Table Of ContentPHOTOMESIC AND PHOTONUCLEAR PROCESSES
FOTOMEZONNYE I FOTOYADERNYE PROTSESSY
<l>OTOME30HHbIE II <l>OTOH.L\EPHbIE TIPOll,ECCbI
The Lebedev Physics Institute Series
Editor: Academician Do V. Skobel'tsyn
Director, P. N. Lebedev Physics Institute, Academy of Sciences of the USSR
Volume 25 Optical Methods of Investigating Solid Bodies
Volume 26 Cosmic Rays
Volume 27 Research in Molecular Spectroscopy
Volume 28 Radio Telescopes
Volume 29 Quantum Field Theory and Hydrodynamics
Volume 30 Physical Optics
Volume 33 Studies of Nuclear Reactions
Volume 34 Photomesic and Photonuclear Processes
Volume 36 Photo disintegration of Nuclei in the Giant Resonance Region
In preparation:
Volume 31 Quantum Radiophysics
Volume 32 Plasma Physics
Volume 35 Electronic and Vibrational Spectra of Molecules
Volume 37 Electrical and Optical Properties of Semiconductors
Proceedings (Trudy) of the P. N. Lebedev Physics Institute
Volume 34
PHOTOMESIC AND
PHOTONUCLEAR PROCESSES
Edited by
Academican D. V. Skobel'tsyn
Director, P. N. Lebedev Physics Institute
Academy of Sciences of the USSR, Moscow
Translated from Russian
®
Springer Science+Business Media, LLC 1967
ISBN 978-1-4899-2719-4 ISBN 978-1-4899-2717-0 (eBook)
DOI 10.1007/978-1-4899-2717-0
The Russian text was published by Nauka Press in Moscow in 1966 for the
Academy of Sciences of the USSR as Volume XXXIV of the Proceedings
(Trudy) of the P. N. Lebedev Physics Institute.
OoTOMeaoHHbie u $OTOHRepnbie npoqeccu
Tpynu d>H3HiecKoro HHCTHiyTa HM. n. H. JIe6e«eBa
TOM XXXIV
Library of Congress Catalog Card Number 67-27904
© Springer Science+Business Media New York 1967
Originally published by Consultants Bureau New York in 1967
All rights reserved
No part of this publication may be reproduced in any
form without written permission from the publisher
CONTENTS
PHOTOPRODUCTION OF lTo-MESONS IN DEUTERIUM NEAR THRESHOLD. A. I. Lebedev and
E. I. Tamm . .. . . • . . . •. . . . • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .• . . . 1
Introd uction. • . . . . . . . . . • • . . • • . . • . . . . . . . . . . . . . . . . . • • . . . . . . . . . . . . . . . . . . . . 1
Chapter I. Short Review of Theoretical and Experimental Work on lTo-Meson Photoproduction . . . . . . 2
1. Meson PhotoFIOduction on Free Nucleons. . . . . . • . . . . . . . . . . . . . . . • . . . . . . . . . . . 2
2. Theory of lTo -Meson Photoproduction in Deuterium • . . . . . . . . . • . . . . • . . . . . . . . . . . 5
3. Experimental Investigations •...•........•.•.....••.••................
Chapter II. Calculations of Differential Cross Sections for ~o -Meson Photoproduction on Deuterons. • . 10
1. Approximations Employed • • • . . . . . . • . • . . . . • . . . • . . . • . . • . . . . . . . . . • . . . . . 10
2. Elastic Photoproduction of 11'0 -Mesons (r td-.d + 11'0). • • • • • • • • • • • • • • • • • • • • • • • • • • 11
3. Inelastic Photoproduction of lTo-Mesons (r +d-+p+n+!I'°) . . . . • . •• • . . . . . . . . • . . . . . 14
Chapter III. Experimental Investigations of 11'0 -Meson Photoproduction . • . • • . . . . • . • • • • • . . . . . 18
A. Measurement of Differential Cross Section by the Direction of One Decay Photon
of the 1I'°-Meson • . • • • . . . • . • . • . . • . . • • . . • • . • . • • . • . • . . . • . • . . . . . . . . . . 18
B. Measurement of Differential Cross Sections at Small Angles by the Detection
r
of Two Decay -Quanta. • • . • • . . . . . • . • . . • . . . . . . . . • . . . . . . . • • . . • . . . . . . 31
Chapter IV. Comparison of Obtained Experimental Data for Processes 'Y +d-+d(pn)tlTo with Results
of Theoretical Calculations. • • • . • • . . • . . . . . . . . . . . . . . . . . • . • . . . . . . . • . . . • 41
Conclusion. • • . . . . . . . . . . . . • • . . . . . . . . . . . . . . . . . . . . . . . . • . . • • • . . . . . . . . • . . • . 45
Literature Cited . . • . . • • • • • • • • • • • • . • • • • • . . • . . . . . . . . . . . . . . . • . . . . . . . . . . . • . . 46
PHOTOPRODUCTION OF lTt -MESONS ON PROTONS NEAR THRESHOLD. M. I. Adamovich.
