Sensitivity of analyzing power to distorting potentials in the quasifree reaction ${}^{40}\mathrm{Ca}(p,p\alpha ){}^{36}\mathrm{Ar}$ at 100 MeV incident energy: Comparison with ${}^9\mathrm{Be}$ and ${}^{12}\mathrm{C}$ targets

Background: The ($p,p\alpha$) knockout reaction is useful for the study of preformed $\alpha$ clusters in atomic nuclei. At quasifree kinematic conditions above an incident energy of about 100 MeV the cross section and analyzing-power angular distributions extracted from the ($p,p\alpha$) knockout reaction are anticipated to resemble its free two-body counterparts. Several ($p,p\alpha$) knockout studies in the incident-energy range of 100–150 MeV on targets up to ${}^{12}\mathrm{C}$ confirm the predicted equivalence. However, the only experiment on ${}^{40}\mathrm{Ca}(p,p\alpha ){}^{36}\mathrm{Ar}$ appears to fail the expectation spectacularly.

Purpose: The reason for the drastic discrepancy between the experimental analyzing-power angular distribution for ${}^{40}\mathrm{Ca}(p,p\alpha ){}^{36}\mathrm{Ar}$ and the trend of free elastic scattering of protons from ${}^4\mathrm{He}$ is investigated.

Method: Guidance in general from the distorted-wave impulse approximation (DWIA) theory is employed. Specific focused theoretical calculations are performed.

Results: As expected, for the ($p,p\alpha$) reaction on several light target masses up to ${}^{12}\mathrm{C}$, comparable cross section and analyzing-power angular distributions resemble free ${}^4\mathrm{He}(p,p){}^4\mathrm{He}$ elastic scattering to a remarkable extent. The DWIA treatment for the ${}^{40}\mathrm{Ca}(p,p\alpha ){}^{36}\mathrm{Ar}$ reaction, however, needs a more careful selection of the distortion optical-model parameters in the $\alpha \text{−}\mathrm{Ar}$ outgoing channel. Global optical-model potentials used in the published work reproduce neither analyzing-power distribution of the ${}^{40}\mathrm{Ca}(p,p\alpha ){}^{36}\mathrm{Ar}$ reaction, nor $\alpha \text{−}{}^{36}\mathrm{Ar}$ elastic scattering cross-section angular distributions. Use of appropriate optical potentials resolves the problem.

Conclusions: The use of appropriate optical-model potentials which describe elastic scattering of $\alpha$ particles from ${}^{36}\mathrm{Ar}$ correctly appears to be crucial. The problem reported previously in the literature is resolved to a remarkable extent. There is a need to explore the two-body aspects of the quasifree ($p,p\alpha$) reaction for heavier targets further.

Figure 1

Intranuclear two-body projectile-cluster cross sections extracted from the experimental $(p,p\alpha )$ reaction data (circles) at incident energies as indicated for targets ${}^9\mathrm{Be}$ [15] and ${}^{12}\mathrm{C}$ [17, 18]. Results are displayed as a function of the two-body $p\text{−}\alpha$ center-of-mass scattering angle. The lines are smooth curves through experimental $p+{}^4\mathrm{He}$ elastic scattering data of Refs. [24, 25], respectively, at incident energies of 100 and 150 MeV.

Figure 2

Experimental analyzing-power angular distributions for the $(p,p\alpha )$ reaction on ${}^9\mathrm{Be}$ at an incident energy of 150 MeV [15], and ${}^{12}\mathrm{C}$ at 100 MeV [17, 18] (circles with statistical error bars). Results are displayed as a function of the two-body $p\text{−}\alpha$ center-of-mass scattering angle. The lines represent smooth curves drawn through experimental analyzing-power angular distributions for ${}^4\mathrm{He}(p,p){}^4\mathrm{He}$ elastic scattering from Refs. [25, 26] at the same incident energies as for the quasifree knockout reaction.

Figure 3

Experimental analyzing-power angular distributions for the $(p,p\alpha )$ reaction on ${}^{40}\mathrm{Ca}$ [19] at an incident energy of 100 MeV (circles with statistical error bars). Results are displayed as a function of the two-body $p\text{−}\alpha$ center-of-mass scattering angle. The continuous curve in (a) represent results of DWIA calculations with distorted waves derived from optical-model potentials as listed by Carey et al. [14]. For comparison an experimental analyzing-power distribution for elastic scattering of protons from ${}^4\mathrm{He}$ at the same incident energy is shown in (a) as a smooth dashed line drawn through the data of Ref. [26]. In (b) the same experimental distribution for the $(p,p\alpha )$ reaction on ${}^{40}\mathrm{Ca}$ is compared with a modified implementation of the DWIA as described in the text.

Figure 4

Energy sharing cross section distribution for the ${}^{40}\mathrm{Ca}(p,p\alpha ){}^{36}\mathrm{Ar}$ reaction as a function of the outgoing proton energy. Experimental data (circles with statistical error bars) are from Ref. [14]. The curve represents the result of a DWIA calculation as described in the text. The arrow indicates the proton energy at which the recoil momentum of the heavy residual nucleus is zero.