Direct Nuclear Reactions

The following sections are included:

• Contents

• Preface

• Acknowledgments

• Notational Conventions

The following sections are included:

• THE OBSERVABLES

• DIRECT AND COMPOUND NUCLEAR REACTIONS

• COMPETITION BETWEEN DIRECT AND COMPOUND NUCLEAR REACTIONS

• HISTORICAL NOTE

The difference between direct and compound nuclear reactions has been discussed. In the direct reaction, the incident particle interacts with the target nucleus only several times at most. Therefore the change produced in the target must be a simple rearrangement of one or several nucleons or collective degrees of freedom. Because of the conservation laws, the change produced in the nucleus must be reflected in the energy and angular momentum carried by the outgoing particle…

The following sections are included:

• MOTIVATION

• THE NUCLEAR SHELL MODEL

• REACTION CHANNELS OR PARTITIONS

• INTEGRAL EQUATIONS AND THE SCATTERING AMPLITUDE

• ASYMPTOTIC FORM OF THE COMPLETE WAVE FUNCTION

• THE FIRST BORN APPROXIMATION

• CROSS SECTION

• Notes to Chapter 3

The following sections are included:

• RATIONALE FOR THE OPTICAL POTENTIAL

• PARTIAL WAVE EXPANSION, THE RADIAL WAVE FUNCTION, ITS ASYMPTOTIC BEHAVIOR

• ELASTIC SCATTERING AMPLITUDE

• COULOMB AND NUCLEAR POTENTIALS

• PARAMETERIZATION OF THE OPTICAL POTENTIAL

• ELASTIC SCATTERING OF ALPHA PARTICLES

• SPIN-ORBIT INTERACTION AND NUCLEON ELASTIC SCATTERING

• ELASTIC SCATTERING OF HEAVY IONS

• THE IMAGINARY POTENTIAL AND MEAN FREE PATH

• SYSTEMATICS OF THE PARAMETERS

• NONLOCALITY OF THE OPTICAL POTENTIAL

• CONVERGENCE OF THE PARTIAL WAVE SUM

• Notes to Chapter 4

The following sections are included:

• INTRODUCTION

• DISTORTED-WAVE GREEN'S FUNCTIONS

• THE GELL-MANN–GOLDBERGER TRANSFORMATION

• TWO-POTENTIAL FORMULA

• THE DWBA TRANSITION AMPLITUDE

• DISCUSSION OF THE APPROXIMATIONS

• ANTISYMMETRIZATION

• MULTIPOLE EXPANSION OF THE TRANSITION AMPLITUDE

• Notes to Chapter 5

The following sections are included:

• INTRODUCTION

• LIPPMANN–SCHWINGER EQUATlON

• FORMAL SOLUTION

• TRANSITION AMPLITUDE

• TRANSITION OPERATOR T

• GELL-MANN–GOLDBERGER TRANSFORMATION

• DISTORTED-WAVE GREEN'S FUNCTION

• DISTORTED-WAVE BORN APPROXIMATION

• SECOND DISTORTED-WAVE BORN APPROXIMATION

• MULTIPLE-SCATTERING SERIES OF WATSON

• GREEN'S THEOREM AND THE HERMITIAN H

• Notes to Chapter 6

The following sections are included:

• INTRODUCTION

• THE (d, p) STRIPPING REACTION

• ZERO-RANGE APPROXIMATION

• EXAMPLES

• IMPROVEMENTS WITHIN THE FRAMEWORK OF THE DWBA

• SPECTROSCOPIC FACTORS FOR ONE-NUCLEON TRANSFER

• PAIRING THEORY IN NUCLEAR STRUCTURE

• INELASTIC EXCITATION OF SURFACE VIBRATIONS

• INELASTIC EXCITATION OF NUCLEAR ROTATIONAL LEVELS

• INELASTIC EXCITATION OF SINGLE-NUCLEON STATES

• CHARGE-EXCHANGE REACTIONS

• DISTORTED-WAVE IMPULSE APPROXIMATION

• COULOMB EXCITATION

• Notes to Chapter 7

The following sections are included:

• COUPLED EQUATIONS FOR INELASTIC SCATTERING

• TRUNCATION AND EFFECTIVE INTERACTIONS

• THE EFFECTIVE INTERACTION

• NONLOCALITY

• MULTIPLE-SCATTERING SERIES FOR THE EFFECTIVE INTERACTION

• PARTIAL-WAVE EXPANSION

• BOUNDARY CONDITIONS

• DISTORTED-WAVE BORN APPROXIMATION

• CROSS SECTIONS

The following sections are included:

• THE RICHNESS OF NUCLEAR STRUCTURE

• DISCUSSION OF THE INTERACTIONS IN THE COUPLED EQUATIONS

• MATRIX ELEMENTS OF THE EFFECTIVE INTERACTION

• SELECTION RULES

• NUCLEAR FORM FACTOR

• SINGLE-PARTICLE FORM FACTORS

• NUCLEAR STRUCTURE AMPLITUDES

• SHELL-MODEL CONFIGURATIONS

• PARTICLE CREATION AND DESTRUCTION OPERATORS

• PARTICLE-HOLE CONFIGURATIONS

• QUASI-PARTICLE CONFIGURATIONS

• RECAPITULATION

• THE DIRECT INTERACTION AND ITS SPIN DEPENDENCE

• SELECTION RULES AND THE DIRECT INTERACTION

• APPLICATION OF THE THEORY

• Notes to Chapter 9

In the introduction to Chapter 9, it was mentioned that a discussion of nuclear reactions may, in general, require corrections arising both from a truncation of the channel space in which the scattering problem is solved as well as from the truncation of the configuration space in which the nuclear problem is solved. The general formulation of effective operators within a truncated shell-model space would parallel the development in Chapter 8. However, instead we now discuss a simple model, introduced by Love and Satchler (1967), that is a particular case of the general theory…

