Apparent temperatures of neutron-poor and neutron-rich compound nuclei

The possibility of the dependence of the nuclear caloric curve on neutron excess sets a limit on the accuracy of our knowledge of the nuclear equation of state, and thus impacts predictive capabilities of nuclear reaction and nuclear astrophysics models. To date, theoretical models have not reached consensus on the magnitude or sign on the asymmetry dependence. To provide constraints, we have measured evaporated particles and heavy residues for complete and incomplete fusion-evaporation reactions in inverse kinematics. The temperatures extracted from the observed light charged particles tend to favor higher temperatures for the neutron-rich fused systems, though they are near the limits of the systematic uncertainty. The present measurement may be used as an upper limit to constrain the asymmetry dependence of the nuclear caloric curve.

Figure 1

Velocity distributions of $\alpha$ particles predicted by HIPSE for ${}^{86}\mathrm{Kr}+{}^{12}\mathrm{C}$ at 15 MeV/u (top), at 25 MeV/u (middle), at 35 MeV/u (bottom).

Figure 2

Particle identification by $\mathrm{\Delta }E\text{−}E$ in a representative detector (21) of FAUST.

Figure 3

Measured charged particle multiplicity in FAUST as a function of beam energy per nucleon (left) and excitation energy per nucleon (right) for ${}^{78}\mathrm{Kr}+\mathrm{C}$ (red) and ${}^{86}\mathrm{Kr}+\mathrm{C}$ (blue).

Figure 4

Velocity distributions of fusion-evaporation residues measured in the QTS in coincidence with a charged particle in FAUST. Top, from left to right: ${}^{78}\mathrm{Kr}+\mathrm{C}$ at 15, 25, 35 MeV/u; bottom, from left to right: ${}^{86}\mathrm{Kr}+\mathrm{C}$ at 15, 25, 35 MeV/u. The dotted and dashed lines matched to the height of the nearest distribution indicate the velocity of the beam and the velocity corresponding to complete fusion, respectively.

Figure 5

Velocity spectra for $\alpha$ particles measured in FAUST for ${}^{86}\mathrm{Kr}+\mathrm{C}$ at 15 MeV/u (top), ${}^{86}\mathrm{Kr}+\mathrm{C}$ at 25 MeV/u (middle), and ${}^{86}\mathrm{Kr}+\mathrm{C}$ at 35 MeV/u (bottom).

Figure 6

Same as Fig. 5, with the requirement that a heavy residue be measured in coincidence in the QTS, and transforming the $\alpha$ particle velocity to the frame of the residue. Lines and arcs indicate the region of complete kinematic coverage used for subsequent Maxwell-Boltzman fits.

Figure 7

Energy distributions of $\alpha$ particles in the frame of the coincident evaporation residue for reactions of ${}^{86}\mathrm{Kr}+\mathrm{C}$ at 35 MeV/u. Uppermost distribution is summed from ${10}^{\circ }$ to ${70}^{\circ }$. Each distribution below this corresponds to an angular range ${10}^{\circ }$ wide; from the top down: $0^{\circ }$ to ${10}^{\circ }, {10}^{\circ }$ to ${20}^{\circ }, {20}^{\circ }$ to ${30}^{\circ }$, etc. The magenta curve is a Maxwell-Boltzman with a diffuse barrier fit to the upper most data series, and scaled and superimposed on top of the distributions that comprise it.

Figure 8

$\alpha$ particle kinetic energy spectra in the frame of the evaporation residue for ${}^{78}\mathrm{Kr}+\mathrm{C}$ (red) and ${}^{86}\mathrm{Kr}+\mathrm{C}$ (blue) at 15 MeV/u (top), at 25 MeV/u (middle), at 35 MeV/u (bottom). Curves show Maxwell-Boltzmann fits with diffuse barriers.

Figure 9

Same as Fig. 8 but for ${}^6\mathrm{He}$ nuclei.

Figure 10

Slope temperatures for $\alpha$ particles (left) and ${}^6\mathrm{He}$ nuclei (right) for ${}^{78}\mathrm{Kr}+\mathrm{C}$ (red) and ${}^{86}\mathrm{Kr}+\mathrm{C}$ (blue).

Figure 11

Primary slope temperatures for alpha particles (left) and ${}^6\mathrm{He}$ nuclei (right) for ${}^{78}\mathrm{Kr}+\mathrm{C}$ (red) and ${}^{86}\mathrm{Kr}+\mathrm{C}$ (blue).

Figure 12

In reading order of panels: MQF temperatures for protons, deuterons, tritons, helions, $\alpha$ particles, and ${}^6\mathrm{He}$ nuclei for ${}^{78}\mathrm{Kr}+\mathrm{C}$ (red) and ${}^{86}\mathrm{Kr}+\mathrm{C}$ (blue).

Figure 13

Albergo temperatures for {$p,d,h,a$} (left) and {$d,t,h,a$} (right) for ${}^{78}\mathrm{Kr}+\mathrm{C}$ (red) and ${}^{86}\mathrm{Kr}+\mathrm{C}$ (blue).