Final Nucleon Research Articles

Antiprotonic deuterium annihilation into two spin-zero mesons and a nucleon

The decay of antiprotonic deuterium into two spin-zero mesons and a nucleon is calculated analytically in terms of threshold values of the helicity amplitudes for the two-particle annihilation process. After averaging over the final state nucleon spin projection, we obtain the differential decay width as a function of the nucleon momentum and its direction with respect to the relative momentum of the two mesons. Both the angular distribution and momentum dependence is studied in detail for the case of two pions for each fine structure state of the 2P-level. The characteristic behaviour is discussed and approximate selection rules established. Numerical results are given based on Coulomb atomic wavefunctions and on helicity amplitudes from in-flight data. We outline a procedure to determine threshold values of the helicity amplitudes from measurements of anti-protonic deuterium decay. It is in principle, and perhaps in practice, possible to completely determine four of the amplitudes with their relative phases. This is, to our knowledge, the only process where this information is apparently accessible.

MEDIUM EFFECTS ON KNOCKOUT OF DEEPLY BOUND NUCLEONS

MEDIUM EFFECTS ON KNOCKOUT OF DEEPLY BOUND NUCLEONS

Spectral function of the p3/2 nucleons in 6Li.

The internal momentum spectrum of p+n pairs produced in the /sup 6/Li(/alpha/,2/alpha/)pn reaction at 118 MeV was measured for those pairs whose c.m. was at rest after the reaction. This spectrum was calculated with a plane wave impulse approximation model, having no free parameters, for two p/sub 3/2/ nucleons initially bound in a harmonic oscillator potential. The calculation gave reasonable agreement with measured values of both the normalization of the spectrum and its dependence upon the p+n internal energy, when the final nucleons were described by Yamaguchi, Paris, or Reid wave functions and the data were reduced by the final-state energy prescription. Less satisfactory fits were obtained with p+n plane waves and/or the initial-state energy prescription.

Scaling variables for coincident electron scattering

The cross section for quasi-free nucleon knockout by inelastic electron scattering (e, e′N) is shown to depend on two scaling variables: y used in inclusive (e, e′) reactions and z = ( p f / M) sin θ p , the transverse component of the initial and final nucleon velocity. We show that for given y and z the coincidence cross section is determined by a single spectral function of y 2 + z 2. A sum rule relates the spectral function to the nuclear response measured in inclusive reactions.

Pion production from hydrogen bombarded by polarized protons at intermediate energies

Angular distributions of differential cross sections and polarization analyzing powers are presented for the 1 H( p , π +) 2 H reaction for incident proton energies between 305 and 425 MeV. The pions were detected in a single-arm configuration employing a magnetic spectrograph. Pions associated with both bound (deuteron) and unbound final nucleon states were detected simultaneously. These data provide the first indication of the contribution of d-wave pions in this energy region. Some data concerning the analyzing power for the inclusive pions from the 1 H( p , π +) pn reaction are also presented. An interesting feature of these results is the similarity of the analyzing power for the 1 H( p , π +) pn reaction (when the relative kinetic energy in the pn system is 10–20 MeV) to that for 1 H( p , π +) 2 H .

(π,πn) puzzle above the (3,3) resonance

We calculate the corrections due to pion production, Fermi motion, and the Pauli principle on the ratio of $^{12}\mathrm{C}({\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}},\ensuremath{\pi}N)^{11}\mathrm{C}$ total cross sections for particle-stable final states. These corrections are important above 400 MeV. When they are combined with those estimated earlier for final state nucleon charge exchange interactions, good agreement is obtained with the data, which cover the energy region from 40 to 550 MeV.[NUCLEAR REACTIONS $^{12}\mathrm{C}({\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}},\ensuremath{\pi}N)^{11}\mathrm{C}$, calculated ratio of knockout cross sections 40 - 1000 MeV, impulse approximation, nucleon final state charge exchange interactions, pion production corrections, Pauli principle and Fermi motion effects.]

Equilibration in relativistic nuclear collisions. A Monte Carlo calculation

A relativistic Monte Carlo calculation of the nucleus-nucleus interaction in the GeV range is presented. The interaction process is described as a sequence of classical, binary, on-shell baryon-baryon collisions. Pion production is introduced via the formation of Δ-resonances. The latter are given a definite mass and a lifetime against pion emission larger than the collision time. They are, however, assumed to scatter or disappear in collisions with nucleons. At the end of the collision process, they are allowed to decay. The model is used to study the equilibration during a head-on collision between two 40 Ca nuclei. The system is found to be compressed up to a time 6–8 fm/ c and to decompress very rapidly. The final nucleon and pion momentum distributions are not completely thermalized. They are, however, tentatively described by effective temperatures. The rapidity distributions show larger temperatures than the perpendicular momentum distributions. Also, nucleon temperatures are generally larger than pion temperatures. The theoretical transverse temperatures and the pion multiplicities agree fairly well with the experimental data. The role of the delta particles is investigated. It is shown that the delta production quickens the equilibration process by transforming longitudinal kinetic energy into mass energy. Furthermore, it favours high compression of the system. Non-central collisions are studied. The results are consistent with the concept of geometrical separation between participant and spectator nucleons. However, our model predicts more transparency than the so-called fireball model. The participant part is shown to decompress very rapidly, while the spectator parts are slightly kicked off for intermediate impact parameters. Finally, some results are shown for the case of a head-on collision of a 20 Ne projectile by a 60 Ni target. A strong shock wave propagates into the target for several fm/ c , after which all the matter is dispersed.

