Formation and decay of toroidal and bubble nuclei and the nuclear equation of state

Abstract

Multifragmentation, following the formation of toroidal and bubble nuclei, is observed with an improved Boltzmann-Uehling-Uhlenbeck model for central Mo+ Mo collisions. With a stiff equation of state, simultaneous explosion into several nearly equal fragments in a ringlike manner occurs due to the formation of metastable toroidal nuclei. In contrast, with a soft equation of state, simultaneous explosion into several nearly equal fragments in a volumelike manner occurs due to the formation of metastable bubble nuclei. Experimental signatures for the formation of these exotic shapes are discussed. PACS number(s): 25.70.Pq, 21.65.+f, 24.10.Cn, 25.70.Gh Two decades ago, in connection with the stability of nuclei with new types of topology proposed by Wheeler [1] and Siemens and Bethe [2], Wong systematically studied the instabilities of toroidal and spherical bubble nuclei within the context of liquid drop, shell, and Hartree-Fock models [3]. He subsequently argued that higher nuclear temperatures enhance the possibility for the formation of toroidal and bubble nuclei [4]. Toroids have been seen in collisions between water drops [5]. Bubbles were observed in one-dimensional hydrodynamical collisions [6,7] as well as in hot dense matter [8,9] and Thomas-Fermi and Hartree-Fock calculations [10]. Recently, theoretical research in this area was revived when it was suggested that the formation of toroids and bubbles could provide new decay modes for multifragment disintegration [11 -15]. To investigate the dependence on the equation of state (EOS) and to look for experimental observables, we I have performed improved Boltzmann-Uehling-Uhlenbeck (BUU) calculations [15 -17] for Mo+ Mo collisions. In our calculations, we have included Coulomb interactions and have used a lattice Hamiltonian method [18] to propagate test particles.In the present calculations for the 2Mo+ Mo system, we find that, depending on the nuclear equation of state, a metastable toroidal or bubble nucleus can be formed. The decays of these unstable states are simultaneous, yet very slow. We predict a significant increase in the cross sections of nearly equal fragments with small center-of-mass energies as a result of the cold breakup of a bubble or toroidal nucleus. These two shapes can further be separated by the coplanarity of the nearly equal fragments with similar energies, which, in turn, could provide information about the nuclear equation of state. We simulate the Boltzmann-Uehling-Uhlenbeck equation [19] 0fg 4 s do"" Bt (2vr) s dA 4-v V'" fg -V"U Tp fi -d k2dA "vq2[fs f4(1fq) (1 -f2)fq f2(1fs) (1 -f4)], with the lattice Hamiltonian method of Lenk and Pandharipande [18]. In Eq. (1), "&&" and vq2 are the inmedium cross section and relative velocity for the colliding nucleons, and U is the total mean-field potential consisting of the Coulomb potential and a nuclear potential with isoscalar and symmetry terms [16]. In our calculations, we use two parameter sets [19] for the EOS which correspond to values of nuclear compressibility at K = 200 MeV (so...

Hollow nuclear matter

“…The formation of bubble or toroidal nuclear matter was in fact predicted by nuclear transport model at lower incident beam energy [15,[27][28][29][30]. It is thus also interesting to see if such internally hollow nuclear matter is also formed in nucleus-nucleus collisions by our isospindependent transport model.…”

Multifragmentation: Surface instabilities or statistical decay?

“…It has been brought to our attention that in some cases rather thin skinned bubbles are formed (Bauer et al, 1992, Borderie et al, 1992, Xu et al, 1992. It appears that these striking objects break up much in the same way as the disks described above, possibly due to the same instabilities.…”

Common Approaches in Description of Ordinary Liquids

“…9) and bubble ( Fig. 10) structures in the head-on HIC was studied extensively with the help of microscopic transport models [63,64]. Within the BoltzmannUehling-Uhlenbeck (BUU) model, it was shown that, at the energy interval 60-75 MeV/A, the different exotic topologies of the formed objects can be observed, depending on the stiffness of the nuclear mater EOS.…”