Influence of medium modified angular distributions and mean field on the quasielastic and inelastic peaks of neutrons induced by $1.2\mathrm{GeV}$ protons on targets with $27⩽A⩽232$

An analysis of the quasielastic and inelastic peaks of neutrons induced by $1.2\mathrm{GeV}$ protons on targets with $27⩽A⩽232$ is presented using the ultrarelativistic quantum molecular dynamics (UrQMD) model. Two distinct contributions of the nuclear medium are studied in the UrQMD framework, referred to as “in-medium” and “mean field” effects. The former only includes modifications to the $NN$-elastic and $NN\to N\Delta$ angular distributions as well as changes to the $\Delta$-mass distribution. The latter incorporates the (QMD) interaction potential between nucleons. It is shown that in-medium effect produces an important role for enhancing the quasi-inelastic peak, while the mean field effect enhances the intensity of both peaks and becomes important in the quasielastic region. The introduction of both effects in the UrQMD calculations improves the intensity and location of the quasielastic and inelastic peaks. A rather smooth dependence of the integrated cross sections of the quasielastic and inelastic peaks on the mass number at both angles is also found and shown to be in qualitative agreement with the UrQMD incorporating these two effects.

Figure 1

(Color online) The delta mass distribution $⟨m_{\Delta }⟩$ as a function of the total energy of a two particle system in free space $\left(s\right)$.

Figure 2

(Color online) The angular distribution of the neutron calculated using Eq. (B9) for the reaction $p+p\to n+{\Delta }^{++}\to n+p+{\pi }^{+}$ at $0.97\mathrm{GeV}$. (a) Shows the calculations with different delta mass distributions. (b) The contributions of the direct and exchange terms. The solid histograms show the data from Ref. 19.

Figure 3

(Color online) Neutron energy spectra at $0°$ (left panels) and $10°$ (right panels) from $1.2\mathrm{GeV}$ proton interactions with targets of (from the bottom): ${}^{232}\mathrm{Th}$, ${}^{208}\mathrm{Pb}$, ${}^{184}\mathrm{W}$, ${}^{91}\mathrm{Zr}$, ${}^{56}\mathrm{Fe}$, and ${}^{27}\mathrm{Al}$. The bold solid histograms denote the UrQMD/C calculations with the simulated mass distribution of Eq. (9), while the dotted histograms are those with $⟨m_{\Delta }⟩=m_N+m_{\pi }$. The thin solid histograms represent the UrQMD/C calculations with free parametrizations. The experimental data (solid circles with error bars) are taken from Ref. 1.

Figure 4

(Color online) The predicted angular distributions of neutrons evaluated at different laboratory energies for $p+n\to p+n$ (left panels) and $N+N\to N+N+\pi$ (right panels). (a) and (b) are the results calculated by the free Cugnon parametrizations, Eqs. (B1, B2, B3), while (c) and (d) are those calculated by Eqs. (B4, B9), respectively.

Figure 5

(Color online) Same as Fig. 3, but here the bold solid and small dashed histograms denote the UrQMD/MM and UrQMD/CM calculations, respectively. The thin solid histograms denote the UrQMD/MM calculations that includes the $N+\Delta \to N+N$ process.

Figure 6

(Color online) Plot of the cross sections integrals $[\int (d^2\sigma ∕d\Omega dE)dE]$ at $0°$ (left panels) and $10°$(right panels) of the quasielastic and inelastic associated regions of the neutron spectra versus the mass number of the target. Solid circles with error bars represent results extracted from experimental data shown in Figs. 3, 5. The solid lines give the results of the power law fits to the present data (solid circles with error bars) for the two regions at both angles. Results of the UrQMD/MM calculation of the quasielastic and inelastic cross sections for each nucleus are plotted as open circles.