Inclusive Reactions Research Articles

An analytic theory of inclusive high-energy atomic reaction cross sections

We present a first Born approximate method for evaluating cross sections for collisions of one-electron projectile ions with one-electron target atoms. We consider those reactions in which the projectile electron is excited to a specific state but no measurement is made of the target electron in regard to its final disposition. Comparison with accurate first Born calculations is made. The approximation scheme involves evaluation of a one-dimensional integral. Explicit analytic forms are given for the asymptotic region. The method is applied to shed light on an interesting result obtained from the static mean field model.

Super-high-energy neutrino spectra in the atmosphere derived from the latest JACEE, MSU, SOKOL and CRN primary spectrum usingZ-factors for p-air collisions estimated from Fermi national accelerator data

The absolute spectra of atmospheric neutrinos in the vertical direction and at large zenith angle have been estimated directly from the primary cosmic-ray nucleon spectrum based on the latest JACEE, MSU, SOKOL and CRN data surveyed by Swordy. The Fermi National Accelerator Laboratory results for pp→K±X, pp→K±X and pp→pX inclusive reactions have been used for theZ-factor calculations for meson production and these were modified for p-air and A-A collisions. The derived muon and electron neutrino spectra at 0° and 89° from non-prompt meson decay are found comparable with the results of Volkova and Zatsepin, and Butkevichet al. An estimate of the prompt muon neutrino spectra at 0° and 89° fromtthe charmed-meson decay has been given along with the earlier results of different authors. The present result for muon neutrino spectra at zenith angles 0° and 89° is found in approximate agreement with the EAS-TOP results of the Gran Sasso group.

Study of the inclusive reaction at a momentum of 4.3 GeV/c per incident nucleon

A detailed study of pion production in central Mg - Mg collisions at a momentum of 4.3 GeV/c per incident nucleon was carried out using the GIBS set-up. It has been shown that the dependence of the average kinematical characteristics ( and ) of mesons on multiplicity differs from that for NN collisions at the same energy, which is due to nuclear effects. The temperatures of mesons have been estimated using two different selection criteria: in the rapidity interval and at angles in the CMS. A satisfactory fit for mesons can be achieved by using a form involving two temperatures and . The relative yield of the high-temperature component is . The results obtained by the intranuclear cascade model CASIMIR coincide with the experimental data estimated with both methods. From the analysis of angular distributions of mesons the anisotropy coefficient a was obtained. The anisotropy coefficient increases linearly with the kinetic energy (in the CMS). CASIMIR reproduces the increase of a with , but the slope is less steep than from experimental results.

Glauber theory of initial- and final-state interactions in (p, 2p) scattering

We develop the Glauber theory description of initial- and final-state interactions (IFSI) in quasielastic A(p,2p) scattering. We study the IFSI-distortion effects both for the inclusive and exclusive conditions. In inclusive reaction the important new effect is an interaction between the two sets of the trajectories which enter the calculation of IFSI-distorted one-body density matrix for inclusive (p,2p) scattering and are connected with incoherent elastic rescatterings of the initial and final protons on spectator nucleons. We demonstrate that IFSI-distortions of the missing momentum distribution are large over the whole range of missing momentum both for inclusive and exclusive reactions and affect in a crucial way the interpretation of the BNL data on (p,2p) scattering. Our numerical results show that in the region of missing momentum $p_{m}\lsim 100-150$ MeV/c the incoherent IFSI increase nuclear transparency by 5-10\%. The incoherent IFSI become dominant at $p_{m}\gsim 200$ MeV/c.

Charged current neutrino-nucleus reaction cross sections at intermediate energies.

Inclusive and semi-inclusive neutrino-nucleus reaction cross sections at intermediate energies (20 MeV\ensuremath{\le}${\mathit{E}}_{\ensuremath{\nu}}$\ensuremath{\le}500 MeV) are calculated throughout the Periodic Table for the most interesting nuclei from an experimental point of view. The method used had previously proved to be very accurate in calculating the inclusive reaction cross section for light nuclei ${(}^{12}$C and $^{16}\mathrm{O}$) and in the study of other similar processes and has been further improved to deal with low energy neutrinos. The electron neutrino (${\ensuremath{\nu}}_{\mathit{e}}$) and muon neutrino (${\ensuremath{\nu}}_{\mathrm{\ensuremath{\mu}}}$) cross sections weighted by their energy distributions are also calculated and discussed in conjunction with the existing experimental results at LAMPF and the KARMEN Collaboration. \textcopyright{} 1996 The American Physical Society.

INCLUSIVE TRITIUM STRIPPING REACTION THEORY

The angular and energy distributions and the integrated cross-section of the inclusive two-nucleon transfer reaction with the participation of three-nucleon nucleus were calculated at intermediate energies.

