Participant and spectator scaling of spectator fragments in Au + Au and Cu + Cu collisions at $\sqrt{s_{NN}}=19.6$ and 22.4 GeV

Spectator fragments resulting from relativistic heavy ion collisions, consisting of single protons and neutrons along with groups of stable nuclear fragments up to nitrogen $\left(Z=7\right)$, are measured in PHOBOS. These fragments are observed in Au+Au $\left(\sqrt{s_{{}_{NN}}}=19.6\mathrm{GeV}\right)$ and Cu+Cu (22.4 GeV) collisions at high pseudorapidity $\left(\eta \right)$. The dominant multiply-charged fragment is the tightly bound helium $\left(\alpha \right)$, with lithium, beryllium, and boron all clearly seen as a function of collision centrality and pseudorapidity. We observe that in Cu+Cu collisions, it becomes much more favorable for the $\alpha$ fragments to be released than lithium. The yields of fragments approximately scale with the number of spectator nucleons, independent of the colliding ion. The shapes of the pseudorapidity distributions of fragments indicate that the average deflection of the fragments away from the beam direction increases for more central collisions. A detailed comparison of the shapes for $\alpha$ and lithium fragments indicates that the centrality dependence of the deflections favors a scaling with the number of participants in the collision.

Figure 1

Transverse momentum and rapidity coverage of charged particles in the silicon Ring detectors in PHOBOS. The main figure shows the $p_T/m$-rapidity acceptance for charged particles in each Ring (different shaded bands). The boundary on the rightmost edge of the shaded region depends on the beam energy. The dashed line shows the boundary for $p_z/m=p_{\mathrm{beam}}/m_{\mathrm{Au}}$ for $\sqrt{s_{{}_{NN}}}=19.6\mathrm{GeV}$ Au+Au collisions. The right-hand axis shows the $p_T$ scale for $\alpha$ particles, i.e., $m=3.727\mathrm{GeV}/c^2$. The inset figure shows the Ring-detector $p_T$ and pseudorapidity coverage.

Figure 2

Correlation between the summed energy recorded in each of the Ring detectors (ERing) and the summed energy deposited in the Octagon barrel (EOct) in Au+Au collisions at $\sqrt{s_{{}_{NN}}}=19.6\mathrm{GeV}$. Filled (open) symbols illustrate the measured distributions from data (simulation). Spectators have been explicitly excluded from the simulation distributions. The bands show the centrality class selection bins used in this analysis, with darker bands corresponding to more central events. See text for discussion.

Figure 3

The distribution of the relative energy loss in Au+Au collisions as $\sqrt{s_{{}_{NN}}}=19.6\mathrm{GeV}$ averaged over the centrality range 0%–70% and $5.0<|\eta <5.4$. The blue distribution shows data, the error bars indicate statistical uncertainties only and the data are not corrected for acceptance. The red distribution shows the results from a MC simulation of singly charged particles with spectator fragments explicitly excluded. See text for discussion.

Figure 4

(a) shows the $E_{\mathrm{rel}}$ distribution after subtracting the $Z=1$ component. The dominant peak at $E_{\mathrm{rel}} \sim 4$ corresponds to $Z=2 \left(\alpha \right)$ fragments. The red line depicts the fit to determine fragment yields—the solid part shows the region over which the fit was made and the dashed is the extrapolation under the higher-$Z$ peaks. (b) shows the same as (a) but with the contribution from the $\alpha$ spectrum [red line in (a)] removed, highlighting the distribution from $Z\ge 3$ fragments. The red line shows a fit to the lithium peak, similar to that described in (a). (c) shows the same as (b), but with the contribution from $Z=3$ particles removed, and the $x$ axis is extended to show the presence of $Z=6$ and $Z=7$ fragments. The error bars are statistical only; data are not corrected for acceptance. See text for discussion.

Figure 5

Pseudorapidity dependence of $\alpha$ [(a)–(g)], lithium [(h)–(n)], beryllium [(o)–(u)], and boron [(v)–(ab)] fragments measured in Au+Au collisions at $\sqrt{s_{{}_{NN}}}=19.6\mathrm{GeV}$. Data are presented in bins of centrality (more central in the rightmost panels) and are averaged over both hemispheres, i.e., the number of fragments per colliding nucleus. The error bars represent the statistical uncertainty, the error bands represent 90% C.L. systematic uncertainties in the yield.