Space-time structure of weak neutral currents: (II). Elastic scattering

The elastic scattering of neutrinos and antineutrinos on nucleons in which the initial and final nucleon polarizations are measured, is studied from the point of view of the space-time properties of the currents. Structure functions are defined and experimentally measurable quantities which can be usual to disentangle the Lorentz structure of the currents are given. Second class current effects are also examined.

Symmetry Relations Among Pionization Cross Sections

From Mueller's Regge analysis of the pionization region, symmetry relations to order ${s}^{\ensuremath{-}\frac{1}{4}}$ among invariant cross sections at $x=0$, in which a final pion is observed, are derived. SU(3) and quark universality are assumed to relate the Regge residues at the projectile-Reggeon vertex. There is good agreement with experiment to 10-50% indicating that the approximate symmetry pattern at nonasymptotic energies is that of total cross sections. The rising of the invariant cross sections to their asymptotic forms as $c\ensuremath{-}b{s}^{\ensuremath{-}\frac{1}{4}}$ can be understood in terms of known $j$-plane singularities if the $f$-Pomeron central vertex ${g}_{\mathrm{fP}}^{{\ensuremath{\pi}}^{+}}({{q}_{\ensuremath{\perp}}}^{2})l0$. Symmetry relations valid for final kaons and nucleons and for both the pionization and the target-fragmentation regions are also given.

Amplitude Analysis of πNBackward Scattering at 6 GeV/cand the Peripherality

An amplitude analysis of πN backward scattering is performed at plab=6 GeV/c from the viewpoint of the peripherality (the dominance of peripheral waves). A functional form Aexp (Bu')Jν(R√-u') is assumed for Im Δ+± and Im N+- where Δ and N denote Iu=3/2 and Iu=1/2 exchange amplitudes, respectively, and ++(+-) denotes the final and initial nucleon helicities and corresponds to ν=1 (ν=0). The resultant Im N++ is shown to be consistent with the above Bessel function representation, too. The parameters B and R can be taken as B ∼1.5 (GeV/c)-2 and R ∼1 fm commonly for Im Δ+± and Im N+±, of which values are consistent with those obtained previously by amplitude analyses of various meson-baryon scattering and photo-vector-meson production process in the forward region. The results for Δ++ and N+- are consistent with the Regge phase of Δδ trajectory for u \gtrsim-0.15 (GeV/c)2 and of Nα trajectory for u \gtrsim-0.6 (GeV/c)2, respectively. The spin rotation parameters for π±p elastic scattering and the polarization for charge exchange scattering in the backward direction are given as predictions.

Effects of exchange, final-state interactions, and distorted waves in the reactions 2H( 3He, 3H p)p and 2H( 3He, 3He p)n

A systematic treatment of the 2H( 3He 3H p)p and 2H( 3He, 3He p)n reactions by the Born approximation is carried out for conditions at which Warner et al. (WBDFF) observed spectator peaks juxtaposed with final-state interaction (FSI) effects. WBDFF fitted the spectator peaks with plane-wave Born approximation (PWBA) using two interaction matrix elements, but encountered difficulties in predicting relative yields, absolute cross sections and the shape modifications due to FSI. We first add full antisymmetry to PWBA in order to account properly for relative yields. This step connects all reaction mechanisms (break-up, knock-out, and pick-up), and their seven distinct interaction matrix elements. Next, the FSI shape modifications are successfully accounted for by using scattering wave functions for the final free nucleons in one of the matrix elements and by inferring the FSI properties in all matrix elements through a scattering-length approximation. When juxtaposed to simple spectator poles the FSI effects are shown to be interesting interference dips and amplitude peaks which are dominated by the sign and size of the singlet and triplet nueleon-nucleon scattering lengths. Finally, the effects of distorted waves on absolute cross sections are briefly discussed.

Tests of Hadronic Bremsstrahlung Production at Large Nucleon Momentum Transfer

It is suggested that hadronic bremsstrahlung may become the dominant production process in nucleon-nucleon reactions at large momentum transfer to the final nucleons. Correlation tests are proposed to distinguish the model from other models of inclusive processes.

