Complete sets of polarization transfer observables for the ${}^{208}$Pb$(\vec{p},\vec{n})$ reaction at 296 MeV and Gamow-Teller and spin-dipole strengths for ${}^{208}$Pb

We report measurements of cross sections and analyzing powers for reaction angles of ${\theta }_{\mathrm{lab}}={0.0}^{\circ }$–${10.0}^{\circ }$ and complete sets of polarization transfer observables and induced polarizations at ${\theta }_{\mathrm{lab}}={0.0}^{\circ }$–${7.0}^{\circ }$ for the ${}^{208}\mathrm{Pb}(\vec{p},\vec{n})$ reaction at a bombarding energy of $T_p=296$ MeV. A multipole decomposition technique was applied to the data to extract the Gamow-Teller (GT) and spin-dipole (SD) components from the continuum. The polarization observables were also used, for the first time, to separate the SD components into different spin-parity transfer ($\Delta J^{\pi }=0^{-}$, $1^{-}$, and $2^{-}$) contributions. A significant strength with $\Delta J^{\pi }=1^{+}$ is identified in the continuum beyond the GT giant resonance, which is due to configuration mixing effects and the isovector spin monopole (IVSM) contribution. The SD strength distributions were clearly dependent on $\Delta J^{\pi }$, which is reasonably reproduced by Hartree-Fock (HF) plus random phase approximation (RPA) calculations that include the Skyrme interaction with tensor components [Phys. Rev. C 83, 054316 (2011)].

Figure 1

Polarization transfer observables $D_{LL}\left(0^{\circ }\right)$ for the ${}^2\mathrm{H}(p,n)$ reaction at $0^{\circ }$ as a function of incident energy $T_p$. The filled square indicates the present result and the open circles represent data from McNaughton et al. [32]. The solid curve is a fit of the data using a second-order polynomial.

Figure 2

Cross sections (left panels) and analyzing powers (right panels) for the ${}^{208}\mathrm{Pb}(p,n)$ reaction at $T_p=296$ MeV and ${\theta }_{\mathrm{lab}}=0^{\circ }$–$4^{\circ }$. The cross sections and analyzing powers are binned in steps of 0.1 and 1 MeV, respectively. The solid curves show the results of DWIA calculations employing RPA response functions.

Figure 3

As described in Fig. 2 for the range of ${\theta }_{\mathrm{lab}}={5.5}^{\circ }$–${10}^{\circ }$.

Figure 4

Polarization transfer observables $D_{NN}$ (left panels) and induced polarization $P$ (right panels) for the ${}^{208}\mathrm{Pb}(p,n)$ reaction at $T_p=296$ MeV and ${\theta }_{\mathrm{lab}}={0.0}^{\circ }$–${7.0}^{\circ }$. The data are binned in 1 MeV steps. The solid curves denote the results of DWIA calculations employing RPA response functions.

Figure 5

As described in Fig. 4, but for the polarization transfer observables $D_{S^{\prime }S}$ (left panels) and $D_{L^{\prime }L}$ (right panels).

Figure 6

As described in Fig. 4, but for the polarization transfer observables $D_{L^{\prime }S}$ (left panels) and $D_{S^{\prime }L}$ (right panels) at ${\theta }_{\mathrm{lab}}={2.0}^{\circ }$–${7.0}^{\circ }$.

Figure 7

Cross sections for the ${}^{208}\mathrm{Pb}(p,n)$ reaction at $T_p=296$ MeV and ${\theta }_{\mathrm{lab}}=0^{\circ }$. The dashed, solid, and dotted curves denote the $\text{DWIA}+\text{RPA}$ results obtained with ${\varepsilon }_0=18$, 26, and 30 MeV, respectively. See text for details.

Figure 8

Cross sections for the ${}^{208}\mathrm{Pb}(p,n)$ reaction at $T_p=296$ MeV for ${\theta }_{\mathrm{lab}}=0^{\circ }$ (a) and $4^{\circ }$ (b). The shaded, cross-hatched, hatched, and unfilled regions represent the results of $\text{DWIA}+\text{RPA}$ calculations for the $\Delta J^{\pi }=1^{+}$, $0^{-}$, $1^{-}$, and $2^{-}$ components, respectively. The dashed curves show the total cross sections, including contributions up to $\Delta J^{\pi }=9^{+}$.