V. G. Larionova. A. 1. Lebedev. S. P. Kharlamov. and F. R. Yagudina. . . . . . . . . . . . . . . 49
Introduction. • • • • • • • • • . . . • . . . . • • . . . . . . . . . . . . . . . . • • • . . . . . . . . . . . . . . . . . . . . 49
1. Basic Ideas Regarding Pion Photoproduction on Nucleons. . . . . . . . . . . • . . . . . . . . . . . . 50
2. Investigation of Meson Photoproduction on the Basis of Dispersion Relations. . . . . . . . . . . . 54
3. Review of Experimental Work. . . • . . . . . . . . . • . . . . . . . • . . . . . . . . . . . . . . . . . . . 57
4. Experimental Setup and Method .....•........ ; . . . . . . . . . . . . . . . . . . . . . . . . . 62
5. Experimental Results. • . . • . . . . • • • . . . • . . . . . . . . . . . • • . • . . . . . . . . . . . . . . . . 66
6. Calculation of Differential Cross Sections of !I'+ - Meson Photoproduction . . . • . . . . . . . . . 73
7. Discussion. • . . . . . . • . . • • • . . . • . . . . . . • . . . . . • . . . • • . . . . • . . . . . . . . . . • . . 76
Literature Cited . • . • . . . . • . • . . . . . • • . . . • . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . 79
NUCLEAR PHOTOEFFECT IN THREE-PARTICLE NUCLEI. A. T. Varfolomeev. A. N. Gorbunov.
and V. N. Fetisov . . . . . . . . • . • . . . . . . . . . • . . . . . . . • • . . . . . . . • • . • • . • . . • . 81
Introduction. . . . • . . . . • . . • . . . . • • • • . . . . • . • • • • • • • . • . . . • . . . . . . . . . . . . . . . • . . 8.1
Section 1. Experimental Method • . . . . . . • . . . . . . . . . • . . . . . . . • . . . . . . . . . . • . . . . . . . . 84
Section 2. Results of Measurements. • . . . . . . . . • • . • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
1. Yields of He3(r. p)D and He3(r. n)2p Reactions. • . . . . . . • . . . • . . . . . • . . • . . . . . . . . 86
v
vi CONTENTS
2. Two-Particle Disintegration [He3(y, p)d Reaction] . . . • . . . . . . . . . . . . . . . . . • . . . . . . 87
3. Three-Particle Disintegration [He3(y, nl2p Reaction] • . . . . . . . . . • . . . . . . . . . . . . . . . 88
Section 3. Rule of Sums and Dimensions of Three-Particle Nuclei. • . . . . . . . . . . . . . . . . . . . . . . 95
1. Rule of Sums for the Integral Cross Section. . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . 95
2. Rule of Sums for the Integral Cross Section Weighted with Respect to the Bremsstrahlung
Spectrum. . . . . • • . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3. Radii of Charge Distribution in Three-Particle Nuclei. . • . . . . . . . . . . . . . . . • • . . . . . . 98
Section 4. Comparison between Experimental Data and Theoretical Calculations of Effective Cross
Sections . . . . . . . . • . . • • • . . • . . . . . . . . . . . . • . . . . . . . . . . • • . . . . . . . . . . . . 99
1. Two-Particle Channel for Absorption of y-Quanta by the Nucleus. . • . • . • . • . . . . . . . . . 99
2. Three-Particle Disintegration of H3 . . • . . . • • . . • . . . . . . . • . . . . . • . . . . . . . . . . . . 102
Section 5. Experimental Results of Other Authors. . . • . . . . . . • . . • . . . • . . • . . . • . . • . . . . . . . 106
1. Two-Particle Disintegration .•.............••...•...•..•.....•... ; . . . . 106
2. Three-Particle Disintegration. • . . . . . . . . • . • . . . . . . . . . . . . . . . . . . • . . . . . . . . . 110
Conclusions . . . . . . . . . • • . . • . . . . . • . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . 11 0
Literature Cited • • . . . • . . . . . . . . • . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . 111
STUDY OF NUCLEAR REACTIONS AT HIGH ENERGIES BY THE RECOIL-NUCLEUS METHOD.
