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Experimental results are presented on the scattering of 250-MeV electrons by ${\mathrm{Ca}}^{40}$, ${\mathrm{Ca}}^{42}$, ${\mathrm{Ca}}^{44}$, ${\mathrm{Ca}}^{48}$, and ${\mathrm{Ti}}^{48}$, and of 500-MeV electrons by ${\mathrm{Ca}}^{40}$ and ${\mathrm{Ca}}^{48}$. An analysis is made in terms of a phenomenological three-parameter shape, and a new, more accurate charge distribution is obtained for ${\mathrm{Ca}}^{40}$. The experiments also lead to a detailed exploration of the radial dependence of the differences in charge distributions of the various isotopes. Implications for nuclear theory are discussed. Comparison is made with the results of other electron scattering and of muonic x-ray experiments. The latter comparison permits an independent determination of an upper limit on the muon electromagnetic radius ${{〈{r}^{2}〉}_{\ensuremath{\mu}}}^{\frac{1}{2}}\ensuremath{\lesssim}0.35$ F.

The elastic scattering peak in carbon-12 is accompanied by a number of additional peaks corresponding to inelastic scattering of electrons from the various excited levels of the carbon nucleus. Three levels have been investigated by this method and correspond to the three known states at 4.43 Mev, 7.68 Mev, and 9.61 Mev. Angular distributions of the inelastically-scattered electrons have been obtained as well as the angular distribution of the elastically-scattered electrons. The angular distributions of the inelastic peaks fall off less steeply with angle than the elastic peak. By comparing the scattering from carbon with scattering from the proton, and using the theoretical value of the cross section of electrons scattered from the proton, it is possible to obtain "absolute" values for the elastic and inelastic scattering cross sections. From the elastic-scattering curve, information about the size and charge distribution in the carbon-12 nucleus may be derived. The charge distribution lies halfway between a Gaussian and a uniform model. The root mean square radius of the resultant charge distribution is (2.40\ifmmode\pm\else\textpm\fi{}0.25)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm.

Thallium-activated sodium iodide crystals may be used as efficient detectors of gamma-rays and other ionizing radiations. The crystals are used in combination with a photo-multiplier after the manner of Kallmann. Curves are given which show the duration of the light emission process, the distribution of light pulse sizes, the energy discrimination possibilities, and the dependence of number of counting events on photo-multiplier voltage and amplifier gain. Comparison curves are shown for NaI(Tl) and anthracene. A description is given of the method of preparation of polycrystalline samples and single crystal specimens of the sodium iodidethallium phosphor. A few remarks are made concerning the combination of alkali halide phosphor crystals with photographic plates.

The elastic scattering of 188-Mev electrons from gaseous targets of hydrogen and helium has been studied. Elastic profiles have been obtained at laboratory angles between 35\ifmmode^\circ\else\textdegree\fi{} and 138\ifmmode^\circ\else\textdegree\fi{}. The areas under such curves, within energy limits of \ifmmode\pm\else\textpm\fi{}1.5 Mev of the peak, have been measured and the results plotted against angle. In the case of hydrogen, a comparison has been made with the theoretical predictions of the Mott formula for elastic scattering and also with a modified Mott formula (due to Rosenbluth) taking into account both the anomalous magnetic moment of the proton and a finite size effect. The comparison shows that a finite size of the proton will account for the results and the present experiment fixes this size. The root-mean-square radii of charge and magnetic moment are each (0.74\ifmmode\pm\else\textpm\fi{}0.24)\ifmmode\times\else\texttimes\fi{}${10}^{13}$ cm. In obtaining these results it is assumed that the usual laws of electromagnetic interaction and the Coulomb law are valid at distances less than ${10}^{\ensuremath{-}13}$ cm and that the charge and moment radii are equal. In helium, large effects of the finite size of the alpha-particle are observed and the rms radius of the alpha particle is found to be (1.6\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm.

