Interplay of short-range correlations and nuclear symmetry energy in hard-photon production from heavy-ion reactions at Fermi energies

Within an isospin- and momentum-dependent transport model for nuclear reactions at intermediate energies, we investigate the interplay of the nucleon-nucleon short-range correlations (SRCs) and nuclear symmetry energy $E_{\text{sym}}\left(\rho \right)$ on hard-photon spectra in collisions of several Ca isotopes on ${}^{112}\mathrm{Sn}$ and ${}^{124}\mathrm{Sn}$ targets at a beam energy of 45 MeV/nucleon. It is found that over the whole spectra of hard photons studied, effects of the SRCs overwhelm those owing to the $E_{\text{sym}}\left(\rho \right)$. The energetic photons come mostly from the high-momentum tails (HMTs) of single-nucleon momentum distributions in the target and projectile. Within the neutron-proton dominance model of SRCs based on the consideration that the tensor force acts mostly in the isosinglet and spin-triplet nucleon-nucleon interaction channel, there are equal numbers of neutrons and protons, thus a zero isospin asymmetry in the HMTs. Therefore, experimental measurements of the energetic photons from heavy-ion collisions at Fermi energies have the great potential to help us better understand the nature of SRCs without any appreciable influence by the uncertain $E_{\text{sym}}\left(\rho \right)$. These measurements will be complementary to but also have some advantages over the ongoing and planned experiments using hadronic messengers from reactions induced by high-energy electrons or protons. Because the underlying physics of SRCs and $E_{\text{sym}}\left(\rho \right)$ are closely correlated, a better understanding of the SRCs will, in turn, help constrain the nuclear symmetry energy more precisely in a broad density range.

Figure 1

Nucleon momentum distribution $n\left(k\right)$ of ${}_{26}{}^{56}\mathrm{Fe}$ with normalization condition ${\int }_0^{\lambda k_F}n\left(k\right)k^{2}dk=1$.

Figure 2

Nucleon momentum distribution $n\left(k\right)$ in (a) ${}_{20}{}^{40}\mathrm{Ca}$ and (b) ${}_{20}{}^{48}\mathrm{Ca}$. For a comparison, the nucleon Fermi distribution is also shown.

Figure 3

The corresponding density-dependent symmetry energy in Eq. (5). $x=-1,1$ are for the stiff and soft symmetry energies, respectively.

Figure 4

(a) HMT effects on hard-photon productions in head-on ${}^{40}\mathrm{Ca}+{}^{112}\mathrm{Sn}$ reactions at 45 MeV/nucleon with the default value of $x=1$. (b) The ratio of hard-photon spectra with the HMTs and without HMT.

Figure 5

Same as Fig. 4, but with an impact parameter of $b=5$ fm.

Figure 6

(a) Hard-photon productions in head-on collisions of Ca isotopes on ${}^{112}\mathrm{Sn}$ target at 45 MeV/nucleon with the default value of $x=1$. (b) The ratio of hard-photon productions in reactions with ${}^{56,48}\mathrm{Ca}$ projectiles over that with ${}^{40}\mathrm{Ca}$.

Figure 7

Same as Fig. 6, but with an impact parameter of $b=5$ fm.

Figure 8

Effects of the symmetry energy on the ratio of hard-photon productions in neutron-rich and neutron-deficient reactions at a beam energy of 45 MeV/nucleon with different impact parameters.