https://link.springer.com/content/pdf/10.1007/s41365-021-00944-5.pdf

Further developments of a multi-phase transport model for relativistic nuclear collisions

The reaction {sup 3}He({pi}{sup +},{ital pp}){ital p} was measured at {ital T}{sub {pi}}=350 and 500 MeV in a kinematically complete experiment. Separate contributions from two-body and three-body pion absorption are clearly seen in recoil momentum distributions. The two-body angular distributions closely follow the shape of the free {pi}{ital d}{r arrow}{ital pp} cross section, although the number of deuterons estimated from the two-body yield is larger than the value 1.5 expected from isospin coupling and observed previously at lower energies. Comparison with a simple impulse approximation model suggests some of the enhancement may arise from binding of the quasideuteron, although absorption on {ital T}=1 ({ital pn}) pairs and the higher density of {sup 3}He may also be a factor. The strength of the three-body component falls off with bombarding energy with roughly the same slope as for the two-body component, and accounts for {approx}45% of the total absorption cross section, a larger fraction than reported previously below the (3,3) resonance. The three-body matrix element {vert bar}{ital M}{sub 3}{vert bar}{sup 2} displays an angular dependence at both energies which is suggestive of initial-state interactions. No evidence of final-state interactions is seen.

Reaction 3He( pi +,pp)p at T pi =350 and 500 MeV.

Precision measurements of the analyzing powers for the reaction p/sub pol/+p..-->..d+..pi../sup +/ have been made at approx. =550, 600, 650, 700, and 800 MeV. The data have been analyzed in terms of Legendre polynomials. It is found that excitation functions for both even and odd Legendre coefficients exhibit very similar resonant behaviors. It is concluded that the triplet amplitudes are as strongly dominated by the ..delta..(1232) as the well-known singlet amplitude, /sup 1/D/sub 2/, and that the data do not exhibit any anomalous behavior suggestive of dibaryon resonances.

Energy Variation of the Analyzing Power in the Reaction p pol +p-->d+π +

Unified description of hadronic and electromagnetic reactions of the two-nucleon system

The energy dependence of pp to d pi is calculated for the Delta -resonance range (400<or approximately=Tp<or approximately=800 MeV) extending a preceding relativistic study at Tp=578 MeV. The leading graph is the exchange of a pion and a nucleon. Input are elastic pi N amplitudes (off shell) and relativistic pi NN and dpn vertex functions. Single-neutron exchange is added and distortion factors for the pp and pi d channels are applied. Only moderate sensitivity to variations of the input is found. Comparing with the existing body of data, good agreement is found for the total and differential cross sections. The relative spin observables are reproduced to within 10% of the possible range of variation. The remaining discrepancies can be traced to insufficient strength of pp spin-triplet channels.

Energy dependence of relativistic predictions for pp→dπ in the Δ-resonance region

We have measured the reactions $^{3,4}\mathrm{He}({\ensuremath{\pi}}^{\ensuremath{-}}, n)^{2,3}\mathrm{H}$ at ${T}_{\ensuremath{\pi}}=285, 428, 525, \mathrm{and} 575$ MeV over an angular range ${\ensuremath{\theta}}_{n}=18\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}134\ifmmode^\circ\else\textdegree\fi{}$ in the center-of-momentum frame, and the reaction $^{3}\mathrm{He}({\ensuremath{\pi}}^{\ensuremath{-}}, {\ensuremath{\pi}}^{0})^{3}\mathrm{H}$ at ${T}_{\ensuremath{\pi}}=285, 428, \mathrm{and} 525$ MeV over an angular range ${\ensuremath{\theta}}_{{\ensuremath{\pi}}^{0}}=60\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}140\ifmmode^\circ\else\textdegree\fi{}$. The pion absorption is found to proceed by a two-nucleon mechanism, with an energy dependence consistent with the formation of an $I=\frac{1}{2}$ resonance in the intermediate state. The pion single-charge exchange is discussed within the framework of the optical and Glauber models, and the dependence on the $^{3}\mathrm{He}$ electromagnetic form factors is discussed. We also examine the isospin dependence of the $\ensuremath{\pi}$-nuclear Hamiltonian.NUCLEAR REACTIONS $^{3,4}\mathrm{He}({\ensuremath{\pi}}^{\ensuremath{-}}, n)^{2,3}\mathrm{H}$, ${T}_{\ensuremath{\pi}}=285\ensuremath{-}575$ MeV, ${\ensuremath{\theta}}_{n}=18\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}134\ifmmode^\circ\else\textdegree\fi{}$; and $^{3}\mathrm{He}({\ensuremath{\pi}}^{\ensuremath{-}}, {\ensuremath{\pi}}^{0})^{3}\mathrm{H}$,, ${T}_{\ensuremath{\pi}}=285\ensuremath{-}525$ MeV, ${\ensuremath{\theta}}_{{\ensuremath{\pi}}^{0}}=60\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}140\ifmmode^\circ\else\textdegree\fi{}$; measured $\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}$; discussed reaction mechanism, effects of form factors.

/sup 3,4/He(. pi. /sup -/,n)/sup 2,3/H and /sup 3/He(. pi. /sup -/,. pi. /sup 0/)/sup 3/H at 285--575 MeV

Differential cross sections were measured for the reaction, ${\ensuremath{\pi}}^{+}d\ensuremath{\rightarrow}\mathrm{pp}$, at seven energies, 80, 100, 140, 182, 230, 323, and 417 MeV. Sufficient data were taken for a 1% statistical uncertainty at eleven different angles for most of these energies. The elastic ${\ensuremath{\pi}}^{+}p$ reaction was used to normalize the ${\ensuremath{\pi}}^{+}d\ensuremath{\rightarrow}\mathrm{pp}$ data. Legendre polynomial fits of the data are presented. The increased accuracy and energy of these data require an addition of a ${{cos}^{6}\ensuremath{\theta}}^{*}$ term in the traditional low energy form of the differential cross section: $C(A+{{cos}^{2}\ensuremath{\theta}}^{*}+B{cos}^{4}{\ensuremath{\theta}}^{*})$. The coefficients, $A$ and $B$, are used to compare the present data with a survey of previous experiments and the theoretical work of Niskanen. Agreement is usually within uncertainties, but some diagreement remains even among recent experiments.NUCLEAR REACTIONS $d(\ensuremath{\pi},pp)$, $E=80\ensuremath{-}417$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$; calculated Legendre polynomial fits; compared to earlier work.

Differential cross section for the π + d → pp reaction from 80 to 417 MeV

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/sup 3,4/He(. pi. /sup -/,n)/sup 2,3/H and /sup 3/He(. pi. /sup -/,. pi. /sup 0/)/sup 3/H at 285--575 MeV

Differential cross section for the π + d → pp reaction from 80 to 417 MeV