Aspects Of Nuclear Structure Research Articles

Spin dependence in the nucleus-nucleus optical potential

The general multipole decomposition of a complete nucleon-nucleon interaction containing central, tensor, and spin-orbit components is presented in a form suitable for double-folding calculations of arbitrary nucleus-nucleus elastic scattering and transition potentials. This multipole decomposition is used to derive a general expression for the optical potential for the elastic scattering of two complex nuclei with arbitrary spin. The relationships between the terms in the nucleus-nucleus potential, the components of the nucleon-nucleon interaction, and various aspects of nuclear structure are discussed. These results are applied to obtain an estimate of the cross section and vector and tensor analyzing powers for the elastic scattering of 7Li + 58Ni at E 7 Li = 20.3 MeV which has recently been investigated experimentally. A realistic nucleon-nucleon interaction is employed in the calculations and a coupled-equations formalism is used to obtain the scattering observables. A reasonable description of the available experimental data is obtained.

Excitation of giant electric isovector resonances in pion charge exchange reactions

Pion single charge-exchange reactions exciting giant electric isovector resonances are studied for a series of nuclei. The reaction mechanism is treated in the distorted-wave impulse approximation. Emphasis is put on the nuclear structure aspects probed in these reactions. Transition densities for charge-exchange excitations are calculated using the sum-rule method and microscopically, in the Hartree-Fock---random-phase-approximation framework. The resulting cross sections are sensitive to the nuclear structure input. Double differential cross sections as functions of the nuclear excitation energy are calculated.NUCLEAR REACTIONS Pion single charge exchange exciting giant isovector resonances.

( π, d) Pick-up reaction

The reaction π + A → d + B at low energy is studied in a one-step DWBA framework. The nuclear structure aspects of the reaction are investigated. The reaction involves mostly neutron or proton pairs of the target nucleus with large total momentum and with total spin equal to zero. In the case of even-even nuclei with a partially filled shell, the coherence of the contributions from different orbitals produces an enhancement of the ground state to ground state transitions. Distortion effects are found to be very large. The final-state interaction is crucial in bringing the magnitude of the differential cross section into satisfactory agreement with the experimental value.

On Nonstatistical Effects in Nuclear Reactions

AbstractDifferent types of nonstatistical effects in nuclear reactions are discussed on the basis of a unified description of nuclear reaction and nuclear structure aspects. Particular attention is devoted to the problem of nuclear molecular states.

Spectroscopic investigation of decaying states

The relation between decay widths, partial widths and spectroscopic amplitudes is investigated in the framework of the continuum shell model allowing a unified description of nuclear reaction and nuclear structure aspects. The channel coupling is shown to be important in many cases.

Dynamical polarization in pionic atoms

Dynamical nuclear polarization occurs in pionic atoms when a nuclear excitation of appropriate multipolarity is nearly degenerate with de-excitation of a pion atomic level. This phenomenon has been studied in several nuclei, one goal being to test the pion optical potential for pion atomic states normally "hidden" because of pion absorption. We find that, in addition to Coulomb mixing of the atomic and nuclear levels; strong interaction mixing and nuclear excitations above the lowest collective quadrupole mode are important for understanding the experimental results. All cases except $^{110}\mathrm{Pd}$ can then be understood. For $^{110}\mathrm{Pd}$, additional nuclear structure information is needed to determine whether or not the conventional pion optical potential will suffice again. We discuss the sensitivity of dynamical polarization measurements to the parameters of the optical potential and to various aspects of nuclear structure. In particular, we find that pionic $^{150}\mathrm{Sm}$ provides a test of the interacting boson model and that the difference in neutron and proton radii predicted by Hartree-Fock calculations affects the mixing appreciably.NUCLEAR REACTIONS Dynamical nuclear polarization in pionic atoms $^{48}\mathrm{Ti}$, $^{104}\mathrm{Ru}$, $^{110}\mathrm{Pd}$, $^{112}\mathrm{Cd}$, $^{150}\mathrm{Sm}$; nuclear structure effects.

