Asymptotic estimation of some multiple integrals and the electromagnetic deuteron form factors at high momentum transfer

TL;DR

This paper develops a new asymptotic estimation theorem for certain multiple integrals and applies it to analyze the high-momentum transfer behavior of deuteron electromagnetic form factors, highlighting relativistic effects.

Contribution

It introduces a novel theorem for asymptotic estimation of integrals with boundary-peaking integrands and applies it to improve understanding of deuteron form factors at high energies.

Findings

Relativistic effects slow the decline of deuteron form factors.

The asymptotic expansion aligns with experimental data at high momentum transfers.

The theorem addresses integrals peaking at domain boundaries, not extrema.

Abstract

A theorem about asymptotic estimation of multiple integral of a special type is proved for the case when the integrand peaks at the integration domain bound, but not at a point of extremum. Using this theorem the asymptotic expansion of the electromagnetic deuteron form factors at high momentum transfers is obtained in the framework of two-nucleon model in both nonrelativistic and relativistic impulse approximations. It is found that relativistic effects slow down the decrease of deuteron form factors and result in agreement between the relativistic asymptotics and experimental data at high momentum transfers.