arXiv · 0707.4076
We present predictions of the thermal model for hadron ratios in central Pb+Pb collisions at LHC.
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A. Andronic, P. Braun-Munzinger, J. Stachel. 2007-07-27. Thermal model predictions of hadron ratios at LHC. https://arxiv.org/abs/0707.4076
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In this work, we calculate the binding energies of an equal-mass fermion--antifermion system in the $0^{-+}$ and $1^{--}$ channels from the ladder Bethe--Salpeter (BS) equation with scalar, pseudoscalar, and vector exchange. The results are compared with those of the Schrödinger equation with the corresponding leading static interaction in two regimes: pointlike massless exchange at weak coupling and finite-mass exchange with monopole form factors at stronger coupling. For the BS calculation, we use two independent numerical methods based on momentum-space integral equations and coordinate-space differential equations. The differential-equation method gives estimated relative binding-energy errors below $10^{-9}$ in both regimes. For massless vector exchange in Coulomb gauge, the numerical results are consistent with the uncrossed-ladder perturbative spectrum through the $O(mα^5)$ terms. The results for massless scalar exchange and vector exchange in Feynman gauge are consistent with the common Wick--Cutkosky expansion through order $mα^3$. For finite exchange masses, the differences from the leading static Schrödinger spectra at the same masses, couplings, and form factors depend strongly on the exchange and channel. Scalar exchange gives nearly degenerate channels with much weaker binding than the Schrödinger reference. In contrast, vector exchange with only the metric term retained gives stronger binding than the Schrödinger reference in $0^{-+}$ and weaker binding in $1^{--}$. Notably, retaining the full Proca numerator substantially increases the vector binding in both channels. Pseudoscalar exchange also supports bound states and favors $1^{--}$, although its leading static central interaction vanishes.
The shell structure of nuclei beyond N=126 relevant to the third peak at A ~ 195 in r-process nuclear abundances in investigated. Within the framework of the relativistic Hartree-Bogoliubov theory in deformed space, a comparative study of the response of nuclei with three different model Lagrangians NL-SV1, SVI-2 and NL3 is made. Ground-state properties of even-even nuclei in the isotopic chains of Z=58-72$= in the highly neutron-rich region are investigated. A comparison of binding energies with mass formulas shows that in the extreme region of the r-process path, the RMF model SVI-2 without nonlinearities of sigma and omega mesons shows an excellent agreement with the mass formula HFB-24. It is shown that in all the above Lagrangian models, in the neutron rich region between the shell closures N=126 and N=184, there is a preponderance of nuclides exhibiting coexistence of well-deformed prolate and oblate shapes in the ground state. A prolate ground state is shown to evolve smoothly to a coexisting oblate ground state via a near degeneracy with successive addition of neutrons. Induced by an onset of deformation for $N \ge 130$, nuclei approaching the r-process path are shown to exhibit enhanced stability in many isotopic chains (Z > 60). This has the effect of shifting the expected neutron drip line significantly farther into the neutron-rich region especially for the higher Z chains. Consequences of the enhanced stability, the shape co-existence and degeneracy of shapes in nuclei on the r-process nucleosynthesis are discussed.
Characterized by central density depletion, bubble nuclei represent an important class of exotic nuclear structures. Collective flow in the $^{40}$Ca+$^{9}$Be projectile fragmentation reaction at 140 MeV/u is investigated using the extended quantum molecular dynamics (EQMD) model with a parameter on of the isoscalar monopole excitation strength $\varepsilon$. The projectile $^{40}Ca$ is initialized as a relaxed ten-$α$ cluster configuration exhibiting a bubble-like density distribution. The results reveal that increasing $\varepsilon$ modifies the density distribution and the size of the depleted central region of bubble, producing pronounced changes in fragment yields and collective flow around $\varepsilon\approx0.5$. Below this value, heavy-fragment production plays a significant role, while the directed flow $v_1$ of protons and neutrons remains predominantly negative, indicating preferential emission toward the target side. Above $\varepsilon\approx0.5$, enhanced expansion of the central low-density region suppresses heavy residues and drives $v_1$ toward positive values. In contrast, preformed $α$ clusters show different responses, reflecting their origin in the initial cluster configuration rather than solely in secondary decay. At low excitation, the cluster flow exhibits a pronounced impact-parameter dependence, whereas stronger excitation weakens cluster binding and suppresses directional anisotropy, driving the flow close to zero. The rapidity slopes of the flow coefficients also vary systematically with $\varepsilon$, tracing changes in emission anisotropy during expansion. These findings extend traditional static descriptions by probing the dynamical evolution of exotic structures in heavy-ion reactions and the contrasting collective-flow behavior of preformed clusters and single nucleons constitutes a sensitive dynamical probe of bubble-like structures.