Kaon inelastic scattering and charge exchange on nuclei

We present the results of calculations of kaon inelastic and charge exchange reactions on nuclei, based on the microscopic particle-hole shell model. Both ${K}^{+}$ and ${K}^{\ensuremath{-}}$ inelastic scattering on $^{12}\mathrm{C}$ are discussed for incident momenta ${p}_{\mathrm{lab}}=300 \mathrm{MeV}/c \mathrm{and} 800 \mathrm{MeV}/c$. In addition, we examine the charge exchange process $^{30}\mathrm{Si}$(${K}^{\ensuremath{-}}$,${\overline{K}}^{0}$)$^{30}\mathrm{Al}$ at 300 MeV/c. We employ the distorted wave impulse approximation, using a transition operator constructed from free space ${K}^{\ifmmode\pm\else\textpm\fi{}}$-nucleon amplitudes taken from analyses of two-body data. For the off-shell extrapolation of the two-body $t$ matrix, required in the many-body problem, we use a separable form factor obtained by solving the inverse scattering problem. The inelastic scattering results are found to be insensitive to the presence of the off-shell form factor. We find that normal parity $T=0 \mathrm{and} 1$ states dominate the nuclear response to both ${K}^{+}$ and ${K}^{\ensuremath{-}}$. At 300 MeV/c, some qualitative differences in the inelastic scattering predictions arise from choosing different elementary amplitudes from the literature. Thus kaon-nucleus scattering may shed some light on ambiguities in the low energy free space interactions of kaons. At 800 MeV/c, there is much less uncertainty in the two-body $t$ matrix, so we can focus our attention on nuclear structure aspects. We compare the kaons with pions, electrons, protons, and $\ensuremath{\alpha}$ in terms of their inelastic scattering and charge exchange properties. By emphasizing nuclear structure aspects such as the excitation of high spin states and the splitting of the ${T}_{<}$ and ${T}_{>}$ components of giant resonances, we show that kaons are very promising as a nuclear probe.NUCLEAR REACTIONS, NUCLEAR STRUCTURE $^{12}\mathrm{C}$(${K}^{\ifmmode\pm\else\textpm\fi{}}$,${K}^{\ifmmode\pm\else\textpm\fi{}\ensuremath{'}}$)$^{12}\mathrm{C}$* ${p}_{\mathrm{lab}}\ensuremath{\approx}300\ensuremath{-}800$ MeV/c; $^{30}\mathrm{Si}$(${K}^{\ensuremath{-}}$, ${\overline{K}}^{0}$)$^{30}\mathrm{A}1$*, ${p}_{\mathrm{lab}}=300$ MeV/c theoretical estimates based on DWIA for kaon inelastic and charge exchange $\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}$; virtues of kaons as nuclear structure probe.

Level structure and lifetimes of excited states in 48Ti

The properties of excited states in 22 48Ti 26 populated by means of the 45Sc(α, pγ) 48Ti reaction were investigated. The Doppler-shift attenuation method was employed to determine the mean lives of 16 levels up to an excitation energy of 4073 keV. Proton-γ coincidence techniques were used to record simultaneously the Doppler-shifted de-excitation γ-rays emitted at 26 and 154 degrees to the incident beam direction. A comprehensive level and decay scheme is proposed. Detailed shell-model calculations have been made of M1 and E2 transition matrix elements for depopulation of states whose lifetimes have been measured. Salient nuclear structure aspects of this “self-cross-conjugate” nucleus are examined in light of critical comparisons of measured and calculated Ml and E2 reduced transition probabilities.

Nuclear muon capture - theoretical aspects

In the first two lectures, we discuss what can be learned about the particle physics and nuclear structure aspects from the study of the nuclear muon capture. In the third lecture, we examine the adequacy of the naive impulse approximation approach in describing the capture reaction in complex nuclei and related processes.

Kaonic atoms and the Λ(1405)

Kaonic shifts and widths for 12C and 32S are analysed using an optical potential, which selectively incorporates nuclear shell structure aspects as well as effects of Λ(1405) dynamics inside the nucleus. Good agreement with data is found and suggests a moderately repulsive interaction of the Λ(1405) with surrounding nucleons.

