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Light Nuclei embedded in a Nuclear Medium: Clustering and Mott Transitions

Qi Meng, Chang Xu

TL;DR

This work investigates how light clusters with $A=2$–$4$ form and dissolve when embedded in nuclear matter, focusing on Pauli blocking and Mott transitions. It develops a microscopic in-medium few-body framework using a multi-Gaussian variational basis and a density-dependent, Pauli-blocked Volkov NN interaction, solved at zero $T$ and zero total momentum to obtain intrinsic energies $E^{intr}$ and Mott densities for the clusters in symmetric and asymmetric matter. The results show the deuteron remains bound to higher densities than $^3$H, $^3$He, and α, with its rms radius expanding to about $4.8$ fm prior to dissolution, while the α-particle has a lower Mott density that decreases slightly in neutron-rich environments; the $^3$H and $^3$He Mott densities lie around $0.013$ fm$^{-3}$ and $0.0126$ fm$^{-3}$, respectively. These findings provide quantitative constraints on cluster formation at nuclear surfaces and in intermediate-energy heavy-ion collisions, with implications for neutron-star crusts and astrophysical nucleosynthesis.

Abstract

The clustering of nucleons is a fundamental phenomenon with broad implications for nuclear physics and astrophysics. In this work, we employ a microscopic in-medium few-body approach to systematically investigate the formation and dissolution of light clusters (deuteron, $\rm{^3H}$, $\rm{^3He}$, $α$-particle) embedded in nuclear medium. The medium-modified cluster structures under the Pauli blocking and the picture of Mott transitions in nuclear medium are discussed in detail. We find that the weakly bound deuteron survives to higher densities as compared with the more compact $α$-particle in symmetric nuclear matter, with its r.m.s. radius expanding markedly prior to its dissolution. Moreover, the Mott density of $α$-particle is slightly lower in neutron-rich matter than in symmetric matter. These results may provide useful constraints for the formation of light clusters at nuclear surface and the cluster yields in intermediate-energy heavy-ion collisions.

Light Nuclei embedded in a Nuclear Medium: Clustering and Mott Transitions

TL;DR

This work investigates how light clusters with – form and dissolve when embedded in nuclear matter, focusing on Pauli blocking and Mott transitions. It develops a microscopic in-medium few-body framework using a multi-Gaussian variational basis and a density-dependent, Pauli-blocked Volkov NN interaction, solved at zero and zero total momentum to obtain intrinsic energies and Mott densities for the clusters in symmetric and asymmetric matter. The results show the deuteron remains bound to higher densities than H, He, and α, with its rms radius expanding to about fm prior to dissolution, while the α-particle has a lower Mott density that decreases slightly in neutron-rich environments; the H and He Mott densities lie around fm and fm, respectively. These findings provide quantitative constraints on cluster formation at nuclear surfaces and in intermediate-energy heavy-ion collisions, with implications for neutron-star crusts and astrophysical nucleosynthesis.

Abstract

The clustering of nucleons is a fundamental phenomenon with broad implications for nuclear physics and astrophysics. In this work, we employ a microscopic in-medium few-body approach to systematically investigate the formation and dissolution of light clusters (deuteron, , , -particle) embedded in nuclear medium. The medium-modified cluster structures under the Pauli blocking and the picture of Mott transitions in nuclear medium are discussed in detail. We find that the weakly bound deuteron survives to higher densities as compared with the more compact -particle in symmetric nuclear matter, with its r.m.s. radius expanding markedly prior to its dissolution. Moreover, the Mott density of -particle is slightly lower in neutron-rich matter than in symmetric matter. These results may provide useful constraints for the formation of light clusters at nuclear surface and the cluster yields in intermediate-energy heavy-ion collisions.
Paper Structure (10 sections, 43 equations, 5 figures, 4 tables)

This paper contains 10 sections, 43 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Framework
  3. Results
  4. Summary
  5. Calculation of Matrix Elements
  6. Symmetric nuclear matter
  7. Deuteron
  8. $\rm{^3H}$ and $\rm{^3He}$
  9. $\alpha$-particle
  10. Asymmetric nuclear matter

Figures (5)

  • Figure 1: Rearrangement channels of 3-nucleon cluster Jacobi momenta.
  • Figure 2: Rearrangement channels of 4-nucleon cluster Jacobi momenta.
  • Figure 3: The intrinsic energies (solid curves) of deuteron ($d$), $\rm{^3 H}$, $\rm{^3 He}$ and $\alpha$-particle in isospin symmetric nuclear matter as functions of nucleon density $n_b=n_n+n_p$. The dashed curves denote the continuum edges of $A$ uncorrelated nucleons ($Z$ protons and $N$ neutrons). Note that $\rm{^3 H}$ and $\rm{^3 He}$ share the same continuum edge in symmetric nuclear matter.
  • Figure 4: The proton point r.m.s. radius $\sqrt{\langle r^2_p \rangle}$ of deuteron as a function of the nucleon density $n_b$ in isospin symmetric nuclear matter. The insets provide schematic illustrations of the deuteron in free space and when embedded in nuclear matter.
  • Figure 5: The intrinsic energy of $\alpha$-particle in nuclear matter with isospin asymmetry $\delta$ as a function of density $n_b=n_n+n_p$ (solid curves). The dashed curves denote the continuum edges of four uncorrelated nucleons (two protons and two neutrons). The inset illustrates the dependence of the Mott density on the isospin asymmetry $\delta$.