Damped oscillation regular structures from the deuteron effective electromagnetic form factor data

The deuteron “D” is the simplest nucleus with the spin <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>S</a:mi> <a:mo>=</a:mo> <a:mn>1</a:mn> </a:mrow> </a:math> , therefore its electromagnetic structure is completely described by three different form factors: the charge <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>G</c:mi> <c:mi>C</c:mi> </c:msub> <c:mo stretchy="false">(</c:mo> <c:mi>t</c:mi> <c:mo stretchy="false">)</c:mo> </c:math> , magnetic <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>G</g:mi> <g:mi>M</g:mi> </g:msub> <g:mo stretchy="false">(</g:mo> <g:mi>t</g:mi> <g:mo stretchy="false">)</g:mo> </g:math> , and quadrupole <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>G</k:mi> <k:mi>Q</k:mi> </k:msub> <k:mo stretchy="false">(</k:mo> <k:mi>t</k:mi> <k:mo stretchy="false">)</k:mo> </k:math> , where <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>t</o:mi> <o:mo>=</o:mo> <o:mo>−</o:mo> <o:msup> <o:mi>q</o:mi> <o:mn>2</o:mn> </o:msup> </o:math> is the momentum transfer squared of the electrons or the deuterons in the elastic scattering of electrons on deuterons. All three deuteron form factors are theoretically related to the functions <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>A</q:mi> <q:mo stretchy="false">(</q:mo> <q:mi>t</q:mi> <q:mo stretchy="false">)</q:mo> </q:math> , <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>B</u:mi> <u:mo stretchy="false">(</u:mo> <u:mi>t</u:mi> <u:mo stretchy="false">)</u:mo> </u:math> , and <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msub> <y:mi>T</y:mi> <y:mn>20</y:mn> </y:msub> <y:mo stretchy="false">(</y:mo> <y:mi>t</y:mi> <y:mo stretchy="false">)</y:mo> </y:math> to be numerically evaluated with errors, whereby <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mi>A</cb:mi> <cb:mo stretchy="false">(</cb:mo> <cb:mi>t</cb:mi> <cb:mo stretchy="false">)</cb:mo> </cb:math> and <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mi>B</gb:mi> <gb:mo stretchy="false">(</gb:mo> <gb:mi>t</gb:mi> <gb:mo stretchy="false">)</gb:mo> </gb:math> in a measurement of the differential cross section of elastic scattering of unpolarized electrons on unpolarized deuterons, and <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:msub> <kb:mi>T</kb:mi> <kb:mn>20</kb:mn> </kb:msub> <kb:mo stretchy="false">(</kb:mo> <kb:mi>t</kb:mi> <kb:mo stretchy="false">)</kb:mo> </kb:math> in measurements of the elastic scattering of the longitudinally polarized electrons, respectively also on the polarized deuteron target. The obtained data are utilized to fix parameters of the deuteron electromagnetic form factors to be constructed in the form of the unitary and analytic model. Afterwards these form factors are analytically continued into the timelike region, with the aim to predict artificial behavior of the total cross section <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:msub> <ob:mi>σ</ob:mi> <ob:mi>tot</ob:mi> </ob:msub> <ob:mo stretchy="false">(</ob:mo> <ob:msup> <ob:mi>e</ob:mi> <ob:mo>+</ob:mo> </ob:msup> <ob:msup> <ob:mi>e</ob:mi> <ob:mo>−</ob:mo> </ob:msup> <ob:mo stretchy="false">→</ob:mo> <ob:mi>D</ob:mi> <ob:mover accent="true"> <ob:mi>D</ob:mi> <ob:mo stretchy="false">¯</ob:mo> </ob:mover> <ob:mo stretchy="false">)</ob:mo> <ob:mo stretchy="false">(</ob:mo> <ob:mi>s</ob:mi> <ob:mo stretchy="false">)</ob:mo> </ob:math> . By means of the latter, artificial data with errors on the deuteron “effective” electromagnetic form factor are produced theoretically. Finally, such data render a possibility to investigate the deuteron damped oscillation regular structures.