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Nuclear cross sections for charged-particle-induced reactions
NUCLEAR DATA, Section A, Volume 3, Number 2, September 1967 NUCLEAR CROSS SECTIONS FOR CHARGED.PARTICL E.INDUCED REACTIONS Nand 0
Compiled by H. J. Kim, W. T. Milner, and F. K. McGowan
Chcrqed-Porrl cle Crc s s-Sect icn Data Center" Oak Ridge National Laboratory Oak Ridge, Tennessee
ABSTRACT Nuclear cross sections for charged-particle-induced reactions of isotopes of Nand
o
are presented in tabular and graphical fonn. This compilation includes experimental
cross-section data available in the literature before January 1, 1965, for nuclear reactions of the type A(a, b)B at all energies, where Ma2: one nucleon mass. Nuclear reactions involving mesons in the exit channel are not included. This collection supplements a previous compilation, Los Alamos Scientific Laboratory Report LA·2014 (see following page for bibliographic information). A large amount of the cross-section data is not presented either in tabular or graphical form in order to limit the size of the present compilation to a manageable one. A number of annotated bibliographies are included in the appendixes to provide a brief summary of these data.
CONTENTS 3.2 Isolated Values of Nuclear Cross Sections for Charged-Particle-Induced Reactions
1. INTRODUCTION 1.1 Notation
3.3 Bibliography for Energy Spectra
1.2 Tabular Data
3.4 Bibliography for Relative Data
1.3 Graphs
3.5 Bibliography for Energy Correlation Data 2. TABULAR DATA AND GRAPHS
3.6 Numerical Factors for the Computation of the Nonrelativistic Rutherford Scattering Cross Sections
Nitrogen and Oxygen 3. APPENDIXES 3.1 Bibliography for Data Not Plotted
*Sponsored by Oak Ridge National Laboratory. operated by Union Carbide Corporation for the U.S. Atomic Energy Commission.
123
KIM, MILNER, AND McGOWAN
REPORTS PREVIOUSLY ISSUED Reports previously issued in this series, which summarize nuclear cross sections for chargedparticle-induced reactions, are as follows: 'Charged-Particl e Cross Se ctions, Los Alamos Report LA-2014 (1957), edited by Nelson Jarmie and John D. Seagrave. Out of print. Charged-Particle Cross Sections, Neon to Chromium, Los Alamos Report LA-2424 (1961), compiled and edited by Darryl B. Smith. Available for $2.50 from Clearinghouse for Federal Scientific and Technical Information, 5285 Port Royal Road, Springfield, Va. 22151. Nuclear Cross Sections for Charged-Particle-Induced R eactions - Mn, Fe, Co, ORNL-CPX-1 (july 1964), compiled by F. K. McGowan, W. T. Milner, and H. J. Kim. Available on request to the Charged-Particle Cross-Section Data Center, Oak Ridge National Laboratory, P.O. Box X, Oak Ridge, Tennessee 37830. Nuclear Cross Sections for Charged-Particle-Induced Reactions - Ni, Cu, ORNL-CPX-2 (September 1964), compiled by F. K. McGowan, W. T. Milner, and H. J. Kim. Available on request to the Charged-Particle Cross-Section Data Center, Oak Ridge National Laboratory, P.O. Box X, Oak Ridge, Tennessee 37830. Nuclear Cross Sections for Cherged-Perticle-Induced Reactions - Li, Be, B, compiled by H. J. Kim, W. 'r . Milner, and F. K. McGowan, Nucleet Deie , A1, 203-389 (1966), issues 3 and 4 combined $6.00 , Academic Press, 111 Fifth Avenue, New York, N.Y. 10003. Nuclear Cross Sections for Charged-Particle-Induced Reactions - C, compiled by H. J. Kim, W. T. Milner, and F. K. McGowan, Nuclear Data, A2, 1-241 (1966), issues 1 and 2 combined $6.00, Academic Press, 111 Fifth Avenue, New York, N.Y. 10003.
