Missing Energy Spectra Research Articles

Short range interaction of nucleons inside the nucleus via 4He(e,e'p)R reactions.

Cross sections for the $^{4}\mathrm{He}$(e,e'p)R reaction have been measured for recoil momenta between 225 and 500 MeV/c. We find (1) that in the continuum channel a peak in the missing energy spectrum appears which shifts with increasing recoil momentum in a predictable way, and (2) that for the highest recoil momenta (above 300 or 350 MeV/c) overall agreement is obtained with microscopic calculations in which the scattering on nucleon pairs predominates. These results strongly suggest that the highest recoil momenta are generated by the scattering on one of a pair of nucleons. This interpretation is reinforced by an observed continuum momentum distribution which, for high recoil momenta, resembles the momentum distribution of deuterium. We infer that the high momentum part of the momentum distributioon of a nucleon pair appears unmodified when embedded in a nuclear medium.

Extrapolating (e,e'p) to (e,e').

Unexplained anomalies in quasielastic (e,e') measurements motivated (e,e'p) experiments to determine the reaction mechanisms (single-nucleon knockout, multinucleon knockout, delta production, etc.) involved in quasielastic electron scattering. In this paper we use various models to extrapolate from C(e,e'p) measurements, where an outgoing proton is detected in a small solid angle centered around the virtual photon angle, to C(e,e') measurements, which integrate over all knockedout particles at all angles. Extrapolated single nucleon knockout (p and s shell) only accounts for 25% of the (e,e') cross section in the dip region and only 40--60 % in the quasielastic region. This indicates that the ``quasielastic'' region has a large nonquasielastic component. Various multinucleon knockout models (two-nucleon correlations, six-quark bags, and qualitative final state rescattering) are compared to C(e,e'p) missing energy spectra and to the difference between the (e,e') cross section and the extrapolated single-nucleon knockout; none completely describe the data.

The 16O(γ, 2N) reaction measured with tagged photons

The results of tagged photon measurements of the 16O(γ, pn) and 16O(γ, pp) reactions, carried out with photons of energies of 80–131 MeV, are presented. Missing energy spectra for both reactions, with an energy resolution of 7 MeV have been obtained. The 16O(γ, pn) missing energy spectrum is very similar to that recently measured for the 12C(γ, pN) reaction. In both cases the recoil momentum distributions are quantitavely described by a quasideuteron mechanism. Using normalisation factors based on this mechanism the average cross section for the 16O(γ, pn) reaction, for nucleons ejected from the 1p shell, is 510 ± 95 μb. The corresponding cross section for the 16O(γ, pp) reaction is 10.0 ± 3.0 μb.

Quasielastic reaction mechanism studied using the reaction 12C(e,e'p).

We have measured missing-energy spectra for the reaction $^{12}\mathrm{C}$(e,e'p) in the quasielastic region in parallel kinematics at momentum transfers q of 585, 775, and 827 MeV/c. We observed $^{1}$p and $^{1}$s single-proton knockout peaks and large broad strength attributed to multinucleon knockout. We saw no increase in strength at pion threshold. The ratio of single-particle knockout to a distorted-wave impulse-approximation calculation is approximately constant with q. Multinucleon knockout is 25%--40% of the total cross section; it increases with q. This quasielastic non-single-nucleon knockout is much stronger than previously observed.

Multinucleon knockout in electron scattering

The exclusive (e,e'p) reaction and the inclusive (p,p') reaction for /sup 12/C at intermediate energy are studied in order to understand the reaction mechanism leading to multinucleon knockout in electron scattering. We focus on the effect of the final-state interaction in the missing-energy spectrum measured (under parallel kinematics) in a coincidence (e,e'p) experiment in the dip region, where the many-body process is the dominant channel. To disentangle complex many-body processes and understand the final-state interaction quantitatively, we first study the inclusive (p,p') reaction at the corresponding proton energy, which represents the final-state interaction in the on-shell limit. We show that the single scattering process, which means that the incident proton interacts inelastically with the target nucleon only once before coming out, is dominant at small proton scattering angles and can be treated within the framework of distorted-wave impulse approximation by using the effective nucleon-nucleon (NN) interaction. This prescription is able to be applied to the (e,e'p) reaction, since the forward proton scattering in the final state is important under parallel kinematics. Based on the knowledge obtained from the study of the (p,p') reaction, we examine the two-body type of final-state interaction in electron scattering within the above approach. We indicatemore » limitations of the two-body process as a mechanism for understanding the (e,e'p) reaction.« less

Many-body effects in the (e,e'p) reaction.

We present the first quantitative study of the final-state-interaction effect in the missing-energy spectrum measured in a coincidence /sup 12/C(e,e'p) experiment in the dip region. It is found that the calculated cross section for the two-body type of final-state interaction is very small compared with the data. Furthermore, it decreases with increasing missing energy; this qualitative behavior does not agree with the data. From qualitative investigation, the presence of the many-body mechanism involving more than two nucleons is suggested.

