Internal Momentum Distribution Research Articles

6Li(e,e′α) and (e,e′d) reactions

The correlation cross sections for the quasifree scattering in the 6Li(e,e′α) and (e,e′d) reactions are calculated in the microscopic model. The internal momentum distributions of clustering particles play an important role for explaining experimental data.

π−Photoproduction from Deuterium at Laboratory Energies 600 to 1250 MeV

The differential cross section for the reaction $\ensuremath{\gamma}+n\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}+p$ was measured for laboratory photon energies between 600 and 1250 MeV, using a liquid deuterium target. The internal nucleon momentum distribution of the deuteron was used to calculate the major effect of using deuterium as a neutron target. The data show that the amplitude to excite the ${F}_{15}(1688)$ resonance is small, in agreement with a recent quark-model prediction.

Quasi-Deuteron Model and the Internal Momentum Distribution of Nucleons inC12

The quasi-deuteron model was assumed in computing the internal momentum distribution of nucleons in ${\mathrm{C}}^{12}$ using the monoergic photodata of Cence and Moyer and the bremsstrahlung photodata of the Purdue group. The computed quasi-deuteron momentum distribution has the form $\frac{A\mathrm{exp}(\ensuremath{-}\frac{{p}^{2}}{4M{E}_{1}})}{{(4\ensuremath{\pi}M{E}_{1})}^{1.5}}+\frac{B{p}^{2}\mathrm{exp}(\ensuremath{-}\frac{{p}^{2}}{4M{E}_{2}})}{1.5{\ensuremath{\pi}}^{1.5}{(4M{E}_{2})}^{2.5}}$, where ${E}_{1}$ is 1.5 MeV and ${E}_{2}$ is 5 MeV. The ratio $\frac{B}{A}$ is approximately 2. These two components resemble the ($1s$) and ($1p$) wave functions of the shell model. The ($1s$) component is associated with a binding energy 40 MeV while the ($1p$) component is associated with a binding energy 10 MeV. The internal momentum distribution of nucleons in ${\mathrm{C}}^{12}$ was calculated from this quasideuteron momentum distribution assuming that the nucleons exist in proton-neutron pairs in the nucleus.

Photoproduction of Pions in Carbon

Positive and negative pions were produced by photons on a carbon target and observed at laboratory angles of 35\ifmmode^\circ\else\textdegree\fi{}, 73\ifmmode^\circ\else\textdegree\fi{}, and 121\ifmmode^\circ\else\textdegree\fi{}. At each angle the yield of mesons of constant energy was observed by a magnetic spectrometer as a function of peak bremsstrahlung energy. Seven values of the latter ranging from 205 to 335 Mev were used. Yields and $\frac{{\ensuremath{\pi}}^{\ensuremath{-}}}{{\ensuremath{\pi}}^{+}}$ ratios corrected for various systematic experimental errors are presented. By using a photon difference method the bremsstrahlung spectra were unfolded from the yield curves to give meson cross sections versus photon energy at fixed pion energies. These functions are compared with predicted yields which consider the internal momentum distribution of the target nucleons; the agreement is adequate.

Photoproduction of Negative Mesons in Deuterium

A 24-in. diffusion cloud chamber filled to 14 atmospheres with tritium-free deuterium gas, operating in a magnetic field of 6 kilogauss, has been placed in the 1040-Mev "hardened" bremsstrahlung beam of the Cornell synchrotron. A total of 310 events of the type $\ensuremath{\gamma}+d\ensuremath{\rightarrow}p+p+{\ensuremath{\pi}}^{\ensuremath{-}}$ have been observed and analyzed. Using the "spectator model," a total cross section has been determined for the reaction $\ensuremath{\gamma}+n\ensuremath{\rightarrow}p+{\ensuremath{\pi}}^{\ensuremath{-}}$ from threshold to 1 Bev, in good agreement with the results obtained from the measurement of the negative-to-positive pion ratio together with the measured cross section for the reaction $\ensuremath{\gamma}+p\ensuremath{\rightarrow}n+{\ensuremath{\pi}}^{+}$.The momentum distribution of the low-energy protons in the laboratory system compares very favorably with the internal momentum distribution of the deuteron as calculated from the Hulth\'en or Gartenhaus wave functions. The validity of the spectator model for photons above 200 Mev is experimentally justified, as is expected in consideration of the assumptions of the impulse approximation.A study of the forward-backward asymmetry of the spectator protons in the laboratory system indicates that above photon energies of 250 Mev, there is a 15% deviation from isotropy, favoring the forward beam direction, indicating that the spectator proton is being "pulled along" with the net forward momentum of the rest of the system, through an average forward momentum transfer of about 10 Mev/c.

