Table Of ContentIntermediate-Energy
Nuclear Physics
A. S. Iljinov
M. V. Kazarnovsky
E. Ya. Paryev
Institute for Nuclear Research of the
Academy of Sciences of Russia
Moscow, Russia
Boca Raton London New York
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Library of Congress Cataloging-in-Publication Data
Il’inov, A. S., 1944-
Intermediate-energy nuclear physics/A.S. Iljinov, M.V. Kazarnovsky, E. Ya. Paryev.
p. cm.
Includes bibliographical references and index.
ISBN 0-8493-4827-7
1. Nuclear reactions. 2. Hardron Interactions. I. Kazarnovskii,
M. V. II. Par’ev, E. IA. III. Title.
Qc794.144 1993
539.7’5--dc20 93-9456
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PREFACE
During the last two decades, qualitatively new high-intensity proton accelerators
up to 1 GeV with mean current of about 1 rnA have been created. These are the
so-called "meson facilities". The "kaon facilities", i.e., high-intensity proton
accelerators which produce particles with energies of several tens Ge V, are currently
being constructed. As a result of the interaction of such protons with various targets,
intensive secondary beams of neutrons, pions, kaons, antinucleons and other par-
ticles, as well as radionuclides, are generated. All such particles are usually called
intermediate-energy particles and their interaction with nuclei is referred to as
intermediate-energy nuclear reactions.
The high intensity of beams of intermediate-energy particles makes it possible
to carry out experimental investigations of their interaction with nuclei with a high
degree of statistical reliability. Owing to the considerable advances made in in-
strument design and the methods used for registering the products of nuclear re-
actions and computerization of the experimental procedure, the possibilities to
obtain, process, and analyze a large body of experimental data have grown con-
siderably. All this ensures a rapid influx of data (and a significantly higher order
of accuracy) on nuclear reactions in the intermediate-energy range. A large body
of such information has been accumulated so far.
In turn, these developments have given impetus to intensive theoretical studies
in this field, especially to the study of deep inelastic processes, such as branched
nucleonic-mesonic cascade and break-up of highly-excited nuclei, which are char-
acteristic of the energy range under consideration. On the other hand, the entire
body of this information has not been systematized. Our monograph aims at
r.IIing this gap.
In this connection, it should be emphasized that intermediate-energy nuclear
physics has two peculiar features which make it a separate line of scientific inves-
tigation.
Indeed, nuclear reactions in the domain of low energies have, as a rule, a
relatively small number of open channels (witb the only exception being that of
fission of heavy nuclei). Therefore, the exclusive experimental and corresponding
theoretical investigation of a reaction is quite possible and often realized in practice.
As the energy increases, new channels readily open and, in particular, channels
involving the emission of an every-increasing number of particles. In this case,
complete, exclusive experimental investigation of a reaction involves considerable
difficulties and, finally, becomes practically impossible in spite of the previously
mentioned achievements of the experimental technique. This is just the case in the
domain of intermediate energies. This is the first peculiarity that distinguishes this
energy range.
The second peculiarity is associated with specific features of the theoretical
description of nuclear reactions in this energy range. In this instance a statistical
approach must be used to describe such a complicated and branched nuclear process
involving a large number of different states of the system at the same energy.
Moreover, in this energy range the wavelength of an incident hadron is small as
compared to the separation between nucleons in a nucleus; its energy is large as
compared to the mutual interaction energy and the kinetic energy of intranuclear
nucleons. Therefore, to describe the behavior of intermediate-energy particles in a
nucleus we can use simplified approaches (such as semiclassical, eikonal, and other
approximations) which are characteristic of this energy range.
The monograph is devoted mainly to the interaction of hadrons with nuclei
which leads to the excitation of a large number of degrees of freedom in a nucleus
and, as a result, to the emission of several particles during an intranuclear cascade
and subsequent decay of a highly-excited residual nucleus. These processes are
described on the basis of a unified approach which reflects the peculiar features of
intermediate-energy nuclear physics as outlined. Namely, the stage of an intranuclear
cascade and the characteristics (distributions over the number of protons and neu-
trons, over the excitation energy, etc.) of a residual nucleus are treated by the
method of classical (more precisely, semiclassical) kinetic equations, whereas the
decay of a residual nucleus is described within the framework of a statistical model.
The methods and results of the calculation of probabilities of various processes
initiated by intermediate-energy hadrons in nuclei and experimental data are set
forth and discussed. The possibility of obtaining information on the structure and
properties of nuclei, in particular on the properties of highly-excited nuclear matter,
by comparing the experimental data with the theoretical results is analyzed. Special
attention is paid to new issues, like analytic methods for solution of kinetic equations
describing the cascade. In particular, the exclusive description of an intranuclear
cascade on the basis of the Liouville equation is given for the first time, to our
knowledge, in Chapter 1. Other new areas of attention are nuclear absorption of
hadrons from bound states of hadronic atoms, interaction of antinucleons with
nuclei, multifragmentation of highly-excited residual nuclei, and polarization phe-
nomena. These also have not been previously discussed in detail in the current
literature.
