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Project List » Exotic nuclear matter in the explosive stage of supernovae

Exotic nuclear matter in the explosive stage of supernovae

Acronym: ENMES
Contracting Authority: Executive Agency for Higher Education, Research, Development and Innovation Funding (UEFISCDI)
Number / Date of the contract: 55/2011 / 2011-10-05
Idei PN-II-ID-PCE-2011-3-0427
Project Manager: Dr. Florin Carstoiu
Partners: -
Starting date / finishing date: 2011-10-05 / 2014-10-05
Project value: 1500000 RON
Abstract: Understanding the properties of α matter has retained a lot of attention in recent years. This situation is mainly due to the believe that this type of hadronic matter occurs in astrophysical environment in deconfined form. In the debris of a supernovae explosion, a substantial fraction of hot and dense matter resides in α particles and therefore the equation of state of alpha matter is essential in simulating the supernovae collapse and explosions and is also important for the formation of the supernovae neutrino signal. An old neutron star is a compact, massive and cold object. If such a neutron star travels through the interstellar medium it will accrete mass on its surface which, after reaching a high enough density, will evolve owing to pycnonuclear triple α fusion reactions and two-stage electron capture. Finally, this evolution may lead to density instability at the interface of the freshly evolved crust and the original outer layers of the old neutron star resulting in a starquake which releases some 1040 erg of gravitational and nuclear energy where the latter had been stored in neutron-rich nuclei during the crust evolution. Recently Blaes et al. have proposed such a starquake scenario as the possible energy source of γ-ray bursts. From the various nuclear reaction rates the model most sensitively depends on the rate at which three α-particles fuse to form a 12C nucleus (pycnonuclear triple-α fusion rate). Adopting the "slow" rate estimated by Cameron for a triple-α reaction taking place in a Wigner-Seitz crystal the evolution of the neutron star crust produces material up to 28Si and the density instability is found at a 28Mg/62Ni interface; while the "fast" rate, predicted by Fushiki and Lamb within a coupled-channel S-matrix approach using a WKB approximation for the two-particle tunneling amplitudes, results in a production of elements up to 16O, in which case subsequently a 16C/56Ti interface becomes unstable owing to gravitational turnover. However, under the conditions governing the evolution of a neutron star crust (high densities ρ9 ~ 0.1-1.0, where ρ9 measures the density in 109~g/cm3, and low temperatures T < 106 K) the helium plasma forms a quantum fluid rather than a Wigner-Seitz crystal owing to the strong zero-point motion of the relatively light 4He nuclei, which had not been appropriately taken into account in the previous estimations of the pycnonuclear triple- α rate. Further noting that the α-particle plasma is a rather dilute system in this density regime, the Hypernetted Chain Approximation (HNC) might be an adequate formalism to describe the helium plasma under the conditions appropriate for the evolving neutron star crust with the electrons treated as a homogeneous neutralizing background. Renewed interest in the properties of α matter is manifest in the literature especially in connection with α-particle Bose-Einstein condensation (BEC) in α-like nuclei. Calculations reported in this reference are pointing to the existence of a Bose-Einstein condensate of α-particles at low densities. It was also noted by these authors, that with increasing density the condensate fraction is reduced such that at density corresponding to the saturation of nuclear matter (~ 0.04 α particles/fm3), the condensate fraction is reduced to roughly one half. The estimation of the condensate fraction was done in the lowest approximation, i.e. the radial distribution function (RDF) is approximated by the square of the two-body correlation function (CFN), and therefore it is less justified for higher densities. There is however an old estimation by Clark and Johnson for three values around the saturation density of nuclear matter using the Hypernetted Chain Approximation in the lowest order (HNC/0), i.e. taking into account only nodal diagrams in the infinite density expansion of the RDF. It provides a severe reduction of the condensate fraction (~15%) compared to the lowest-order cluster expansion at the same density. On the other hand calculations of the cold α matter equation of state (EOS) reported by the same authors within the HNC/0 approximation and using the soft core α-α potential of Ali and Bodmer are predicting the saturation point at a high density (ρ α ~0.085 α particles per fm 3 and a corresponding incompressibility much lower than the normal nuclear matter incompressibility. These benchmark calculations of the α matter EOS were very recently compared to results obtained in the frame of the scalarφ 6 effective field theory with negative quartic and positive sextic interactions, to simulate the attractive character at long distances and repulsive at short distances, and found to be in a very good agreement . Though no estimations of the condensate fraction are provided for this high density saturation point, from the estimation made at lower densities, as quoted above, we expect a stronger depletion of the BEC. One is then confronted with the problem that at low densities the α matter condensate is far from equilibrium, whereas at the saturation point the condensate fraction is small. It was advocated that beyond a critical density (ρα ~0.03 nucleons/ fm3), due to the strong overlap of the wave-functions and the unavoidable action of the Pauli principle, a total extinction of the α structure should occur . Also at high densities strong polarization effects may occur and three-body interactions must be taken into account. The phenomenological α-α potentials used in the past are systematically predicting saturation of α matter at densities considerably larger than this critical density. It would then be important to establish if the saturation of the α matter takes place below this critical density if one employs other types of potentials that incorporate more microscopic input. The aim of this project is to analyze the α matter EOS over a wide range of densities and try to find the optimal two body correlation functions which reflects the interplay between the strong short-range and the long-range correlations that ultimately would lead to saturation. Gaining insight in the saturation properties of α matter could also shed light on the condensate fraction reduction issue as well as the clustering phenomenon in light nuclei. We investigate the ground state of a uniform, extended system of alpha particles at zero temperature in a neutralizing background by using variational methods borrowed from quantum Bose liquids. We consider the thermodynamic limit of an infinite system, defined as the limit of N particles in a box of volume V, where N goes to infinity with the density ρ=N/V kept constant. The alpha particles are treated as elementary bosons and are assumed to interact through strong two-body potentials fitting the alpha-alpha elastic scattering data. A cluster expansion will be used to evaluate the expectation value of the energy for a trial ground state wave function of Jastrow form. The conventional Bose cluster expansion is modified to cope with the rather strong radial dependence of the best phenomenological and microscopic α - potentials. Numerical calculations of the two- and three-body cluster diagrams, as well as some high order diagrams contributing to the ground state energy will be performed over a wide range of densities. Estimates of the four-body diagrams as well as five body diagrams contributing to Perkus -Yevick expansion of the ground state energy will be made and convergence properties of the cluster expansion for the optimal two-body correlation functions will be studied. The ground state of alpha matter will be also studied using high order Hypernetted Chain Approximation (HNC/0 and HNC/4) and comparison with cluster expansion method will be made. Optimal two body correlation functions and radial distribution will be studied in the context of the Paired Phonon Analysis (PPA) method .The resulting equations of state for zero-temperature alpha-matter are of interest in relation to the theory of low-density nuclear matter and, more specifically, the problems of nucleon clustering in the nuclear surface.


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4. Two body correlation function for strongly interacting bosons. Particle hole interaction in the paired phonon analysis  (2014-12-15) Results
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