New upper limits for H-particle production in p̄Xe annihilation at low energy

A study of the reactions p Xe → K +K +X , p Xe → K +H(H → Σ −p)X and p Xe → K +K +H(H → Σ −p)X was performed using the 700-litre xenon bubble chamber DIANA, exposed to the 1 GeV/ c antiproton beam of ITEP (Moscow). From a sample of 7.8 · 10 5 antiproton annihilations at low energy in xenon nuclei 4 events were observed for the reaction p Xe| → K +K +X at rest ( P p ≤ 400 MeV/c ) and 8 for the same reaction in flight ( 400 ≤ P p ≤ 900 MeV/c ). The corresponding probabilities turned out to be 3.1 · 10 −5 and 3.4 · 10 −5, respectively. No H-event was found in the two semi-inclusive reactions p Xe → K +HX and p Xe → K +K +HX . This lead to the upper limits 6 · 10 −6 and 8 · 10 −6 (90% C.L.), respectively. The corresponding upper limit for the fully inclusive reaction p Xe → HX turned out to be 1.2 · 10 −5 (90% C.L.), which is about one order of magnitude lower than the actual value reported in the literature.

The inclusive muon neutrino reaction in 12C

We calculate the charged current inclusive cross section for the reaction, v(sub)u +12C ->u^- + X, from the threshold to 300 MeV.In addition we obtain the average cross section over the spectrum currently being produced at LAMPF.We discuss our results with respect to the current experimental work and consider the possible contributions from higher l states.

Tests of time-reversal invariance in nuclear and particle physics.

There is a theorem that states that there can be no null test of time-reversal invariance (T symmetry) in exclusive reactions; that is, T symmetry does not require any single observable to vanish. This theorem is extended to inclusive reactions. Also, a general argument, that an experimental observable vanishes from T symmetry if a corresponding operator changes sign under time reversal, is shown to be invalid.

Role of final state interactions in quasielastic 56Fe(e,e') reactions at large ||q

A relativistic finite nucleus calculation using a Dirac optical potential is used to investigate the importance of final state interactions [FSI] at large momentum transfers in inclusive quasielastic electronuclear reactions. The optical potential is derived from first-order multiple scattering theory and then is used to calculate the FSI in a nonspectral Green's function doorway approach. At intermediate momentum transfers excellent predictions of the quasielastic $^{56}$Fe$(e,e')$ experimental data for the longitudinal response function are obtained. In comparisons with recent measurements at $|{\vec q|}=1.14$~GeV/c the theoretical calculations of $R_L$ give good agreement for the quasielastic peak shape and amplitude, but place the position of the peak at an energy transfer of about $40$~MeV higher than the data.

Reactive scattering theory for molecular transitions in time-dependent fields

A new approach is introduced for computing probabilities of molecular transitions in time-dependent fields. The method is based on the stationary (t,t′) representation of the Schrödinger equation and is shown to be equivalent to infinite order time-dependent perturbation theory. Bound-to-bound (i.e., photoexcitation) and bound-to-continuum (i.e., photoreaction) transitions are regarded as reactive collisions with the ‘‘time coordinate’’ as the reaction coordinate in an extended Hilbert space. A numerical method based on imposing absorbing boundary conditions for the time coordinate in a discrete variable representation framework is introduced. A single operation of the Green’s operator provides all the state-specific transition probabilities as well as partial state-resolved (inclusive) reaction probabilities. Illustrative numerical applications are given for model systems.

INCLUSIVE (3He, t) REACTION IN DELTA EXCITATION REGION

Using the one step reaction mechanism, calculations are presented for the overall features of the inclusive (3 He , t) reaction on various target nuclei in the delta excitation region. The interaction for the elementary pp→nΔ++ process is given by one-pion-exchange, and is written in the covariant relativistic form. The values of the parameters in the interaction are chosen such that the interaction successfully describes the spin averaged experimental elementary cross-sections. The distortion in the entrance and exit channels is described in the eikonal approximation, and the nuclear response is described in the “distorted wave Fermi gas model”. The cross-sections for the triton energy spectrum, angular distribution, and the total events at 0° on several nuclei, are calculated and compared with the corresponding experimental data. The main features of the measured cross-sections are reproduced.

Inclusive neutrino reactions in 127I

Inclusive neutrino reactions in 127I

Final state interactions and relativistic effects in y scaling.

The role of final state interactions in [ital y] scaling in quasielastic electronuclear reactions is investigated in a physically realistic model, which incorporates the final state interactions via the optical model Green's function. Relativistic and nonrelativistic complex optical potentials are utilized in finite nucleus, fully-off-shell, momentum space calculations to represent the final state interactions in an approach which has been shown to provide realistic descriptions of the separate response functions in the inclusive reaction. Analyses of the effects of Dirac dynamical degrees of freedom and final state interactions upon the separate longitudinal and transverse scaling functions are presented along with a discussion of the high momentum transfer dependence.

