Probing the neutron-skin thickness by photon production from reactions induced by intermediate-energy protons

The photon from neutron-proton bremsstrahlung in $p+\mathrm{Pb}$ reactions is examined as a potential probe of the neutron-skin thickness in different centralities and at different proton incident energies. It is shown that the best choice of reaction environment is about 140 MeV for the incident proton and the 95%–100% centrality for the reaction system since the incident proton mainly interacts with neutrons inside the skin of the target and thus leads to different photon production to a maximal extent. Moreover, considering two main uncertainties from both photon production probability and nucleon-nucleon cross section in the reaction, I propose to use the ratio of photon production from two reactions to measure the neutron-skin thickness because of its cancellation effects on these uncertainties simultaneously, but preserved about 13%–15% sensitivities on the varied neutron-skin thickness from 0.1 to 0.3 fm within the current experimental uncertainty range of the neutron-skin size in ${}^{208}\mathrm{Pb}$.

Figure 1

The neutron and proton density profiles for ${}^{208}\mathrm{Pb}$ target with the neutron-skin thickness of 0.1 and 0.3 fm.

Figure 2

The time evolution of photon multiplicity with different energies (upper panel) and total photon multiplicity (lower panel) in the $p$+Pb reaction with 95%–100% centrality at the proton incident energy of 140 MeV within the neutron-skin thickness of 0.1 and 0.3 fm. The probability formula $p_{\gamma }^b$ and in-medium nucleon-nucleon cross section are used.

Figure 3

Total photon multiplicity and the corresponding relative sensitivity on the neutron-skin thickness in different centralities but with the given proton incident energy of 140 MeV within the neutron-skin thickness of 0.10 and 0.30 fm. The probability formula $p_{\gamma }^b$ and in-medium nucleon-nucleon cross section are used.

Figure 4

Total photon multiplicity and the corresponding relative sensitivity on the neutron-skin thickness in different proton incident energies but the given centrality of 95%–100% within the neutron-skin thickness of 0.10 and 0.30 fm. The probability formula $p_{\gamma }^b$ and in-medium nucleon-nucleon cross section are used.

Figure 5

The time evolution of total photon multiplicity with free-space and in-medium nucleon-nucleon cross section in the proton incident energy of 140 MeV and the centrality of 95%–100% within the probability formula $p_{\gamma }^b$ and neutron-skin thickness of 0.10 and 0.30 fm.

Figure 6

The time evolution of total photon multiplicity with probability formulas $p_{\gamma }^a$ and $p_{\gamma }^b$ in the proton incident energy of 140 MeV and the centrality of 95%–100% within the in-medium nucleon-nucleon cross section and neutron-skin thickness of 0.10 and 0.30 fm.

Figure 7

The ratio of photon multiplicity from two reactions and the corresponding relative sensitivity on the neutron-skin thickness with free-space and in-medium nucleon-nucleon cross section within the probability formula $p_{\gamma }^b$ and neutron-skin thickness of 0.10 and 0.30 fm.

Figure 8

The ratio of photon multiplicity from two reactions and the corresponding relative sensitivity on the neutron-skin thickness with different photon production probability within the in-medium nucleon-nucleon cross section and neutron-skin thickness of 0.10 and 0.30 fm.

Figure 9

The ratio of photon multiplicity from two reactions and the corresponding relative sensitivity on the neutron-skin thickness with two kinds of setting in the $p$+Pb reaction, i.e., free-space cross section with photon production probability formula $p_{\gamma }^b$ and in-medium cross section with photon production probability formula $p_{\gamma }^a$ within the neutron-skin thickness of 0.10 and 0.30 fm.

Figure 10

Same as Fig. 9 but with a centrality of 90%–100%.