Signatures of $\alpha$ clustering in ultrarelativistic collisions with light nuclei

We explore possible observable signatures of $\alpha$ clustering of light nuclei in ultrarelativistic nuclear collisions involving ${}^{7,9}\mathrm{Be}$, ${}^{12}\mathrm{C}$, and ${}^{16}\mathrm{O}$. The clustering leads to specific spatial correlations of the nucleon distributions in the ground state, which are manifest in the earliest stage of the ultrahigh energy reaction. The formed initial state of the fireball is sensitive to these correlations, and the effect influences, after the collective evolution of the system, the hadron production in the final stage. Specifically, we study effects on the harmonic flow in collisions of light clustered nuclei with a heavy target (${}^{208}\mathrm{Pb}$), showing that measures of the elliptic flow are sensitive to clusterization in ${}^{7,9}\mathrm{Be}$, whereas triangular flow is sensitive to clusterization in ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$. Specific predictions are made for model collisions at energies available at the CERN Super Proton Synchrotron. In another exploratory development we also examine proton-beryllium collisions, where the $3/2^{-}$ ground state of ${}^{7,9}\mathrm{Be}$ nuclei is polarized by an external magnetic field. Clusterization leads to multiplicity distributions of participant nucleons which depend on the orientation of the polarization with respect to the collision axis, as well as on the magnetic number of the state. The obtained effects on multiplicities reach a factor of a few for collisions with a large number of participant nucleons.

Figure 1

Schematic view of the cluster structure of light nuclei. The dark blobs indicate $\alpha$ clusters (in the case of ${}^7\mathrm{Be}$, also the ${}^3\mathrm{He}$ cluster). The additional open circle in ${}^9\mathrm{Be}$ indicates the extra neutron.

Figure 2

Diagram of ultrarelativistic ${}^{7,9}\mathrm{Be}+{}^{208}\mathrm{Pb}$ collisions. The clustered beryllium creates a fireball whose initial transverse shape reflects the deformed intrinsic shape of the projectile (left panel). Subsequent collective evolution leads to faster expansion along the direction perpendicular to the symmetry axis of the beryllium, and slower expansion along this axis, as indicated by the arrows (right panel). The effect generates specific signatures in the harmonic flow patterns in spectra of the produced hadrons in the final state.

Figure 3

Nuclear density profiles of the considered light nuclei. The points correspond to our Monte Carlo generation of the nuclear distributions in glissando, with parameters listed of Table 1 adjusted in such a way that the results from variational Monte Carlo (VMC) studies [18, 19] (dashed lines) are properly reproduced. We use the normalization $4\pi {\int }_0^{\infty }{r}^{2}dr\rho \left(r\right)=1$.

Figure 4

Ratios of the four- to two-particle cumulants for ${}^7\mathrm{Be}+{}^{208}\mathrm{Pb}$ collisions, plotted as functions of the total number of the wounded nucleons. Clustered nuclei (thick lines) are compared with the case where the nucleons are distributed uniformly with the same one-body radial distributions (thin lines). The vertical lines indicate the multiplicity percentiles (centralities) corresponding to the indicated values of $N_W$. The upper horizontal axis shows the corresponding values of RDS of Eq. (4).

Figure 5

The same as in Fig. 4 but for ${}^9\mathrm{Be}+{}^{208}\mathrm{Pb}$ collisions.

Figure 6

The same as in Fig. 4 but for ${}^{12}\mathrm{C}+{}^{208}\mathrm{Pb}$ collisions.

Figure 7

The same as in Fig. 4 but for ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$ collisions.

Figure 8

Ratios of the four- to two-particle cumulants for ${}^7\mathrm{Be}+{}^{208}\mathrm{Pb}$ collisions with clustered nuclei, plotted as functions of the total number of the wounded nucleons. Results with constant strength sources (thick lines) are compared to the case where the strength fluctuates with the $\mathrm{\Gamma }$ distribution with $\kappa =0.9$ (thin lines). The vertical lines indicate the multiplicity percentiles (centralities) corresponding to the indicated values of $N_W$. The upper horizontal axis shows the corresponding values of RDS.

Figure 9

Ratios of the four- to two-particle cumulants for ${}^7\mathrm{Be}+{}^{208}\mathrm{Pb}$ collisions, clustered nuclei case, simulated for the backward, central, and forward rapidity regions, plotted as functions of the total number of the wounded nucleons. Thick lines correspond to elliptic coefficients, $n=2$, and thin lines correspond to the triangular coefficients, $n=3$. The upper horizontal axis shows the corresponding values of the transverse entropy.

Figure 10

The distributions of the intrinsic symmetry axes of ${}^{7,9}\mathrm{Be}$ vs the polar angle $\theta$, Eq. (20), following from the Peierls-Yoccoz projection method.

Figure 11

Schematic representation of collisions of protons with polarized ${}^{7,9}\mathrm{Be}$. The sphere represents the $\alpha$ or ${}^3\mathrm{He}$ clusters and the clouds indicate the quantum washing-out of the symmetry axis of the intrinsic states, in accordance with Eq. (14). The tube represents the proton beam with the area given by the total inelastic proton-proton cross section. Arrows show the direction of the magnetic field, which corresponds to the quantization axis of spin. Details are in the text.

Figure 12

Results of Monte Carlo simulations of $p$+${}^7\mathrm{Be}$ collisions. We note that for $N_W\ge 3$ the probability of wounding $N_W$ nucleons is higher for $m=1/2$ than for $m=3/2$ in the case when $\vec{B}$ is parallel to $z$ axis [panel (a)]. For the situation when $\vec{B}$ is perpendicular to $z$, we observed more wounded nucleons for $m=3/2$ than for $m=1/2$ [panel (b)].

Figure 13

The same as in Fig. 12 but for $p$+${}^9\mathrm{Be}$ collisions.