Electroexcitation of the Delta resonance in the (e,e'p) reaction.

The /sup 12/C(e,e'p) reaction at the delta resonance has been measured for protons detected parallel to the momentum transfer at two kinematical situations: at the maximum and the low-energy-loss side of the peak. The cross section was measured for missing energies up to 320 and 220 MeV, respectively. In the missing energy spectrum two distinct structures are observed, which correspond to multinucleon knockout and quasifree pion production processes. In addition, there is a remnant of the quasifree knockout process.

Weak transitions in the quasi-elastic reaction 12C(e, e′p) 11B

In a high-resolution quasi-elastic 12C(e, e'p) 11B experiment several weak transitions have been observed to excited final states with spin and parity characteristic of direct knockout from orbitals above the 1p shell. The momentum distributions, which have been measured in parallel kinematics at an outgoing-proton energy of 70 MeV in the range of missing momentum −170 ⩽ p m ⩽ 210 MeV c, show the shape expected for a single-step knockout process. It is demonstrated that the interference between a direct-knockout process and a two-step process leading to the same final state in the (e, e'p) reaction may cause important modifications of the deduced spectroscopic factors. Explicit coupled-channels (CC) calculations show that the spectroscopic factor for the transition to the 7 2 − state at 6.743 MeV is reduced by a factor of 6, whereas the spectroscopic factors of the other weak transitions observed in the present experiment are uncertain by a factor of 2 due to CC-effects. Since the strength of these transitions is larger than can be explained by a pure two-step process, we interpret the observation of these transitions as direct evidence for the existence of ground-state correlations in 12C. The total spectroscopic strength in the E x region between 6 and 12 MeV amounts to 0.1, or 4.1 % of the observed strength for 1p knockout in the low E x region. Two peaks have been identified in the missing-energy spectrum that hitherto have not been reported: a narrow peak at E x = 9.82 (3) MeV with an l = 0 character and a broad structure centered at about 11.5 MeV with an l = 1 character. The missing-energy spectrum between E x = 12 and 24 MeV corresponding to 1 s 1 2 knockout has also been analyzed. The deduced momentum distribution shows evidence for the onset of a two-nucleon mechanism beyond the two-particle emission threshold.

Production and decay of neutralinos in e +e − annihilation

We study in detail production and decay of neutralinos in e +e − annihilation. Formulae for the cross section, the single lepton, lepton pair, and missing energy spectra are given. Particular attention is paid to the mixing of gauginos and higgsinos. In order to illustrate its importance numerical results for four different mixing scenarios are presented.

Signatures of chargino production ine + e − collisions

We treat the production of charged gauginos ine+e− annihilation and their most important decays. Mixing of charged as well as of neutral gauginos in a general form is included. Formulae for the cross section, the lepton and missing energy spectrum are presented. We also give numerical results for three distinct mixing possibilities.

Monte Carlo study of proton multiple scattering in (e, e′p) reactions

Distorition effects on the spectral function extracted from (e, e′p) experiments, because of the multiple scattering of the proton with the residual nucleus, have been evaluated by means of a Monte Carlo code. The calculation was carried out for the16O(e, e′p)15N reaction, under the kinematical conditions of an experiment performed in Saclay. The results obtained indicate that about 50% of the knock-out protons undergo a second scattering. The missing-energy spectrum is largely distorted, while the momentum distributions are slightly mofidied. Koltun's sum rule is better satisfied by taking into account the multiplescattering contributions.

Angular correlations and missing energy spectrum in quasifree electron scattering

The angular correlations and missing energy spectrum in quasifree electron scattering are studied in the unfactorized distorted wave impulse approximation. The present approach, in the nonrelativistic description, effectively includes the finer aspects of the process, namely the off-energy-shell effect and the spin-orbit coupling, which are neglected or approximated in the usual factorization methods. A comparative study between the factorized and unfactorized methods reveals that the unfactorized cross section not only accounts for the absolute value but also a possible asymmetry in its distribution. The study of the off-shell influence on spherical and nonspherical nuclei indicates that the off-shell effect is to increase with the increase of nuclear deformation.

Quasi-free electron scattering and the independent particle model

The missing-energy spectrum for the reaction 12C(e, e'p) 11B is studied using the independent particle model. It is shown that this cross-section is quite sensitive to the bound-state wavefunction. The apparent incompatibility between quasi-free and elastic electron scattering data is removed if realistic wavefunctions are used. For 12C, there is no need to invoke short-range correlations for comparing the two processes, at least for the momentum transfers for which experimental data are available.

Microscopic description of the absorption of bound pions

The absorption rates of bound 1s and 2p pions in some light nuclei have been investigated on the basis of a shell model picture modified by short range nucleonnucleon correlations. It turns out that the total absorption rate, the missing energy spectra and the single neutron energy spectra depend sensitively on the details of the correlation functions. The results of the present analysis indicate that one can obtain informations on the short range correlations from pion absorption experiments.