In-medium effects for nuclear matter in the Fermi-energy domain

Background: By looking specifically at free nucleons (here protons), we present for the first time a comprehensive body of experimental results concerning the mean free path, the nucleon-nucleon cross-section and in-medium effects in nuclear matter.

Purpose: Using the large dataset of exclusive measurements provided by the $4\pi$ array INDRA, we determine the relative degree of stopping as a function of system mass and bombarding energy. We show that the stopping can be directly related to the transport properties in the nuclear medium.

Methods: We perform a systematic study of protons nuclear stopping in central collisions for heavy-ion induced reactions in the Fermi-energy domain, between $15A$ and $100A$ MeV.

Results: It is found that the mean free path exhibits a maximum at ${\lambda }_{NN}=9.5\pm 2$ fm, around $E_{\mathrm{inc}}=35A-40A$ MeV incident energy and decreases toward an asymptotic value ${\lambda }_{NN}=4.5\pm 1$ fm at $E_{\mathrm{inc}}=100A$ MeV.

Conclusions: After accounting for Pauli blocking of elastic nucleon-nucleon collisions, it is shown that the effective in-medium $NN$ cross section is further reduced compared to the free value in this energy range. Therefore, in-medium effects cannot be neglected in the Fermi-energy range. These results bring new fundamental inputs for microscopic descriptions of nuclear reactions in the Fermi-energy domain.

Figure 1

Isotropy ratio $R_E$ as a function of total charged multiplicity $M_{ch}$ for Xe+Sn at $15A,25A,39A$, and $65A$ MeV. The black histograms show the mean values and the grey (red) symbols indicate the event selection. All $M_{ch}$ bins have been normalized to the same number of entries.

Figure 2

c.m. transverse versus parallel velocities for protons (left) and $\alpha$ particles (right) in invariant cross section, for the selected central events of the ${}^{129}\mathrm{Xe}+{}^{124}\mathrm{Sn}$ system at $65A$ MeV.

Figure 3

Mean isotropy ratio for protons $R_E^p$ as a function of energy. The symbols represent the different studied systems. The lower dashed curve represents the expected value for the entrance channel (no stopping) and the upper straight line for the full stopping.

Figure 4

Stopping ratio $\mathcal{S}$ (see text) as a function of incident energy. Symbols are the same as for Fig. 3.

Figure 5

Correlation between the probability $\mathcal{C}$ of accepted collisions and the stopping ratio $\mathcal{S}$ for two Fermi spheres separated by relative energies of $30A,60A,90A,110A$ MeV (symbols). The curves correspond to the fits $S^{\beta }$, with the $\beta$ values displayed in the inserted table and their corresponding reduced ${\chi }^2$ values.

Figure 6

Scaled quantity $\mathcal{C}/A_{\mathrm{tot}}^{\gamma }$ (see text), here multiplied by 100, as a function of incident energy for $\gamma =0.25$, 0.333,0.5,0.667. Symbols are the same as for Fig. 3.

Figure 7

Mean free path for a nucleon in nuclear matter as a function of incident energy. Symbols are the same as for Fig. 3.

Figure 8

In-medium nucleon-nucleon cross section as a function of incident energy for $\rho =1.2{\rho }_0$ (see text). Symbols are the same as for Fig. 3.

Figure 9

In-medium nucleon-nucleon cross section corrected from Pauli effects (see text) as a function of incident energy. The different curves correspond to the free values for $nn/pp,np$, and $NN$ cross section for two isospin ratios $N/Z=1,1.38$. Symbols are the same as for Fig. 3.

Figure 10

In-medium factor $\mathcal{F}={\sigma }_{NN}^{\mathrm{in}\text{−}\mathrm{medium}}/{\sigma }_{NN}^{\mathrm{free}}$ for the nucleon-nucleon cross section in nuclear matter. The different curves correspond to some parametrizations used in transport models. Symbols are the same as for Fig. 3.