Theoretical investigation of two-particle two-hole effects on spin-isospin excitations through charge-exchange reactions

Background: Coherent one-particle one-hole (1p1h) excitations have given us effective insights into general nuclear excitations. However, the two-particle two-hole (2p2h) excitation beyond 1p1h is now recognized as critical for the proper description of experimental data of various nuclear responses.

Purpose: The spin-flip charge-exchange reactions ${}^{48}\mathrm{Ca}(p,n){}^{48}\mathrm{Sc}$ are investigated to clarify the role of the 2p2h effect on their cross sections. The Fermi transition of ${}^{48}\mathrm{Ca}$ via the $(p,n)$ reaction is also investigated in order to demonstrate our framework.

Methods: The transition density is calculated microscopically with the second Tamm-Dancoff approximation, and the distorted-wave Born approximation is employed to describe the reaction process. A phenomenological one-range Gaussian interaction is used to prepare the form factor.

Results: For the Fermi transition, our approach describes the experimental behavior of the cross section better than the Lane model, which is the conventional method. For spin-flip excitations including the GT transition, the 2p2h effect decreases the magnitude of the cross section and does not change the shape of the angular distribution. The $\mathrm{\Delta }l=2$ transition of the present reaction is found to play a negligible role.

Conclusions: The 2p2h effect will not change the angular-distributed cross section of spin-flip responses. This is because the transition density of the Gamow-Teller response, the leading contribution to the cross section, is not significantly varied by the 2p2h effect.

Figure 1

(a) Strength functions of the GT and IAS resonances of ${}^{48}\mathrm{Ca}$ calculated with the STDA and TDA. The filled and slash-shaded bars are the results of the GT transition calculated with the TDA and STDA, respectively, and the cross-shaded bars are for the IAS resonance. (b) Strength functions of the $\mathrm{SQ}-1^{+}$ transition.

Figure 2

The cross sections of the ${}^{48}\mathrm{Ca}{(p,n)}^{48}\mathrm{Sc}\left(\mathrm{IAS}\right)$ reaction at $E_{\mathrm{lab}}=25$, 35, and 45 MeV. The solid lines are the calculated results from the TDA form factor, while the dashed lines are ones from the Lane form factor. The measured data are taken from Refs. [33, 34]. The lines and the dots are multiplied by ${10}^{-2}$ (${10}^{-4}$) at 35 (45) MeV.

Figure 3

The differential cross section of the ${}^{48}\mathrm{Ca}(p,n){}^{48}\mathrm{Sc}\left(\mathrm{GT}\right)$ reaction at $E_{\mathrm{lab}}=295\mathrm{MeV}$ for the low-lying $1^{+}$ resonance state. The calculated result with (without) the 2p2h configuration shown by the solid (dashed) line is compared with the experimental data (open circle) taken from Ref. [8].

Figure 4

The transition density of the low-lying $1^{+}$ resonance state of ${}^{48}\mathrm{Sc}$ calculated with the STDA (thick solid line for $l=0$, thin solid line for $l=2$) and TDA (thick dashed line for $l=0$, thin dashed line for $l=2$).

Figure 5

The cross section of ${}^{48}\mathrm{Ca}(p,n){}^{48}\mathrm{Sc}$ at 295 MeV for the low-lying $1^{+}$ resonance state calculated with the STDA transition density of the GT and $\mathrm{\Delta }l=2$ transitions (solid line), the GT transition only (dashed line), and $\mathrm{\Delta }l=2$ transition only (dotted line).

Figure 6

Same as Fig. 3 but for the giant resonance.

Figure 7

Same as Fig. 4 but for the giant resonance.

Figure 8

Same as Fig. 5 but for the giant resonance.