The renormalization of the shell-model Gamow-Teller operator starting from effective field theory for nuclear systems

For the first time, we approach in this work the problem of the renormalization of the Gamow-Teller decay operator for nuclear shell-model calculations by way of many-body perturbation theory, starting from a nuclear Hamiltonian and electroweak currents derived consistently by way of the chiral perturbation theory. These are the inputs we need to construct microscopically the effective shell-model Hamiltonians and decay operators. The goal is to assess the role of both electroweak currents and many-body correlations as the origins of the well-known problem of the quenching of the axial coupling constant $g_A$. To this end, the calculation of observables related to the Gamow-Teller transitions has been performed for several nuclear systems outside the ${}^{40}\mathrm{Ca}$ and ${}^{56}\mathrm{Ni}$ closed cores and compared with the available data.

Figure 1

Diagrams illustrating the contributions up to ${\mathrm{N}}^3\mathrm{LO}$ to the axial current we have considered in the present work. The wavy lines represent the external weak field, the dashed lines the pion exchange, the square in diagram (b) represents relativistic corrections, while the dot in diagram (c) denotes a vertex induced by subleading terms in the $\pi$-nucleon chiral Lagrangian.

Figure 2

Comparison between experimental and calculated SP spectra of ${}^{57}\mathrm{Ni}$ and ${}^{57}\mathrm{Cu}$.

Figure 3

Experimental and calculated excitation energies of the yrast $J^{\pi }=2^{+}$ states for nickel isotopes from $N=30$ to 48. The black dashed line refers to results obtained with the $H_{\mathrm{eff}}$ for the $A=58$ system (see text for details).

Figure 4

Experimental and calculated two-neutron separation energies for nickel isotopes from $N=30$ to 48. The black dashed line refers to results obtained with the $H_{\mathrm{eff}}$ for the $A=58$ system (see text for details). Data are taken from [71]; open circles correspond to estimated values.

Figure 5

Neutron ESPEs from $H_{\mathrm{eff}}$ TBMEs for nickel isotopes as a function of the neutron number, calculated from the CD-Bonn potential and from chiral two- and three-body potential (see the text for details).

Figure 6

Same as in Fig. 3, but the theoretical results are here obtained with $H_{\mathrm{eff}}$ reported in Ref. [10] (see text for details).

Figure 7

Experimental and calculated spectra of ${}^{48}\mathrm{Ca}$ and ${}^{48}\mathrm{Ti}$. $B\left(E2\right)$ strengths (in $e^2{\mathrm{fm}}^4$) are also reported (see text for details).

Figure 8

Same as in Fig. 7, but for ${}^{76}\mathrm{Ge}$ and ${}^{76}\mathrm{Se}$ (see text for details).

Figure 9

Same as in Fig. 7, but for ${}^{82}\mathrm{Se}$ and ${}^{82}\mathrm{Kr}$.

Figure 10

Correlation plots between experimental ($y$ axis) and calculated ($x$ axis) values of the GT nuclear matrix elements of a few decay processes in the $0f1p$ shell region. The experimental values are taken from Ref. [80].

Figure 11

Running sums of the ${}^{48}\mathrm{Ca}B\left(\mathrm{GT}\right)$ strengths as a function of the excitation energy $E_x$ up to 6.5 MeV (see text for details).

Figure 12

Running sums of the ${}^{76}\mathrm{Ge}B\left(\mathrm{GT}\right)$ strengths as a function of the excitation energy $E_x$ up to 5 MeV.

Figure 13

Same as in Fig. 12, but for ${}^{82}\mathrm{Se}$.