Statistical production and binding energy of hypernuclei

High-energy nuclear reactions enable us to produce a large variety of hypernuclei through the capture of hyperons by nuclear residues. We explore the statistical disintegration of such hypernuclear systems and the connection of fragment production to the binding energies of hyperons. It has been demonstrated that the hyperon binding energies can be effectively evaluated from the yields of different isotopes of hypernuclei by using the double ratio method. The advantages of this procedure are its universality and the possibility to involve many different isotopes. This method can also be applied for multistrange nuclei, for which binding energies were very difficult to measure in previous hypernuclear experiments. Corrections caused by secondary deexcitation processes are also discussed.

Figure 1

The difference of binding energies of hyperons in nuclei extracted from the double yield ratio ($\mathrm{\Delta }{E}_{\mathrm{bh}}$) divided by the temperature $T$ versus the mass number difference of these nuclei $\mathrm{\Delta }A$, as calculated with the statistical model at different temperatures relevant for multifragmentation reactions. Baryon composition and temperatures (for groups of curves) of the initial system are given in the figure. The results for involved isotopes (see the text) are demonstrated by different color symbols connected with lines, where circles (solid lines) are for single hypernuclei, inverse triangles (dotted lines) are for double hypernuclei, squares (dashed lines) are for triple hypernuclei.

Figure 2

The difference of binding energies of hyperons in nuclei ($\mathrm{\Delta }{E}_{\mathrm{bh}}$) versus the mass number difference of these nuclei $\mathrm{\Delta }A$ for single hypernuclei. The statistical calculations are performed involving the double ratio yields shown in the figure for temperatures $T=2\mathrm{MeV}$ (dashed line), 4 MeV (thin solid line, circle symbols), and 6 MeV (dotted line). The stars (thick solid line) are the direct calculation of $\mathrm{\Delta }{E}_{\mathrm{bh}}$ according to the adopted hyperfragment formula (2, 3, 4, 5, 6, 7) at $T=0$ and $V\to \infty$. The initial parameter of the hypernuclear system are as in Fig. 1.

Figure 3

The temperature versus the excitation energy for the disintegration of the hypernuclear system with parameters given in the figure. The statistical calculations including different initial numbers of hyperons (0, 2, and 4) are shown by different symbols and lines. (For better view the symbols are shifted slightly along the horizontal axis being at the same $E^{*}$.) The helium-lithium isotope temperature (see the text) calculated within the standard multifragmentation model are represented by diamonds.

Figure 4

Influence of the secondary deexcitation on the difference of binding energies of hyperons in nuclei $\mathrm{\Delta }{E}_{\mathrm{bh}}$ as function of their mass number difference $\mathrm{\Delta }A$, by taking single hypernuclei (which are the same as in Fig. 2). The calculations of double ratio yields for primary hot nuclei are shown for temperature 4 MeV (solid line, color circle symbols). The triangles, squares, and stars stand for the calculations with modified double ratios after the secondary deexcitation (via nuclear evaporation) of primary nuclei at excitation energies of 1.5, 2.0, and 3.0 MeV/nucleon, respectively. The same color symbols show the modification of $\mathrm{\Delta }{E}_{\mathrm{bh}}$ and $\mathrm{\Delta }A$ after the deexcitation evolution of many nuclei leading to the same daughter ones (see the text).

Figure 5

The same as in Fig. 4, however, for double hypernuclei (see the text).