Nuclear Pairing Correlations Research Articles

Inelastic electron scattering from fluctuations in the nuclear charge distribution

This paper concerns itself with the cross section σ( q, ω) for scattering of electrons through momentum transfer q and energy loss ω from heavy nuclei. This cross section is related to the four-dimensional Fourier transform of the nuclear time-dependent pair correlation function; this latter function gives a measure of the fluctuation of the charge density about its mean value. In an infinite medium there are regions of the q- ω plane where scattering is possible only if dynamical (in contrast to statistical) correlations are present. We present an argument which leads to the conclusion that even for finite nuclei there is still a fairly well defined boundary outside of which the scattering is due solely to correlations impressed on the ground state by the nuclear forces. Since one would only carry out such experiments on heavy nuclei, we also discuss the break down of the Born approximation and conclude that one may readily and quite reliably correct for this. A general discussion of some possible methods for computing the relevant correlation function is given. We also present a detailed calculation of the cross section σ( q, ω) for scattering from a gas of nucleons with hard core interactions. This calculation is expected to give the qualitative features of the cross section for real nuclei when the values of q and ω are properly chosen. Furthermore, it leads to estimates of the relative importance of various diagrams which should be useful in calculations with more realistic nuclear models.

Evidence of Nuclear Structures fromK−-Meson Absorption

The characteristics of the multinucleon capture of ${K}^{\ensuremath{-}}$ mesons in nuclei have been investigated in both normal and water-soaked $G5$ nuclear emulsion. It has been found that the emission of fast (⋝ 60 MeV) hyperons is more often associated with ${K}^{\ensuremath{-}}$ captures in light (C,N,O) than in heavy (Ag,Br) nuclei. Further, considering the relative absorptions of $\ensuremath{\Sigma}$ hyperons in the parent nucleus in which they are produced, we inferred that the rate of multinucleon ${K}^{\ensuremath{-}}$ absorptions is approximately the same for all nuclei of nuclear emulsion and corresponds to \ensuremath{\sim}17% of all ${K}^{\ensuremath{-}}$ absorptions at rest. From those events which can be definitely assigned to interactions in light nuclei, by virtue of energy and momentum conservation, it was found that the reaction ${K}^{\ensuremath{-}}+(n, n)\ensuremath{\rightarrow}{\ensuremath{\Sigma}}^{\ensuremath{-}}+n$ is of comparable intensity with the reaction ${K}^{\ensuremath{-}}+(n, p)\ensuremath{\rightarrow}{\ensuremath{\Sigma}}^{\ensuremath{-}}+p$, and that in light nuclei, the major mode of multinucleon ${K}^{\ensuremath{-}}$ absorption in C,N,O appears to be on a pair of nucleons in an $\ensuremath{\alpha}$-particle cluster. Comparison of the characteristics of the ${K}^{\ensuremath{-}}$ multinucleon absorptions in light and heavy nuclei shows that $\ensuremath{\alpha}$-particle clusters are less likely to be involved in (Ag,Br) than in (C,N,O). An attempt to estimate the nuclear pair correlation function was also made.

The determination of the nuclear pair correlation function and momentum distribution

This paper presents a critical discussion of some of the suggestions which have been put forward for measuring the nuclear momentum distribution F( p) and pair correlation function C(r 1r 2). On the basis of qualitative arguments we conclude that a majority of the measurements of F and C are based on dubious analysis of the experimental data. In particular, the use of the impulse approximation in these analyses is brought into question. Although we do not question the conclusion that F( p) has many high momentum components, we argue that we have no reliable quantitative knowledge regarding F( p) at this time. We discuss various experiments related to the measurement of C, in particular inelastic electron scattering, and the (γ, pn) reaction. Here too we conclude that our present knowledge is virtually nil. Some rigorous formulae for the cross sections measured in pursuit of F and C are also given.

The determination of the nuclear pair correlation function and momentum distribution: Kurt Gottfried. Harvard University, Cambridge, Massachusetts

The determination of the nuclear pair correlation function and momentum distribution: Kurt Gottfried. Harvard University, Cambridge, Massachusetts

Binding energies of Λ particles and the Λ-N interaction

The implications of Λ-binding energies for the Λ-nucleon interaction have been considered when three-body forces are included in addition to two-body Yukawa forces. In part I the light hypernuclei with baryon number ≦ 5 are considered. For ΛH 3 the effect of three-body forces is small and may be obtained by a perturbation procedure; the binding energy of ΛH 3 being almost entirely determined by the two-body forces. For ΛH 5 the He 4 core is assumed to be undistorted by the Λ. The binding energies of ΛH 4, ΛHe 4 do not seem capable of yielding significant information about the interaction strenghts. The two-body system ΛH 2 is not bound unless the three-body forces are very strongly attractive. In part II the potential felt by a Λ in nuclear matter, this being considered as a Fermi gas, is calculated using perturbation theory. Both direct and exchange two-body forces are considered. The second order contributions, the effect of nuclear pair correlations and the velocity dependence are all small. The nucleon exchange factor used for the three-body forces strongly suppresses their effect in nuclear matter. The implications of ‘empirical’ values of the Λ-potential depth are considered. In particular if the pion-baryon couplings predominate then strongly attractive three-body forces of not too large a range are favoured, corresponding to a larger singlet than triplet two-body volume integral.

π−Capturel in Complex Nuclei and Nuclear Pair Correlations

Scintillation counters in coincidence were used as detectors of neutrons and protons produced in pi /sup -/ capture by complex nuclei. By measuring neutrons, it was hoped to establish whether pi /sup -/ capture in complex nuclei involves two nucleons, and if it does, to use the process to study the ratio of neutron--proton pairs to proton--proton pairs. The pi /sup -/ mesons were stopped in Li, C, Al, S, Cu, and Pb targets. In order to test the spatial correlation of the ejected nucleons, measurements were made with the counters 90 and 180 deg from each other. The results obtained are given as coincidences as a function of angle. If corrections are made for relative probability of detecting neutrons and protons, the following ratios of n--n events (a) STA pi / sup -/ + p + n yields n + n! to n--p events (b) STA pi /sup -/ + p + p yields n + p! are obtained: carbon, a/b = 5.0 plus or minus 1.5; aluminum, a/b = 3.9 plus or minus 1.2. Due to background subtractions and secondary events contributing more to the proton coincidence runs, it is felt that these observed ratios are to bemore » taken as lower limits on the ratio of reaction. (B.O.G.)« less

On the determination of the nuclear pair correlation function from the high energy photo-effect

In accordance with Levinger's predictions, the absorption of a high energy photon frequently results in the simultaneous ejection of a neutron and proton. The present paper provides a theoretical analysis of this direct reaction which starts from first principles and is based on the following assumptions: (i) the impulse and closure approximations are valid, (ii) the photo-nuclear interaction is a sum of two-nucleon operators, and (iii) the pair correlation function is given by ∂ s ( r 1, r 2)|g( r 1 − r 2)| 2 where ∂ s is the shell model correlation function and g( x) contains those correlations directly due to nuclear forces. The cross section is then shown to be proportional to the probability for finding two nucleons with a certain total momentum in a relative S-state, the contributions from P-states being demonstrably small. The further assumptions required to relate the nuclear cross section to the one for photodissociation of deuterium are examined, while final state interactions are treated with an optical model. The theory is compared with the present data and found to be in good agreement. The type of further information required for ascertaining the validity of assumptions (ii) and (iii) is discussed, and a method for acquiring it suggested.