Nuclear Internal Momentum Distributions

The nuclear internal momentum distributions of protons in light nuclei have been studied with the 340-Mev scattered proton beam from the synchrocyclotron. The two protons from a quasi-elastic scattering event are detected in coincidence, and the energy of one of them is magnetically analyzed. In the limit of the impulse approximation, conservation of energy and momentum can be employed to solve for the momentum of the struck proton. The best fit to the experimental data for beryllium was obtained with a Gaussian momentum density distribution with a $\frac{1}{e}$ value of about 20 Mev. Fermi (rectangular) and Chew-Goldberger distributions did not fit so well. Qualitative differences were observed between lithium, beryllium, and boron. The observed lithium spectrum was interpreted as being caused by two types of protons in lithium; two core protons that have a large momentum distribution and a third proton that has a rather low kinetic energy. This speculation was supported by the shape of the observed lithium spectrum, and by the relative yields from lithium, beryllium, and deuterium. The spectrum observed from beryllium indicated that the protons in beryllium have a larger momentum than the protons in the lighter elements studied. There were some indications that the fifth proton in boron may behave similarly to the third proton in lithium.

Fast Protons from 270-Mevn−dCollisions

The differential cross section for production of high energy protons in $n\ensuremath{-}d$ scattering, using the 270-Mev neutron beam of the 184-in. cyclotron, has been measured at scattering angles between 4\ifmmode^\circ\else\textdegree\fi{} and 58\ifmmode^\circ\else\textdegree\fi{}. For normalization, yields of protons from $n\ensuremath{-}p$ scattering were measured at each scattering angle. In all cases, only protons above a cut-off energy of 200 Mev ${cos}^{2}\ensuremath{\Theta}$ were accepted by the counter system. In addition, through the use of a magnetic analyzer, energy distributions of the $n\ensuremath{-}d$ protons were measured at 4\ifmmode^\circ\else\textdegree\fi{} and 22.5\ifmmode^\circ\else\textdegree\fi{}. The energy distributions closely resembled, in shape, the energy distributions of $n\ensuremath{-}p$ protons at the same angles, confirming the similarity in nature between collisions of high energy neutrons with free protons and collisions with protons bound in deuterium. Total yield of protons above the cut-off energy is lower for $n\ensuremath{-}d$ than for $n\ensuremath{-}p$ collisions, however, the ratio of the two being about 0.7 at all angles observed. Effects of the exclusion principle, of the internal momentum distribution of the deuteron, and of the difference in average potential energy between the dineutron and the deuteron are discussed as possible causes of the lowering of the $n\ensuremath{-}d$ proton yield below that from $n\ensuremath{-}p$ scattering.

Production of Mesons by Photons on Nuclei

The total cross section, energy spectrum, and angular distribution of mesons produced by photons incident on a target nucleus have been expressed in terms of the nucleon momentum distribution within the nucleus. The theory used here is valid for photon energies greater than approximately 1.2 times threshold, and for all but the lightest nuclei. These results have been applied to carbon employing Goldberger and Chew's momentum distribution for the protons in carbon. Excellent agreement is obtained for the meson energy spectrum at 90\ifmmode^\circ\else\textdegree\fi{} and the decrease in efficiency of meson production compared to free protons as targets. The change in efficiency with photon energy, and the meson spectrum at various angles can be used to determine the internal nucleon momentum distribution. Positive mesons yield the proton distribution, negative mesons the neutron distribution.