Probing the density dependence of the quantum molecular dynamics potential with spallation neutrons induced by 1.2 GeV protons on Al, Fe, Zr, and Pb

The dependence of spallation neutron production double-differential cross sections on the density of the quantum molecular dynamics potential is investigated in $p$+Al, Fe, Zr, and Pb reactions at 1.2 GeV. It is shown that the cascade component of the neutron spectra is largely unaffected by the parameters of the density-dependent potential. As for the evaporative part ($<20$ MeV), some differences are marked only for Pb. Calculated results with a Skyrme-type equation of state of $K=300$ MeV reproduce the neutron spectra for the reactions under study.

Figure 1

Time evolution of binding energy (a) and (c) and root mean square radius (b) and (d) of the ground state of Fe and Pb computed by ImUrQMD using three different parameter sets. The lines are the best fit to the results.

Figure 2

(a) Profile density distribution $\rho (r)$ and (b) momentum distribution $g(p)$of the ground state of Fe and Pb obtained by set 1 (solid red histograms), set 2 (short-dotted green histograms), and set 3 (dash-dotted blue histograms) averaged over 100 events. The smooth solid lines designate the empirical Woods-Saxon density (left panels) and the two Gaussian momentum distributions (right panels).

Figure 3

Neutron energy-angle double-differential cross sections for 1.2 GeV protons on Al, Fe, and Zr. Predictions by ImUrQMD using sets 1 and 3 are given by solid (red) and short-dashed (blue) histograms, respectively. Data (solid circles with error bars) are from [4]. For clarity, only the histograms and data for the smallest angles are given in absolute value. The others have been multiplied by ${10}^{-2},\hspace{1em}\hspace{1em}{10}^{-4},\dots$ for other angles in increasing order.

Figure 4

Same as Fig. 3, but for Pb target. Also shows results for (b) set 2 and (c) set 4.

Figure 5

Low- and high-energy cascade neutrons as predicted by ImUrQMD (SDM is switched off) using set 1 (solid red histograms) and set 3 (short-dashed blue histograms) for the reactions $p$+Fe and $p$+Pb. Spectra are scaled by the factors ${10}^0,{10}^{-1},{10}^{-2},{10}^{-3},{10}^{-4}$, and ${10}^{-5}$ from top to bottom.

Figure 6

Normalized neutron multiplicities as a function of density at the space coordinates where the neutrons have been collided more than once. $p$+Fe and $p$+Pb reactions are considered, ImUrQMD calculations are performed with sets 1 and 3.

Figure 7

(a) Multiplicity distributions and (b) excitation energy distributions of prefragments in the $p$+Fe, Zr, and Pb interactions with different parameter sets.