Correlated Fermion Pairs in Nuclei and Ultracold Atomic Gases

Abstract

Background: The high momentum distribution of atoms in two spin-state ultra-cold atomic gases with strong short-range interactions between atoms with different spins, which can be described using Tan's contact, are dominated by short range pairs of different fermions and decreases as $k^{-4}$. In atomic nuclei the momentum distribution of nucleons above the Fermi momentum ($k>k_F\approx 250$ Mev/c) is also dominated by short rangecorrelated different-fermion (neutron-proton) pairs. Purpose: Compare high-momentum unlike-fermion momentum distributions in atomic and nuclear systems. Methods: We show that, for $k>k_F$ MeV/c, nuclear momentum distributions are proportional to that of the deuteron. We then examine the deuteron momentum distributions derived from a wide variety of modern nucleon-nucleon potentials that are consistent with $NN$-scattering data. Results: The high momentum tail of the deuteron momentum distribution, and hence of the nuclear momentum distributions appears to decrease as $k^{-4}$. This behavior is shown to arise from the effects of the tensor part of the nucleon-nucleon potential. In addition, when the dimensionless interaction strength for the atomic system is chosen to be similar to that of atomic nuclei, the probability for finding a short range different-fermion pair in both systems is the same. Conclusions: Although nuclei do not satisfy all of the conditions for Tan's contact, the observed similarity of the magnitude and $k^{-4}$ shape of nuclear and atomic momentum distributions is remarkable because these systems differ by about $20$ orders of magnitude in density. This similarity may lead to a greater understanding of nuclei and the density dependence of nuclear systems.

Accepted for publication in PRC. 8 pages, 3 figures, 1 table. Revised version: 6-Oct-15

References in corpus (28)

• Chiral effective field theory and nuclear forces
• Similarity Renormalization Group for Nucleon-Nucleon Interactions
• Probing Cold Dense Nuclear Matter
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Molecular Probe of Pairing in the BEC-BCS Crossover
• Momentum sharing in imbalanced Fermi systems
• Evidence for the Strong Dominance of Proton-Neutron Correlations in Nuclei
• Verification of universal relations in a strongly interacting Fermi gas
• Tensor Forces and the Ground-State Structure of Nuclei
• Number of closed-channel molecules in the BEC-BCS crossover
• Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory
• Nuclear Structure in the Framework of the Unitary Correlation Operator Method
• Measurement of the Homogeneous Contact of a Unitary Fermi gas
• Probing the Repulsive Core of the Nucleon-Nucleon Interaction via the 4He(e,e'pN) Triple-Coincidence Reaction
• Comparing and contrasting nuclei and cold atomic gases
• Precise determination of the structure factor and contact in a unitary Fermi gas
• Density and isospin asymmetry dependence of high-momentum components
• Dominant contributions to the nucleon-nucleon interaction at sixth order of chiral perturbation theory
• BEC-BCS crossover and universal relations in unitary Fermi gases
• Quantum Monte Carlo approaches to nuclear and atomic physics
• Universal contact of strongly interacting fermions at finite temperatures
• Extracting the Mass Dependence and Quantum Numbers of Short-Range Correlated Pairs from A(e,e'p) and A(e,e'pp) Scattering
• Stylized features of single-nucleon momentum distributions
• Short-range correlations in nuclei with similarity renormalization group transformations
• Experimental evaluation of the nuclear neutron-proton contact
• Quantifying short-range correlations in nuclei
• Decoupling of Spurious Deep Bound States with the Similarity Renormalization Group
• High-precision covariant one-boson-exchange potentials for np scattering below 350 MeV

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• Generalized nuclear contacts and the nucleon's momentum distributions
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• The interplay of short-range correlations and nuclear symmetry energy in hard photon productions from heavy-ion reactions at Fermi energies
• Constraining nucleon high momentum in nuclei
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• Multi-Nucleon Short-Range Correlation Model for Nuclear Spectral Functions: I. Theoretical Framework
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• Impacts of symmetry energy slope on the oscillation frequencies of neutron stars with short-range correlation and admixed dark matter
• Deuteron electrodisintegration with unitarily evolved potentials
• Isospin dependence of nucleon effective masses in neutron-rich matter
• Short range correlations - The important role of few-body dynamics in many-body systems
• Nucleon Effective E-Mass in Neutron-Rich Matter from the Migdal-Luttinger Jump
• Role of the effective range in the density-induced BEC-BCS crossover
• Contact formalism for coupled channels
• Relativistic self-energy decomposition of nuclear symmetry energy and equation of state of neutron matter within QCD sum rules
• Precise Measurement of Short-Range Correlations in Nuclei from Bremsstrahlung Gamma Ray Emission in Low-Energy Heavy-Ion Collisions
• A local-density-approximation description of high-momentum tails in isospin asymmetric nuclei
• Proton-proton momentum correlation function as a probe of the high momentum tail of the nucleon momentum distribution
• Nucleon momentum gap in asymmetric nuclear matter
• Universal laws for nuclear contacts
• Neutron matter within QCD sum rules
• Nucleon Short-Range Correlations and High-Momentum Dynamics: Implications on the Equation of State of Dense Matter
• Discovery vs. Precision in Nuclear Physics- A Tale of Three Scales
• Meaning of the nuclear wave function
• Neutron Star Equation of State with Nucleon Short-Range Correlations: A Concise Review and Open Issues