Two-body currents at finite momentum transfer and applications to M1 transitions

TL;DR

This work develops a multipole decomposition of leading order two-body currents at finite momentum transfer within ab initio VS-IMSRG calculations and applies it to magnetic dipole transitions in medium mass nuclei. Using a broad set of chiral NN+3N Hamiltonians, including the 1.8/2.0 EM interaction, the study finds that 2BCs produce small net enhancements for the $^{48}$Ca 10.23 MeV M1 transition due to cancellations between seagull and pion-in-flight terms, while axial-vector 2BCs substantially affect Gamow-Teller strengths. In $^{48}$Ti, 2BCs yield more pronounced increases in the tested M1 strengths, reflecting a clear but nucleus dependent separation between M1 and GT responses. The framework enables momentum transfer dependent assessments for processes such as neutrinoless double beta decay and neutrino/nucleus scattering, and the authors emphasize that a universal quenching factor is not supported by first-principles results.

Abstract

We explore the impact of two-body currents (2BCs) at finite momentum transfer with a focus on magnetic dipole properties in $^{48}$Ca and $^{48}$Ti. To this end, we derive a multipole decomposition of 2BCs to fully include the momentum-transfer dependence in $\mathit{ab\,initio}$ calculations. As application, we investigate the effects of 2BCs on the strong M1 transition at 10.23$\,$MeV in $^{48}$Ca using the valence-space in-medium similarity renormalization group (VS-IMSRG) with a set of non-implausible interactions as well as the 1.8/2.0 (EM) interaction. Experiments, such as $(e,e')$ and $(γ,n)$, disagree on the magnetic dipole strength $B$(M1) for this transition. Our VS-IMSRG results favor larger $B$(M1) values similar to recent coupled-cluster calculations. However, for this transition there are larger cancellations between the leading pion-in-flight and seagull 2BCs, so that future calculations including higher-order 2BCs are important. For validation of our results, we investigate additional observables in $^{48}$Ca as well as M1 transitions in $^{48}$Ti. For these, our results agree with experiment. Finally, our results show that for medium-mass nuclei 2BC contributions to M1 and Gamow-Teller transitions are, as expected, very different. Therefore, using similar quenching factors for both in phenomenological calculations is not supported from first principles.

Figures (5)

• Figure 1: Many-body convergence with respect to the basis parameters $e_\mathrm{max}$ and $E_\mathrm{3max}$ for the M1 strength (top) and the $1^+$ excitation energy (bottom) of $^{48}$Ca using the VS-IMSRG for the 1.8/2.0 (EM) interaction. The left (right) panels show the variation with $e_\mathrm{max}$ ($E_\mathrm{3max}$) for $E_\mathrm{3max}=24$ ($e_\mathrm{max}=12$).
• Figure 2: Top panel: Transition form factor $F^2_\mathrm{T}(Q^2)$ as a function of the momentum transfer $Q$. Results are shown for the non-implausible interactions with only 1BCs (open blue circles) and including also 2BCs (1BCs+2BCs, filled red circles). The blue (red) filled diamonds show the result for the 1.8/2.0 (EM) interaction. In order to better compare the VS-IMSRG results to the $(e,e')$ experimental data Steffen1983 (black points with error bars), we interpolate our results using scipy.interpolate.CubicSplineVirtanen2020. Bottom panel: Ratio between the transition form factor with 2BCs and without, $F^2_\mathrm{T}(Q^2)_\mathrm{1BC+2BC}/F^2_\mathrm{T}(Q^2)_\mathrm{1BC }$ as function of momentum transfer $Q$ for the same interactions as in the top panel.
• Figure 3: Correlations for $^{48}$Ca between the studied $B$(M1) and the largest $B$(GT) (see text for details) as well as between the $B$(M1) and the $1^+$ excitation energy $E^*_{1^+}$ and ground-state energy $E_\mathrm{gs}$ (in the left, middle and right panel, respectively). The gray bands show the $B(M1)$ to the 10.23 MeV $1^{+}$ state measured with either the $(e,e')$ experiment Steffen1983 (lower gray band) or the $(\gamma,n)$ experiment Tompkins2011 (upper gray band). The dashed gray line in each panel shows the experimental $B$(GT) (from $^{48}$Ca($^3$He,t)$^{48}$Sc at 2.53 MeV Grewe2007), $1^+$ excitation energy $E^*_{1^+}=10.23$ MeV, and the ground-state energy $E_\mathrm{gs}$ of $^{48}$Ca Nndc. The green bar shows the prediction of the $B$(M1) from coupled-cluster calculations using different NN+3N interactions Acharya2024. Our results using the non-implausible interactions with 1BCs and 2BCs (or 1BCs only) are given by the red filled circles (blue open circles). The red and blue filled diamonds are the results using the 1.8/2.0 (EM) interaction with and without 2BCs, respectively.
• Figure 4: Ratio between the $B$(M1) and $B$(GT) strengths computed with and without 2BCs. The result with only 1BCs is denoted as $B$(M1/GT)$_{\rm 1BC}$. Likewise, the result with the 2BCs is given by $B$(M1/GT)$_{\rm 1BC+2BC}$. The circles show the results obtained with the non-implausible interactions, and the diamond is for the 1.8/2.0 (EM) interaction result.
• Figure 5: Correlation between the M1 strength $B$(M1) in $^{48}$Ca and $^{48}$Ti (top panels) and between the $1^+$ excitation energy $E^*_{1^+}$ and the M1 strength in $^{48}$Ti (bottom panels). The left (right) panels show the correlations with the M1 strength in $^{48}$Ti at 3.742 MeV (7.22 MeV) Guhr1990. The gray bands show the M1 strength in $^{48}$Ca at 10.23 MeV either measured with the $(e,e')$ experiment Steffen1983 (lower gray band) or the $(\gamma,n)$ experiment Tompkins2011 (upper gray band). The dashed grey lines and the vertical grey bands show the experimental values for the $1^+$ excitation energies and the $B$(M1) strengths in $^{48}$Ti NndcGuhr1990. The green bar shows the prediction of the M1 strength from coupled-cluster calculations using different NN+3N interactions Acharya2024. Our results for the non-implausible interactions including only 1BCs (including 1BCs and 2BCs) are given by the blue open circles (red filled circles) and for the 1.8/2.0 (EM) interaction by the blue (red) filled diamonds.