Microscopic optical potential for ${}^6\mathrm{He}$

The microscopic optical potential for ${}^6\mathrm{He}$ with no free parameters is obtained by folding the microscopic optical potentials of its constituent nucleons with the internal wave function of ${}^6\mathrm{He}$. We use the isospin-dependent nucleon microscopic optical potential, which is derived by using the Green's function method through the nuclear matter approximation and the local density approximation based on the Skyrme nucleon-nucleon effective interaction. The internal wave function of ${}^6\mathrm{He}$ is described in a harmonic-oscillator form. The ${}^6\mathrm{He}$ microscopic optical potential is used to calculate the reaction cross sections and elastic-scattering angular distributions for target nuclei in the mass range $12\le \mathrm{A}\le 209$ at incident energies up to 350 MeV. The results are compared with the experimental data and those calculated by a global phenomenological optical potential; in most cases, the microscopic optical potential reproduces the experimental data less well than the global potential. The sensitivity of scattering to the potentials as a function of radius has been investigated by using the notch perturbation method. The investigation shows that the scattering is sensitive to the optical potential in the nuclear surface region. It is concluded from the discussion that the microscopic optical potential can be improved by increasing the surface absorption contribution.

Figure 1

The relation of the coordinates of each nucleon in ${}^6\mathrm{He}$ with the internal relative coordinates $\mathbf{\xi }$.

Figure 2

Radial probability distributions of $1s$-state protons and neutrons (dashed line), $1p$-state neutrons (solid line), all neutrons (dash-dot-dotted line), and all nucleons (dash-dotted line) relative to the full nucleon probability distribution of ${}^6\mathrm{He}$. The arrows denote the corresponding most-probable radii.

Figure 3

Radial dependence of the MOP for ${}^6\mathrm{He}+{}^{208}\mathrm{Pb}$ reaction.

Figure 4

Calculated differential cross sections relative to Rutherford cross section for ${}^6\mathrm{He}$ elastic scattering from ${}^{12}\mathrm{C}$ at incident energies from 8.79 to 250 MeV compared with experimental data. The solid lines and dashed lines denote the results calculated by the MOP and the GOP [22], respectively. The data are shifted downward by factors of ${10}^0$, ${10}^{-2}$, ${10}^{-4}$, and so on.

Figure 5

Same as Fig. 4 but for ${}^6\mathrm{He}$ elastic scattering from ${}^{27}\mathrm{Al}$ at incident energies from 9.54 to 13.4 MeV. The data are shifted downward by factors of ${10}^0$, ${10}^{-1}$, ${10}^{-2}$, and ${10}^{-3}$.

Figure 6

Same as Fig. 4 but for ${}^6\mathrm{He}$ elastic scattering from ${}^{51}\mathrm{V}$ at incident energies of 15.4 and 23.0 MeV. The data are shifted downward by factors of ${10}^0$ and ${10}^{-1}$.

Figure 7

Same as Fig. 4 but for ${}^6\mathrm{He}$ elastic scattering from ${}^{58}\mathrm{Ni}$ at incident energies from 9.0 to 21.7 MeV. The data are shifted downward by factors of ${10}^0$, ${10}^{-1}$, ${10}^{-2}$, ${10}^{-3}$, and ${10}^{-4}$.

Figure 8

Same as Fig. 4 but for ${}^6\mathrm{He}$ elastic scattering from ${}^{65}\mathrm{Cu}$ at incident energies from 19.56 to 30.05 MeV. The data are shifted downward by factors of ${10}^0$, ${10}^{-1}$, and ${10}^{-2}$.

Figure 9

Same as Fig. 4 but for ${}^6\mathrm{He}$ elastic scattering from ${}^{64}\mathrm{Zn}$ at incident energies of 10.0 and 13.6 MeV. The data are shifted downward by factors of ${10}^0$ and ${10}^{-1}$.

Figure 10

Same as Fig. 4 but for ${}^6\mathrm{He}$ elastic scattering from ${}^{120}\mathrm{Sn}$ at incident energies from 17.4 to 20.05 MeV. The data are shifted downward by factors of ${10}^0$, ${10}^{-1}$, ${10}^{-2}$, and ${10}^{-3}$.

Figure 11

Same as Fig. 4 but for ${}^6\mathrm{He}$ elastic scattering from ${}^{197}\mathrm{Au}$ at incident energies of 10.1 and 27.0 MeV. The data are shifted downward by factors of ${10}^0$ and ${10}^{-1}$.

Figure 12

Same as Fig. 4 but for ${}^6\mathrm{He}$ elastic scattering from ${}^{208}\mathrm{Pb}$ at incident energies from 14.0 to 56.6 MeV. The data are shifted downward by factors of ${10}^0$, ${10}^{-1}$, ${10}^{-2}$, and so on.

Figure 13

Same as Fig. 4 but for ${}^6\mathrm{He}$ elastic scattering from ${}^{209}\mathrm{Bi}$ at incident energies from 14.71 to 22.5 MeV. The data are shifted downward by factors of ${10}^0$, ${10}^{-1}$, ${10}^{-2}$, and so on.

Figure 14

Calculated total reaction cross sections for ${}^6\mathrm{He}+{}^{28}\mathrm{Si}$ compared with experimental data. The results calculated by MOP and GOP are denoted by the solid line and dashed line, respectively.

Figure 15

Same as Fig. 4 but for ${}^6\mathrm{He}$ elastic scattering from ${}^9\mathrm{Be}$ at incident energies from 16.2 to 150 MeV. The data are shifted downward by factors of ${10}^0$, ${10}^{-2}$, and ${10}^{-4}$.

Figure 16

Comparison of the MOP (solid lines), GOP [22] (dashed lines), and KD-fold (dash-dotted lines) for ${}^6\mathrm{He}+{}^{209}\mathrm{Bi}$ reaction at the incident energy of 22.5 MeV.

Figure 17

Radial sensitivity of the differential cross sections of ${}^6\mathrm{He}$ elastic scattering from ${}^{209}\mathrm{Bi}$ at the incident energy of 22.5 MeV to the MOP and GOP. The solid and dashed lines show the results of perturbing the real and imaginary parts of the MOP, respectively, while the dash-dotted and dash-dot-dotted lines denote the results of perturbing the real and imaginary parts of the GOP, respectively.

Figure 18

The differential cross sections relative to Rutherford cross section for ${}^6\mathrm{He}$ elastic scattering from ${}^{209}\mathrm{Bi}$ at the incident energy of 22.5 MeV. The solid and dashed lines denote the results calculated by the MOP and GOP [22], respectively. The dash-dot-dotted line denotes the result calculated by the MOP with the real part replaced by the GOP in the radial region of 5–14 fm. The dash-dotted line denotes the result calculated by the MOP with the imaginary part replaced by the GOP in the radial region of 11–15 fm.

Figure 19

The differential cross sections relative to Rutherford cross section for ${}^6\mathrm{He}$ elastic scattering from ${}^{209}\mathrm{Bi}$ at the incident energy of 22.5 MeV. The solid, dashed, and dash-dotted lines denote the results calculated by the MOP, GOP, and KD-fold, respectively.