Light clusters in nuclear matter: Excluded volume versus quantum many-body approaches

The formation of clusters in nuclear matter is investigated, which occurs, e.g., in low-energy heavy-ion collisions or core-collapse supernovae. In astrophysical applications, the excluded volume concept is commonly used for the description of light clusters. Here we compare a phenomenological excluded volume approach to two quantum many-body models, the quantum statistical model and the generalized relativistic mean-field model. All three models contain bound states of nuclei with mass number $A\le 4$. It is explored to which extent the complex medium effects can be mimicked by the simpler excluded volume model, regarding the chemical composition and thermodynamic variables. Furthermore, the role of heavy nuclei and excited states is investigated by use of the excluded volume model. At temperatures of a few MeV the excluded volume model gives a poor description of the medium effects on the light clusters, but there the composition is actually dominated by heavy nuclei. At larger temperatures there is a rather good agreement, whereas some smaller differences and model dependencies remain.

Figure 1

The mass fractions of protons, deuterons, helions, tritons, and alphas, and the mass fraction $X^{\prime }$, defined by Eq. (13), for symmetric nuclear matter at $T=4$ MeV. The results of the generalized relativistic mean-field model GRMF and of the quantum statistical model QS from Ref. [2] are compared to the excluded volume model ExV [12]. “ExV, LC” shows the results if only the same light clusters with $A\le 4$ as in Ref. [2] are considered and no excited states are taken into account. For “ExV, all” all available nuclei are used. “ExV, all, g(T)” also takes all available nuclei into account, but this time with the internal partition function of excited states. The vertical gray lines show the density where the fraction $X^{\prime }>0.1$ for “ExV, all, g(T).”

Figure 2

The free energy per baryon and internal energy per baryon with respect to the averaged rest mass of neutrons and protons at $T=4$ MeV. Otherwise, notation is as in Fig. 1.

Figure 3

As in Fig. 1, but now for $T=10$ MeV.

Figure 4

As in Fig. 2, but now for $T=10$ MeV.

Figure 5

As in Fig. 1, but now for $T=20$ MeV.

Figure 6

As in Fig. 2, but now for $T=20$ MeV.