International Review of Cytology. Supplement 4. Aspects of Nuclear Structure and Function.G. H. Bourne, J. F. Danielli

Previous articleNext article No AccessNew Biological BooksInternational Review of Cytology. Supplement 4. Aspects of Nuclear Structure and Function. G. H. Bourne, J. F. DanielliDominic L. PocciaDominic L. Poccia Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The Quarterly Review of Biology Volume 50, Number 4Dec., 1975 Published in association with Stony Brook University Article DOIhttps://doi.org/10.1086/408783 Copyright 1975 Stony Brook Foundation, Inc.PDF download Crossref reports no articles citing this article.

Calculations of harmonic oscillator brackets

Oscillator brackets are used in various aspects of nuclear structure and reaction calculations. The program calculates these very rapidly. The method is to use a closed form for an oscillator bracket as given by Baranger and Davies (1966), and then to calculate simultaneously a large number of brackets that have different sets of principal quantum numbers for a given set of angular-momentum quantum numbers. Restrictions come about only through the size of the core storage assigned by the DIMENSION statements. The storage presently assigned will meet the needs of most present-day nuclear physics calculations. The running time of the program ranges roughly from 600 to 1000 brackets per second of CP time on the CDC 6600 computer at the computer center of the University of Texas. (NL)

Hydrogen burning of 20Ne and 22Ne in stars

Abstract The 20 Ne(p, γ) 21 Na capture reaction has been studied in the energy range E p = 0.37–2.10 MeV. Direct-capture transitions to the 332 ( 5 2 + ) and 2425 keV ( 1 2 + ) states have been found with spectroscopic factors of C 2 S (1d) = 0.77±0.13 and C 2 S (2s) = 0.90±0.12, respectively. The high-energy tail of the 2425 keV state, bound by 7 keV against proton decay, has also been observed in the above energy range as a subthreshold resonance. The excitation function for this tail is consistent with a single-level Breit-Wigner shape for a γ-width of Γ γ = 0.31±0.07 eV at E x = 2425 keV. The extrapolation of these data to stellar energies gives an astrophysical S -factor of S (0) = 3500 keV · b. Two new resonances at E p = 384±5 and 417± 5 keV have been observed with strengths of ωγ = 0.11±0.02 and 0.06±0.01 meV, corresponding to the known states at E x (J π) = 2798 ( 1 2 − ) and 2829 keV (presumably 9 2 + ), respectively. For the known E p = 1830 keV resonance, a strength of ωγ = 1.0± 0.3 eV and a total width of Γ = 180± 15 keV were found. Branching ratios as well as transition strengths have been obtained for these three states. The Q -value for the 20 Ne(p, γ ) 21 Na reaction ( Q = 2432.3 ± 0.5 keV) as well as excitation energies for many low-lying states in 21 Na have been measured. No evidence was found for the existence of the state reported at E x = 4308±4 keV. In the case of 22 Ne(p, γ) 23 Na, direct-capture transitions to six final bound states have been observed revealing sizeable spectroscopic factors for these states. The astrophysical S -factor extrapolated from these data to stellar energies, is S (0) = 67 ± 12 keV · b. The astrophysical as well as the nuclear structure aspects of the present results are discussed.

A few uses of elementary particles in nuclear structure studies

A selective review is given of some of the ways in which “elementary particles” and the techniques of high energy physics in general may be used for the investigations of nuclear structure. It is pointed out that our ability to extract new nuclear structure information from such experiments is often limited by our present ignorance on other aspects of nuclear structure.

Rotation of Elongated Atomic Nuclei

Many nuclei exhibit rotational spectra much as molecules do. A rotational spectrum is recognized by the ratios of the successive spacings between the levels. The magnitude of this spacing is inversely proportional to the moment of inertia of the rotating object. For a molecule, the moment of inertia is quite simply determined by the fairly definite positions of the atomic nuclei where practically all the mass is concentrated. In nuclei there are no fixed masses and the very possibility of rotation depends on the nuclear shape being out-of-round. The moment of inertia is determined by the way the internal motions of the nucleons are influenced by the rotation. The hydrodynamic calculation based on treating the nuclear “fluid” like water with no friction gives too small a moment of inertia, which means calculated levels are more widely spaced than observed, by about a factor five. Among all the complicated aspects of nuclear structure, one aspect of the motion of nucleons that can be described in simple graphic terms is the influence of rotation. It is shown that this leads to large contributions to the moment of inertia by the few nucleons not in closed shells. Thus it is possible to understand in fairly simple terms how the moment of inertia can be greater than that calculated for a distorted droplet of “nuclear fluid,” though one manner of estimating the effect somewhat overshoots the experimental result.