The study of the interaction between nuclei, which is closely related to the
previously mentioned issues, is a separate, large problem which is extensively
studied in the literature. Therefore, we shall not dwell on this problem here. How-
ever, a peculiar nature of physics of hadron-nucleus interactions which bridges the
gap between low-energy nuclear and heavy-ions physics will be demonstrated.
This range of issues can be useful in the analysis of problems associated with
the evolution of the early (hot) universe, neutron stars and supernovas, and in
solving a number of applied problems (e.g., the problems associated with the after-
burning of radioactive waste in nuclear energy installations and with electronuclear
breeding of energy).
In conclusion, the authors would like to express their thanks to Andrei R.
Isaakian who worked laboriously and skillfully to present this book in English.
Additionally, A. S. I1jinov is grateful to his co-authors, V. S. Barashenkov, A. S.
Botvina, E. A. Cherepanov, S. E. Chigrinov, F. G. Gereghi, Ye. S. Golubeva,
K. K. Gudima, S. G. Mashnik, M. V. Mebel, I. N. Mishustin, V. I. Nazaruk,
I. A. Pshenichnov, N. M. Sobolevsky, and V. D. Toneev, with whom he developed
models of nuclear reactions, for helpful discussions and fruitful collaboration.
THE AUTHORS
A. S. Iljinov, Ph.D., is a head of the radioisotope laboratory at the Institute
for Nuclear Research of the Academy of Sciences of Russia. He has been associated
with the institute since 1974. This site is the Moscow meson facility. Prior to 1970
he was associated with the Joint Institute for Nuclear Research, Dubna. He received
his first doctoral degree in physics in 1971 while working at the Laboratory of
Theoretical Physics of the Joint Institute for Nuclear Research, Dubna. He received
his second doctoral degree in 1985 while at the Institute for Nuclear Research.
His current interests focus on the theory of nuclear reaction. Together with his
colleagues he has formulated the optical-cascade model of nuclear absorption of
stopped pions and antiprotons and has also developed the statistical model of multi-
fragmentation of nuclei by intermediate energy particles. He has also participated
in the discovery and study of the cold fusion of two nuclei which has been used
in the synthesis of chemical elements 106 through 109. In 1984 he proposed the
use of the Moscow meson facilty for production of high intensity radioactive nuclear
beams.
Dr. Iljinov is the author or co-author of 140 scientific articles. He is co-author,
along with Professor G. N. Flerov, of On the Way to Super-Elements (Pedagogics
Publishers, Moscow, 1982) which has been translated into several languages, and
of the handbook of Production ofR adionuclides ofI ntermediate Energies (Landolt-
Bornstein, Vol. 13, Springer-Verlag, Berlin, 1991).
M. V. Kazarnovsky, Ph.D., is the head of one of the theoretical laboratories
of the Institute for Nuclear Research of the Russian Academy of Sciences and has
been associated with the institute since 1970. He is also a Professor at the Moscow
Physical-Technical Institute, where he is a lecturer in nuclear physics. Prior to 1970
he was associated with the Lebedev Physical Institute of the Academy of Sciences
of the U.S.S.R. He received his first doctoral degree in 1955, a second doctoral
degree in 1971, and the title of professor in 1987.
Dr. Kazarnovsky is the author or co-author of more than 120 scientific works
and two monographs, primarily on the following topics: the theory of non-stationary
neutron transport, the theory of nuclear reactions at intermediate energies, and the
physics of ultracold nuetrons.
E. Ya. Paryev, Ph.D., is a senior scientist at the Institute for Nuclear Research
of the Academy of Sciences of Russia and has been associated with the institute
since 1974. He received his doctoral degree in 1985; the subject of his thesis was
the application of the kinetic equations method in theory of nucleon-nucleus re-
actions at intermediate energies.
Together with Professor M. V. Kazarnovsky, he has developed, on the basis
of these equations, the new analytic approach for the description of inclusive in-
termediate-energy nucleon-nucleus reactions, which take into account the spin de-
pendence of the NN-interaction and quantum-mechanical effects at the initial state
of this reaction as well.
He has also worked out various problems in the field of applied nuclear physics:
transport of neutrons, charged particles in solids, and radiation protection of high-
current accelerators. His current focus of interest is on the theory of production of
various mesons (K"', 11, w) in the nucleon-nucleon and nucleon-nucleus collisions
at different energies.
Dr. Paryev has published 40 scientific papers and has presented reports at a
variety of international conferences.
TABLE OF CONTENTS
INTRODUCTION ............................................................... 1
I. Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
II. Classification of Cross-Sections of NRs ................................. 2
III. Quantum Formulation of Collision Problem ............................. 5
A. Reaction Channels ................................................ 5
B. Transition Probabilities and S-Matrix ............................. 6
C. S-Matrix and Cross-Sections-Scattering Amplitude ............. 8
D. Quantum-Mechanical Models of NRs ........................... 10
IV. Statistical Description of Dynamical Many-Particle Systems ............ 14
A. Phase Density and Liouville Equation ........................... 14
B. Density Matrix-Quantum Liouville-von Neumann
Equation ......................................................... 16
C. Wigner Probability Function ..................................... 18
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. 9. . . . . . . . . . . . .
