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Alpha-Particle Monopole Form Factors with Ab Initio No-Core Shell Model

P. Yin, A. M. Shirokov, H. Li, B. Zhou, X. Zhao, S. Bacca, J. P. Vary

Abstract

The state-of-the-art ab initio nuclear many-body approaches with modern nuclear forces are challenged by the recent experimental measurement of the monopole form factor of the $0^+_1\rightarrow 0^+_2$ transition in the $α$ particle [Kegel et al., Phys. Rev. Lett. 130, 152502 (2023)]. We investigate the elastic and inelastic $0^+_1\rightarrow 0^+_2$ transition form factors using the ab initio no-core shell model (NCSM). We observe a good convergence of both form factors with respect to the basis size employing the Daejeon16 nucleon-nucleon ($NN$) interaction. Our NCSM results are very close to the effective interaction hyperspherical harmonic calculations using $NN$ plus three-nucleon interactions based on the chiral effective field theory which take into account the continuum effects via the Lorentz integral transform. The significant difference between the ab initio results with various modern nuclear interactions and of some of them with the recent experimental data provides motivations for deeper investigation of this observable.

Alpha-Particle Monopole Form Factors with Ab Initio No-Core Shell Model

Abstract

The state-of-the-art ab initio nuclear many-body approaches with modern nuclear forces are challenged by the recent experimental measurement of the monopole form factor of the transition in the particle [Kegel et al., Phys. Rev. Lett. 130, 152502 (2023)]. We investigate the elastic and inelastic transition form factors using the ab initio no-core shell model (NCSM). We observe a good convergence of both form factors with respect to the basis size employing the Daejeon16 nucleon-nucleon () interaction. Our NCSM results are very close to the effective interaction hyperspherical harmonic calculations using plus three-nucleon interactions based on the chiral effective field theory which take into account the continuum effects via the Lorentz integral transform. The significant difference between the ab initio results with various modern nuclear interactions and of some of them with the recent experimental data provides motivations for deeper investigation of this observable.

Paper Structure

This paper contains 4 equations, 3 figures.

Figures (3)

  • Figure 1: (Color online) Point-proton density [panel (a)] and elastic monopole form factor [panel (b)] of the $^4$He ground state calculated with the NCSM using the Daejeon16 $NN$ interaction for $\hbar\Omega=10$ MeV at $N_{\rm max}=16{-}20$ (line+symbol) and $\hbar\Omega=15$ MeV at $N_{\rm max}=20$ (red solid diamond). In panel (b), the experimental data along with the quoted uncertainty (black solid dots with error bars) are taken from Ref. Frosch:1967pz; EIHH results calculated with AV18+UIX and chiral $NN$ (N$^3$LO)+3$N$ (N$^2$LO) interactions from Ref. Bacca:2012xv are shown for comparison.
  • Figure 2: (Color online) Monopole form factor of the $0^+_1\rightarrow 0^+_2$ transition in $^4$He calculated with the NCSM using the Daejeon16 $NN$ interaction for $\hbar\Omega=5$ [panel(a)], $7$ [panel (b)] and $10$ [panel (c)] MeV.
  • Figure 3: (Color online) Monopole form factor of the $0^+_1\rightarrow 0^+_2$ transition in $^4$He calculated with the NCSM using the Daejeon16 $NN$ interaction for $\hbar\Omega=7$ MeV at $N_{\rm max}=20$ (solid line). The experimental data along with their quoted uncertainties (solid dots with error bars) from Ref. Kegel:2021jrh, the EIHH results from Ref. Bacca:2012xv obtained with the AV18+UIX interactions (dash-dotted line) and the chiral $NN$(N$^3$LO) + 3$N$(N$^2$LO) interactions adopting the cutoff $\Lambda=500$ MeV (blue band), and the HH results from Ref. Viviani:2024yej obtained with chiral $NN$ (N$^3$LO) and differently parameterized 3$N$ (N$^2$LO) interactions adopting cutoffs $\Lambda=500$ MeV (dashed line, denoted as $\Lambda500^{*}$ in the legend) and $\Lambda=600$ MeV (dotted line, denoted as $\Lambda600^{*}$ in the legend) are shown for comparison.