Effect of the repulsive core in the proton-neutron potential on deuteron elastic breakup cross sections

The role of the short-range part (repulsive core) of the proton-neutron ($pn$) potential in deuteron elastic breakup processes is investigated. A simplified one-range Gaussian potential and the Argonne $\text{V4}{}^{\prime }$ ($\text{AV4}{}^{\prime }$) central potential are adopted in the continuum-discretized coupled-channels (CDCC) method. The deuteron breakup cross sections calculated with these two potentials are compared. The repulsive core is found not to affect the deuteron breakup cross sections at energies from 40 MeV to 1 GeV. To understand this result, an analysis of the peripherality of the elastic breakup processes concerning the $pn$ relative coordinate is performed. It is found that for the breakup processes populating the $pn$ continua with orbital angular momentum $\ell$ different from 0, the reaction process is peripheral, whereas it is not for the breakup to the $\ell =0$ continua (the $s$-wave breakup). The result of the peripherality analysis indicates that the whole spatial region of deuteron contributes to the $s$-wave breakup.

Figure 1

Schematics of the three body system in deuteron scattering.

Figure 2

(a) $\text{AV4}{}^{\prime }$ (solid) and 1G-av4 (dashed) potentials. (b) Radial wave functions of deuteron multiplied by $r$.

Figure 3

Differential deuteron breakup cross sections on ${}^{58}\mathrm{Ni}$ at 80 MeV as a function of the relative $pn$ momentum (solid lines). The $s$-, $d$-, and $g$-wave components are shown by the dashed, dotted, and dash-dotted lines, respectively. The thick (thin) lines represent the results calculated with the $\text{AV4}{}^{\prime }$ (1G-av4) potential. The microscopic folding potential is used as $U_N$.

Figure 4

Same as Fig. 3 but at 1 GeV.

Figure 5

Deuteron wave functions normalized to the exponential function at 6 fm.

Figure 6

$f$ for each partial-wave component of the breakup cross section on ${}^{58}\mathrm{Ni}$ at 80 MeV. The horizontal axis is the rms radii of the deuteron adopted. The values of $f$ are normalized to the value at $r_{\mathrm{rms}}=1.7$ fm. The microscopic folding potential is used as $U_N$.

Figure 7

Same as Fig. 6 but at 1 GeV.