F. P. Denisov . • . . . . . . . • • . . . • . . . . • . . . . . • . . . • . . . . . . • . . . . • . . . . . . . . . 115
Introduction. . . • • • . . • • . . • . • . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . 115
Chapter 1. Experimental. • . . . • . . . . . . • . . . . . • . . . . . . . . • • . . . . . . • . . . . . . . . . . . . . . . 119
1. Method . . . . . . • . • • • . . . . . . . . . • • . . . . . . . . • . . . . • . . . . . . . . . . . . . . . . . . • 119
2. Apparatus. • . . • . • . . . . . . . . . . . • . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . 120
3. Measurement. • . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • • . . 122
4. Yield and Effective Cross Sections of the Photonuc!ear Reactions AI27 -.Na24, Co59 __ Mn56,
and p31 __ Na24 for y-Quantum Energies up to 260 MeV. . . . . . . . . . . . . . . . . . . . . . . . . 125
5. Yields of Recoil Nuclei from Thick Targets. Range and Angular Distributions
of the Recoil Nuclei. . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . • . . . . • . . . . . . . . . 126
Chapter II. Discussion. Compound Nucleus and Evaporation. . . . . • . . . . . . . . . . . . . . . . . . . . . . 130
1. Mean-Square Momentum and Angular and Energy Distributions of
Recoil Nuclei on the Model of the Compound Nucleus. . . . . . . . . . . . . . . . . . . . . . . . . 131
2. Range-Energy Relation, Straggling, and Multiple Scattering of Heavy Ions. Range
Distribution of Recoil Nuclei. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
3. Yield of Recoil Nuclei from Thick Targets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4. Comparison of Calculations with Experiment and Conclusions. . . . . . . . . . . . . . . . . . . . . 136
Chapter III. Discussion. Cascade Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
1. General Arrangement and Initial Data of the Nuclear-Cascade Calculations . . . . . . . . . . . 140
2. Photonuclear Cascade. . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . 142
3. Results of Calculations and Comparison with Experiment. . . . • . . . . . . . . . . . . . . . . . . . 143
4. Interaction with Correlated Groups of Nucleons. . . . . • . . . . . . . . . . . . . . . . • . . . . . . . 148
Appendices . . • . . . . . . . . . • • . . . . . . . • • . . . . . . . . • . . . . . . . . . . . . . . . . . . . • . . . . . . . 150
Appendix I. Activation Method of Measuring the Thicknesses of Thin Films and Foils . . . . . . . 150
Appendix II. Correction for the Decay of Radioactivity in the Case of the Successive
Irradiation of Several Monitors. . . . . . . . . • • . . • . . . . . . . • . . . . . . . . . . . . . . . . . . 152
Appendix III. Mean-Square Momentum and Angular Distribution of Recoil Nuclei on the
Compound-Nucleus Model. • . . . . • • . . . . . . . . • . . • . . . . . . • . . . . . . . . . . . . . . . . 153
Appendix IV. Energy Distributions of Recoil Nuclei on the Ev aporation of Two and
Three Nucleons. • . . . . . . . . • • • • . . . . • . . . . • . . . . . . • . . . . . . . . . . . . . . . . . . . 155
Appendix V. Yield of Recoil Nuclei from Thick Targets. Effective Thickness. . . • • . . . . • . . 158
Literature Cited . • . . • . • • • • • . . . . • . . . • . . . • . • . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . 159
CONTENTS vii
A STUDY OF THE ANGULAR DISTRIBUTION OF FRAGMENTS IN THE PHOTOFISSION OF URANIUM
ISOTOPEU233, N. M. Kulikova, N. V. Nikitina, and N. V. Popov. . . . . .. . . . . . . . .. . . 163
Literature Cited . • . . . . . . . . . . . . . . . . . . . . . . • • . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . 166
SHOWER-TYPE GAMMA SPECTROMETERS, THEORY AND CALCULATION OF THE PRINCIPAL
CHARACTERISTICS. V. F. Grushin and E. M. Leikin. • . . . . . . . . . . . . . . . . . . . . . . . . 167