124
1. INTRODUCTION
ucts (other than photons) which accompany the detected products but are not observed or recorded, then the emerging product subscript should be followed with a y (up ,ny). Photons are not indicated as part of the outgoing product unless they are the only outgoing product (capture reaction) or are observed (reactions involving angular correlations), in which case the symbol for photons, y, need not have a coefficient. Examples in this case are:
1.1 Notation
The following scheme for cross-section terminology and associated notation is taken from a nomenclature scheme suggested by Goldstein. 1 The terminology is particularly formulated for reporting experimental re~ sults. The nuclear reaction is denoted by A(a, b)B, where A and B are the target nucleus and the residual nucleus, a is the bombarding charged particle, and b is the outgoing product particle or particles in the re~ action. In the cross-section notation, the type of re~ action is indicated by subscripts. The variables of the reaction (energy, angle, etc.) are indicated in parentheses following the cross-section symbol, in the usual mathematical functional notation, Whether a cross section is total or differential for a given type of reaction is indicated by the variables shown. Examples are: u p,p (E;e)
Differential elastic proton scattering cross section as a function of proton energy
u p,n (E)
Total (p,n) cross section as a function of proton energy
oP,y(E)
Cross section for radiative capture of a proton as a function of energy E
u d,py
Cross section for the (d,p) reaction in which the protons are observed with gamma rays
2. When the cross section represents a sum over a number of possible partial reaction cross sections, the subscripts consist of a letter or symbol designating the incident projectile followed by an uppercase letter chosen more or less arbitrarily. Examples are:
up, R(E)
Reaction cross section for protons as a function of energy E. The reaction cross section is defined as the cross section for all interactions between the target nucleus and the incident projectile that leave the nucleus in a state different from the original ground state. This includes all direct reactions and all events that lead to the formation of the compound nucleus, including compound elastic scattering
ap, Q(E)
Sum of the partial proton-induced reaction cross section, as a function of proton energy E, in which a charged particle is emitted
Variables of the Reaction
For a given type of reaction, the only variable present in the total cross section is the bombarding energy indicated by E without a subscript. For differential cross sections, there will be more variables indicating the energies or angles of the emerging particles. Variables for a given particle are separated by commas, and groups of variables for the various particles are separated by semicolons. In this cornpilation all energies are in the laboratory frame of reference, since this is customary for most crosssection measurements. The symbol e is used for the emerging particle angle in the frame of reference indicated by the abbreviated subscripts C.M. (center of mass frame) and Lab (laboratory frame).
3. The remaining class of subscripts consists of a few symbols of long usage in the literature; for ex~ ample, the Rutherford differential scattering cross section a R (8) and the cross section for compound elastic scattering u e E(e). The argument E is suppressed when we are dealing with monoenergetic projectiles.
Types of Reaction Subscripts
1. When both the bornbarding and outgoing particles are specified for a reaction, they are indicated by symbols with a comma following the bombarding particle or projectile (op,n ). Each product particle produced in a reaction must have a coefficient to indicate the number of product particles involved if there is more than one (uF, 2 n ). If only the type of product particle is observed without regard to number, then the coefficient should be a k (op, k n ). If there are other prod-
Abbreviated Notation
In this compilation the above general principles of notation have been abbreviated for the tabular and
125
KIM, MILNER, AND McGOWAN
graphical presentation of the data as follows: 1. The subscripts in the cross-section notation indicating the projectile and emerging particle or particles are suppressed whenever the reaction types are given explicitly as separate entities. 2. Since the caption for the tabular presentation gives explicitly the type of reaction and the energy of the projectile, the argument E of the projectile is suppressed in the cross-section notation for elastic and inelastic scattering and for angular distributions. 3. Since the bombarding energy is conserved in the center-of-mass system for elastic scattering, the argument E of the emerging particle is suppressed. 4. For the angular distributions of emerging particles with monoenergetic projectiles and for inelastic scattering distributions, the energy of the outgoing particle leaving the residual nucleus in a definite state in the center-of-mass system is suppressed. The labeling of the energy of the emerging particle is included in the caption; for example, the Q of the reaction. For the sake of definiteness, the term inelastic scattering refers to those situations in which the incident projectile transfers energy to the nucleus (nuclear excitation) in the center-of-mass system, all of which appears eventually as deexcitation gamma rays emitted by the residual nucleus. 5. In many cases of high-energy reaction cross sections, it is impossible to distinguish the sequence of particle emission. Although we have in many instances given a reaction sequence for the emerging particles, we do not mean to imply that is the correct or the only reaction sequence for the emerging particles in the nuclear reaction. In general for these reactions, only the induced activity in the residual nucleus is observed. This fact is always indicated in the caption to the tabular data.
