Examination of experimental conditions for the production of proton-rich and neutron-rich hypernuclei

After the demonstration of the feasibility of hypernuclear spectroscopy with heavy-ion beams, the HypHI Collaboration will next focus on the study of proton- and neutron-rich hypernuclei. The use of a fragment separator for the production and separation of rare-isotope beams is a crucial aspect to producing hypernuclei far from the stability line. Precise spectroscopy of exotic hypernuclei is planned to be carried out at the GSI and later at the FAIR facility with the FRS and Super-FRS fragment separators. A systematic study and an optimization analysis were performed to determine optimal experimental conditions for producing hypernuclei with high isospin. The optimal conditions are obtained based on theoretical models for the heavy-ion induced reaction and hypernuclei production. Experimental efficiencies for the production of exotic secondary beams were also taken into account via Monte Carlo simulations of the fragment separator. The developed methodology is presented to deduce the expected yields of ${}_{\mathrm{\Lambda }}{}^8\mathrm{Be}$ and subsequently other proton-rich and neutron-rich hypernuclei.

Figure 1

Super-FRS fragment separator layout. The primary beam from the synchrotron, represented by the yellow arrow on the beam line, bombards the primary target to produce the exotic beam of interest. The pre-separator of Super-FRS, highlighted in red, is used to select and produce a high quality exotic beam. The main separator, filled in blue, acts as the high-resolution forward spectrometer. A second target is installed for the production of hypernuclei at the focal plane of the main separator FMF2.

Figure 2

Beam kinetic energy distribution and transmission distribution of the fragments propagated in the mocadi simulations. (a) Projected beam energy distribution. (b) Candle plot of the beam energy distribution as a function of the transmission. For each transmission bin, the box represents the underlying distributions: the bold line represents the quantile at 50%, the left and right sides of the box are the 75% and 25% quantile. The maximum and the minimum of the distributions are represented by the vertical segments of the dotted line. The open circle is the position of the mean value of the distributions.

Figure 3

Intensity of the secondary beam ${}^{10}\mathrm{C}$ at the FMF2 experimental area of the Super-FRS as a function of the production target thickness, the primary beam, and the target isotope. Only ten entries of the results of the mocadi simulations are displayed out of the whole data set. The intensity of the primary beam was set to $5\times {10}^9$ ions/s, which will be available at the Super-FRS. The legend is ordered from highest to lowest intensity.

Figure 4

Production cross sections in $\mu \mathrm{b}$ of $\mathrm{\Lambda }$-hypernuclei from the collision of (a) ${}^9\mathrm{C}+{}^{12}\mathrm{C}$ at $2A$ GeV, (b) ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$, (c) ${}^{15}\mathrm{C}+{}^{12}\mathrm{C}$, and (d) ${}^{12}\mathrm{B}+{}^{12}\mathrm{C}$. The neutron and proton numbers of the $\mathrm{\Lambda }$-hypernucleus core are represented by the horizontal and vertical axis, respectively. The systematic uncertainty of the production cross sections is estimated to the level of 0.1 $\mu \mathrm{b}$.

Figure 5

Production cross sections in $\mu \mathrm{b}$ of (a) ${}_{\mathrm{\Lambda }}{}^8\mathrm{Be}$ and (b) ${}_{\mathrm{\Lambda }}{}^{11}\mathrm{Be}$ hypernuclei, according to the collision of different exotic secondary beams ${}^{Z+N}\mathrm{Z}$ on a ${}^{12}\mathrm{C}$ target at $2A$ GeV. The systematic uncertainty of the production cross sections is estimated to the level of 0.1 $\mu \mathrm{b}$.

Figure 6

Evolution of the cost function maximum as a function of the $\alpha$ and $\beta$ weight coefficients for the multivariate data set optimization of the studied case of ${}_{\mathrm{\Lambda }}{}^8\mathrm{Be}$. The red dot represents the position of the maximum of the maxima within the $\alpha -\beta$ space.

Figure 7

Results of the multivariate data-set optimization for the studied case of ${}_{\mathrm{\Lambda }}{}^8\mathrm{Be}$ as a function of the target thickness, beam energy, beam intensity, hypernuclear yield, exotic beam, primary beam, and target species. Figures (a) to (f) represent the evolution of the variables, the primary beam and target species, the thickness in centimeters, the selected exotic beam species and its kinetic energy in $A\mathrm{GeV}$, and the ${}_{\mathrm{\Lambda }}{}^8\mathrm{Be}$ yield per second, respectively. Each red dot represents the position of the overall maximum within the $\alpha -\beta$ space.