Scaling behavior of the momentum distribution of a quantum Coulomb system in a confining potential

Abstract

We calculate the single-particle momentum distribution of a quantum many-particle system in the presence of the Coulomb interaction and a confining potential. The region of intermediate momenta, where the confining potential dominates, marks a crossover from a Gaussian distribution valid at low momenta to a power-law behavior valid at high momenta. We show that for all momenta the momentum distribution can be parametrized by a $q$-Gaussian distribution whose parameters are specified by the confining potential. Furthermore, we find that the functional form of the probability of transitions between the confined ground state and the $n^{th}$ excited state is invariant under scaling of the ratio $Q^2/{\nu }_n$, where $Q$ is the transferred momentum and ${\nu }_n$ is the corresponding excitation energy. Using the scaling variable $Q^2/{\nu }_n$ the maxima of the transition probabilities can also be expressed in terms of a $q$-Gaussian.

arXiv comment6 pages, 5 figures

References in corpus (8)

• Pair distribution function of the spin-polarized electron gas: A first-principles analytic model for all uniform densities
• Operator Evolution via the Similarity Renormalization Group I: The Deuteron
• Quantifying short-range correlations in nuclei
• High-momentum tails from low-momentum effective theories
• Universality of nucleon-nucleon short-range correlations: two-nucleon momentum distributions in few-body systems
• Counting the number of correlated pairs in a nucleus
• Short-distance properties of Coulomb systems
• Scaling behavior of the Compton profile of alkali metals