1.2 Tabular Data The arrangement of the reactions A(a, h)B is according to (1) increasing Z of the target and (2) increasing Z and mass number of the projectile. For a given type of reaction, the arrangement is in order of increasing energy of the projectile. For a given reaction and projectile energy, the information on the naturally occurring element comes first, and the various isotopes follow in order of increasing mass number. For a given projectile, elastic scattering reactions come first, inelastic scattering reactions come next, and all other reactions follow according to decreasing Z and mass number of the residual nucleus.
The angular dependence of the polarization in the elastic scattering reaction is placed after elastic scattering data of the same energy or nearly the same energy. Further differentiation is given by differential excitation functions preceding angular distributions and ground-state reactions preceding excited-state reactions of the residual nucleus. The recent style of placing the isotope mass number as a superscript at the upper left of the element symbol has been adopted for the reaction notation. The energy E appearing below the reaction is always in the laboratory frame of reference. The symbol P(O) is the notation for angular dependence of the polarization produced in the elastic scattering reaction. Below the energy E of the projectile, a labeling of the energy of the emerging particle or particles is given by the Q value of the reaction. Sometimes the excitation energy of the residual nucleus is given in parentheses following the Q value. The quoted Q values are taken from Ref. 2. The caption to the tabular data gives the reference, laboratory, a few experimental details, errors, and source of tabular data. Insofar as possible the abbreviations for journals conform with those adopted by Chemical Abstracts and the American Institute of Physics. In the case of references to Russian literature, an attempt has been made to present the original Russian reference. The location of the laboratory at which the data originated follows the reference in brackets. The experimental details include accelerator, detectors, energy resolution, angular resolution, and target thickness. Occasionally one or more of these details are omitted if they are not available in the paper. Usually some expression of the errors for the cross sections is included either in the caption or the tabular information. In the caption this expression is the fractional standard deviation of the cross section. Frequently the type of error is not indicated by the authors of the paper. In these cases, we have arbitrarily taken the errors to mean standard deviations. The tabular information for the elastic scattering reaction is always given in the formo(O)juR , where u R is the nonrelativistic Rutherford scattering cross section. The expression of error for 0(0) in the caption does not reflect the error introduced by the uncertainty in when the elastic scattering cross section is expressed in units of u R ' that is, u(O)/uR • Whether the tabular data were supplied by the authors or obtained from figures in the published paper is also stated in the caption.
e
126
INTRODUCTION
In many cases' of early cross-section data, the only sources of the information are from the small figures in the journals. A Moseley model 25 X-V point plotter was modified to read data points from small published figures. Helipots were coupled to the cables which drive the pen and carriage of the plotter. The coordinates of the data points are displayed in analog form by a Hewlett-Packard model 40SCR automatic de digital voltmeter which also drives a Hewlett-Packard model 561B digital recorder. The X and Y ranges may be adjusted to yield 2000 increments of information in analog form for any size figure. The components of the data-point reader provide an overall accuracy of to.25% of full scale. For example, the reading error in 0 from an angular distribution would be to.5°. In general, the accuracy of the data points read from small figures depends entirely on the accuracy of the original drawing and on distortions introduced by the publisher. Enlargements of the small figures in the journal would be of no va lue with regard to avoiding these possible sources of errors. The coordinates of the data points in analog form are key punched directly from the tapes of the digital recorder onto IBM cards. Computer programs process the analog information ; transform, if necessary, the cross-section data from the laboratory frame of reference to the center-of-mass system by a nonrelativistic kinematics program ; list the data in tabular form; and prepare a magnetic tape for plotting the data by a Calcomp model 570 plotter. This mechanization means a saving of labor and reduces the chance of error. The captions as well as the tabul ar data are composed and arranged by using a computer code, and the resulting machine compositions are listed by an IBM model 1405 on-line printer and presented directly. In this compilation the differential cross-section data are given in the center-of-mass system. There are a few exceptions, and these cases are noted in the caption preceding the tabul ar data . When several sets of data are presented in a single graph, the symbol associated with each set of data points is placed either near the caption or above tabular data, whichever is appropriate, for iden tification purposes.