The mirror nuclei of tritium and helium-3 have been studied by the method of elastic electron scattering. Absolute cross sections have been measured for incident electron energies in the range 110-680 MeV at scattering angles lying between 40 and 135\ifmmode^\circ\else\textdegree\fi{} in this energy range. The data have been interpreted in a straightforward manner and form factors are given for the distributions of charge and magnetic moment in the two nuclei over a range of four-momentum transfer squared 1.0-8.0 ${\mathrm{F}}^{\ensuremath{-}2}$. Model-independent radii of the charge and magnetic-moment distributions are given and an attempt is made to deduce form factors describing the spatial distribution of the protons in tritium and helium-3.

The study of electrons scattered inelastically from the deuteron has been extended to 600 Mev. Data at 500 Mev were reported in an earlier paper. Results are presented for seven scattering angles between 45\ifmmode^\circ\else\textdegree\fi{} and 135\ifmmode^\circ\else\textdegree\fi{}. A comparison of the deuteron's cross section at these angles with the corresponding free proton cross sections permits a determination of the form factor associated with the magnetic moment distribution of the neutron. Two different methods of analyzing the data are described, and the rms radius of the neutron for an exponential density distribution of the magnetic cloud can be shown to lie between the limits of 0.75\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm and 0.95\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm. The rms radius of the neutron may be taken to be (0.80\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm and is very close to the value found for an exponential model of the magnetic cloud in the proton.

The scattering of high-energy electrons from ${\mathrm{C}}^{12}$, reported previously, has been extended to 420 Mev. The elastic and inelastic scattering from the first excited level at 4.43 Mev has been studied between 33\ifmmode^\circ\else\textdegree\fi{} and 70\ifmmode^\circ\else\textdegree\fi{}. The new data are in good agreement with what one would expect from the earlier measurements on ${\mathrm{C}}^{12}$ performed at 187 Mev. Additional measurements of the elastic ${\mathrm{O}}^{16}$-scattering cross sections of 240-, 360-, and 420-Mev electrons as functions of the scattering angle furnish information on the size and shape of the ${\mathrm{O}}^{16}$ nucleus. Pronounced diffraction minima in the angular distributions were observed for ${\mathrm{C}}^{12}$ and ${\mathrm{O}}^{16}$. The experimental results are compared with the predictions of a theoretical phase-shift analysis derived for the harmonic-well independent-particle model of the nucleus. Preliminary best fits confirm the shell-model predictions for the charge density distribution of these $p$-shell nuclei. The preliminary analysis of the data shows that the length parameter of the well is 1.66\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm for ${\mathrm{C}}^{12}$, and 1.76\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm for ${\mathrm{O}}^{16}$, thus indicating a slight variation of the curvature of the harmonic well as the $p$ shell is filled in.

Measurements are reported of the inelastic scattering of electrons from the mirror nuclei of tritium and helium - 3. The ratio of the quasi-elastic electron-tritium and electron-helium -3 cross sections was measured to a precision of about 3% for values of the square of the four-momentum transfer, equal to 2.5 and 4.6/F sq. Detailed measurements of the shape of the entire inelastic spectra and estimates of the total inelastic cross sections were made. While these data are primarily intended to furnish additional experimental information which will be of use in determining the structure of the three-body nuclei, it is also pointed out that such data are a possible source of information on the structure of the neutron. (Author)

The electron scattering at high momentum transfer has been measured from the nucleons in Be, in C, and from the free proton. The data yield the cross section of the average nucleon and of the neutron in relation to that of the proton. $\frac{{\ensuremath{\sigma}}_{n}}{{\ensuremath{\sigma}}_{p}(\ensuremath{\theta})}$ is found to be 1.16\ifmmode\pm\else\textpm\fi{}0.3 at 500 Mev and 135\ifmmode^\circ\else\textdegree\fi{}; it decreases, as expected, for smaller angles and lower energies. If the assumption is made that meson-exchange effects and interactions in the final state are not important, the form factors obtained indicate an apparent root-mean-square radius of the neutron's magnetic-moment distribution of (0.53\ifmmode\pm\else\textpm\fi{}0.15)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm. It is possible that the apparent small size of the neutron in Be and C is due to the neglect of meson-exchange effects and interactions in the final state. The present result is smaller than a neutron size, given by Yearian and Hofstadter, who compared the cross sections of deuteron and proton and found equal sizes for neutron and proton. If one accepts the latter result, the present experiment can be used to yield a measure of the above neglected effects.