Section 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Section 2. Calculation of the Mathematical Expectancy and Dispersion. Energy Resolurion. . . . . . . . 168
Section 3. Line Shape of the Shower Gamma Spectrometer . . . . • . . . . . . . . . . . . . . . . . . . . . . . 172
Section 4. Numerical Calculation of the Characteristics of Cerenkov Gamma Spectrometers. . . . . . . 174
Section 5. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Literature Cited . • • . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
DETERMINA TION OF THE SHOWER EFFICIENCY OF SCINTILLA TION DETECTORS. V. N. Bolotov,
M. I. Devishev, and V. M. Knyazev. . . • . . . • . . . . . . . . . . . • . . . . . . . . . . . . . . . . . 181
Literature Cited . . • . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
A LIQUID-HYDROGEN TARGET. Yu. M. Aleksandrov, A. N. Zinevich, and E. M. Leikin . . . . . . • . . 185
Literature Cited . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
APPARA TUS FOR INVESTIGA TING 1[+ -MESON PHOTOPRODUCTION. Yu. M. Aleksandrov,
V. F. Grushin, V. A. Zapevalov, and E. M. Leikin. . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Literature Cited . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
USE OF STATIC CHARACTERISTICS OF GAS-DISCHARGE GAPS IN THE DESIGN OF DECATRON
COUNTING CIRCUITS. V. A. Zapevalov. • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
1. Transfer of Discharge from Cathode to First Guide ....•......... , . . . . . . . . . . . . 197
2. Transfer of Discharge from First to Second Guide. . . . . . . . . • . . • . . . . . . . . . . . . . . . 200
3. Transfer of Discharge from the Second Guide to Following Cathode. . . . . . . . . . . . . . . . 201
4. Plotting the Shape of Current Pulses at the Decatron Electrodes. • • . . . • . . . . . . . . . . . . 202
5. Resetting the Decatron to Zero . . . . . • . . . . . . . . . . . . . • . . . . . . • . . . . . . . . . . . . 205
Selection of Guide Bias Voltage . . . . . . . . . . . • . . . . . . • . . . . . . . . . . . . . . . . . . . 205
Selection of Zero-Cathode Resistance ...............•............. ' . . . . 205
Pulsed Zero Reset . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . ' . . . . . . . . . . . . . 206
6. The Principle of Amplitude Matching. . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . 207
7. Transistorized Decatron Scalers. • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
8. Selection of Coupling and Control Circuits Ensuring Reliable Decatron Operation. . . . . . . 211
Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
CONTRIBUTION TO THE DESIGN OF THREE-MESH BANDPASS FILTERS. V. S. Voronin and
S. S. Semenov . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . 215
Literature Cited . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
SYSTEM FOR STABIliZING THE SUPPLY CURRENT OF AN ELECTROMAGNET. V. S. Voronin
and S. S. Semenov. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
1. Requirements Laid on the Supply System .••.......................... ' . . . 219
2. Voltage-Stabilizing System for the DC Generators. . . . . . . . . . . . . . . . . . . . . . . . . . . 220
3. DC Amplifier for the Comparison Circuit and the Suppression of Pulsations. . . . . . . . . . . 225
Literature Cited . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
PHOTOPRODUCTION OF 1To-MESONS IN
DEUTERIUM NEAR THRESHOLD
A. 1. Lebedev and E, 1. Tamm
INTROD UC TION
Photoproduction and scattering of rr -mesons on nucleons are among the simplest processes involving
strongly interacting particles - the rr-meson and nucleon. An investigation of the nature of strong interaction
is a central problem in modem physics.
A complete study of rro-meson photoproduction on nucleons entails an investigation of meson production
both on protons and neutrons (we will not consider the prospects of an investigation of the reverse reactions).
