Effect of deuteron breakup on the deuteron-$\mathrm{\Xi }$ correlation function

Background: The hadron-deuteron correlation function has attracted much interest as a potential method to access three-hadron interactions. However, the weakly bound nature of deuterons has not been considered in the preceding studies.

Purpose: The breakup effect of deuterons in the deuteron-${\mathrm{\Xi }}^{-}$ $(d-{\mathrm{\Xi }}^{-})$ correlation function $C_{d{\mathrm{\Xi }}^{-}}$ is investigated.

Methods: The $d-{\mathrm{\Xi }}^{-}$ scattering is described by a nucleon-nucleon-$\mathrm{\Xi }$ three-body reaction model. The continuum-discretized coupled-channels method, which is a fully quantum-mechanical and nonperturbative reaction model, is adopted.

Results: $C_{d{\mathrm{\Xi }}^{-}}$ turns out to be sensitive to the strong interaction and enhanced by the deuteron breakup effect by 6%–8% for a $d\text{−}{\mathrm{\Xi }}^{-}$ relative momentum below about 70 MeV/$c$. Low-lying neutron-neutron continuum states are responsible for this enhancement.

Conclusions: Within the adopted model, the deuteron breakup effect on $C_{d{\mathrm{\Xi }}^{-}}$ is found to be appreciable but not very significant. Except for the enhancement by several percent, studies on $C_{d{\mathrm{\Xi }}^{-}}$ without the deuteron breakup effect can be justified.

Figure 1

The $d-{\mathrm{\Xi }}^{-}$ correlation function as a function of the relative momentum $q$. The solid red, dashed green, dotted blue, and dash-dotted purple lines represent the result of the CDCC method, that with the ${}^{13}S_1$ breakup states only, the result of the single-channel calculation (without breakup states), and the result with the strong interactions switched off, respectively. Inset: Enlarged result for $30\mathrm{MeV}/c\le q\le 120\mathrm{MeV}/c$.

Figure 2

Convergence of the $d-\mathrm{\Xi }$ correlation function regarding $k_{\max }$. The horizontal axis is the $d\text{−}{\mathrm{\Xi }}^{-}$ relative momentum. The solid red, dashed green, dotted blue, and dash-dotted purple lines correspond to $k_{\max }=0.2$, 0.5, 1.0, and 2.0 ${\mathrm{fm}}^{-1}$, respectively.

Figure 3

Convergence of the $d-\mathrm{\Xi }$ correlation function regarding ${\mathrm{\Delta }}_c$ for the $nn$ continuum; ${\mathrm{\Delta }}_c$ for the $pn$ continuum is taken to be 0.2 ${\mathrm{fm}}^{-1}$. The horizontal axis is the $d\text{−}{\mathrm{\Xi }}^{-}$ relative momentum. The solid red, dashed green, dotted blue, and dash-dotted purple lines correspond to ${\mathrm{\Delta }}_c=1.0$, 0.5, 0.2, and 0.005 ${\mathrm{fm}}^{-1}$, respectively.

Figure 4

Same as Fig. 1 but with different values of the source size $b$ of the source function. (a) $b=1.6$ fm and (b) $b=3.0$ fm.

Figure 5

(a) $NNs$-wave scattering phase shift as a function of the c.m. scattering energy in the ${}^{13}S_1$ (solid red line) and ${}^{31}S_0$ (dashed green line) channels. (b) $NN$ discretized continuum states in the ${}^{13}S_1$ channel as a function of the distance of the two nucleons. The dashed green, dotted blue, and dash-dotted purple lines correspond to the first, third, and sixth bin states, respectively, with the bin size of 0.2 ${\mathrm{fm}}^{-1}$. The solid red line represents the bound-state wave function of the deuteron. (c) Same as (b) but in the ${}^{31}S_0$ channel; there is no bound state in this channel.

Figure 6

(a) $N-\mathrm{\Xi }$ interaction as a function of their distance. The solid red, dashed green, dotted blue, and dash-dotted purple lines correspond to the ${}^{11}S_0$, ${}^{31}S_0$, ${}^{13}S_1$, and ${}^{33}S_1$ channels, respectively. (b) Same as (a) but folded by the deuteron ground-state density.

Figure 7

Coupling potentials $U_{c{c}^{\prime }}^{(1/2)}\left(R\right)$. (a) Diagonal components for the deuteron ground state ($d$), the third bin state in the ${}^{13}S_1$ channel ($pn$), the first bin state in the ${}^{31}S_0$ channel (${}^{2}n$), and the third bin state in the ${}^{31}S_0$ channel ($nn$) are represented by the solid red, dashed green, dotted blue, and dash-dotted purple lines, respectively. (b) Potentials for the $d-pn$ (solid red line), $d-{}^{2}n$ (dashed green line), and $d-nn$ couplings.

Figure 8

The $d-d$ diagonal, $d-pn$ coupling, and $pn-pn$ diagonal potentials with $\sigma =3/2$ are shown by the solid red, dashed green, and dotted blue lines, respectively.

Figure 9

The $s$-wave phase shift of the $NN-\mathrm{\Xi }$ scattering as a function of the c.m. scattering energy. The solid red and dashed green lines correspond to the $d-{\mathrm{\Xi }}^{-}$ scattering in the ${}^{22}S_{1/2}$ and ${}^{24}S_{3/2}$ channels, respectively. The $nn-\mathrm{\Xi }$ scattering phase shift in the ${}^{22}S_{1/2}$ (${}^{22}S_{1/2}$) channel is shown by the dotted blue (dash-dotted purple) line; the discretized $nn$ continuum state corresponding to the wave number between 0.0 and 0.2 ${\mathrm{fm}}^{-1}$ is adopted as an internal $nn$ wave function. All results are obtained by the single-channel calculation.

Figure 10

Absolute square of the $NN-\mathrm{\Xi }$ scattering wave function for $\sigma =1/2$ at $q=30$ MeV/$c$. The solid red line represents the elastic channel component, whereas the dotted blue line shows the sum of the components for the $nn$ closed channel; both are obtained by the CDCC method. The dash-dot-dotted brown line shows the total contributions of the channels included. The dash-dotted purple line represents the result of the single-channel calculation.

Figure 11

Same as Fig. 10 but at $q=60$ MeV/$c$. The dashed green line shows the sum of the contributions from the $nn$ open breakup channels.

Figure 12

Same as Fig. 11 but at $q=100$ MeV/$c$.