Figure 6

Pseudorapidity dependence of $\alpha$ (filled symbols) and lithium fragments (open symbols) measured in Cu+Cu collisions at $\sqrt{s_{{}_{NN}}}=22.4\mathrm{GeV}$. Lithium fragment yields are scaled up by a factor of 10 for clarity. Data are presented in bins of centrality and are averaged over both hemispheres, i.e., the number of fragments per colliding nucleus. The error bars represent the statistical uncertainty, the error bands represent 90% C.L. systematic uncertainties in the yield.

Figure 7

Comparison between the PHOBOS charged particle multiplicity measured at positive $\eta$ in Au+Au collisions at $\sqrt{s_{{}_{NN}}}=19.6\mathrm{GeV}$ and the yield of $\alpha$ and lithium fragments, averaged over positive and negative $\left|\eta \right|$. (a), (b), (c), and (d) show the distributions in centrality bins 0%–10%, 10%–20%, 20%–30%, and 30%–40%, respectively. The open squares/light grey bands represents the PHOBOS multiplicity [20], filled (open) circles represent the measured $\alpha$ (Li) yields.

Figure 8

Comparison between the measured PHOBOS charged particle multiplicity in Cu+Cu collisions at $\sqrt{s_{{}_{NN}}}=22.4\mathrm{GeV}$ and the yield of $\alpha$ fragments. (a), (b), (c), and (d) show the distributions in centrality bins 10%–20%, 20%–30%, 30%–40%, and 40%–50%, respectively. The open squares/light grey bands represents the PHOBOS multiplicity [20], filled circles represent the measured $\alpha$ yields.

Figure 9

Comparison of $\alpha$ yields between PHOBOS data from Au+Au collisions $\left(\sqrt{s_{{}_{NN}}}=19.6\mathrm{GeV}\right)$ and Au+Em $\left(\sqrt{s_{{}_{NN}}}=4.6\mathrm{GeV}\right)$ [4] and Pb+Pb $\left(\sqrt{s_{{}_{NN}}}=17.2\mathrm{GeV}\right)$ [7] collisions. PHOBOS data are averaged over positive and negative $\eta$ and over the most central 0%–70% cross section (filled circles and shaded band which represent the 90% C.L. systematic uncertainties in the yield) for $\alpha$ particles. The pseudorapidity ($x$ axis) is relative to the rest frame of the target nucleus for each energy, as discussed in Appendix pp1.

Figure 10

Centrality dependence of $\alpha$ [(a)–(e)], lithium [(f)–(j)], beryllium [(k)–(o)], and boron [(p)–(t)] fragments measured in Au+Au collisions at $\sqrt{s_{{}_{NN}}}=19.6\mathrm{GeV}$. Data are presented in bins of pseudorapidity, $\eta$, with the lowest $\eta$ shown in the leftmost panels. The data are averaged over both hemispheres, i.e., the number of fragments per colliding nucleus. The error bars represent the statistical uncertainty, the error bands represent 90% C.L. systematic uncertainties in the yield. The errors associated with the centrality variables (here $N_{\mathrm{part}}/2$) are not shown on the figures, see Tables 2, 3, 4, 5, 6, 7.

Figure 11

Centrality dependence of $\alpha$ fragments (filled symbols) for $\sqrt{s_{{}_{NN}}}=22.4\mathrm{GeV}$ Cu+Cu collisions for four $\left|\eta \right|$ bins [(a)–(d)]. For clarity, lithium (open symbols) are scaled up by a factor of 10 and are only shown for the highest two pseudorapidity bins [(c) and (d)]. The data are averaged over both hemispheres, i.e., the number of fragments per colliding nucleus. The error bars (typically smaller than the symbol height) represent the statistical uncertainty, the error bands represent 90% C.L. systematic uncertainties in the yield.

Figure 12

Spline polynomial fits (lines) to $\alpha$ yields from Au+Au peripheral (60%–70%) data (filled circles). Interpolated points at ${\eta }^{\prime }=1.57$ and ${\eta }^{\prime }=2.02$ are shown as open circles. The scale on the upper $x$ axis shows ${\eta }^{\prime }\equiv \left|\eta \right|-y_{\mathrm{beam}}$. The dashed and green lines show fits using polynomials of different order. The outer dotted lines represent a fit to points at the extreme of the systematic uncertainty bands.

