Deuteron breakup $\mathit{pd}\to \{\mathit{pp}\}{}_{s}n$ with forward emission of a fast ${}^1{S}_0$ diproton

The deuteron breakup reaction $\mathit{pd}\to \{\mathit{pp}\}{}_{s}n$, where $\{\mathit{pp}\}{}_s$ is a fast proton pair emitted in forward direction with small excitation energy $E_{\mathit{pp}}<3$ MeV, has been studied at proton beam energies of $0.5–2.0$ GeV using the ANKE spectrometer at COSY-Jülich. The differential c.m. cross sections are measured in complete kinematics and provide angular distributions of the neutron emission angle in the range ${\theta }_n={168}^{°}$–${180}^{°}$, the dependence on beam energy at ${\theta }_n={180}^{°}$, angular distributions of the direction of the proton in the $\mathit{pp}$ rest frame, and distributions of the excitation energy $E_{\mathit{pp}}$ of the proton pair. The obtained data are analyzed on the basis of theoretical models previously developed for the $\mathit{pd}\to \mathit{dp}$ process in a similar kinematics and properly modified for the diproton channel in $\mathit{pd}\to \{\mathit{pp}\}{}_{s}n$. It is shown that the measured observables are highly sensitive to the short-range part of the nucleon-nucleon interaction.

Figure 1

Top view of the ANKE setup at COSY, showing the components used in the present experiment. The positions of the dipole magnets D1, D2, and D3; the cluster target spot; and the forward detector system (FD) are shown. The $\mathit{xyz}$ coordinate system is indicated.

Figure 2

Single-particle acceptance of the ANKE forward detector at $T_p=0.8$ GeV, showing the polar angle projection ${\theta }_{\mathit{xz}}$ as a function of particle momentum. The curves show the kinematical loci for different processes (the detected particles are labeled in boldface). For the $\mathit{pd}\to \{\mathit{pp}\}{}_{s}n$ reaction, the dashed box corresponds to $E_{\mathit{pp}}<3$ MeV and the solid curve is for $E_{\mathit{pp}}=0$.

Figure 3

Recorded momentum distributions at $T_p=0.8$ GeV: protons with ${\mathrm{H}}_2$ target (thin line), protons with ${\mathrm{D}}_2$ target (thick line), deuterons with ${\mathrm{D}}_2$ target (filled histogram). (The relative normalization of the distributions is arbitrary.)

Figure 4

Upper panel: Kinematics of the $\mathit{pd}\to \{\mathit{pp}\}{}_{s}n$ reaction in the $\mathit{pd}$ c.m. system. Lower panel: ${\mathrm{P̂}}_p$ and ${\mathrm{P̂}}_{\mathit{pp}}$ denote the directions of the incoming beam proton and the outgoing proton pair, respectively. In the rest frame of the proton pair, protons have the momenta $\mathbf{k}$ and $-\mathbf{k}$; polar and azimuthal angles ${\theta }_k$ and ${\varphi }_k$ are indicated.

Figure 5

Resolution of the kinetic energy $E_{\mathit{pp}}$ of proton pairs, obtained from a simulation.

Figure 6

Two-dimensional acceptance factor $A({\theta }_{\mathit{pp}},E_{\mathit{pp}})$ at $T_p=0.6$ GeV.

Figure 7

Distribution of double-particle events showing the measured $\Delta t_{\mathrm{meas}}$ vs the calculated time differences $\Delta t_{\mathrm{calc}}$ at $T_p=0.5$ GeV.

Figure 8

Missing-mass distributions of two-particle events at three beam energies. The thin line shows all events, the thick line corresponds to proton pairs selected by the time-difference $\Delta t$ criterion (Fig. 7), and the filled histograms show proton pairs with $E_{\mathit{pp}}<3$ MeV.

Figure 9

Momentum correlation of two particles detected in the FD at beam energies of 0.5, 1.1, and 1.97 GeV. Loci populated by events from the following processes are indicated: $\mathit{pd}\to \mathit{ppn}$ (A), quasifree $\mathit{pN}\to \mathit{pp}\pi$ (B), $\mathit{pd}\to d{\pi }^{+}n$ (C), $\mathit{pd}\to {}^{3}H{\pi }^{+}$ (D), and quasifree $\mathit{pp}\to \mathit{pn}{\pi }^{+}$ (E). The upper panels show all pairs of particles, while the lower ones depict proton pairs selected by the time-difference $\Delta t$ criterion. The distributions were symmetrized with respect to the bisecting line $p_1=p_2$.

Figure 10

Differential cross section $d\sigma /d{E}_{\mathit{pp}}$ as a function of $E_{\mathit{pp}}$, integrated in the interval $\cos {\theta }_{\mathit{pp}}=0.98$–1 and ${\varphi }_{\mathit{pp}}=0$–$2\pi$. The solid lines correspond to the Migdal-Watson approach, and the dotted lines depict phase-space distributions.

Figure 11

Dependence of the differential c.m. cross section on $\cos {\theta }_k$. The curves show Legendre polynomial fits using Eq. (3); their parameters are listed in Table .

