[Paper Review] Spin effects and relative momentum spectrum of two protons in deuteron charge-exchange breakup

R. Lednický, V. L. Lyuboshitz+1 more|ArXiv.org|Feb 14, 2003

Atomic and Subatomic Physics Research1 references3 citations

TL;DR

This paper investigates the charge-exchange breakup of a fast polarized deuteron on a proton target, $d + p \rightarrow (pp) + n$, using the impulse approximation to calculate the relative momentum spectrum of the two protons. It rigorously accounts for Fermi-statistics, Coulomb and strong interactions in the final state, and the deuteron's $d$-wave admixture, showing that the differential cross section at zero momentum transfer depends solely on the spin-flip amplitude of the $n+p\rightarrow p+n$ reaction, enabling separation of spin-dependent terms and their phase difference via polarization measurements.

ABSTRACT

The relation between the differential cross section of the charge-exchange breakup of a fast deuteron d+p -> (pp)+n and the differential cross section of the charge transfer process n+p -> p+n is discussed taking into account the effects of the proton identity and of the Coulomb and strong interactions of protons in the final state. The distribution of the relative momenta of the protons is found in the framework of the impulse approach. It is shown that the use of polarized initial deuterons and protons allows one to separate two spin-dependent terms in the amplitude of the charge transfer reaction n+p -> p+n at zero angle and to determine their phase difference. The influence of the deuteron d-wave state is investigated.

Motivation & Objective

• To establish a precise theoretical relation between the differential cross section of deuteron charge-exchange breakup and the $n+p\rightarrow p+n$ charge transfer reaction.
• To account for Fermi-statistics, Coulomb, and strong interactions in the final two-proton state with high accuracy.
• To investigate the influence of the deuteron's $d$-wave component on the proton momentum spectrum and polarization observables.
• To demonstrate that polarized deuteron beams on polarized proton targets allow separation of spin-dependent terms and measurement of their phase difference in the $n+p\rightarrow p+n$ amplitude.

Proposed method

• The impulse approximation is applied to the $d + p \rightarrow (pp) + n$ process, assuming short collision time compared to internal deuteron motion.
• The final two-proton wave function is constructed from the deuteron wave function and momentum transfer, incorporating Pauli exclusion via antisymmetrization.
• The Schr"{o}dinger equation is solved exactly for the two-proton system to include Coulomb and strong interactions in the final state.
• The spin structure of the $n+p\rightarrow p+n$ amplitude is decomposed into spin-nonflip and spin-flip parts, with the latter dominating at zero momentum transfer.
• The $d$-wave admixture in the deuteron is included via expansion of the deuteron wave function in terms of $s$- and $d$-wave components.
• Polarization observables are derived by projecting the two-proton state onto the singlet state due to Fermi-statistics, leading to explicit dependence on deuteron and proton polarization parameters.

Experimental results

Research questions

• RQ1 How does the two-proton relative momentum spectrum in $d + p \rightarrow (pp) + n$ depend on final-state interactions and Fermi-statistics?
• RQ2 What is the role of the deuteron's $d$-wave component in shaping the momentum spectrum and polarization effects in forward charge-exchange breakup?
• RQ3 Can the spin-flip and spin-nonflip components of the $n+p\rightarrow p+n$ amplitude be separated experimentally using polarized deuteron beams and targets?
• RQ4 How accurate is the impulse approximation when exact final-state interactions are included in the two-proton system?
• RQ5 What is the quantitative influence of the $d$-wave admixture on the differential cross section and polarization observables at zero momentum transfer?

Key findings

• The differential cross section for $d + p \rightarrow (pp) + n$ at zero momentum transfer is determined exclusively by the spin-flip part of the $n+p\rightarrow p+n$ amplitude.
• Due to Fermi-statistics, the two protons are forced into a singlet state, making the cross section sensitive only to the spin-dependent amplitude of the charge transfer process.
• The inclusion of exact final-state interactions (Coulomb and strong) improves the accuracy of the soft momentum spectrum ($k < 50$ MeV/$c$) to within a few percent.
• The $d$-wave component of the deuteron modifies the polarization observables, with the effective polarization parameters of the neutron-proton pair scaled by $\beta^2 - \frac{1}{2}\gamma^2$ and $\beta^2 + \frac{1}{10}\gamma^2$.
• Polarized deuteron beams on polarized proton targets allow, in principle, the separation of two spin-dependent terms in the $n+p\rightarrow p+n$ amplitude and the determination of their phase difference.
• Glauber corrections are estimated to be small (<5%) at low relative momenta but may reach ~20% at $k > 100$ MeV/$c$, indicating a need for inclusion in high-momentum regions.