Neutron Stars, Bubble Nuclei and Quantum Billiards
Aurel Bulgac
University of Washington / Seattle
日時：2001年09月14日（金） 16:15-
場所：東北大学理学部物理A棟504号室
The positioning of a bubble inside a many fermion system does not affect the volume, surface or curvature terms in the liquiddrop expansion of the total energy. Besides possible Coulomb effects,the only other contribution to the ground state energy of such asystem arises from quantum effects, often called in nuclear physicsshell correction energy effects. Related phenomena could be observedin infinite systems. Homogeneous neutron matter at subnuclear densitiesbecomes unstable towards the formation of inhomogeneities. Dependingon the average value of the neutron one can observe the appearanceof either bubbles, rods, tubes or plates embedded in a neutron gas.We estimate the quantum corrections to the ground state energy(which could be termed either shell correction or Casimir energy)of such phases of neutron matter. The calculations are performed by evaluating the contribution of the shortest periodic orbits in the Gutzwillertrace formula for the density of states. The magnitude of the quantumcorrections to the ground state energy of neutron matter are of thesame order as the energy differences between various phases and thuscan lead to changes in the sequence of the nuclear shape transitionsin the neutron star crust. We discuss also the dependence of thesecorrections on a number of physical parameters (density, filling factor, temperature, lattice distortions). Similar phenomena are expected to occur as well in atomic clusters, condensed matter systems, dilute atomic fermi condensates and quark--gluon plasma.
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