Related papers: Sum rule of the correlation function
We derive a sum rule satisfied by the correlation function of two particles with small relative momenta, which results from the completeness condition of the quantum states.
A correlation function of two particles with small relative velocities obeys a sum rule - the momentum integral of the function is determined due to the completeness of quantum states of the particles. The original sum rule derived in 1995…
We consider an ionic fluid made with two species of mobile particles carrying either a positive or a negative charge. We derive a sum rule for the fourth moment of equilibrium charge correlations. Our method relies on the study of the…
A Coulomb sum rule is derived for the response of nuclei to $(e,e^\prime)$ scattering with large three-momentum transfers. Unlike the nonrelativistic formulation, the relativistic Coulomb sum is restricted to spacelike four-momenta for the…
A sum rule has been derived for the static pair correlation function. This rule is the extension of the well-known equation that relates density fluctuation to compressibility. The obtained sum rule is applied to the Bose and Fermi ideal…
Some present day results for few-nucleon bound state, two-nucleon correlation functions and scattering observables are briefly reviewed. The old idea of the Coulomb sum rule as a way to extract the pp correlation function is reconsidered.…
This paper is the continuation of a previous one [L. {\v{S}}amaj and B. Jancovici, 2007 {\it J. Stat. Mech.} P02002]; for a nearly classical quantum fluid in a half-space bounded by a plain plane hard wall (no image forces), we had…
In simple models of the nuclear charge operator, measurements of the Coulomb sum and the charge form factor of a nucleus directly determine the proton-proton correlations. We examine experimental results obtained for few-body nuclei at…
The status of our understanding of relativistic sum rules is reviewed. The recent development of new theoretical methods for the evaluation of these sum rules offers hope for further advances in this challenging field. These new techniques…
This paper concerns the equilibrium bulk charge and current density correlation functions in quantum media, conductors and dielectrics, fully coupled to the radiation (the retarded regime). A sequence of static and time-dependent sum rules,…
The correlations in classical multi-component ionic mixtures with spatial dimension $d\geq 2$ are studied by using a restricted grand-canonical ensemble and the associated hierarchy equations for the correlation functions. Sum rules for the…
The neutron and proton single-particle spectral functions in asymmetric nuclear matter fulfill energy weighted sum rules. The validity of these sum rules within the self-consistent Green's function approach is investigated. The various…
A new approach of the QCD sum rule is proposed in which positive and negative-parity baryons couple with each other. With positive and negative-parity states explicitly taken into account, sum rules are derived by means of the dispersion…
We have addressed here the problem of calculating the correlation function of a stable particle with a resonance, in particular one resonance that qualifies as a molecular state of two components. The formalism used requires to evaluate the…
The nucleon spectral function in nuclear matter fulfills an energy weighted sum rule. Comparing two different realistic potential, these sum rules are studied for Green's functions that are derived self-consistently within the $T$ matrix…
There may be a link between the quantum properties of the vacuum and the parameters describing the properties of light propagation, culminating in a sum over all types of elementary particles existing in Nature weighted only by their…
A generalized Friedel sum rule is derived for a quantum dot with internal orbital and spin degrees of freedom. The result is valid when all many-body correlations are taken into account and it links the phase shift of the scattered electron…
In this paper, we study the truncated two-particle correlation function in particle systems with long range interactions. For Coulombian and soft potentials, we define and give well-posedness results for the equilibrium correlations. In the…
For inhomogeneous classical Coulomb fluids in thermal equilibrium, like the jellium or the two-component Coulomb gas, there exists a variety of exact sum rules which relate the particle one-body and two-body densities. The necessary…
We prove the bijectivity of the constraints of normalization and of the Fermi-Coulomb hole charge sum rule at each electron position for approximate wave functions. This bijectivity is surprising in light of the fact that normalization…