrophic destruction of heavy target nuclei might provide an opportunity for testing the various models proposed for explaining the mechanism of multiparticle production in high-energy hadron-hadron (h-h) collisions and the formation of anomalous nuclei; it also offers a unique possibility for understanding the production of shock waves in nuclear matter (1)(2)(3)(4)(5)(6)(7)(8). However, relatively little attention has been paid to the study of this phenomenon (9)(10)(11)(12)(13)(14) compared with its interest and importance.…”

Collective Excitation of Nuclear Matter

“…This situation is analogous to the interaction potential between a nucleon and an anti-nucleon. 4 ) Glassgold, Heckrotte and Watson 2 ) studied a similar problem, but they did not take HJ (2).…”