A scintillation counter telescope, employing three NaI(Tl) crystals in coincidence, has been used to study the energy losses experienced by mu-mesons in traversing one of the crystals. The magnitude of the light flash in NaI(Tl) has been assumed to be proportional to the energy lost in the crystal by the meson. The observed pulse distribution is compared with one calculated on the basis of the Bethe-Bloch theory without the density correction and also with the Halpern-Hall theory which includes the effect of the dielectric shielding. Each calculated curve employs a fold of the Landau straggling theory with the cosmic-ray mumeson spectrum. Comparison of the data with the two theories definitely favors the Halpern-Hall theory both in respect to absolute value of the most probable energy loss as well as the shape of the distribution.

A new method is described for determining gamma-ray energies and intensities. The basis of the method is the observation of narrow pulse distributions (lines) in the scintillations of NaI(T1). Due to the presence of the iodine component, pair production and the photoelectric process produce relatively sharp lines in the pulse distributions. The Compton process may also be used in determining gamma-energies. Approximate theoretical curves of the pulse distribution are shown. Experimental spectra resemble the theoretical patterns, except for differences in intensities discussed in the text. Electronic as well as photographic techniques for obtaining spectra are described. With these methods well known spectra are confirmed and new results in the case of ${\mathrm{Ga}}^{66}$ are given. With a source of less than ${10}^{\ensuremath{-}9}$ curie of ${\mathrm{K}}^{40}$ the energy of the gamma-ray has been determined to within two percent. The method described should make possible a new approach to the study of weak gamma-radioactivities and unknown gamma-ray spectra.

Electron scattering from the bound neutron and proton in the deuteron has been studied at various scattering angles between 75\ifmmode^\circ\else\textdegree\fi{} and 135\ifmmode^\circ\else\textdegree\fi{} for 500-Mev and 600-Mev electrons. A comparison of these scattering cross sections with those of the free proton permits a determination of the density distribution of the magnetic cloud around the neutron. By using theories developed by Jankus and Blankenbecler, the root-mean-square radius of the neutron is shown to lie between the limits 0.80\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm and 0.90\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm. The choice between these radii depends on whether the deuteron total cross sections or differential (peak) cross sections are compared with the protonic scattering cross section. Since presently available theory has not yet developed sufficiently to decide definitely between these possibilities, the root-mean-square size may be taken to be (0.85\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm with small error. The neutron's magnetic cloud clearly does not have the small size obtained by measurement of its charge cloud from experiments on the neutron-electron interaction, and this anomaly challenges the present concepts of nucleon size.

The structure and size of the proton have been studied by means of high-energy electron scattering. The elastic scattering of electrons from protons in polyethylene has been investigated at the following energies in the laboratory system: 200, 300, 400, 500, and 550 Mev. The range of laboratory angles examined has been 30\ifmmode^\circ\else\textdegree\fi{} to 135\ifmmode^\circ\else\textdegree\fi{}. At the largest angles and the highest energy, the cross section for scattering shows a deviation below that expected from a point proton by a factor of about nine. The magnitude and variation with angle of the deviations determine a structure factor for the proton, and thereby determine the size and shape of the charge and magnetic-moment distributions within the proton. An interpretation, consistent at all energies and angles and agreeing with earlier results from this laboratory, fixes the rms radius at (0.77\ifmmode\pm\else\textpm\fi{}0.10) \ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm for each of the charge and moment distributions. The shape of the density function is not far from a Gaussian with rms radius 0.70\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm or an exponential with rms radius 0.80\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm. An equivalent interpretation of the experiments would ascribe the apparent size to a breakdown of the Coulomb law and the conventional theory of electromagnetism.

