<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>D</mml:mi> </mml:math> -shell mixing in light baryons and its effect on the orbital motion

The standard description of the nucleon in the nonrelativistic quark model is an <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>1</a:mn> <a:mi>S</a:mi> <a:mo>,</a:mo> <a:mi>L</a:mi> <a:mo>=</a:mo> <a:mn>0</a:mn> </a:math> state without orbital motion. Yet, there are several indications from phenomenology that an admixture of states with nonzero orbital motion maybe substantial. In this paper we focus on the “second shell” of the nucleon excitations (D-shell), for which we give a modern description of the wave functions. We follow it by investigating what we call a “maximal mixing” scenario, assuming a hypothetical long-range tensor force. We give the explicit wave functions for all states, before and after mixing, and reassess many predictions such as the magnetic moments, the standard and transitional form-factors from the nucleon to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msup> <c:mi>N</c:mi> <c:mo>*</c:mo> </c:msup> </c:math> . Unexpectedly, in this scenario we can reproduce the long-puzzling features of the Roper resonance <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mi>N</e:mi> <e:mo>*</e:mo> </e:msup> <e:mo stretchy="false">(</e:mo> <e:mn>1440</e:mn> <e:mo stretchy="false">)</e:mo> </e:math> . But even in this extreme case, the admixture of the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mn>1</i:mn> <i:mi>D</i:mi> <i:mo>,</i:mo> <i:mi>L</i:mi> <i:mo>=</i:mo> <i:mn>2</i:mn> </i:math> state to a nucleon remains significantly smaller than expected from phenomenology.