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arXiv:1105.3110 · Physical Review C

Non-Abelian behavior of α bosons in cold symmetric nuclear matter

Hua Zheng, Aldo Bonasera A

Published May 31, 2011• 5 citations
arXivHTMLPDF

Abstract

The ground-state energy of infinite symmetric nuclear matter is usually described by strongly interacting nucleons obeying the Pauli exclusion principle. We can imagine a unitary transformation which groups four nonidentical nucleons (i.e., with different spin and isospin) close in coordinate space. Those nucleons, being nonidentical, do not obey the Pauli principle, thus their relative momenta are negligibly small (just to fulfill the Heisenberg principle). Such a cluster can be identified with an $\ensuremath{\alpha}$ boson. But in dense nuclear matter, those $\ensuremath{\alpha}$ particles still obey the Pauli principle since are constituted of fermions. The ground state energy of nuclear matter $\ensuremath{\alpha}$ clusters is the same as for nucleons, thus it is degenerate. We could think of $\ensuremath{\alpha}$ particles as vortices which can now braid, for instance making $^{8}\mathrm{Be}$ which leave the ground state energy unchanged. Further braiding to heavier clusters ($^{12}\mathrm{C}$, $^{16}\mathrm{O}$$,\dots{}$) could give a different representation of the ground state at no energy cost. In contrast $d$-like clusters (i.e., $N=Z$ odd-odd nuclei, where $N$ and $Z$ are the neutron and proton number, respectively) cannot describe the ground state of nuclear matter and can be formed at high excitation energies (or temperatures) only. We show that even-even, $N=Z$, clusters could be classified as non-Abelian states of matter. As a consequence an $\ensuremath{\alpha}$ condensate in nuclear matter might be hindered by the Fermi motion, while it could be possible a condensate of $^{8}\mathrm{Be}$ or heavier clusters.

