Elastic scattering of ${}^{17}\mathrm{F},{}^{17}\mathrm{O}$, and ${}^{19}\mathrm{F}$ on a heavy target in a microscopic continuum discretized coupled-channels method

Background: In the traditional continuum discretized coupled-channels (CDCC) method, the clusters of the projectile are structureless. Exotic nuclei exhibit unusual properties and often show significant couplings to the continuum. Therefore, reaction models that consider a more accurate structure of the projectile are often preferable. A microscopic description of the projectile, based on an effective nucleon-nucleon (NN) interaction, in a microscopic CDCC (MCDCC) model [Descouvemont and Hussein, Phys. Rev. Lett. 111, 082701 (2013)] has been successfully applied to ${}^7\mathrm{Li}+{}^{208}\mathrm{Pb}$ scattering.

Purpose: The MCDCC method is applied to low-energy elastic scattering of ${}^{17}\mathrm{F},{}^{17}\mathrm{O}$, and ${}^{19}\mathrm{F}$ on ${}^{58}\mathrm{Ni}$ and ${}^{208}\mathrm{Pb}$ targets. The goal of the calculations is twofold: to test the adequacy and the accuracy of the MCDCC model for heavier projectiles and to study the contribution of various channels to the elastic scattering cross sections.

Methods: The elastic scattering cross sections are calculated by using the MCDCC method. The nucleon-target optical potential is folded with the projectile densities resulting from an effective NN interaction, which includes central nuclear, spin-orbit, and Coulomb terms. Discretization of the continuum is achieved via the pseudostate method. Coupled equations are solved by using the $R$-matrix method on a Lagrange mesh.

Results: For the test case of ${}^{17}\mathrm{F}$ at 10 MeV/nucleon, the cross sections are weakly sensitive to the choice of the effective NN interaction. Three different energy-dependent optical nucleon-target potentials provide a similar reasonable agreement with data. Just below the Coulomb barrier, the MCDCC significantly underestimates the cross sections at larger angles. The coupling to the continuum is not significant in most of the assessed cases.

Conclusions: The MCDCC is very satisfactory in the sense that it includes the microscopic properties of the projectile in a reaction model. Well above the Coulomb barrier, the cross sections are in a good agreement with the data. The reasons for the discrepancy between the data and the calculated cross sections at the lower energies, which is also observed in a traditional CDCC, are unclear.

Figure 1

Bound states of ${}^{19}\mathrm{F}$ with respect to the ${}^{15}\mathrm{N}$ + $\alpha$ threshold, resulting from a Minnesota effective NN interaction with parameters $u=0.8185$ and $S_0=35.0\mathrm{MeV}{\mathrm{fm}}^5$.

Figure 2

${}^{17}\mathrm{F}$ states included in the MCDCC calculation.

Figure 3

Differential elastic cross sections, relative to the Rutherford cross section, for the scattering of ${}^{17}\mathrm{F}$ on ${}^{208}\mathrm{Pb}$. The top and bottom panels show the scattering at $E_{\mathrm{lab}}=170$ MeV and at $E_{\mathrm{lab}}=90.4$ MeV, respectively. The solid line shows the single-channel calculation that uses the Koning-Delaroche [14] nucleon-target potential (KD02), the dashed line corresponds to the CH89 [15] potential, and the dotted line corresponds to the Bechetti-Greenlees (BG69) [16] potential. Quasielastic scattering data at $E_{\mathrm{lab}}=170$ MeV and $E_{\mathrm{lab}}=90.4$ MeV are from Ref. [17] and Ref. [18], respectively.

Figure 4

(a) Differential elastic cross sections, relative to the Rutherford cross section, for the proton scattering of ${}^{208}\mathrm{Pb}$ at 11 MeV and for the neutron scattering of ${}^{208}\mathrm{Pb}$ at (b) 10 and (c) 5.5 MeV, respectively. The solid line corresponds to a Koning-Delaroche [14] nucleon-target potential (KD02), the dashed line results from the CH89 [15] potential, and the dotted line is for the Bechetti-Greenlees (BG69) [16] potential. The proton scattering data are taken from Ref. [20], and the neutron scattering data are from Refs. [21] and [22] as in Ref. [14] at 10 and 5.5 MeV, respectively.

