Intermediate Nuclear States Research Articles

Corrections to high-energy electron-nucleus scattering

The effect of excitation of intermediate nuclear states on both elastic and inelastic electron scattering is examined. The method employed is the DWBA carried to second order in the transition potential. For high incident energy ( E e ⪆ 200 MeV ) the second-order terms can be simplified by ignoring the nuclear excitation energy, and by using simple forms for the transition charge densities. The dispersion corrections are then independent of the details of the level structure of the target nucleus. Sample calculations are presented for scattering processes from 40Ca, 58Ni and 208Pb, to which intermediate dipole states may contribute. The effect of quadrupole states is also included for elastic scattering. The most important corrections (⪆ 20%) occur in elastic scattering at high momentum transfer ( q ⪆ 500 MeV/c ) and are more pronounced in light nuclei than heavy ones.

Si28(d, pγ)Si29Angular Correlations from 4 to 6 MeV

A study of the ($p, \ensuremath{\gamma}$) angular correlations involving the 1.28- and 2.03-MeV states in ${\mathrm{Si}}^{29}$ populated by the ${\mathrm{Si}}^{28}(d, p){\mathrm{Si}}^{29}$ reaction has been carried out at five deuteron bombarding energies between 4 and 6 MeV. Angular-correlation measurements were carried out in the reaction plane and in that plane perpendicular to the reaction plane which contains the incident-beam direction. The data were analyzed by means of the distorted-wave stripping formalism. Statistical tensors, describing the orientation of the intermediate excited nuclear states, were calculated at each energy. Since the reaction-plane measurements on the 2.03-MeV state alone were sufficient for determining the statistical tensors describing the correlation over the sphere, comparison has been made between the measured perpendicular-plane correlations and the correlations predicted from these statistical tensors. In addition, a combined set of statistical tensors has been calculated utilizing data from the reaction-plane and perpendicular-plane correlations. The magnitudes of the proton polarizations have also been calculated for the 2.03-MeV excited-state reaction using the combined set of statistical tensors. The observed correlations are in agreement with the predictions of a distorted-wave theory and not with those of the plane-wave theory.

Nuclear structure effects in bremsstrahlung

The cross section for bremsstrahlung is calculated in the Born approximation, taking into account the emission by the nucleus of the bremsstrahlung photon, as well as the emission of the bremsstrahlung photon by the electron. The formal results, which are expressed in terms of various form factors, are applicable to an arbitrary nucleus. Nuclear matrix elements for the specific case of 16O are evaluated in the long wavelength limit, using the j− j coupling particle- hole model. Excited states included in evaluating the summations over intermediate nuclear states are limited to one-particle, one-hole configurations coupled by electric dipole transitions to the ground state. Effects in the bremsstrahlung spectrum due to the intrinsic structure of the 16O nucleus are found to be strikingly apparent, at least in the coincidence arrangement in which scattered electron and photon are observed simultaneously, in the form of peaks superimposed on the background from electron bremsstrahlung. The relative magnitude of the nuclear effects depends strongly on the scattering angles and on the photon energy, essentially a resonance effect, and varies over a wide range from one nuclear level to another.

Microscopic Theory of the Optical-Model Potential and the Hole-Particle Model in Nuclear Spectroscopy

Approximate expressions for the optical-model potential ${\mathcal{U}}_{\mathrm{opt}}$ in terms of the nucleon-nucleon interaction are discussed. The identity of all the $A+1$ nucleons of the scattering problem is approximately taken into account in our final formulas. The imaginary part of ${\mathcal{U}}_{\mathrm{opt}}$ is calculated for the case of $^{12}\mathrm{C}$ and the incident-nucleon energy of 20 MeV. The spherical-model random-phase-approximation (RPA) eigenvalues and eigenvectors are assumed for the complete set of intermediate nuclear states involved. The results are rather insensitive to the exchange-force mixture assumed for our zero-range nucleon-nucleon potential. The anti-symmetrization of our $V$-matrix elements is extremely important as it reduces our $\mathrm{Im}{\mathcal{U}}_{\mathrm{opt}}$ by a factor of 2-3. For a reasonable set of our RPA intermediate eigenvalues and eigenvectors we obtain a semiquantitative agreement with the best phenomenological $\mathrm{Im}{\mathcal{U}}_{\mathrm{opt}}$ available for our case. The most important contribution to $\mathrm{Im}{\mathcal{U}}_{\mathrm{opt}}$ corresponds to the first excited $T=0, {2}^{+}$ state in $^{12}\mathrm{C}$.

