Production of nuclei and hypernuclei in pion-induced reactions near threshold energies

The ultrarelativistic quantum molecular dynamics model is employed to simulate ${\pi }^{-}+\mathrm{C}$ and ${\pi }^{-}+\mathrm{W}$ collisions at $p_{\mathrm{lab}}=1.7$ GeV motivated by the recent HADES results. By comparing the proton and $\mathrm{\Lambda }$ transverse momentum spectra, it was observed that the data and transport model calculation show a good agreement, if cluster formation is included to obtain the free proton spectra. Predictions of light cluster ($d, t, {}^3\mathrm{He}, {}^4\mathrm{He}$, as well as ${}_{\mathrm{\Lambda }}{}^3\mathrm{H}$ and $\mathrm{\Xi }\mathrm{N}$) multiplicities and spectra are made using a coalescence mechanism. The resulting multiplicities suggest that the pion beam experiment can produce a substantial amount of ${}_{\mathrm{\Lambda }}{}^3\mathrm{H}$, especially in ${\pi }^{-}+\mathrm{W}$ collisions due to the stopping of the $\mathrm{\Lambda }$ inside the large tungsten nucleus. The findings are supplemented by a statistical multifragmentation analysis suggesting that even larger hyperfragments are produced copiously. It is suggested that even double strange hypernuclei are in reach and might be studied in more detail using a slightly higher pion beam momentum.

Figure 1

Upper panel: The transverse momentum differential cross section $d^2\sigma /d{p}_{\mathrm{T}}dy$ in $\mu \mathrm{b}/\left(\mathrm{GeV}\mathrm{\Delta }y\right)$ of free protons as a function of transverse momentum in different rapidity bins (from $0\le y<0.1$ to $0.9\le y<1.0$, the curves are successively multiplied by factors of 10 from bottom to top) for minimum bias ${\pi }^{-}+\mathrm{C}$ (left) and ${\pi }^{-}+\mathrm{W}$ (right) collisions from UrQMD (v3.5). The solid lines with symbols show the calculations and the open symbols show the recent HADES measurements [32]. The dotted line shows the extrapolation function used by HADES. Lower panel: The percentage error between the UrQMD simulations and the experimental data.

Figure 2

Upper panel: The transverse momentum differential cross section $d^2\sigma /d{p}_{\mathrm{T}}dy$ in $\mu \mathrm{b}/\left(\mathrm{GeV}\mathrm{\Delta }y\right)$ of $\mathrm{\Lambda }$ as a function of transverse momentum in different rapidity bins (from $0\le y<0.15$ to $0.9\le y<1.05$, the curves are successively multiplied by factors of 100 from bottom to top) for minimum bias ${\pi }^{-}+\mathrm{C}$ (left) and ${\pi }^{-}+\mathrm{W}$ (right) collisions from UrQMD (v3.5). The solid lines with symbols show the calculations and the open symbols show the recent HADES measurements [32]. Lower panel: The percentage error between the UrQMD simulations and the experimental data (the last rapidity bin is scaled by a factor of 0.2 for visibility).

Figure 3

The rapidity differential cross section $d\sigma /dy$ in $\mu \mathrm{b}/\mathrm{\Delta }y$ of protons (red), $\mathrm{\Lambda }$'s (orange), and $\mathrm{\Xi }$'s (black) as a function of the rapidity for minimum bias ${\pi }^{-}+\mathrm{C}$ (left panel) and ${\pi }^{-}+\mathrm{W}$ (right panel) collisions. The results from UrQMD are shown as colored lines with symbols, while the open black symbols without lines depict the recent HADES measurements [32].The blue crosses show the result using the experimental fit function for the $p_{\mathrm{T}}$ extrapolation.