Figure 5

(a) Differential elastic cross sections, relative to the Rutherford cross section, for the scattering of ${}^{17}\mathrm{F}$ on ${}^{208}\mathrm{Pb}$ at 10 MeV/nucleon. The solid line shows the full MCDCC calculation and the dashed line shows the single-channel ${}^{17}\mathrm{F}$ + ${}^{208}\mathrm{Pb}$ calculation. The dotted line shows a full MCDCC calculation with a renormalized Koning-Delaroche potential. The scaling factor for the real part of the potential is 0.65. Quasielastic scattering data are taken from Ref. [17]. Cross sections for the same system at 98 and 90.4 MeV are shown in (b) and (c), respectively. The solid line shows the full MCDCC calculation and the dashed line shows a single-channel ${}^{17}\mathrm{F}$ + ${}^{208}\mathrm{Pb}$ calculation. Quasielastic scattering data are taken from Ref. [18].

Figure 6

The inelastic cross section, relative to the Rutherford cross section, for the scattering of ${}^{17}\mathrm{F}$ on ${}^{208}\mathrm{Pb}$ at 10 MeV/nucleon.

Figure 7

Differential elastic cross sections, relative to the Rutherford cross section, for the scattering of ${}^{17}\mathrm{F}$ on ${}^{208}\mathrm{Pb}$ at 10 MeV/nucleon, showing the full MCDCC calculation with the real (a) and imaginary (b) parts of the Koning-Delaroche [14] potential scaled by 1.2, 1.0, 0.8, and 0.6. The quasielastic scattering data are taken from Ref. [17].

Figure 8

(a) Differential elastic cross sections, relative to the Rutherford cross section, for the scattering of ${}^{17}\mathrm{F}$ on ${}^{58}\mathrm{Ni}$ at 10 MeV/nucleon. The solid line shows the full MCDCC calculation and the dashed line shows the single-channel ${}^{17}\mathrm{F}$ + ${}^{208}\mathrm{Pb}$ calculation. The dotted line shows a full MCDCC calculation with a renormalized Koning-Delaroche potential. The scaling factor for the real part of the potential is 0.8. Quasielastic scattering data are taken from Ref. [17]. (b) Differential elastic cross sections for scattering at 58.5 MeV. The solid line shows the full MCDCC calculation, the dashed line shows the single-channel ${}^{17}\mathrm{F}$ + ${}^{208}\mathrm{Pb}$ calculation, and the dotted line shows the cross sections that include the inelastic and breakup contributions. Quasielastic scattering data are taken from Ref. [8].

Figure 9

Differential elastic cross sections, relative to the Rutherford cross section, for the scattering of ${}^{17}\mathrm{O}$ on ${}^{58}\mathrm{Ni}$ at $E_{\mathrm{lab}}=55$ MeV. The solid line shows the full MCDCC calculation and the dashed line shows the single-channel ${}^{17}\mathrm{O}$ + ${}^{58}\mathrm{Ni}$ calculation. Quasielastic experimental data are taken from Ref. [25].

Figure 10

Differential elastic cross sections, relative to the Rutherford cross section, for the scattering of ${}^{17}\mathrm{O}$ on ${}^{208}\mathrm{Pb}$ at $E_{\mathrm{lab}}=78$ MeV. The solid line shows the full MCDCC calculation; the dashed line and the dotted line show a single-channel ${}^{17}\mathrm{O}$ + ${}^{208}\mathrm{Pb}$ and a two-channel ${}^{17}\mathrm{O}$(g.s., first excited state) + ${}^{208}\mathrm{Pb}$ calculation, respectively. Experimental data are taken from Ref. [26].

Figure 11

Differential elastic cross sections, relative to the Rutherford cross section, for the scattering of ${}^{19}\mathrm{F}$ on ${}^{208}\mathrm{Pb}$ at (a) $E_{\mathrm{lab}}=102$ MeV and (b) $E_{\mathrm{lab}}=91$ MeV, respectively. The dashed line shows the single-channel ${}^{19}\mathrm{F}$ + ${}^{208}\mathrm{Pb}$ calculation, the dotted line shows the two-channel ${}^{19}\mathrm{F}(\mathrm{g}.\mathrm{s}.,5/2^{+})$ + ${}^{208}\mathrm{Pb}$ calculation, and the solid line shows the full MCDCC calculation. Quasielastic scattering experimental data are taken from Ref. [27].