Interplay of projectile breakup and target excitation in reactions induced by weakly bound nuclei

Background: Reactions involving weakly bound nuclei require formalisms able to deal with continuum states. The majority of these formalisms struggle to treat collective excitations of the systems involved. For continuum-discretized coupled channels (CDCC), extensions to include target excitation have been developed but have only been applied to a small number of cases.

Purpose: In this work, we reexamine the extension of the CDCC formalism to include target excitation and apply it to a variety of reactions to study the effect of breakup on inelastic cross sections.

Methods: We use a transformed oscillator basis to discretize the continuum of the projectiles in the different reactions and use the extended CDCC method developed in this work to solve the resulting coupled differential equations. A new code has been developed to perform the calculations.

Results: Reactions ${}^{58}\mathrm{Ni}(d,d){}^{58}\mathrm{Ni}^{*}, {}^{24}\mathrm{Mg}(d,d){}^{24}\mathrm{Mg}^{*}, {}^{144}\mathrm{Sm}({}^6\mathrm{Li},{}^6\mathrm{Li}){}^{144}\mathrm{Sm}^{*}$, and ${}^9\mathrm{Be}({}^6\mathrm{Li},{}^6\mathrm{Li}){}^9\mathrm{Be}^{*}$ are studied. Satisfactory agreement is found between experimental data and extended CDCC calculations.

Conclusions: The studied CDCC method has proven to be an accurate tool to describe target excitation in reactions with weakly bound nuclei. Moderate effects of breakup on inelastic observables are found for the reactions studied. Cross-section magnitudes are not modified much, but angular distributions present smoothing when opposed to calculations without breakup.

Figure 1

(a) Elastic and (b) ${}^{58}\mathrm{Ni}\left(2^{+}\right)$ excitation angular differential cross sections for the ${}^{58}\mathrm{Ni}(d,d){}^{58}\mathrm{Ni}$ reaction at a deuteron energy of $E_d=80\mathrm{MeV}$. In dashed black a calculation including only $l=0$ breakup, while in solid green the calculation includes both $l=0$ and $l=2$ breakup. Experimental data are taken from Ref. [25]. As can be seen, the agreement with the data is improved in the elastic case when including $l=2$ while for the ${}^{58}\mathrm{Ni}\left(2^{+}\right)$ excitation there is only a slight improvement in the agreement. The red squares correspond to the calculation from Ref. [20], which includes only $l=0$ breakup. As can be seen in the figure, the agreement with our $l=0$ calculation is excellent.

Figure 2

Same as Fig. 1. The black solid line includes breakup and target excitation consistently. The red solid line only includes target excitation, while the blue dash-dotted line includes only breakup. The green dotted line excludes both target excitation and breakup. It can be seen that the best agreement with the data is obtained when including both breakup and inelastic excitation consistently.

Figure 3

Elastic (upper) and ${}^{24}\mathrm{Mg}\left(2^{+}\right)$ excitation (lower) differential angular cross sections for ${}^{24}\mathrm{Mg}(d,d^{\prime }){}^{24}\mathrm{Mg}^{*}$ at a deuteron energy of $70\mathrm{MeV}$. CDCC calculations are presented using Köning–Delaroche and CH89 parametrizations. Faddeev calculations are taken from Ref. [26].

Figure 4

Elastic (upper) and ${}^{24}\mathrm{Mg}\left(2^{+}\right)$ excitation (lower) differential angular cross sections for ${}^{24}\mathrm{Mg}(d,d^{\prime }){}^{24}\mathrm{Mg}^{*}$ at a deuteron energy of $70\mathrm{MeV}$ computed including (violet lines) and excluding (green lines) the $4^{+}$ state of ${}^{24}\mathrm{Mg}$, using CH89 (solid lines) and Köning–Delaroche (dashed lines) parametrizations.

Figure 5

Elastic (left) and ${}^{144}\mathrm{Sm}$ excitation (right) differential angular cross sections for ${}^{144}\mathrm{Sm}({}^6\mathrm{Li},{}^6\mathrm{Li}){}^{144}\mathrm{Sm}^{*}$ for incoming energies of $23,28,30$, and $35\mathrm{MeV}$. The red dashed and solid blue lines correspond to different $\alpha -{}^{144}\mathrm{Sm}$ and $d-{}^{144}\mathrm{Sm}$ potentials (see text).

Figure 6

Elastic angular differential cross section for different incident energies for the reaction ${}^{144}\mathrm{Sm}({}^6\mathrm{Li},{}^6\mathrm{Li}){}^{144}\mathrm{Sm}$. The red solid line corresponds to calculations using potentials from Set 1 (see text) including deformation of the target, while the blue dashed line corresponds to calculations using the same potentials without target deformation.

Figure 7

Elastic (left) and ${}^{144}\mathrm{Sm}$ excitation (right) differential cross sections for ${}^{144}\mathrm{Sm}({}^6\mathrm{Li},{}^6\mathrm{Li}){}^{144}\mathrm{Sm}^{*}$ at different incident energies. Coupled-channel calculations are presented using potentials from Set 2 (see text) including (solid blue line) and excluding (dash-dotted green line) breakup states from the calculation. The dashed brown line corresponds to optical model calculations using the Cook potential [42].

Figure 8

Coupling potential $F_{\text{elas,inel}}^{2,0,2}$ for the ${}^6\mathrm{Li}\left(\text{g.s.}\right)+{}^{144}\mathrm{Sm}\left(0^{+}\right)\to {}^6\mathrm{Li}\left(\text{g.s.}\right)+{}^{144}\mathrm{Sm}\left(2^{+}\right)$ inelastic transition, computed from CDCC calculation with Sets 1 and 2 and with the deformed ${}^6\mathrm{Li}+{}^{144}\mathrm{Sm}$ potential, using Cook's parametrization. An incident energy of 30 MeV has been considered. The shaded area corresponds to the distances of closest approach corresponding to Coulomb trajectories leading to scattering angles from ${50}^{\circ }$ to ${150}^{\circ }$, the range spanned by the considered experimental data [19].

Figure 9

Cross sections for (a) elastic scattering and (b) excitation of ${}^9\mathrm{Be}$ ($E_x=2.43$ MeV, $J^{\pi }=5/2^{-}$) and of (c) ${}^6\mathrm{Li}$ (resonant state at $E_x=2.19$ MeV, $J^{\pi }=3^{+}$). Two sets of potentials are presented (see text).

Figure 10

Cross sections for (a) elastic scattering and (b) inelastic scattering of ${}^9\mathrm{Be}$ ($E_x=2.43\mathrm{MeV},J^{\pi }=5/2^{-}$) and of (c) ${}^6\mathrm{Li}$ (resonant state at $E_x=2.19\mathrm{MeV}, J^{\pi }=3^{+}$). Calculations have been performed using the potential from [47] for $V_{n-{}^9\mathrm{Be}}$. The rest of the potentials are those indicated in the text. The dark-green solid line corresponds to the full calculation, while the red dot-dashed line excludes states in which ${}^9\mathrm{Be}$ is in its excited state simultaneously with ${}^6\mathrm{Li}$ being in a breakup state. The blue dashed line excludes all states with ${}^9\mathrm{Be}$ in its excited state while the green dotted line excludes all breakup states of ${}^6\mathrm{Li}$.