Measurement of neutron and proton analyzing powers on C, CH, $CH_2$ and Cu targets in the momentum region 3–4.2 GeV/c

Abstract

The analyzing powers for proton elastic scattering ($\varvec{p} A\rightarrow pX$) and neutron charge exchange ($\varvec{n} A\rightarrow p X$) reactions on nuclei have been measured on C, CH, $CH_2$ and Cu targets at incident neutron momenta 3.0–4.2 GeV/c by detecting one charged particle in forward direction. The polarized neutron measurements are the first of their kind. The experiment was performed using the Nuclotron accelerator in JINR Dubna, where polarized neutrons and protons were obtained from break-up of a polarized deuteron beam which has a maximum momentum of 13 GeV/c. The polarimeter ALPOM2 was used to obtain the analyzing power dependence on the transverse momentum of the final-state nucleon. These data have been used to estimate the figure of merit of a proposed experiment at Jefferson Laboratory to measure the recoiling neutron polarization in the quasi-elastic $^2H(\varvec{e},e'\varvec{n})$ reaction, which yields information on the charge and magnetic elastic form factors of the neutron.

Appendix: calculation of the analyzing powers

The calculation of analyzing power is based on the analysis of the two $(\varphi ,p_t)$-plots corresponding to the two different polarization modes. We denote the bin values as $N_{ij}(1),N_{ij}(2)$, where the first index, i, is related to $\varphi$ and the second one, j, is related to $p_t$.

The values of the vector analyzing power $b_j$ are obtained from a fit that minimizes the following quantity:

$$\begin{aligned} \sum _{i,j} \left( \frac{R_{ij}-b_jf(\varphi )_i}{\varDelta R_{ij}}\right) ^2, \end{aligned}$$

(4)

with

$$\begin{aligned}&R_{ij} = \frac{N_{ij}(2)-C\cdot N_{ij}(1)}{C\cdot N_{ij}(1)P(2)+N_{ij}(2)P(1)}, \end{aligned}$$

(5)

$$\begin{aligned}&\varDelta R_{ij} = \sqrt{\frac{N_{ij}(1)N_{ij}(2)}{[N_{ij}(1)+N_{ij}(2)]^3}}\cdot \frac{2}{|P(2)+P(1)|}, \end{aligned}$$

(6)

where P(k) refers to the beam polarization, $k=1,2$ relates to the polarization mode, and

$$\begin{aligned} C=\frac{I[P(2)]}{I[P(1)]} \end{aligned}$$

is the ratio of intensities (I) in the different polarization modes.

The fit is not equivalent to a number of j independent fits:

$$\begin{aligned} \sum _{i} \left( \frac{R_{ij}-b_jf(\varphi )_i}{\varDelta R_{ij}}\right) ^2 = min, \end{aligned}$$

(7)

because the parameter C is common for all j and can be taken as a free parameter. Such a fit provides reliable results due to the small correlation existing between C and $b_j$ in Eqs. (4) and (5) ($<0.5$%).

This program is included into the latest FUMILIM package, Ref. [59].