Momentum Distribution of Nucleons inIsospin Asymmetric Nuclear Matter

Javier Rufino Jr.1,2

Dr. Jeremy Holt2

Cyclotron Institute – Texas A&M University1

University of Texas at San Antonio2

Motivation-Neutron Stars

• Densest observable objects in the universe• Consist of neutron rich nuclear

matter• Maintain stability from

gravitational collapse from quantum mechanical degeneracy pressure, and nuclear interactions

Neutron star properties sensitive to nucleon momenta• Neutrino propagation in newly born

neutron stars (neutrino-nucleon scattering cross sections)

• Neutron star cooling through neutrino production

𝑛 → 𝑝 + 𝑒 + �̅�(𝑝 + 𝑒 → 𝑛 + 𝜈(

Studying nucleon momentum-distribution• Electron scattering experiments (e,e’n) &

(e,e’p) at Jlab• Theoretical calculations using realistic

nuclear forces

Expectations of nucleon momentum distributions in nuclei/nuclear matter

Short-range repulsive core(Pauli exclusion principle)

(Heisenberg uncertainty principle Δx ∗ Δ𝑝 ≥ ℏ

.)

Modern Theory of Nuclear Forces

• Based on the systematic expansion in terms of one and two pion exchange mechanism constrained by the symmetries of QCD.• We implemented high precision two- and

three-body forces derived from chiral effective field theory.• From the nuclear two- and three-body

forces we compute the self-energies (Σ0,2 (4,5;78,9:;)

.=,.> ) of single-particles up to the first and second order contributions.• 𝛿20 =

ABCD

(0.0 < 𝛿20 < 0.6)• 0.01[fmBM] < 𝜌 < 0.32[fmBM]

Nucleon Self-Energies

The first order and second order contributions of the nucleon self energies are represented diagrammatically provided by Holt et al1. The arrows pointing up and down represent nucleons and holes states, while the wavy lines represent the sum of the 2N and 3N nuclear interactions-where the three body interactions are implemented by a density dependent two body force.

Single-Particle Momentum Distributions

• After computing the self-energies, the potentials are computed by summing up the real parts 𝑉(4,( 4 ) = 𝑅𝑒 Σ(4,( 4 ), which is then used to compute the momentum distribution from the energy portion of the effective mass:

T𝑚(4)(.=)

𝑚 = 1 − W𝜕𝑉 4,Y .=

𝜕𝐸 Y[4\

.]^_( `(a,b a )T𝑚(4)(.>)

𝑚= 1 − W

𝜕𝑉(4,Y)(.>)𝜕𝐸 Y[4

\

]^_( `(a,b a )

𝜌(4) =

T𝑚(4)(.=)

𝑚− 1, 𝑓𝑜𝑟 𝑞 < 𝑞g

2 −T𝑚 4 .>

𝑚, 𝑓𝑜𝑟 𝑞 > 𝑞g

The following curves are proton momentum distribution curves with nuclear densities 𝜌 = .16[fmBM], and arbitrary isospin asymmetries.

The following curves are neutron momentum distribution curves with nuclear densities 𝜌 = .16[fmBM], and arbitrary isospin asymmetries.

The left diagram provided is nucleon scattering data from a collaboration project by CLAS on (e,e’p) and (e,e’n) reactions. The y-axis represents high to low momentum fractions of nucleons vs the neutron excess.The right diagram is our theoretical data representing the linear relationship of high to low momentum fraction of protons vs isospin asymmetry.

𝐻𝑖𝑔ℎ − 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 =∫4gr 𝑞.𝑛 𝑞 𝑑𝑞

∫t4g 𝑞.𝑛 𝑞 𝑑𝑞

Conclusions

• The present work demonstrates that theoretical calculations of nucleon momentum distributions in asymmetric nuclear matter from realistic two- and three-body chiral nuclear forces reproduce trends observed in experimental (e,e'p) and (e,e'n) reactions.• We verified the NP dominance model.• In the future we will consider the role of nuclear short-range

correlation on structure and dynamics of neutron stars.

References

1. J. W. Holt. Microscopic optical potential for exotic isotopes from chiral effective field theory, 10.1103/PhysRevC.93.064603

2. Nature 560. Probing high-momentum protons and neutrons in neutron-rich nuclei. (2018, August 13), https://doi.org/10.1038/s41586-018-0400-z

3. Sartor, R., and C. Mahaux. “Self-Energy, Momentum Distribution, and Effective Masses of a Dilute Fermi Gas.” Physical Review C, vol. 21, no. 4, 1980, pp. 1546–1567., doi:10.1103/physrevc.21.1546.

4. Machleidt, R., and D.r. Entem. “Chiral Effective Field Theory and Nuclear Forces.” Physics Reports, vol. 503, no. 1, 2011, pp. 1–75., doi:10.1016/j.physrep.2011.02.001.

Acknowledgements

• I would like to thank Dr. Holt for guidance and support with this project.• I would like to thank the Cyclotron Institute for allowing me to gain

this experience, and the NSF for funding this REU project

Question?