Nucleon–anti-nucleon intruder state of Dirac equation for nucleon in deep scalar potential well

Abstract

We solve the Dirac radial equation for a nucleon in a scalar Woods–Saxon potential well of depth [Formula: see text] and radius [Formula: see text]. A sequence of values for the depth and radius are considered. For shallow potentials with [Formula: see text] the wave functions for the positive-energy states [Formula: see text] are dominated by their nucleon component [Formula: see text]. But for deeper potentials with [Formula: see text] the [Formula: see text]s begin to have dominant anti-nucleon component [Formula: see text]. In particular, a special intruder state enters with wave function [Formula: see text] and energy [Formula: see text]. We have considered several [Formula: see text] values between 2 and 8[Formula: see text]fm. For [Formula: see text] and the above [Formula: see text] values, [Formula: see text] is the only bound positive-energy state and has its [Formula: see text] closely equal to [Formula: see text], both having a narrow wave packet shape centered around [Formula: see text]. The [Formula: see text] of this state is practically independent of [Formula: see text] for the above [Formula: see text] range and obeys closely the relation [Formula: see text].