Figure 9

Polarization transfer observables (a) $D_{S^{\prime }S}$, (b) $D_{NN}$, and (c) $D_{L^{\prime }L}$ for the ${}^{208}\mathrm{Pb}(p,n)$ reaction at $T_p=296$ MeV and ${\theta }_{\mathrm{lab}}=4^{\circ }$. The dashed, dotted, and dot-dashed curves represent the results of $\text{DWIA}+\text{RPA}$ calculations for the $\Delta J^{\pi }=0^{-}$, $1^{-}$, and $2^{-}$ components, respectively. The solid curves show the total $D_{ij}$, including contributions up to $\Delta J^{\pi }=9^{+}$.

Figure 10

Spin-longitudinal $I{D}_L$ (left panels) and spin-transverse $I{D}_T$ (right panels) polarized cross sections for the ${}^{208}\mathrm{Pb}(p,n)$ reaction at $T_p=296$ MeV and ${\theta }_{\mathrm{lab}}={0.0}^{\circ }$–${7.0}^{\circ }$. The shaded, cross-hatched, hatched, and unfilled regions represent the results of $\text{DWIA}+\text{RPA}$ calculations for the $\Delta J^{\pi }=1^{+}$, $0^{-}$, $1^{-}$, and $2^{-}$ components, respectively. The dashed curves show the total $I{D}_i$, including contributions up to $\Delta J^{\pi }=9^{+}$.

Figure 11

Cross-section results obtained by MD analysis. See text for details.

Figure 12

Analyzing-power results obtained by MD analysis.

Figure 13

Nonspin $I{D}_0$ polarized cross sections obtained by MD analysis.

Figure 14

Spin-longitudinal $I{D}_L$ (left panels) and spin-transverse $I{D}_T$ (right panels) polarized cross sections obtained by MD analysis.

Figure 15

Gamow-Teller unit cross sections ${\widehat{\sigma }}_{\mathit{GT}}$ as a function of $A^{1/3}$. The open circles show the experimental data taken from Ref. [59] and the filled squares represent the DWIA predictions for typical nuclei from ${}^{12}\mathrm{C}$ to ${}^{208}\mathrm{Pb}$. The solid line represents the result of fitting with Eq. (21), and the blue band represents the estimated uncertainty of $\pm 15\%$.

Figure 16

(a) The GT strength $B(\mathit{GT};\omega )$ and (b) its integrated $S_{\mathit{GT}}\left(\omega \right)$ distributions obtained by MD analysis of the ${}^{208}\mathrm{Pb}(p,n)$ reaction. The bands represent the uncertainties arising from the selection of $\alpha$ in Eq. (18). The solid and dashed curves are the theoretical predictions reported by Drożdż et al. [18] and Dang et al. [62], respectively, with a quenching factor $Q=0.86$ [13].

Figure 17

(a) The IVSM strength $B(\mathrm{IVSM};\omega )$ and (b) its integrated $S_{\mathrm{IVSM}}\left(\omega \right)$ distributions obtained by MD analysis of the ${}^{208}\mathrm{Pb}(p,n)$ reaction. The bands represent the uncertainties arising from the selection of $\alpha$ in Eq. (18). The solid curves are the predictions obtained by RPA. See text for details.

Figure 18

The SD strength distributions obtained by MD analysis of the ${}^{208}\mathrm{Pb}(p,n)$ reaction. The separated SD strengths are presented in panels (b)–(d) for $\Delta J^{\pi }=0^{-}$, $1^{-}$, and $2^{-}$, respectively, and the total SD strength is shown in panel (a). The bands represent the uncertainties arising from the selection of $\alpha$ in Eq. (18). The solid curves are the predictions obtained by RPA.

Figure 19

As described for Fig. 18, but including the $\text{HF}+\text{RPA}$ predictions [22] for comparison with the data. The solid, dashed, dotted, and dot-dashed curves represent the results with the SGII, $\text{SGII}+\text{Te}1$, $\text{SGII}+\text{Te}2$, and $\text{SGII}+\text{Te}3$ interactions, respectively. The discrete RPA results have been smoothed by Lorentzian averaging with a width of 1 MeV. See text for details.

Figure 20

The integrated SD strengths defined in Eq. (27). The separated SD strengths are presented in panels (b)–(d) for $\Delta J^{\pi }=0^{-}$, $1^{-}$, and $2^{-}$, respectively, and the total SD strength is shown in panel (a). The bands represent the uncertainties arising from the selection of $\alpha$ in Eq. (18). The solid, dashed, dotted, and dot-dashed curves represent the $\text{HF}+\text{RPA}$ predictions [22] with the SGII, $\text{SGII}+\text{Te}1$, $\text{SGII}+\text{Te}2$, and $\text{SGII}+\text{Te}3$ interactions, respectively.