DOI
10.1103/physrevc.83.057602

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The ground-state energy of infinite symmetric nuclear matter is usually described by strongly interacting nucleons obeying the Pauli exclusion principle. We can imagine a unitary transformation which groups four nonidentical nucleons (i.e., with different spin and isospin) close in coordinate space. Those nucleons, being nonidentical, do not obey the Pauli principle, thus their relative momenta are negligibly small (just to fulfill the Heisenberg principle). Such a cluster can be identified with an \ensuremathα\ensuremath{\alpha}\ensuremathα boson. But in dense nuclear matter, those \ensuremathα\ensuremath{\alpha}\ensuremathα particles still obey the Pauli principle since are constituted of fermions. The ground state energy of nuclear matter \ensuremathα\ensuremath{\alpha}\ensuremathα clusters is the same as for nucleons, thus it is degenerate. We could think of \ensuremathα\ensuremath{\alpha}\ensuremathα particles as vortices which can now braid, for instance making 8Be^{8}\mathrm{Be}8Be which leave the ground state energy unchanged. Further braiding to heavier clusters (12C^{12}\mathrm{C}12C, ^{16}\mathrm{O}$$,\dots{}) could give a different representation of the ground state at no energy cost. In contrast ddd-like clusters (i.e., N=ZN=ZN=Z odd-odd nuclei, where NNN and ZZZ are the neutron and proton number, respectively) cannot describe the ground state of nuclear matter and can be formed at high excitation energies (or temperatures) only. We show that even-even, N=ZN=ZN=Z, clusters could be classified as non-Abelian states of matter. As a consequence an \ensuremathα\ensuremath{\alpha}\ensuremathα condensate in nuclear matter might be hindered by the Fermi motion, while it could be possible a condensate of 8Be^{8}\mathrm{Be}8Be or heavier clusters.
How do protons and neutrons bind to form nuclei?This is the central question of ab initio nuclear structure theory.While the answer may seem as simple as the fact that nuclear forces are attractive, the full story is more complex and interesting.In this work we present numerical evidence from ab initio lattice simulations showing that nature is near a quantum phase transition, a zero-temperature transition driven by quantum fluctuations.Using lattice effective field theory, we perform Monte Carlo simulations for systems with up to twenty nucleons.For even and equal numbers of protons and neutrons, we discover a first-order transition at zero temperature from a Bose-condensed gas of alpha particles ( 4 He nuclei) to a nuclear liquid.Whether one has an alpha-particle gas or nuclear liquid is determined by the strength of the alpha-alpha interactions, and we show that the alpha-alpha interactions depend on the strength and locality of the nucleon-nucleon interactions.This insight should be useful in improving calculations of nuclear structure and important astrophysical reactions involving alpha capture on nuclei.Our findings also provide a tool to probe the structure of alpha cluster states such as the Hoyle state responsible for the production of carbon in red giant stars and point to a connection between nuclear states and the universal physics of bosons at large scattering length.
How do protons and neutrons bind to form nuclei? This is the central question of ab initio nuclear structure theory. While the answer may seem as simple as the fact that nuclear forces are attractive, the full story is more complex and interesting. In this work we present numerical evidence from ab initio lattice simulations showing that nature is near a quantum phase transition, a zero-temperature transition driven by quantum fluctuations. Using lattice effective field theory, we perform Monte Carlo simulations for systems with up to twenty nucleons. For even and equal numbers of protons and neutrons, we discover a first-order transition at zero temperature from a Bose-condensed gas of alpha particles (^{4}He nuclei) to a nuclear liquid. Whether one has an alpha-particle gas or nuclear liquid is determined by the strength of the alpha-alpha interactions, and we show that the alpha-alpha interactions depend on the strength and locality of the nucleon-nucleon interactions. This insight should be useful in improving calculations of nuclear structure and important astrophysical reactions involving alpha capture on nuclei. Our findings also provide a tool to probe the structure of alpha cluster states such as the Hoyle state responsible for the production of carbon in red giant stars and point to a connection between nuclear states and the universal physics of bosons at large scattering length.
We discuss bosonic models with a moat spectrum, where in momentum space the minimum of the dispersion relation is on a sphere of nonzero radius. For spinless bosons with O(N)O(N)O(N) symmetry, we emphasize the essential difference between N=2N=2N=2 and N>2N > 2N>2. When N=2N=2N=2, there are two phase transitions: at zero temperature, a transition to a state with Bose condensation, and at nonzero temperature, a transition to a spatially inhomogeneous state. When N>2N > 2N>2, previous analysis suggests that a mass gap is generated dynamically at any temperature. In condensed matter, a moat spectrum is important for spin-orbit-coupled bosons. For cold nuclear or quarkyonic matter, we suggest that the transport properties, such as neutrino emission, are dominated by the phonons related to a moat spectrum; also, that at least in the quarkyonic phase the nucleons may be a non-Fermi liquid.
The equation of state of symmetric nuclear matter is addressed starting both from a realistic interaction derived from nucleon-nucleon scattering processes and from a low-momentum effective potential. The approach is based on finite temperature Green’s functions. The internal energy per particle is estimated from the summation of diagrams and through the Galitskii-Koltun’s sum rule. At present, there is not a unique and reliable theory of nuclear interactions. From the study of nucleon-nucleon scattering processes different models for the basic interaction between nucleons have been developed, but difficulties arise when they are used in calculations which aim to reproduce the properties of bound nuclei. These models all reproduce the experimental N-N phase shifts up to the threshold for pion production with high accuracy, but differ in the short-wavelength region, where less experimental constraints are available. In deriving the properties of dense nuclear matter, if we start from a bare N-N potential we have to take into account the complex correlations induced
Dense nucleonic matter is of vital importance for understanding compact stars and inferring the transition into deconfined quark phase. We present ab initio exact calculations of infinite nucleonic matter with the state-of-the-art full configuration-interaction quantum Monte Carlo method, enabling us to rigorously benchmark many-body methods and assess the degree to which the nucleonic matter is correlated. Our method has been numerically validated against exact diagonalization within a small model space. Calculations of nucleonic matter using chiral nuclear forces reveal that symmetric nuclear matter is strikingly strongly correlated, raising questions on previous ab initio calculations of nuclear matter with many-body expansion truncations and offering insights into simultaneous descriptions of finite nuclei and infinite nucleonic matter from first principles.
Ground-state energies and superfluid gaps are calculated for degenerate Fermi systems interacting via long attractive scattering lengths such as cold atomic gases, neutron, and nuclear matter. In the intermediate region of densities, where the interparticle spacing $(\ensuremath{\sim}{1/k}_{F})$ is longer than the range of the interaction but shorter than the scattering length, the superfluid gaps and the energy per particle are found to be proportional to the Fermi energy and thus differ from the dilute and high-density limits. The attractive potential increase linearly with the spin-isospin or hyperspin statistical factor such that, e.g., symmetric nuclear matter undergoes spinodal decomposition and collapses whereas neutron matter and Fermionic atomic gases with two hyperspin states are mechanically stable in the intermediate density region. The regions of spinodal instabilities in the resulting phase diagram are reduced and do not prevent a superfluid transition.