1.3 Graphs
All cross-section data, including both angular distribu tions and excitation functions, are presented on semilog graph paper. The angular dependence of the polarization produced in the elastic scattering reaction is presented on linear graph paper. The grid of the X axis is 25 di visions per inch for the semilog graph paper of one, two, and three cycles. This makes possible the presentation of angular distributions (25° lin.) on a 7-in. grid. The reaction label A(a,b)B appears in the upper right corner in the field of the grid. The case number in the upper left corner in the field of the grid is for internal use and represents the location of the data at the CPX Data Center. In general the energy scale for excitation functions does not start with zero at the origin. Occasionally, we find a roll of graph paper in which the registration does not align the grid perfectly with respect to the drum and carriage motions of the plotter. As a result, data points of an angular distribution may be in error by 0.5 ° at the most in the upper third of the grid field. The reader may find a few examples where several data entries in the ta bul ar presentation are not plotted, because these points fall off scale of the graphical presentation. With a few exceptions, only the experimental data points of the original author or authors are presented in this compilation. Data points derived from smooth curves of figures in published papers are noted in the captions. Every effort has been made to ensure the general reliability of the transcription of the data to the graphs. We shall appreciate criticisms, comments, and notes of any errors in the tabular or the graphical presentation of this compilation. References
IH. Goldstein, "Appendix I," p. 2227 in Fast Neutron Physics, vol. IV, part II, ed. by J. B. Marion and J. L. Fowler, Interscience, New York, 1963. 2J. H. E. Mattauch, W. Thiele and A. H. Wapstra, Nucl. Phys. 67, 1 (1965).
127
Compiled by H. J. Kim, W. T. Milner, and F. K. McGowan
Chcrqed-Porrl cle Crc s s-Sect icn Data Center" Oak Ridge National Laboratory Oak Ridge, Tennessee
ABSTRACT Nuclear cross sections for charged-particle-induced reactions of isotopes of Nand
o
are presented in tabular and graphical fonn. This compilation includes experimental
cross-section data available in the literature before January 1, 1965, for nuclear reactions of the type A(a, b)B at all energies, where Ma2: one nucleon mass. Nuclear reactions involving mesons in the exit channel are not included. This collection supplements a previous compilation, Los Alamos Scientific Laboratory Report LA·2014 (see following page for bibliographic information). A large amount of the cross-section data is not presented either in tabular or graphical form in order to limit the size of the present compilation to a manageable one. A number of annotated bibliographies are included in the appendixes to provide a brief summary of these data.
CONTENTS 3.2 Isolated Values of Nuclear Cross Sections for Charged-Particle-Induced Reactions
1. INTRODUCTION 1.1 Notation
3.3 Bibliography for Energy Spectra
1.2 Tabular Data
3.4 Bibliography for Relative Data
1.3 Graphs
3.5 Bibliography for Energy Correlation Data 2. TABULAR DATA AND GRAPHS
3.6 Numerical Factors for the Computation of the Nonrelativistic Rutherford Scattering Cross Sections
Nitrogen and Oxygen 3. APPENDIXES 3.1 Bibliography for Data Not Plotted
*Sponsored by Oak Ridge National Laboratory. operated by Union Carbide Corporation for the U.S. Atomic Energy Commission.