The following sections are included:

• INTRODUCTION

• THE FREE-NUCLEON–NUCLEON INTERACTION

• THE BRUECKNER G MATRIX

• BARE G MATRIX AND CORE POLARIZATION

• EFFECTIVE INTERACTION IN SCATTERING

• LOW-ENERGY DOMAIN

• HIGH-ENERGY DOMAIN (E > 100 MeV)

• MICROSCOPIC CALCULATION OF THE OPTICAL POTENTIAL

The following sections are included:

• INTRODUCTION

• GENERAL FORM OF THE TWO-BODY AMPLITUDE

• LOCAL COORDINATE-SPACE REPRESENTATION OF G OR t

• ENERGY AND MOMENTUM DEPENDENCE OF THE EFFECTIVE INTERACTION IN THE HIGH-ENERGY DOMAIN

• EFFECTIVE OPERATOR FOR THE EXCHANGE CONTRIBUTION

• MULTIPOLE EXPANSION OF THE INTERACTION

• TRANSITION DENSITIES

• CROSS SECTIONS

• APPLICATIONS

The following sections are included:

• WAVE FUNCTIONS OF DEFORMED NUCLEI

• MULTIPOLE EXPANSION OF THE INTERACTION

• COUPLED EQUATIONS

• RELATION BETWEEN OPTICAL POTENTIAL OF SPHERICAL AND DEFORMED NUCLEI

• ALPHA SCATTERING FROM DEFORMED RARE-EARTH NUCLEI

• Notes to Chapter 13

The following sections are included:

• INTRODUCTION

• POTENTIAL COMPONENTS OF A SINGLE LEVEL

• TRIVIALLY EQUIVALENT LOCAL POTENTIAL

• LONG-RANGE ABSORPTION DUE TO COULOMB EXCITATION

The following sections are included:

• CONTRAST BETWEEN ONE- AND TWO-NUCLEON TRANSFER REACTIONS

• TRANSFER FROM A LIGHT-ION PROJECTILE

• SPIN–ISOSPIN SELECTION RULES

• FORM FACTOR

• INTERPRETATION OF THE FORM FACTOR

• TRANSITION AMPLITUDE AND CROSS SECTION

• CORRELATIONS

• PARENTAGE AMPLITUDE FOR TWO NUCLEONS

The following sections are included:

• INTRODUCTION

• THE DWBA AMPLITUDE AND ITS COORDINATE DEPENDENCES

• PARENTAGE EXPANSIONS

• THE (t, p) REACTION

• TWO-NUCLEON TRANSFER BETWEEN HEAVY IONS

The following sections are included:

• BEYOND THE DWBA

• COUPLED-CHANNEL BORN APPROXIMATION (GENERALIZED DWBA)

• SOURCE-TERM METHOD

• DERIVATION OF THE CCBA

• COUPLED REACTION CHANNELS (CRC)

• PARTIAL-WAVE EXPANSIONS AND DERIVATION OF THE CROSS SECTION

• TWO-NUCLEON TRANSFER BETWEEN VIBRATIONAL NUCLEI

• TWO-NUCLEON TRANSFER BETWEEN ROTATIONAL NUCLEI

• INDIRECT TRANSITIONS IN ANALOG REACTIONS

The following sections are included:

• SPECIAL FEATURES

• THE POTENTIAL

• DEFLECTION FUNCTIONS, CLASSICAL CONDITIONS, PLUNGING ORBITS, GRAZING PEAK

• ELASTIC AND INELASTIC SCATTERING AND THE OPTICAL POTENTIAL

• INDIRECT TRANSITIONS IN TWO-NUCLEON TRANSFER, OPPOSITE BEHAVIOR FOR STRIPPING AND PICKUP

• FORWARD-ANGLE RIPPLES, UNCERTAINTY PRINCIPLE

• STRUCTURE OF THE S MATRIX, SPECULATIONS ON FUTURE DEVELOPMENTS

• SUMMARY

• Notes to Chapter 18

The following sections are included:

• INTRODUCTION

• THE EXPERIMENTAL FACTS

• A POSSIBLE EXPLANATION

• ADIABATIC ESTIMATE

• DYNAMICAL DESCRIPTION OF POLARIZABILITY

The following sections are included:

• Appendix Some Useful Reminders
  • LAPLACE OPERATOR
  • SPHERICAL HARMONICS
  • ANGULAR-MOMENTUM COUPLING; CLEBSCH–GORDAN COEFFICIENTS
  • ANGULAR-MOMENTUM RECOUPLING
  • SPHERICAL TENSORS
  • REDUCED MATRIX ELEMENTS—WIGNER–ECKART THEOREM
  • SCALAR PRODUCT OF TWO COMMUTING TENSORS
  • VECTOR PRODUCT OF TWO COMMUTING TENSORS
  • VECTOR AND VECTOR PRODUCT
  • REDUCED MATRIX ELEMENT OF SPIN OPERATOR
  • ROTATION FUNCTIONS
  • OSCILLATOR FUNCTIONS
  • SPHERICAL BESSEL FUNCTIONS
  • Notes to Appendix

• References

• Index