Study of possible DND* bound states

We start from a recently favored picture in which the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi mathvariant="normal">Λ</a:mi><a:mi>c</a:mi></a:msub><a:mo stretchy="false">(</a:mo><a:mn>2940</a:mn><a:mo stretchy="false">)</a:mo></a:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msub><f:mi mathvariant="normal">Λ</f:mi><f:mi>c</f:mi></f:msub><f:mo stretchy="false">(</f:mo><f:mn>2910</f:mn><f:mo stretchy="false">)</f:mo></f:math> correspond mostly to <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>N</k:mi><k:msup><k:mi>D</k:mi><k:mo>*</k:mo></k:msup></k:math> bound states with <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>J</m:mi><m:mi>P</m:mi></m:msup><m:mo>=</m:mo><m:mn>1</m:mn><m:mo>/</m:mo><m:msup><m:mn>2</m:mn><m:mo>−</m:mo></m:msup><m:mo>,</m:mo><m:mn>3</m:mn><m:mo>/</m:mo><m:msup><m:mn>2</m:mn><m:mo>−</m:mo></m:msup></m:math> respectively, and then add a <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>D</o:mi></o:math> as a third particle, looking for the possible binding of the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>D</q:mi><q:mi>N</q:mi><q:msup><q:mi>D</q:mi><q:mo>*</q:mo></q:msup></q:math> three-body system within the framework of the fixed center approximation. We find that the system is bound with respect to the corresponding <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi mathvariant="normal">Λ</s:mi><s:mi>c</s:mi></s:msub><s:mo stretchy="false">(</s:mo><s:mn>2940</s:mn><s:mo stretchy="false">)</s:mo><s:mi>D</s:mi></s:math>, <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:msub><x:mi mathvariant="normal">Λ</x:mi><x:mi>c</x:mi></x:msub><x:mo stretchy="false">(</x:mo><x:mn>2910</x:mn><x:mo stretchy="false">)</x:mo><x:mi>D</x:mi></x:math> thresholds with a binding of about 60 MeV and a width of about 90 MeV. Alternatively we assume a cluster of <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>N</cb:mi><cb:mi>D</cb:mi></cb:math> and a <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msup><eb:mi>D</eb:mi><eb:mo>*</eb:mo></eb:msup></eb:math> meson interacting with the cluster, and we find similar results. The observation of these states of <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msup><gb:mi>J</gb:mi><gb:mi>P</gb:mi></gb:msup><gb:mo>=</gb:mo><gb:mn>1</gb:mn><gb:mo>/</gb:mo><gb:msup><gb:mn>2</gb:mn><gb:mo>+</gb:mo></gb:msup><gb:mo>,</gb:mo><gb:mn>3</gb:mn><gb:mo>/</gb:mo><gb:msup><gb:mn>2</gb:mn><gb:mo>+</gb:mo></gb:msup></gb:math> would provide new and valuable information concerning the <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>D</ib:mi><ib:mi>N</ib:mi></ib:math> and <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:msup><kb:mi>D</kb:mi><kb:mo>*</kb:mo></kb:msup><kb:mi>N</kb:mi></kb:math> interaction, an issue of current debate.