123
KIM, MILNER, AND McGOWAN
REPORTS PREVIOUSLY ISSUED Reports previously issued in this series, which summarize nuclear cross sections for chargedparticle-induced reactions, are as follows: 'Charged-Particl e Cross Se ctions, Los Alamos Report LA-2014 (1957), edited by Nelson Jarmie and John D. Seagrave. Out of print. Charged-Particle Cross Sections, Neon to Chromium, Los Alamos Report LA-2424 (1961), compiled and edited by Darryl B. Smith. Available for $2.50 from Clearinghouse for Federal Scientific and Technical Information, 5285 Port Royal Road, Springfield, Va. 22151. Nuclear Cross Sections for Charged-Particle-Induced R eactions - Mn, Fe, Co, ORNL-CPX-1 (july 1964), compiled by F. K. McGowan, W. T. Milner, and H. J. Kim. Available on request to the Charged-Particle Cross-Section Data Center, Oak Ridge National Laboratory, P.O. Box X, Oak Ridge, Tennessee 37830. Nuclear Cross Sections for Charged-Particle-Induced Reactions - Ni, Cu, ORNL-CPX-2 (September 1964), compiled by F. K. McGowan, W. T. Milner, and H. J. Kim. Available on request to the Charged-Particle Cross-Section Data Center, Oak Ridge National Laboratory, P.O. Box X, Oak Ridge, Tennessee 37830. Nuclear Cross Sections for Cherged-Perticle-Induced Reactions - Li, Be, B, compiled by H. J. Kim, W. 'r . Milner, and F. K. McGowan, Nucleet Deie , A1, 203-389 (1966), issues 3 and 4 combined $6.00 , Academic Press, 111 Fifth Avenue, New York, N.Y. 10003. Nuclear Cross Sections for Charged-Particle-Induced Reactions - C, compiled by H. J. Kim, W. T. Milner, and F. K. McGowan, Nuclear Data, A2, 1-241 (1966), issues 1 and 2 combined $6.00, Academic Press, 111 Fifth Avenue, New York, N.Y. 10003.
124
1. INTRODUCTION
ucts (other than photons) which accompany the detected products but are not observed or recorded, then the emerging product subscript should be followed with a y (up ,ny). Photons are not indicated as part of the outgoing product unless they are the only outgoing product (capture reaction) or are observed (reactions involving angular correlations), in which case the symbol for photons, y, need not have a coefficient. Examples in this case are:
1.1 Notation
The following scheme for cross-section terminology and associated notation is taken from a nomenclature scheme suggested by Goldstein. 1 The terminology is particularly formulated for reporting experimental re~ sults. The nuclear reaction is denoted by A(a, b)B, where A and B are the target nucleus and the residual nucleus, a is the bombarding charged particle, and b is the outgoing product particle or particles in the re~ action. In the cross-section notation, the type of re~ action is indicated by subscripts. The variables of the reaction (energy, angle, etc.) are indicated in parentheses following the cross-section symbol, in the usual mathematical functional notation, Whether a cross section is total or differential for a given type of reaction is indicated by the variables shown. Examples are: u p,p (E;e)
Differential elastic proton scattering cross section as a function of proton energy
u p,n (E)
Total (p,n) cross section as a function of proton energy
oP,y(E)
Cross section for radiative capture of a proton as a function of energy E
u d,py
Cross section for the (d,p) reaction in which the protons are observed with gamma rays
2. When the cross section represents a sum over a number of possible partial reaction cross sections, the subscripts consist of a letter or symbol designating the incident projectile followed by an uppercase letter chosen more or less arbitrarily. Examples are:
up, R(E)
Reaction cross section for protons as a function of energy E. The reaction cross section is defined as the cross section for all interactions between the target nucleus and the incident projectile that leave the nucleus in a state different from the original ground state. This includes all direct reactions and all events that lead to the formation of the compound nucleus, including compound elastic scattering
ap, Q(E)
Sum of the partial proton-induced reaction cross section, as a function of proton energy E, in which a charged particle is emitted
Variables of the Reaction
For a given type of reaction, the only variable present in the total cross section is the bombarding energy indicated by E without a subscript. For differential cross sections, there will be more variables indicating the energies or angles of the emerging particles. Variables for a given particle are separated by commas, and groups of variables for the various particles are separated by semicolons. In this cornpilation all energies are in the laboratory frame of reference, since this is customary for most crosssection measurements. The symbol e is used for the emerging particle angle in the frame of reference indicated by the abbreviated subscripts C.M. (center of mass frame) and Lab (laboratory frame).