Longitudinal and transverse spin response of C12 in the Delta resonance region.

The \ensuremath{\Delta} excitations in nuclei induced by pion and photon scattering are analyzed within the isobar-hole model. The results are compared to those of intermediate energy charge exchange reactions. The similarities and differences between the various probes due to their kinematics and spin-structure are discussed. It is shown that the experimental cross sections for pion and photon induced reactions as well as for the inclusive charge exchange reactions can be consistently described within the isobar-hole model. Of special interest is the coherent pion decay of the \ensuremath{\Delta} resonance which is studied by means of the exclusive reaction ${\mathrm{C}}^{12}$(${\mathrm{He}}^{3}$,t${\mathrm{\ensuremath{\pi}}}^{+}$)${\mathrm{C}}^{12}$ (g.s.), by elastic pion scattering, and by pion photoproduction. It turns out that the coherent pion decay of the ${\mathrm{C}}^{12}$(${\mathrm{He}}^{3}$,t${\mathrm{\ensuremath{\pi}}}^{+}$)${\mathrm{C}}^{12}$ (g.s.) reaction is intimately related to elastic pion scattering. Most interestingly, both the peak energy and the magnitude of the coherent pion production cross section depend very sensitively on the strength of the \ensuremath{\Delta}-hole residual interaction. The observed energy shift is directly proportional to the nuclear density \ensuremath{\rho}. This shows that the coherent pions propagate through the nuclear interior. The coherent pion cross section can be used to determine the Landau-Migdal parameter ${\mathrm{g}}_{\mathrm{\ensuremath{\Delta}}\mathrm{\ensuremath{\Delta}}}^{\ensuremath{'}}$.

Partial and total inelasticities obtained from inclusive reaction data.

We calculate the partial inelasticities referring to the production of pions, kaons, protons, and antiprotons from inclusive reaction data. From the partial inelasticities we also estimate the total inelasticity of a pp collision, which turns out to be rapidly increasing with energy.

Inclusive neutrino reactions in nuclei

The charged-current inclusive reaction for the process nu e+12C to e-+X is calculated from threshold to 100 MeV. The cross sections are calculated via a tensor describing the hadronic part of the interaction, the elements of which are obtained phenomenologically from the total muon capture rates and from electromagnetic-scattering data. Cross sections averaged over the Michel spectrum are also obtained and compared to the existing experimental results.

Inclusive inelastic neutral-current neutrino reactions in 12C and the charged-current reaction

The inclusive neutral-current cross section for the process v e + 12 C → v e + X is calculated for energies from threshold to 100 MeV. Averages for the cross section over the Michel spectrum are also obtained. The relationship between this cross section and the charged-current cross section for the reaction ν e + 12 C → e − + X is also discussed.

Multinucleon mechanisms in ( gamma,N) and ( gamma,NN) reactions.

The similarities in the experimental indications for multinucleon mechanisms in (\ensuremath{\gamma},p) and (e,e'p) processes are pointed out. For both types of reactions, the substantial role of two-nucleon emission processes for transitions to high excitation energies in the residual nucleus is stressed. A microscopic model for the calculation of the two-body knockout contributions to the inclusive (\ensuremath{\gamma},N) reaction is presented. It is based on an unfactorized formalism for the calculation of electromagnetically induced two-nucleon emission cross sections. The model is shown to yield a reasonable description of the overall behavior of the $^{12}\mathrm{C}$(\ensuremath{\gamma},p) and $^{12}\mathrm{C}$(\ensuremath{\gamma},n) data at high excitation energies in the residual nucleus. In the calculations, effects from nonresonant and resonant pion exchange currents are included. Photoabsorption on these currents is predicted to produce the major contributions to the exclusive $^{16}\mathrm{O}$(\ensuremath{\gamma},${\mathit{n}}_{0}$${)}^{15}$O process at photoenergies above the pion threshold. Double differential cross sections for photon induced pp and pn emission from $^{16}\mathrm{O}$ are calculated and compared with the data.

Preequilibrium (p,p') measurements and calculations for 90Zr and neighboring nuclei for incident energies up to 200 MeV.

Double differential cross sections have been measured for inclusive (p,p') reactions on targets of $^{89}\mathrm{Y}$, $^{90}\mathrm{Zr}$, and the even-mass Mo isotopes from A=92 to 98 at incident proton energies of 120, 160, and 200 MeV. Comparisons are made with calculations based on the statistical multistep direct theory of Feshbach, Kerman, and Koonin. In general it is found that the theory gives a good description of the angular distributions. Possible explanations for the deviation of the predicted cross sections from experiment at very low and very high excitation energies of the residual nucleus are given.