Figure 12

Dependence of the differential c.m. cross section of the $\mathit{pd}\to \{\mathit{pp}\}{}_{s}n$ reaction on the neutron emission angle ${\theta }_n$ in the c.m. system for the interval $E_{\mathit{pp}}=0$–3 MeV. The lines represent linear fits in the interval $\cos {\theta }_n=-0.985$ to $-1.00$.

Figure 13

Energy dependence of the differential c.m. cross sections of the deuteron breakup $\mathit{pd}\to \{\mathit{pp}\}{}_{s}n$ at ${\theta }_n={180}^{°}$ and of backward $\mathit{pd}$ elastic scattering ([38, 44, 45, 46, 47, 50] and Refs. therein). The previously obtained data of Ref. [25] are shown by open circles ($○$), and the new data are shown by bullets ($•$). The solid line represents a quadratic fit to $\log (d\sigma /d\Omega )$ of the $\mathit{pd}\to \mathit{dp}$ data, the dashed line is obtained by scaling the solid line by a factor $r=8.8\times {10}^{-3}$, introduced in Eq. (4).

Figure 14

Mechanisms included in the $\mathrm{ONE}+\mathrm{SS}+\mathrm{\Delta }$ model of the $\mathit{pd}\to \{\mathit{pp}\}{}_{s}n$ reaction: (a) one-nucleon exchange within the plane-wave Born approximation (ONE), (b) single scattering (SS), and (c) double $\mathit{pN}$-scattering with excitation of the $\Delta$ or ${\mathrm{N}}^{*}$ isobar ($\Delta$). Rescatterings within the distorted-wave Born approximation (DWBA) are shown for ONE in the initial (d), final (e), and initial plus final (f) states.

Figure 15

Excitation energy $E_{\mathit{pp}}$ of proton pairs from the $\mathit{pd}\to \{\mathit{pp}\}{}_{s}n$ reaction. The data were summed in the interval $T_p=0.5$–1.4 GeV. The curves show fits with the $\mathrm{ONE}+\mathrm{SS}+\mathrm{\Delta }$ approximation (solid line) and the Migdal-Watson approach (dashed line).

Figure 16

Differential c.m. cross section averaged over the angular interval ${172}^{°}$–${180}^{°}$ vs beam energy [26]. The curves are the result of calculations using the CD-Bonn $\mathit{NN}$ potential with the ONE (dashed line) and $\Delta$ mechanisms (solid thin line), both without distortions and Coulomb effects. The $\mathrm{ONE}(\mathrm{DWBA})+\mathrm{SS}+\mathrm{\Delta }$ is the dotted line, and the ONE(DWBA) $+\Delta$ (solid thick line) contributions are obtained with a Coulomb suppression factor of 0.83 [26]. The previously obtained data of Ref. [25] are shown by open circles ($○$), and the new data are shown by bullets ($•$). The upper scale shows the internal momentum $q$ of the nucleons in the deuteron for ONE at ${\theta }_n={180}^{°}$.

Figure 17

Angular dependence of the differential c.m. cross section at $0.5$ GeV. The curves show the results of calculations within the $\mathrm{ONE}(\mathrm{DWBA})+\mathrm{SS}+\mathrm{\Delta }$ approach using the CD-Bonn $\mathit{NN}$ potential without Coulomb interaction: ONE (dashed line), ONE(DWBA) (dashed-dotted line), $\Delta$ (solid thin line), $\mathrm{ONE}(\mathrm{DWBA})+\mathrm{SS}+\mathrm{\Delta }$ (dotted line), and $\mathrm{ONE}(\mathrm{DWBA})+\mathrm{\Delta }$ (solid thick line). The Coulomb repulsion in the $\mathit{pp}$ system, which would scale all the curves by a factor of 0.83, is not introduced here.

Figure 18

Angular dependence of the differential c.m. cross section for different beam energies. The curves are for the $\mathrm{ONE}(\mathrm{DWBA})+\mathrm{SS}+\mathrm{\Delta }$ description. The results of the calculations are scaled at $1.4$ and $1.97$ GeV by factors of 0.5 and 0.7, respectively. The Coulomb repulsion in the $\mathit{pp}$ system, which would scale all the curves by a factor of 0.83, is not introduced here.

Figure 19

Mechanisms of the $\mathit{pd}\to \mathit{dp}$ (a, c) and $\mathit{pd}\to \{\mathit{pp}\}{}_{s}n$ (b, d) processes for the OPE-I (a, b) and OPE-II (c, d) models.

Figure 20

Differential cross section $\ln (d\sigma /\mathit{dt})$ as a function of $\ln (s)$ for $\mathit{pd}$ backward elastic scattering and the $\mathit{pd}\to \{\mathit{pp}\}{}_{s}n$ reaction. The previously obtained data of Ref. [25] are shown by open circles ($○$), and the new data are shown by bullets ($•$). The fits in the range 0.95–2.0 GeV for $\mathit{pd}$ backward elastic scattering and $\mathit{pd}\to \{\mathit{pp}\}{}_{s}n$ yield exponents of $n=11.70\pm 0.32$ (${\chi }^2/\mathrm{ndf}=18/9$) and $n=11.88\pm 0.53$ (${\chi }^2/\mathrm{ndf}=56/4$), respectively. The upper scale indicates the incident proton beam energy.