Figure 4

The transverse momentum differential cross section $d^2\sigma /d{p}_{\mathrm{T}}dy$ in $\mu \mathrm{b}/\left(\mathrm{GeV}\mathrm{\Delta }y\right)$ of deuterons as a function of transverse momentum in different rapidity bins (from $0\le y<0.1$ to $0.8\le y<0.9$, the curves are successively multiplied by factors of 100 from bottom to top) for minimum bias ${\pi }^{-}+\mathrm{C}$ (left panel) and ${\pi }^{-}+\mathrm{W}$ (right panel) collisions from UrQMD.

Figure 5

The transverse momentum differential cross section $d^2\sigma /d{p}_{\mathrm{T}}dy$ in $\mu \mathrm{b}/\left(\mathrm{GeV}\mathrm{\Delta }y\right)$ of tritons as a function of transverse momentum in different rapidity bins (from $0\le y<0.1$ to $0.5\le y<0.6$, the curves are successively multiplied by factors of 100 from bottom to top) for minimum bias ${\pi }^{-}+\mathrm{C}$ (left panel) and ${\pi }^{-}+\mathrm{W}$ (right panel) collisions from UrQMD.

Figure 6

The transverse momentum differential cross section $d^2\sigma /d{p}_{\mathrm{T}}dy$ in $\mu \mathrm{b}/\left(\mathrm{GeV}\mathrm{\Delta }y\right)$ of ${}^3\mathrm{He}$ as a function of transverse momentum in different rapidity bins (from $0\le y<0.1$ to $0.5\le y<0.6$, the curves are successively multiplied by factors of 100 from bottom to top) for minimum bias ${\pi }^{-}+\mathrm{C}$ (left panel) and ${\pi }^{-}+\mathrm{W}$ (right panel) collisions from UrQMD.

Figure 7

The rapidity differential cross section $d\sigma /dy$ in $\mu \mathrm{b}/\mathrm{\Delta }y$ of deuterons (orange), tritons (green), ${}^3\mathrm{He}$ (blue), and ${}^4\mathrm{He}$ (red) as a function of the rapidity for minimum bias ${\pi }^{-}+\mathrm{C}$ (left panel) and ${\pi }^{-}+\mathrm{W}$ (right panel) collisions from UrQMD (v3.5) as denoted by dashed lines with symbols and from SMM as denoted by solid lines without symbols.

Figure 8

The transverse momentum differential cross section $d^2\sigma /d{p}_{\mathrm{T}}dy$ in $\mu \mathrm{b}/\left(\mathrm{GeV}\mathrm{\Delta }y\right)$ of ${}_{\mathrm{\Lambda }}{}^3\mathrm{H}$ (blue) and $N\mathrm{\Xi }$ (black) as a function of transverse momentum at $\left|y\right|\le 0.5$, for minimum bias ${\pi }^{-}+\mathrm{C}$ (left panel) and ${\pi }^{-}+\mathrm{W}$ (right panel) collisions from UrQMD. The extrapolated $N\mathrm{\Xi }$ is shown as a dotted line.

Figure 9

The rapidity differential cross section $d\sigma /dy$ in $\mu \mathrm{b}/\mathrm{\Delta }y$ of the $N\mathrm{\Lambda }$ (blue), $NN\mathrm{\Lambda }$ (green), ${}_{\mathrm{\Lambda }}{}^3\mathrm{H}$ (red), ${}_{\mathrm{\Lambda }}^4\mathrm{H}$ (yellow), ${}_{\mathrm{\Lambda }}^4\mathrm{He}$ (pink), and $N\mathrm{\Xi }$ (black) as a function of the rapidity for minimum bias ${\pi }^{-}+\mathrm{C}$ (left panel) and ${\pi }^{-}+\mathrm{W}$ (right panel) collisions from UrQMD with coalescence (v3.5) denoted as dashed lines with open symbols and SMM denoted as solid lines with full symbols.

Figure 10

The integrated cross section of light nuclei (full symbols) and hypernuclei (single-strange as open symbols) production with different charges $Z$ (denoted by the color) as a function of their mass number $A$ for minimum bias ${\pi }^{-}+\mathrm{C}$ and ${\pi }^{-}+\mathrm{W}$ collisions from a SMM analysis of the UrQMD (v3.5) data.