The electromagnetic form factors of the neutron have been measured in the ${q}^{2}$ range from 1.0 to 30.0 ${\mathrm{F}}^{\ensuremath{-}2}$. It is found that for values of ${q}^{2}$ greater than about 6.0 ${\mathrm{F}}^{\ensuremath{-}2}$ the square of the neutron's charge form factor ${({G}_{\mathrm{En}})}^{2}$ is consistent with zero to within an error of the order of 5% in the existing theoretical cross section. For values of ${q}^{2}$ less than 6.0 ${\mathrm{F}}^{\ensuremath{-}2}$ it is concluded that meaningful values of the neutron form factors cannot be given until the necessary corrections to the theory are better understood. The present results on the neutron form factors are combined with recent measurements of the proton form factors to provide experimental determinations of the isotopic nucleon form factors. It is found that the $\ensuremath{\omega}$ and $\ensuremath{\phi}$ mesons provide a good approximation to the observed isoscalar form factors but that it is difficult to understand the behavior of the isovector form factors in terms of the $\ensuremath{\rho}$ meson alone.

An experimental determination has been made of the radial and longitudinal distribution of energy produced in showers initiated by electrons of 118 Mev and 157 Mev in copper. A small crystal CsBr(Tl) coupled to a thin light pipe and photomultiplier was used as a probe. Graphs of the radial distributions are given from which, by numerical integration, transition curves are determined. Calculations are made for an approximately optimum design of scintillation crystal [e.g., NaI(Tl)] to capture a large fraction of the energy within a shower.

The ${\mathrm{Li}}^{6}$ nucleus has been studied at 426 Mev by electron scattering methods between laboratory angles of 33\ifmmode^\circ\else\textdegree\fi{} and 57.5\ifmmode^\circ\else\textdegree\fi{}. Absolute values of the ${\mathrm{Li}}^{6}$ cross sections have been obtained by comparison with scattering measurements made on the proton at 426 Mev and 40\ifmmode^\circ\else\textdegree\fi{}. Unique values of the experimental form factors are given in tabular form. The results are analyzed in terms of various possible charge distributions. Several examples of models showing a good fit are presented and appropriate radius and skin thickness values are given. Several unsuccessful models are also discussed.

Absolute values of the most probable energy loss and the energy-loss straggling for high-energy muons passing through NaI (T1) have been measured over the muon momentum range from 0.5 to 10.5 $\frac{\mathrm{GeV}}{c}$. The results agree, within the 1% experimental uncertainty, with the theoretical values.

Elastic scattering of 192-Mev electrons from deuterium has been studied using both solid (C${\mathrm{D}}_{2}$) and high-pressure gas targets. The results obtained by these two methods are in agreement and yield the following conclusions: (1) The range of the neutron-proton potential is between 1 and 4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm if a square potential well is assumed and if the deuteron wave functions predicted by the binding energy of the deuteron are used. (2) It is, however, impossible with the present data to eliminate the possibility of other charge distributions for deuterium such as uniform or Gaussian.Inelastic electron scattering from deuterium was also investigated, and promises to give independent information of the deuteron structure.

With apparatus previously described1,2 we have studied the elastic scattering of electrons of energies 100, 188, and 236 MeV from protons initially at rest. At 100 MeV and 188 MeV, the angular distributions of scattered electrons have been examined in the ranges 60°-138° and 35°-138°, respectively, in the laboratory frame. At 236 MeV, because of an inability of the analyzing magnet to bend electrons of energies larger than 192 MeV, we have studied the angular distribution between 90° and 138° in the laboratory frame. In all cases a gaseous hydrogen target was used.