K electron shell ionization and nuclear reactions

TheK-shell ionization probability associated withα-decay and nuclear reactions involving charged particles is calculated. The monopole and dipole term of the Coulomb interaction are considered as well as the nuclear recoil. Relativistic and screening effects are neglected. The theoretical predictions are in good agreement with experiment forα-decay and 52 MeVα-particle X-ray production. A dependence of the ionization probability on the intermediate nuclear state lifetime is found. Coincidence experiments for determining nuclear time delays are discussed.

A method to determine the life-time of a nuclear state by measuring theK-shell ionization probability

TheK-shell ionization probability, due to nuclear reactions like (n, n), (n, p), (p, p) ... is calculated using a first-order perturbation method. It is found that such a probability depends strongly on the life time of the intermediate nuclear state, and on the angle between the incoming and the outgoing particles. Graphs are presented to illustrate the general formulas and an evaluation of the experimental feasibility of the method is given for the particular case of the neutron elastic scattering.

Beta-Gamma Emission through Virtual States

The possibility of observing a combined beta-gamma transition through a virtual intermediate nuclear state in competition with a direct forbidden beta decay is investigated. Such a transition is coherent with ordinary inner bremsstrahlung associated with the direct transition and can therefore be observed through the distortion of the gamma-ray spectrum from the form predicted for inner bremsstrahlung alone. Favorable circumstances occur particularly when the intermediate state of the daughter nucleus is nearly degenerate with the ground state of the parent. The $K$-capture transition in ${\mathrm{Ni}}^{59}$ appears to offer the best possibility for such an observation. The direct observation of negative-helicity gamma rays with appropriate spectrum would be another way of directly establishing the alternate decay mode.

Effects of proton correlations on the scattering of high-energy electrons from nuclei

This paper investigates the extent to which the correlations between protons in nuclear matter manifest themselves in the scattering of high-energy electrons from nuclei. The infinite-order Born series is summed, so that dispersion effects that arise from excitation of virtual intermediate nuclear states are included to all orders. Use is made of a high-energy approximation developed earlier, and of the static or adiabatic approximation for the nuclear protons, and these are justified for incident electrons; their validity for nucleon scattering is also discussed. Expressions for the large-angle elastic and inelastic differential scattering cross-sections are obtained in this way. It is then shown that correlation effects are difficult to identify so long as the final nuclear state is well-defined. On the other hand, if a sum over final states is carried out, the effects of short-range correlations between protons appear in a characteristic way in the summed differential cross-section. These results are in qualitative agreement with those obtained earlier by others on the basis of the first and second Born approximation.

Dispersion Contribution to High-Energy Electron-Deuteron Scattering

An attempt is made to estimate the contribution of the intermediate nuclear virtual states to the high-energy electron elastic scattering cross section in the special case of the deuteron. A method is developed by which the nuclear excited states can be approximated by suitably modified free-nucleon wave functions in the sum over intermediate states. Expressions for the contribution to the cross section arising from the cross terms between the first- (in ${e}^{2}$) and second-order terms of the scattering amplitude are obtained and some numerical results are presented. Some disagreement with previous assumptions as to the magnitude of the "true" dispersion correction is indicated.

Angular Correlation of Nuclear Radiation

We wish in this review to give a short account of the theoretical and ex­ perimental work on angular correlation of successive nuclear radiation. We confine our paper to problems involving a well-defined intermediate nuclear state. Other topics, e.g., simultaneous emission of two or more particles, radiation from aligned nuclei, and angular distribution of nuclear reactions, will be omitted completely.

Lectures on ventilation

Data from the Kstop−A absorption reaction in light nuclei (6,7Li, 9Be, 13C and 16O) have recently been collected by FINUDA at DAΦNE, INFN Laboratori Nazionali di Frascati (LNF), Italy. The studies of kaon absorption on multibaryonic systems have been carried out by examining Λp(d,t) correlations. The observation of a nearly constant rate of Λp(d,t) pairs emitted in opposite direction for the targets examined suggests that the absorption of K− at rest in nuclei proceeds through the formation of an intermediate nuclear state, often named Bound Kaonic Nuclear (BKN) state. The experimental study of such states is based on the behavior of the Λp(d,t) invariant masses, which allow the structure of bound [K−NN(NNN, NNNN)] systems in nuclei to be examined. Missing mass distributions supply complementary information on the dynamics of the K− absorption.