3. The remaining class of subscripts consists of a few symbols of long usage in the literature; for ex~ ample, the Rutherford differential scattering cross section a R (8) and the cross section for compound elastic scattering u e E(e). The argument E is suppressed when we are dealing with monoenergetic projectiles.
Types of Reaction Subscripts
1. When both the bornbarding and outgoing particles are specified for a reaction, they are indicated by symbols with a comma following the bombarding particle or projectile (op,n ). Each product particle produced in a reaction must have a coefficient to indicate the number of product particles involved if there is more than one (uF, 2 n ). If only the type of product particle is observed without regard to number, then the coefficient should be a k (op, k n ). If there are other prod-
Abbreviated Notation
In this compilation the above general principles of notation have been abbreviated for the tabular and
125
KIM, MILNER, AND McGOWAN
graphical presentation of the data as follows: 1. The subscripts in the cross-section notation indicating the projectile and emerging particle or particles are suppressed whenever the reaction types are given explicitly as separate entities. 2. Since the caption for the tabular presentation gives explicitly the type of reaction and the energy of the projectile, the argument E of the projectile is suppressed in the cross-section notation for elastic and inelastic scattering and for angular distributions. 3. Since the bombarding energy is conserved in the center-of-mass system for elastic scattering, the argument E of the emerging particle is suppressed. 4. For the angular distributions of emerging particles with monoenergetic projectiles and for inelastic scattering distributions, the energy of the outgoing particle leaving the residual nucleus in a definite state in the center-of-mass system is suppressed. The labeling of the energy of the emerging particle is included in the caption; for example, the Q of the reaction. For the sake of definiteness, the term inelastic scattering refers to those situations in which the incident projectile transfers energy to the nucleus (nuclear excitation) in the center-of-mass system, all of which appears eventually as deexcitation gamma rays emitted by the residual nucleus. 5. In many cases of high-energy reaction cross sections, it is impossible to distinguish the sequence of particle emission. Although we have in many instances given a reaction sequence for the emerging particles, we do not mean to imply that is the correct or the only reaction sequence for the emerging particles in the nuclear reaction. In general for these reactions, only the induced activity in the residual nucleus is observed. This fact is always indicated in the caption to the tabular data.
1.2 Tabular Data The arrangement of the reactions A(a, h)B is according to (1) increasing Z of the target and (2) increasing Z and mass number of the projectile. For a given type of reaction, the arrangement is in order of increasing energy of the projectile. For a given reaction and projectile energy, the information on the naturally occurring element comes first, and the various isotopes follow in order of increasing mass number. For a given projectile, elastic scattering reactions come first, inelastic scattering reactions come next, and all other reactions follow according to decreasing Z and mass number of the residual nucleus.
The angular dependence of the polarization in the elastic scattering reaction is placed after elastic scattering data of the same energy or nearly the same energy. Further differentiation is given by differential excitation functions preceding angular distributions and ground-state reactions preceding excited-state reactions of the residual nucleus. The recent style of placing the isotope mass number as a superscript at the upper left of the element symbol has been adopted for the reaction notation. The energy E appearing below the reaction is always in the laboratory frame of reference. The symbol P(O) is the notation for angular dependence of the polarization produced in the elastic scattering reaction. Below the energy E of the projectile, a labeling of the energy of the emerging particle or particles is given by the Q value of the reaction. Sometimes the excitation energy of the residual nucleus is given in parentheses following the Q value. The quoted Q values are taken from Ref. 2. The caption to the tabular data gives the reference, laboratory, a few experimental details, errors, and source of tabular data. Insofar as possible the abbreviations for journals conform with those adopted by Chemical Abstracts and the American Institute of Physics. In the case of references to Russian literature, an attempt has been made to present the original Russian reference. The location of the laboratory at which the data originated follows the reference in brackets. The experimental details include accelerator, detectors, energy resolution, angular resolution, and target thickness. Occasionally one or more of these details are omitted if they are not available in the paper. Usually some expression of the errors for the cross sections is included either in the caption or the tabular information. In the caption this expression is the fractional standard deviation of the cross section. Frequently the type of error is not indicated by the authors of the paper. In these cases, we have arbitrarily taken the errors to mean standard deviations. The tabular information for the elastic scattering reaction is always given in the formo(O)juR , where u R is the nonrelativistic Rutherford scattering cross section. The expression of error for 0(0) in the caption does not reflect the error introduced by the uncertainty in when the elastic scattering cross section is expressed in units of u R ' that is, u(O)/uR • Whether the tabular data were supplied by the authors or obtained from figures in the published paper is also stated in the caption.
