Proton-induced deuteron knockout reaction as a probe of an isoscalar proton-neutron pair in nuclei

Background: The isoscalar $pn$ pair is expected to emerge in nuclei having the similar proton and neutron numbers but there is no clear experimental evidence for it.

Purpose: We aim to clarify the correspondence between the $pn$ pairing strength in many-body calculation and the triple differential cross section (TDX) of proton-induced deuteron knockout ($p,pd$) reaction on ${}^{16}\mathrm{O}$.

Methods: The radial wave function of the isoscalar $pn$ pair with respect to the center of ${}^{16}\mathrm{O}$ is calculated with the energy density functional (EDF) approach and is implemented in the distorted wave impulse approximation framework. The $pn$ pairing strength $V_0$ in the EDF calculation is varied and the corresponding change in the TDX is investigated.

Results: A clear $V_0$ dependence of the TDX is found for the ${}^{16}\mathrm{O}(p,pd){}^{14}\mathrm{N}(1_2^{+}$) at 101.3 MeV. The nuclear distortion is found to make the $V_0$ dependence stronger.

Conclusions: Because of the clear $V_0$-TDX correspondence, the ($p,pd$) reaction will be a promising probe for the isoscalar $pn$ pair in nuclei. For quantitative discussion, further modification of the description of the reaction process will be necessary.

Figure 1

Coordinates of the $\mathrm{A}(p,pd)\mathrm{B}$ reaction system.

Figure 2

$S=1pn$-pair removal transition strengths as functions of the excitation energy, where the excitation energy for the unperturbed ${\left(p_{1/2}\right)}^{-2}$ configuration is set as zero. The solid, dashed, and dot-dashed lines correspond to the cases of $V_0=-100, -490$, and $-600$ MeV ${\mathrm{fm}}^3$, respectively.

Figure 3

Radial component of ${\phi }_{pn}\left(\mathit{R}\right)$. The solid, dashed, and dot-dashed lines correspond to the cases of $V_0=-100, -490$, and $-600$ MeV ${\mathrm{fm}}^3$, respectively. Note that each line is multiplied by $R^2$.

Figure 4

Triple differential cross section (TDX) for the ${}^{16}\mathrm{O}(p,pd){}^{14}\mathrm{N}^{*}$ reaction at 101.3 MeV. The solid, dashed, and dot-dashed lines corresponds the results with ${\widehat{\phi }}_{pn}$ of $V_0=-100, -490$, and $-600$ MeV ${\mathrm{fm}}^3$, respectively.

Figure 5

Ratio of the TDX height to that calculated with $V_0=-100$ MeV ${\mathrm{fm}}^3$. The circles (asterisks) represent the results of the DWIA (PWIA) calculations.

Figure 6

Transition matrix density (TMD) corresponding the TDX with $V_0=-490$ MeV ${\mathrm{fm}}^3$ at $T_1^{\text{L}}=52$ MeV. The solid (dashed) line denotes the real (imaginary) part of the TMD.

Figure 7

(a) The solid line is the same as the dashed line in Fig. 3 divided by $R^2$. The dashed line is the wave function obtained by widening the solid line outward by 25% artificially. (b) The corresponding TDXs for the ${}^{16}\mathrm{O}(p,pd){}^{14}\mathrm{N}^{*}$ reaction at 101.3 MeV.