Production of protons and light nuclei in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Au</mml:mi><mml:mo>+</mml:mo><mml:mi>Au</mml:mi></mml:math> collisions at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msqrt><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:msqrt><mml:mspace width="0.16em"/><mml:mo>=</mml:mo><mml:mspace width="0.16em"/><mml:mn>3</mml:mn></mml:mrow></mml:math> GeV with the STAR detector

We report the systematic measurement of protons and light nuclei production in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{NN}}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}3\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}$ by the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The transverse momentum $({p}_{T})$ spectra of protons $(p)$, deuterons $(d)$, tritons $(t)$, $^{3}\mathrm{He}$, and $^{4}\mathrm{He}$ have been measured from midrapidity to target rapidity for different collision centralities. We present the rapidity and centrality dependence of particle yields $(dN/dy)$, average transverse momentum $(\ensuremath{\langle}{p}_{T}\ensuremath{\rangle})$, yield ratios $(d/p,$ $t/p,^{3}\mathrm{He}/p,$ $^{4}\mathrm{He}/p)$, as well as the coalescence parameters $({B}_{2},$ ${B}_{3})$. The $4\ensuremath{\pi}$ yields for various particles are determined by utilizing the measured rapidity distributions, $dN/dy$. Furthermore, we present the energy, centrality, and rapidity dependence of the compound yield ratios $({N}_{p}\ifmmode\times\else\texttimes\fi{}{N}_{t}/{N}_{d}^{2})$ and compare them with various model calculations. The physics implications of these results on the production mechanism of light nuclei and the QCD phase structure are discussed.