Chapter 1
INTRANUCLEAR CASCADE MODEL ....................................... 21
I. Formulation of the Problem and Basic Assumptions .................... 21
A. Prolegomena .................................................... 21
B. Basic Assumptions of the INC-Model ........................... 22
II. Exclusive Description of the INC ....................................... 23
A. Phase Density and Hamiltonian of the INC-Model .............. 23
B. A Streaming and a Collision Term .............................. 24
C. Incorporation of the Pauli Exclusion Principle in the
Collision Term .................................................. 27
D. Formulation of the Equation, the Initial, and the
Boundary Conditions ............................................ 28
E. Integral Forms of the Liouville Equation ........................ 29
F. Solution of the Integral Liouville Equation in the Form
of the von Neumann Series ...................................... 32
G. "Macroapproximation" ......................................... 33
III. Inclusive Description of the INC ........................................ 35
A. Bo1tzmann-Ueh1ing-Uhlenbeck Equation ........................ 35
B. Linearization of the BUD-Equation .............................. 37
IV. Characteristics of NRs .................................................. 39
A. Preliminary Remarks ............................................ 39
B. Total Cross-Section of Inelastic Interaction ...................... 41
C. Topological and Exclusive Cross-Sections ....................... 42
D. Inclusive Cross-Sections ......................................... 43
E. Distribution of Nuclei Produced in the Cascade Over
the Number of Neutrons and Protons, Excitation
Energy, Momentum, and Angular Momentum .................. 43
V. Taking Account of Quantum Effects in the INC-Model. ................ 44
A. Density Matrix-Quantum Liouville-von Neumann
Equation ......................................................... 44
B. Transformation of the Liouville-von Neumann
Equation to the Form Close to the Classical One ................ 45
C. Validity Conditions of the INC-Model .......................... 48
VI. Conclusions ............................................................. 51
References ...................................................................... 53
Chapter 2
METHODS FOR SOLUTION OF THE SYSTEM OF KINETIC
EQUATIONS OF THE INTRANUCLEAR CASCADE MODEL .............. 55
I. Analytic Methods of Solution ........................................... 55
A. Cross-Section of Inelastic Interaction and Quasifree
Nucleons ........................................................ 55
B. Quantum-Mechanical Calculation of a Quasifree
Component of the Inclusive Cross-Section ...................... 60
C. Solution of the System of KEs for Cascade Nucleons
in the Small-Angle Approximation-the Domain of
Relatively High Energies of Secondary Nucleons ............... 64
D. Solution of the System of KEs for Cascade Nucleons
in the P -Approximation-the Domain of Low
1
Energies of Secondary Nucleons ................................ 70
E. Nucleonic Cascade at Low Energies ............................. 75
1. Cross-Section for Production of Quasifree and
Cascade Nucleons at Low Energies ...................... 75
2. Pre-Equilibrium Models of NRs at Low
Energies ................................................. 80
IT. Solution of the System of KEs of the INC-Model by Means
of the Monte Carlo Technique .......................................... 83
A. Standard Monte Carlo INC-Model. .............................. 84
1. General Scheme of the Monte Carlo Simulation
of INCs .................................................. 84
2. Model of a Target Nucleus .............................. 86
3. Characteristics of an Incident Particle Inside a
T-Nucleus ................................................ 87
4. Search of a Partner and an Interaction Point ............. 88
5. Calculation of an Elementary Interaction ................. 88
6. Cut-Off Energy .......................................... 91
7. Characteristics of an R-Nucleus .......................... 92
B. Trawling Effect in the INC ...................................... 93
Ill. Conclusions ............................................................. 95
References ...................................................................... 96
Chapter 3
DECAY AND PROPERTIES OF HIGHLY EXCITED NUCLEI ............... 99
I. Decay of a C-Nucleus with Zero Angular Momentum .................. 99
A. Basic Tenets of Statistical Model of Decay of a
C-Nucleus ....................................................... 99
B. Level Density of Highly Excited Nuclei. ....................... 101
C. Effect of a High Excitation of a Nucleus on its
Structure ........................................................ 106
1. Disappearance of Shell Effects at High Values
of the Excitation Energy ................................ 106
2. Changes in Macroscopic Properties of a
Nucleus Caused by an Increase in its Excitation
Energy .................................................. 111
II. Decay of a C-Nucleus with High Angular Momentum ................. 115
A. Basic Relations of Semiclassical Model ........................ 115
B. The Effect of a High Value of the Angular Momentum
on the Properties of a Nucleus ................................. 117
III. General Pattern of Decay of a Highly Excited Nucleus and
Methods Used in Calculation of the Evaporation Cascade ............. 118
IV. Analysis of Data Concerned with the Properties and Decay of
Excited C-Nuclei. ...................................................... 122
A. Statistical Properties of C-Nuclei Produced in
Reactions with Low-Energy Particles ........................... 122
B. Decay of C-Nuclei Produced in Heavy-Ion-Induced
Reactions ....................................................... 128
V. Explosive Decay of Hot Nuclei ........................................ 130
A. Fermi Breakup of Light Nuclei ................................. 132