Figure 13

Centrality dependence of $\alpha$ (a) and lithium yields (b) in $\sqrt{s_{{}_{NN}}}=19.6\mathrm{GeV}$ Au+Au (filled symbols) and 22.4 GeV Cu+Cu (open symbols) collisions. Note that the centrality variable is not $N_{\mathrm{part}}/2$ but $N_{\mathrm{spec}}$ from a single nucleus—see text for details—and the $x$ axis runs backwards, central collisions are the rightmost data points. The $\alpha$ data are evaluated at ${\eta }^{\prime }=1.57$ (circles/unfilled systematic bands) and ${\eta }^{\prime }=2.02$ (squares/filled systematic bands). Lithium yields are only shown for ${\eta }^{\prime }=2.02$. The bands represent 90% C.L. systematic uncertainties in the yield.

Figure 14

Centrality dependence of the yield of lithium nuclei divided by that of $\alpha$ particles evaluated at ${\eta }^{\prime }=2.02$. Au+Au (filled symbols) and Cu+Cu (open symbols) collision data are shown as a function of (a) $N_{\mathrm{spec}}/2$, (b) $N_{\mathrm{part}}/2$, and (c) the collision geometry $\left(N_{\mathrm{spec}}/2A\right)$. The bands represent 90% C.L. systematic uncertainties in the ratio.

Figure 15

Centrality dependence of the yield of $\alpha$ particles evaluated at ${\eta }^{\prime }=1.57$ divided by the yield measured at ${\eta }^{\prime }=2.02$. Au+Au (filled symbols) and Cu+Cu (open symbols) collision data are shown as a function of (a) $N_{\mathrm{spec}}/2$, (b) $N_{\mathrm{part}}/2$, and (c) the collision geometry $\left(N_{\mathrm{spec}}/2A\right)$. The bands represent 90% C.L. systematic uncertainties in the ratio.

Figure 16

Centrality dependence of the yield of $\alpha$ particles evaluated at ${\eta }^{\prime }=1.21$ divided by the yield measured at ${\eta }^{\prime }=2.02$. Au+Au (filled symbols) and Cu+Cu (open symbols) collision data are shown as a function of (a) $N_{\mathrm{spec}}/2$, (b) $N_{\mathrm{part}}/2$, and (c) the collision geometry $\left(N_{\mathrm{spec}}/2A\right)$. The bands represent 90% C.L. systematic uncertainties in the ratio.

Figure 17

$p_T/m\text{−}{y}^{\prime }$ acceptance for a fixed $1.8<{\eta }^{\prime }<2.0$ window. The upper (lower) bound on each band corresponds to ${\eta }^{\prime }=1.8$ (2.0). The top three panels [(a)–(c)] show the acceptance for PHOBOS ($\sqrt{s_{{}_{NN}}}=19.6\mathrm{GeV}$, and 22.4 GeV), KLMM $\left(E_{\mathrm{beam}}=10.6\mathrm{GeV}\right)$, and KLM ($E_{\mathrm{beam}}$ = 158 GeV), respectively. The lower panel (d) shows an overlay of all distributions. The arrows represent midrapidity ($y=0$ and $\eta =0$) at each energy. See text for discussion.

Figure 18

Estimated $dN/d{p}_T$ distribution for $\alpha$ fragments near beam rapidity for 0%–70% central Au+Au collisions at $\sqrt{s_{{}_{NN}}}=19.6\mathrm{GeV}$. Estimation procedure is described in the text. For comparison, Au+Em $\left(\sqrt{s_{{}_{NN}}}=4.6\mathrm{GeV}\right)$ [4] and Pb+Pb $\left(\sqrt{s_{{}_{NN}}}=17.2\mathrm{GeV}\right)$ [7] collisions are shown, using the same estimation method.

Figure 19

Estimated $dN/d{p}_T$ distribution for $\alpha$ fragments near beam rapidity for Au+Au collisions at $\sqrt{s_{{}_{NN}}}=19.6\mathrm{GeV}$. Estimation procedure is described in the text. The open and closed symbols represent central (0%–10%) and midperipheral (60%–70%) collisions, respectively.