From this viewpoint, an investigation of meson photoproduction on the deuteron, which represents the most
weakly bound system of nucleons, is of fundamental importance. For a complete analysis of the isotopic struc
ture of the meson photoproduction amplitude on nucleons it would be sufficient to confine ourselves to an in
vestigation of the reactions
+ +
y p -;> n n+, (1)
+ +
y p -;> p nO, (2)
+ + +
y d -> p p n-. (3)
In this paper we consider meson photoproduction processes in the near-threshold region of y-ray energies,
where the meson momentWll q in the center-of-mass system satisfies the condition q:'O 1.. This condition is
fulfilled at y-ray energies rt <' 230 MeV.
An investigation of processes (1l-(3) in this energy region shows [1] that errors in the experimental data
do not allow a definite isotopic analySis and a prediction of the amplitude for production of rro -mesons on
neutrons in the S state. The obtention of direct information regarding the process y + n -> n + rro necessitates
an investigation of the reactions
+ + +
y d --> p n nO, (4)
+ +
y d -+ d nO. (5)
An investigation of the latter process can also provide information about the electromagnetic form factor of
the deuteron.
An investigation of the isotopic structure of the photoproduction amplitude assumed particular value in
connection with the study of the role of resonance rr -rr interaction in meson photoproduction. When this inter-
"In this paper we use units with Ii: = I1rro =c =1 .
1
2 A, I. LEBEDEV AND E, I. T AMM
action is associated with the two-meson intermediate state (p -meson), it makes a contribution only to the iso
calar part of the photoproduction amplitude~. When the interaction is associated with the three-meson inter
mediate state (w-or 'i'-mesons) it makes a contribution to the isovector part of the amplitude F+, These con
tributions are characterized by the constants of 'Y'II'P -, 'Y'II'W-, pNN-, and wNN-interactions, which are involved
in a number of effects (lifetime of 11'0 -meson, electromagnetic form factors of nucleons and 'II'-mesons, cross
sections of processes 'Y + N ... N + 11' + 11', 11' + N -+ N + 11' + 'Y, etc, [2]). In this connection a determination of
these constants is of great interest. As we will show below, the discussed reactions can give information about
these constants. An investigation of these reactions can contribute toward a clarification of the question of the
existence of the hypothetical'll'~-meson [3].
For the description of meson photoproduction in deuterium the impulse approximation is used (4], Its ap
plicability for the description of the reaction 'Y + d -+ P + P + 11' - in the near-threshold energy region has been
experimentally confirmed [5]. The case of 11'0 -mesons, however, requires an independent verification of the
impulse approximation, since the cross section for the photoproduction of neutral mesons near threshold is much
smaller than that for charged mesons and the corrections for multiple scattering of 'II'± into 'II'°-mesonsmay be
come significant.
Thus, the problems which may be tackled by an investigation of 'II'°-meson photoproduction in deuterium
in the region of low 'Y-ray energies make this process of exceptional interest for meson physics.
The aim of the present work is to give an account of the results of an experimental investigation of 11'0_
meson photoproduction in deuterium in the near-threshold region of 'Y-ray energies and to discuss these results
from the viewpoint of phenomenological theory using the impulse approximation. We also give the results of
careful calculations of the differential cross sections for the elastic ('Y + d .... d + 11'0) and inelastic ('Y + d ....
p + n + 11'0) photoproduction of 'II'°-mesons on deuterons and suggestions regarding the use of these processes for
a study of 'Y'II'P- and 'Y'II'w-interactions and for the investigation of the process 'Y tn-nt'll'°,
CHAPTER I: SHORT REVIEW OF THEORETICAL AND EXPERIMENTAL WORK
ON 1f °- MESON PHOTOPRODUCTION
1. Meson Photoproduction on Free Nucleons
The operator for meson photoproduction on nucleons in the spin iii matrix representation has the form
(1.1)
where the operators K and L in the meson-nucleon center-of-mass system can be written as
(1.2)
Here, k and e are the momentum and polarization of the photon, ((is the meson momentum, r is the radius
vector of the nucleon, Fi (i = I, 2, 3, 4) are functions of the momentum and angle of emission e of the meson.
Using operators (1.1) arxl (1.2) to determine the matrix element of the photoproduction process, we square it,
sum, and average over the polarizations of the nucleon and 'Y-quantum and thus obtain the following expres
sion for the differential cross section of the process 'Y + N .... N t 11':