On the description of collective motion by the use of superfluous co-ordinates

By introducing superfluous co-ordinates a method is demonstrated for treating the problem of combined collective and individual particle aspects of nuclear structure. The application to the case of the center of mass gives a simple exposition of the method and rigorously defines conditions for the validity of the usual shell-model assumptions regarding the center of mass. The application to rotation gives results similar to those obtained by A. Bohr using a hydrodynamical model and by Inglis using a classical rotating shell model. The present treatment is rigorous except for the fundamental shell-model assumption, the replacement of the inter-particle potential by a single-particle potential which may not be spherically symmetric.

The low energy nuclear excitation spectrum

Various types of nuclear reactions yield information on different aspects of nuclear structure. Inelastic scattering reactions which proceed by direct interaction are especially suited for the study of collective modes of excitation of the nucleus. Most quantitative information is obtained from Coulomb excitation processes. The evidence available from low energy nuclear spectra is summarized. For even-even nuclei, the first few excited levels can in most cases be rather well described in terms of collective modes of motion. In odd-A (or odd-odd) nuclei, the relevant degrees of freedom include also those of the last nucleon(s). The collective modes correspond to oscillations of the nuclear shape and are influenced in an essential manner by the shell structure. For configurations with relatively few particles in unfilled shells, the collective excitations represent vibrations about a spherical equilibrium shape. If the nucleus contains sufficiently many particles in unfilled shells, an ellipsoidal equilibrium shape results. The collective excitations then separate into vibrations about the equilibrium shape and rotations with preservation of shape. While the dominating shape oscillations and deformations are of quadrupole type and give rise to excitations with no parity change, evidence has also recently become available on collective excitations of odd parity.

Approximate Reduction of the Many-Body Problem for Strongly Interacting Particles to a Problem of Self-Consistent Fields

It is shown for systems of strongly interacting particles that in the limit of very many particles a transformation exists leading to an alternative problem which can be solved by a self-consistent field method. The transformed wave function describes "particles" moving in a collectively determined uniform potential; the transformation relating the transformed and original wave functions determines the amount of incoherence and correlation in the original function. The method appears to be more useful for fermion systems and is illustrated by applications to some aspects of nuclear structure.

Theory of Polarization of Nucleons Scattered Elastically by Nuclei

A study of the nucleon polarization to be expected when nucleons are elastically scattered from nuclei is presented. The polarization effect is a consequence of the fact that the nucleon-nucleus interaction may be represented as a complex spin-dependent potential. The existence of such a potential is suggested by the nuclear shell model and the spin dependence of the nucleon-nucleon interaction. Qualitative arguments are advanced to determine this potential in terms of the nucleon-nucleon interaction. Although the polarization effect is by no means confined to elastic scattering, it is in this case particularly useful, since the large diffraction cross sections observed experimentally insure relatively high yields of polarized particles. A number of theoretical studies have been carried out, for both neutron and proton scattering, which show that almost full polarization can occur. The calculations have been carried out by using the W.K.B. approximation as usually applied to the nuclear optical model. The method has been checked by carrying out an exact phase shift analysis for a particular case. The results show that studies of nucleon polarization can illuminate some aspects of nuclear structure, since the polarization depends on the particular nucleus used as a target as well as upon the form of the interaction.

Low Excited States ofF19. I. Proton Inelastic Scattering

The spins, parities, and other properties of the low states of F19 are of considerable interest in connection with the shell model and collective aspects (1) of nuclear structure. Of particular interest in this connection are the first and second excited states of F19 discovered in this laboratory by Mileikowsky and Whaling. (2) In this and the following notes,(3) studies of the excitation of these states in the inelastic scattering of protons and alpha particles by F19 are reported. This note is primarily concerned with the inelastic proton groups and the de-excitation gamma radiation accompanying the inelastic scattering.