Three-body Effect in Short-range Correlations

Abstract

Short-range correlations (SRCs) provide the link between low- and high-energy nuclear physics and can be quantified by two-nucleon densities. We present calculations of the two-nucleon densities using free-space similarity renormalization group (SRG)-evolved operators and in-medium SRG (IMSRG) ground states with softend chiral interaction. Our calculations benchmark well against no-core shell model (NCSM) results with unevolved oparetors and Hamiltonians in $^4\mathrm{He}$. We explicitly include the induced three-body (3b) density operators for the first time which, together with the 3b Hamiltonians, provide the full 3b effects. We show pronounced 3b effects in the $^{16}\mathrm{O}$ two-nucleon densities. Combined with valence-space IMSRG (VS-IMSRG) method, we extend the calculation to the oxygen isotopic chain. This approach enables a consistent \textit{ab initio} description of low-energy properties and SRCs within one framework and offers predictions for the upcoming SRC measurements in unstable nuclei.

Figures (4)

• Figure 1: (a) Coordinate-space two-nucleon density $\rho_2(r)$, (b) momentum-space distribution $\rho_2(k)$, and (c) ground-state energy of $^4\mathrm{He}$, calculated with the chiral NN-N$^4$LO+3$\mathrm{N}_{\mathrm{lnl}}$ interaction. Blue curves are IMSRG results with consistently SRG-evolved Hamiltonians: dashed lines correspond to a two-body truncation ($H^{(2)},O^{(2)}$), and solid lines include full three-body terms ($H^{(3)},O^{(3)}$).. Red curves are J-NCSM benchmark results obtained with the unevolved (bare) interaction: dashed for NN only, solid for NN+3N. Panel (c) shows the ground-state energy as a function of the SRG resolution scale $\lambda$; the dashed horizontal line denotes the experimental value.
• Figure 2: (a) Coordinate-space two-nucleon density $\rho_2(r)$, (b) momentum-space distribution $\rho_2(k)$, and (c) ground-state energy of $^{16}\mathrm{O}$, calculated with the chiral NN-N$^4$LO+3$\mathrm{N}_{\mathrm{lnl}}$ interaction. All results are based on free-space SRG evolution, with bands indicating the variation over the resolution scale $\lambda=2.0$-2.4 fm$^{-1}$. Color denotes the truncation scheme: blue for the two-body truncation ($H^{(2)},O^{(2)}$); orange with three-body terms included only in the Hamiltonian ($H^{(3)},O^{(2)}$); and red with consistent three-body terms in both the Hamiltonian and the operators ($H^{(3)},O^{(3)}$). In coordinate space, the short-range part is dominated by $T=0$ (open circle), while in momentum space the intermediate- and high-momentum tail is dominated by $T=1$ (solid square). Panel (c) shows $E_{\mathrm{gs}}$ versus $\lambda$ and the dashed line denotes the experimental value; including induced 3N terms reduces the $\lambda$ dependence and improves agreement with experiment.
• Figure 3: Correlation function $F^{pp}(r)$ of $^{16}\mathrm{O}$ defined in Eq. \ref{['eq:corfun']}. The numerator $\rho_2$ is calculated using either the bare (dashed lines) or SRG-evolved (solid lines) two-body operator, applied to states obtained from HF (red), second-order many-body perturbation theory (MBPT2, orange), and the IMSRG (blue). The denominator is the HF two nucleon density evaluated with the bare operator.
• Figure 4: (a) Cordinate-space two-nucleon densitises and (b) ground state energies of oxygen isotopes. Calculations use constantly evolved Hamiltonians and operators truncated to 3b. The bands in (a) and error bars in (b) indicate the variation over the resolution scale $\lambda=2.0$-2.4 fm$^{-1}$.