e
126
INTRODUCTION
In many cases' of early cross-section data, the only sources of the information are from the small figures in the journals. A Moseley model 25 X-V point plotter was modified to read data points from small published figures. Helipots were coupled to the cables which drive the pen and carriage of the plotter. The coordinates of the data points are displayed in analog form by a Hewlett-Packard model 40SCR automatic de digital voltmeter which also drives a Hewlett-Packard model 561B digital recorder. The X and Y ranges may be adjusted to yield 2000 increments of information in analog form for any size figure. The components of the data-point reader provide an overall accuracy of to.25% of full scale. For example, the reading error in 0 from an angular distribution would be to.5°. In general, the accuracy of the data points read from small figures depends entirely on the accuracy of the original drawing and on distortions introduced by the publisher. Enlargements of the small figures in the journal would be of no va lue with regard to avoiding these possible sources of errors. The coordinates of the data points in analog form are key punched directly from the tapes of the digital recorder onto IBM cards. Computer programs process the analog information ; transform, if necessary, the cross-section data from the laboratory frame of reference to the center-of-mass system by a nonrelativistic kinematics program ; list the data in tabular form; and prepare a magnetic tape for plotting the data by a Calcomp model 570 plotter. This mechanization means a saving of labor and reduces the chance of error. The captions as well as the tabul ar data are composed and arranged by using a computer code, and the resulting machine compositions are listed by an IBM model 1405 on-line printer and presented directly. In this compilation the differential cross-section data are given in the center-of-mass system. There are a few exceptions, and these cases are noted in the caption preceding the tabul ar data . When several sets of data are presented in a single graph, the symbol associated with each set of data points is placed either near the caption or above tabular data, whichever is appropriate, for iden tification purposes.
1.3 Graphs
All cross-section data, including both angular distribu tions and excitation functions, are presented on semilog graph paper. The angular dependence of the polarization produced in the elastic scattering reaction is presented on linear graph paper. The grid of the X axis is 25 di visions per inch for the semilog graph paper of one, two, and three cycles. This makes possible the presentation of angular distributions (25° lin.) on a 7-in. grid. The reaction label A(a,b)B appears in the upper right corner in the field of the grid. The case number in the upper left corner in the field of the grid is for internal use and represents the location of the data at the CPX Data Center. In general the energy scale for excitation functions does not start with zero at the origin. Occasionally, we find a roll of graph paper in which the registration does not align the grid perfectly with respect to the drum and carriage motions of the plotter. As a result, data points of an angular distribution may be in error by 0.5 ° at the most in the upper third of the grid field. The reader may find a few examples where several data entries in the ta bul ar presentation are not plotted, because these points fall off scale of the graphical presentation. With a few exceptions, only the experimental data points of the original author or authors are presented in this compilation. Data points derived from smooth curves of figures in published papers are noted in the captions. Every effort has been made to ensure the general reliability of the transcription of the data to the graphs. We shall appreciate criticisms, comments, and notes of any errors in the tabular or the graphical presentation of this compilation. References
IH. Goldstein, "Appendix I," p. 2227 in Fast Neutron Physics, vol. IV, part II, ed. by J. B. Marion and J. L. Fowler, Interscience, New York, 1963. 2J. H. E. Mattauch, W. Thiele and A. H. Wapstra, Nucl. Phys. 67, 1 (1965).
127