Acceptance dependence of correlation investigation

The acceptance factorεacc was defined in the three-dimensional space of (k_Y,E_rel,cosθY). In this subsection, the behavior of theεaccis discussed in the(k_Y,E_rel)- and (cosθY,E_rel)-space.

Figure 5.17, the bottom panel of Fig. 5.18, and the bottom panel of Fig. 5.19 show the evaluated experimental acceptances of the present setup as a function of the relative energyE_rel, the internal momentumk_Y, and the opening angle cosθY, respectively.

The acceptance drastically dropped with increasing the internal momentum k_Y, as shown in Fig. 5.18. It was due to the small acceptance for the recoil particles (Sec. 5.11.2). The RPD and the WINDS were placed so as to maximize the acceptance for the events with internal momentum of k_Y = 0, which has a same kinematics with then-pelastic scattering. In such a condition, the scattering angles of the recoil proton and the knocked-out neutron are perfectly correlated; e.g., when the recoil proton has an azimuthal angle ofϕp, the knocked-out neutron has an azimuthal angle ofϕn = ϕp+π. Thus, most of the events with the recoil proton detection in the RPD resulted in the detection of the knocked-out neutron in the WINDS simultaneously, because the azimuthal angular coverage of the WINDS and the RPD were|ϕn| ≲ ±20 degrees and|ϕp+π|≲±20 degrees, respectively. However, by increasing the internal momentumk_Y, in other words, by taking into account the Fermi motion of the knocked-out neutron, the scattering angle between the recoil proton and the knocked-out neutron gradually loses the correlation. In such a case, the knocked-out neutron is often out of the acceptance of the WINDS even if the recoil proton is detected in the RPD, and vice versa.

Although the internal momentum k_Y dependence of the acceptance was large, it had no singularity and the behavior was smooth as shown in Fig. 5.18. Thus, the acceptance could be compensated by dividing the obtained spectrum by the acceptance factorεacc.

As shown in Fig. 5.19, the opening angle cosθY dependence of the acceptance was moderate as compared with the internal momentumk_Y dependence. It was because the definition of the opening angle was not fixed at the laboratory frame; The opening angle was derived from the internal momentumk_Y and the relative momentumK_Y by employing the Eq. (2.7). Although the directions of these two momentum vectors were partly limited by the geometrical acceptance, basically they could head in any direction, and therefore, the opening angle between these two momentum vectors could have any value.

The acceptance had a larger value at cosθY = 1, i.e. θY = 0 degrees, especially with the higher relative energy E_rel. This enhancement came from events where the directions of the both momentum vectors k_Y and K_Y aligned to the beam direction. It could be qualitatively understood as follows. When the yz-component of the internal momentum k_Y was the zero, the probability that both the recoil proton and the knocked-out neutron were detected in the RPD and the WINDS, was maximized because the azimuthal angles of the recoil particles had the same correlation with then-p elastic scattering as ϕn = ϕp +π. Thus, the acceptance is maximized when the direction of the k_Y was parallel or anti-parallel to the beam direction. By

Fri Nov 4 16:13:56 2016

(%)

ε Acceptance

0 0.2 0.4 0.6 0.8 1 1.2

-1

]

Y

[fm k Internal momentum

0 0.5 1 1.5 2 2.5

[MeV]

E Relative energy

0 2 4 6 8 10

Fri Nov 4 16:13:56 2016

-1

]

Y

[fm k Internal momentum

0 0.5 1 1.5 2 2.5

(%)

ε Acceptance

0 0.5 1

1.5

Erel

0<

<2 Erel

1<

<3 Erel

2<

<4 Erel

3<

<5 Erel

4<

<6 Erel

5<

<7 Erel

6<

<8 Erel

7<

<9 Erel

8<

<10 Erel

9<

Figure 5.18: Evaluated experimental acceptance as a function of the internal momentum k_Y. (Top) Two-dimensional plot of the relative energy E_rel versus the internal momentumk_Y. (Bot-tom) The projection onto the internal momentumk_Y distribution at every 1 MeV.

Wed Nov 9 15:12:39 2016

(%)

ε Acceptance

0 0.1 0.2 0.3 0.4 0.5 0.6

θ

Opening angle cos

-1 -0.5 0 0.5 1

[MeV]

E Relative energy

0 2 4 6 8 10

Wed Nov 9 15:12:39 2016

θ

Opening angle cos

-1 -0.5 0 0.5 1

(%)

ε Acceptance

0 0.2 0.4 0.6 0.8

Figure 5.19: Evaluated experimental acceptance as a function of the opening angle cosθY. (Top) Two-dimensional plot of the relative energyE_relversus the opening angle cosθY. (Bottom) The projection onto the opening angle cosθY distribution at every 1 MeV. The color scheme is same as Fig. 5.18.

comparing the parallel and the anti-parallel cases, the angular acceptance was maximized in the former case, because stronger Lorentz boost focused the trajectories of the recoil particles into the effective areas. This tendency was enhanced when the magnitude k_Y was large. In the same manner, the relative momentumK_Y tended to be parallel to the beam direction due to the forward-focused acceptance of the NEBULA used for the decay neutron detection. Therefore, the directions of the k_Y and the K_Y tended to be parallel to the beam direction, when their magnitudes were large. It should be noted that the relative energyE_relwas directly connected to the relative energyK_Y as(E_rel+M_Y)²= K_Y²+M_Y², where theM_Y denotes the reduced mass of the decay neutron and the heavy fragment⁹Li. Thus, the directions of thek_Y and theK_Y tended to be parallel to the beam direction at higher relative energy region. This tendency disappeared at lower relative energy region, as shown in Fig. 5.19.

In common with the internal momentum k_Y, the opening angle θY dependence of the acceptance was also smooth and had no singularity. Thus, the acceptance could be compensated by dividing the obtained spectrum by the acceptance factorεacc.

In conclusion, the acceptance depended on the important observables, the internal momen-tumk_Y and the opening angleθY, but acceptance was smooth and had no singularity. The relative energyE_reldependence of the acceptance was also smooth and had no singularity (Sec. 5.11.3).

Therefore it could be corrected for by employing Eq. (5.46). This correction was applied for further analysis in Chapter 6.