Two-body weak currents in heavy nuclei

In light and medium-mass nuclei, two-body weak currents from chiral effective field theory account for a significant portion of the phenomenological quenching of Gamow-Teller transition matrix elements. Here we examine the systematic effects of two-body axial currents on Gamow-Teller strength and $\beta$-decay rates in heavy nuclei within energy-density functional theory. Using a Skyrme functional and the charge-changing finite amplitude method, we add the contributions of two-body currents to the usual one-body linear response in the Gamow-Teller channel, both exactly and though a density-matrix expansion. The two-body currents, as expected, usually quench both summed Gamow-Teller strength and decay rates, but by an amount that decreases as the neutron excess grows. In addition, they can enhance individual low-lying transitions, leading to decay rates that are quite different from those that an energy-independent quenching would produce, particularly in neutron-rich nuclei. We show that both these unexpected effects are related to changes in the total nucleon density as the number of neutrons increases.

Figure 1

Total quenching trends with proton number for the different sets of LECs in Table 1, with ${\overline{c}}_D=0$. The solid symbols correspond to the lightest isotope of a given element and the open symbols to the heaviest one, at the neutron drip line.

Figure 2

Same as Fig. 1 but for the change in $q$ with ${\overline{c}}_D=\pm 2$.

Figure 3

The difference between the total quenching produced by the density-matrix expansion (DME) and by the full calculation, as a percentage of the full quenching with the RTD parameter set [45]. Blue circles correspond to predictions of the DME exchange current, not supplemented by anything else, while red triangles correspond to those of the DME exchange current together with the full direct current (see text).

Figure 4

Total quenching in the (a) Sn and (b) Gd isotopic chains with the EGM LEC set, and with the full current and the same versions of the DME shown in Fig. 3. Panels (c) and (d) show the respective deformations. Vertical lines indicate the magic numbers $N=82$ and 126.

Figure 5

Comparison of Gamow-Teller rates computed with the full one-plus-two-body current and $g_A=1.27$ to those computed with the one-body current only and $g_A^{\text{eff}}=1.0$, in (a) Sn and (b) Gd isotopes. The percent difference is $({\lambda }_{g_A=1.27}^{\text{1b+2b}}-{\lambda }_{g_A=1.0}^{\text{1b}})/{\lambda }_{g_A=1.0}^{\text{1b}}\times 100\%$, with $\lambda$ representing decay rates. The isotopes ${}^{128}\mathrm{Sn}\text{–}{}^{132}\mathrm{Sn}$ are excluded because the Gamow-Teller strength below the $\beta$-decay threshold is negligible.

Figure 6

Ratio of the one-plus-two-body FAM strength to the one-body strength for Gamow-Teller transitions below the $\beta$-decay threshold energy in the light isotopes (a) ${}^{162}\mathrm{Gd}$ and (b) ${}^{134}\mathrm{Sn}$, as well as the heavy isotopes (c) ${}^{220}\mathrm{Gd}$ and (d) ${}^{174}\mathrm{Sn}$. Arrows indicate the transitions examined in Figs. 7 and 8.

Figure 7

Density of the lowest lying Gamow-Teller transition amplitude in (a) ${}^{134}\mathrm{Sn}$ and (b) ${}^{174}\mathrm{Sn}$ as a function of the radial coordinate $r$. The curves show densities for the one-body, two-body, and one-plus-two-body amplitudes. The factor of $4\pi r^2$ makes the integrated amplitudes equal to the areas under the curves. The vertical line is at the spherical radius $R_0=1.2A^{1/3}$, and the legends show the amplitudes $A$ and quenching factors $q_0$ for the state in question. The overall signs of the amplitudes are arbitrary, but the relative signs between the one- and two-body terms are not. The quenching factor $q_0$ contains the square root of the squared amplitudes and is always positive.

Figure 8

Density of the lowest lying Gamow-Teller transition amplitude in (a) ${}^{162}\mathrm{Gd}$ and (b) ${}^{220}\mathrm{Gd}$ as a function of $r$ and $z$. The figures show densities for the (a1,b1) one-body, (a2,b2) two-body, and (a3,b3) one-plus-two-body amplitudes. The volume element of $4\pi r$ is included (with an extra factor of 2 to account for the lower hemisphere). The curved lines indicate the nuclear surface determined from Eq. (B13), with $r=1.2A^{1/3}$. The titles show the amplitudes $A$ and quenching factors $q_0$ for the state.