Inclusive polarization, two-particle correlation and triple-reggeon phenomenology

The single-particle spectrum in the inclusive reaction induced by a polarized particle, and the polarization of the final nucleon are expressed in terms of the helicity-dependent forward scattering amplitudes of three particles. These spin-dependent analyses allow us to separate some of the two-particle correlation functions kinematically. A triple Regge picture is applied to the reaction π+N→ π( η)+anything.

The transverse and longitudinal cross sections for electroproduction of pions near the Δ(1236)-isobar

The reaction e+ p→ e′+ N ∗ was studied for four momentum transfers up to 2.34 (GeV/ c) 2 in the region of the 1236 MeV isobar. An analysis of the data in terms of the cross sections σ T and σ L for the absorption of transverse and longitudinal photons is given for invariant masses of the final pion nucleon system W=1.220 GeV and W=1.350 GeV.

(p, p) and (n, n) scattering lengths from ( 3He, d) and (t, d) reactions

The triton energy spectrum from the reaction 3He(d, t)2p and the 3He spectrum from t(d, 3He)2n were studied to determine the range of applicability of the Watson-Migdal (W-M) theory of final state interactions as a means of extracting two-nucleon scattering lengths from such experiments. By comparing the predictions of W-M theory to more exact calculations, it was found that the value of scattering length predicted is, in general, too large in magnitude. For the pick-up process where the two final state nucleons originate in the relatively compact t or 3He wavefunction, the usefulness of W-M theory is marginal; for charge exchange where the final state nucleons originate in the deuteron, the W-M prediction is substantially in error. These results are in complete agreement with Watson's original statement of the problem.

Nucleon polarization in elastic lepton or antilepton production by high-energy neutrino or antineutrino

The degrees of polarization of the final nucleon in the processes ν+n→p+μ− and\(\bar \nu + p \to n + \mu ^ + \) are calculated for an unpolarized target nucleon. Three models for this elementary interaction are considered as numerical examples. The degrees of polarization, two transverse and one longitudinal, turn out to be crucial observables to distinguish these models.

Single pion production in proton-proton collisions according to the one-particle exchange model

Single pion production in nucleon-nucleon collisions is calculated in the one-pion exchange approximation. All the possible diagrams of this kind are calculated in the ≪ pole ≫ approximation discussed in the text: also the interferences between them are taken into account. The lab. energy spectra of the final nucleons are calculated and compared with the experimental data at 2.85 GeV. This comparison shows a remarkably good agreement for small values of the squared 4-momentum, of the virtual pion. For higher values the qualitative behaviour is still reproduced, but the theoretical absolute values are larger than the experimental ones.

Positive Pion Production inp−pCollisions at 420 Mev with Polarized Protons

The asymmetry in the production of positive $\ensuremath{\pi}$ mesons in $p\ensuremath{-}p$ collisions has been studied, using a 420-Mev, 62% polarized proton beam from the Chicago synchrocyclotron, with nuclear emulsions as the pion detector. The asymmetry at 65\ifmmode^\circ\else\textdegree\fi{} in the laboratory for the entire spectrum above 20 Mev in the center-of-mass system is found to be 0.151\ifmmode\pm\else\textpm\fi{}0.021, in the direction opposite the elastic scattering that produced the polarized beam. In the region of the spectrum above 40 Mev, results are consistent with those found by other authors for the reaction $p+p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}+d$; at lower energies where pions associated with final nucleon $p$ states become predominant, the asymmetry decreases rapidly and may possibly reverse.

Deuteron-Photospaltung bei niedrigen Energien

Low energy photodisintegration of the deuteron is useful for obtaining information about mesonic corrections to the magnetic dipole operator. Therefore, on the basis of a phenomenological theory of the photodisintegration process, the differential cross section and the polarization of the final state nucleons are calculated. TheD-state admixture of the ground state is taken into account. Using information from neutron-proton scattering, the dependence of the magnetic dipole transition on the force parameters is investigated in detail.

Pion-Pion Interaction and Pion-Nucleon Scattering

Pion-pion interaction is analyzed by using the dispersion relation for pion-nucleon scattering obtained by keeping the momentum transfer between an initial pion and a final nucleon constant. In order to take into account the singularity of two-pion threshold in the dispersion relation, the dispersion relation may be regarded as an integral equation for pion-nucleon scattering amplitude with the kernel of a pion-pion scattering amplitude. When this solution is compared with experiments on pion-nucleon scattering, it is found that the unknown quantity in the dispersion relation is only a pion-pion scattering amplitude. Therefore, if pion-pion amplitude is expressed in terms of an unknown parameter such as . scattering length, then this value can be determined via dispersion relation. Thus we are led to the following conclusion: In the isotopic spin state 1=0 (S-wave) of pion-pion system pion-pion interaction is attractive and the scattering length is of the order of one pion Compton wavelength, while in the isotopic spin state 1=1 (P-wave) of pion-pion state a definite conclusion could not be obtained. Finally the possibility of explaining the momentum dependence of pion-nucleon phase shift a 13 related to the pion-pion interaction is briefly discussed.