Universality of nucleon short-range behavior with chiral forces

TL;DR

The paper tackles how SRG-softened nuclear interactions erase high-momentum short-range information crucial for nucleon-nucleon SRCs. It develops a framework to reconstruct SRG-independent densities from Jacobi-NCSM solutions by back-transforming SRG-evolved two-body relative wave functions, enabling reliable study of short-range physics with chiral SMS $N^4LO^+$+$N^2LO$ forces. The authors reveal universality in short-range behavior: the $np$ $S=1$ two-body density ratio relative to the deuteron is largely interaction-insensitive up to high momenta, and density ratios relative to ${}^4$He are almost independent of the interaction details, despite regulator and SRG variations. This approach provides a robust tool to quantify SRC across light nuclei and can be extended to heavier systems and other many-body methods that employ SRG, such as IMSRG and CC, enhancing our understanding of short-range nuclear structure and its universal aspects.

Abstract

Modern advanced nuclear ab initio approaches with the similarity renormalization group (SRG) softened interactions miss high-momentum information, thus rendering them less suitable for characterizing nucleon-nucleon short-range physics. We introduce a novel framework to construct SRG-independent nuclear wave functions from No-Core Shell Model calculations. Applying our method to densities obtained with semilocal momentum-space-regularized chiral NN and NNN forces, we show key universalities of short-range behavior: (1) The two-body density ratio in the np S=1 channel, relative to the deuteron (d), is remarkably insensitive to interaction details. (2) More strikingly, while the ratio of total two-body densities to the deuteron exhibits cutoff dependence, the same ratio to the $α$-particle (4-He) is almost independent of the interactions.

Figures (23)

• Figure 1: High-momentum and short-range behavior of the ratio ${2\rho_{NN}(^{4}\mathrm{He})}/(4\rho(d))$ for chiral forces SMS N$^{4}$LO$^{+}$ + N$^{2}$LO with different momentum cutoffs ($\Lambda_N=400$, 450, 500, and 550 MeV). The two-body relative densities of $^{4}\mathrm{He}$ are calculated by J-NCSM model in a large HO model space $N_\mathrm{HO}=24$ with the interactions evolved with two flow parameters 1.88 and 2.24 fm$^{-1}$ and by the FY approach with the bare interactions (labeled as "bare"). The ratio between the $^{4}$He densities of the $np$ with $S=1$ channel (circles), the $np$ channel (crosses), and all channels (squares) and the deuteron density is presented.
• Figure 1: Deuteron density distributions in momentum space using the SMS N$^{4}$LO$^{+}$ interaction with a cutoff of $450$ MeV. All results have been obtained using a HO basis. Solid lines are results using directly the wave functions obtained solving the Schrödinger equation for SRG-evolved interactions. Dotted lines and crosses are obtained by using the transformed wave functions of Eq. (\ref{['eq:hoevolvedwf']}). The results for the bare interaction is shown as a black dotted line with circles. The total deuteron densities is normalized to $\int_0^{\infty} dk k^2 \, \rho(k) = 1$.
• Figure 2: High-momentum and short-range behavior of the density ratio in the $np$ with $S=1$ channel (unfilled circles), the $pp$ channel with $S=0$ (unfilled diamonds), and the $nn$ channel with $S=0$ (unfilled squares) for chiral forces SMS N$^{4}$LO$^{+}$ + N$^{2}$LO with different momentum cutoffs ($\Lambda_N=400$, 450, 500, and 550 MeV). $4\rho_{NN}(^{6}\mathrm{Li})/6\rho_{NN}(^{4}\mathrm{He})$ in $p$-space (a) and $r$-space (b). $4\rho_{NN}(^{6}\mathrm{He})/6\rho_{NN}(^{4}\mathrm{He})$ in $p$-space (c) and $r$-space (d). Note for $^{6}$Li, the results for $S=0$$pp$ channel are the same as those in $S=0$$nn$ channel. The horizontal bands represent the range of extracted ratios for four chiral interactions.
• Figure 2: Two-body density distributions of $^{4}$He in momentum space by using two-body HO functions (a) and evolved two-body relative wave functions (b), and the contribution from $np$ channel to the two-body density using our method (c). The adopted interaction is SMS N$^{4}$LO$^{+}$ (450 MeV) + N$^{2}$LO evolved to three different SRG parameters. The two-body density calculated from FY equations using bare interaction (labeled as 'bare') and the deuteron density is also given for comparison.
• Figure 3: Flow parameter independence of the high-momentum and short-range behavior for the $np$-chanal with $S=1$. $2\rho_{NN}({^{6}\mathrm{He}})/6\rho_{NN}(^{4}\mathrm{He})$ for $\Lambda_N=450$ MeV (a) and $\Lambda_N=550$ MeV (b). $2\rho_{NN}({^{6}\mathrm{Li}})/6\rho_{NN}(^{4}\mathrm{He})$ for $\Lambda_N=450$ MeV (c) and $\Lambda_N=550$ MeV (d). The ratio of four selected HO frequencies 12, 16, 20, and 24 are shown. Two flow parameters 1.88 fm$^{-1}$ (unfilled circles) and 2.24 fm$^{-1}$ (crosses) are adopted.