Table Of ContentLandolt-Börnstein
Numerical Data and Functional Relationships in Science and Technology
New Series / Editor in Chief: W. Martienssen
Group I: Elementary Particles, Nuclei and Atoms
Volume 19
Nuclear States from
Charged Particle Reactions
Subvolume A
α
Tables of Proton and -Particle
Resonance Parameters
Part 1
Z = 2 - 18
S.I. Sukhoruchkin
Z.N. Soroko
Edited by H. Schopper
ISSN 1615-1844 (Elementary Particles, Nuclei and Atoms)
ISBN 3-540-41029-5 Springer Berlin Heidelberg New York
Library of Congress Cataloging in Publication Data
Zahlenwerte und Funktionen aus Naturwissenschaften und Technik, Neue Serie
Editor in Chief: W. Martienssen
Vol. I/19A1: Editor: H. Schopper
At head of title: Landolt-Börnstein. Added t.p.: Numerical data and functional relationships in science and technology.
Tables chiefly in English.
Intended to supersede the Physikalisch-chemische Tabellen by H. Landolt and R. Börnstein of which the 6th ed. began publication in 1950 under title:
Zahlenwerte und Funktionen aus Physik, Chemie, Astronomie, Geophysik und Technik.
Vols. published after v. 1 of group I have imprint: Berlin, New York, Springer-Verlag
Includes bibliographies.
1. Physics--Tables. 2. Chemistry--Tables. 3. Engineering--Tables.
I. Börnstein, R. (Richard), 1852-1913. II. Landolt, H. (Hans), 1831-1910.
III. Physikalisch-chemische Tabellen. IV. Title: Numerical data and functional relationships in science and technology.
QC61.23 502'.12 62-53136
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Editor
H. Schopper
CERN, CH-1211 Geneva 23, Switzerland
e-mail: [email protected]
Contributors
S.I. Sukhoruchkin
Z.N. Soroko
Petersburg Nuclear Physics Institute
188350 Gatchina, Leningrad District, Russia
e-mail: [email protected]
Landolt-Börnstein
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Preface
Nuclear resonance parameters for levels created in reactions with incident protons and other light charged
particles are of great interest for nuclear spectroscopy, astrophysical models, thermonuclear calculations
and other applications. In the Landolt-Börnstein volume I/19A the parameters have now been compiled.
No systematic compilation for such data has been performed so far. Parameters for nuclear levels
produced in reactions with incident neutrons were published in volumes I/16B and I/16C.
There is such an abundance of experimental data, a large part of it produced during the last 10 years, that
it had to be distributed over two subvolumes. The present subvolume I/19A1 contains the data for nuclei
up to Z = 18 and subvolume I/19A2 those for nuclei with Z larger than 18.
In agreement with the Publisher's general effort to make the data available to users by modern methods
each subvolume is delivered with a CD-ROM which contains all the data of the printed volume, however,
in view of the large amount of data some of the information is given on the CD-ROM only.
The compilation was prepared as usual by eminent experts in the fields. One of the characteristics of
Landolt-Börnstein is that data are evaluated before they are accepted for compilation. The idea is to
present ‘best values’ which can be used with confidence by non-experts. Preparing such best values also
implied making corrections necessary because of different energy calibrations in various publications.
I should like to thank the authors for their careful work and their flexibility to comply with the wishes of
the editor and publisher. Thanks are also due to the members of the Landolt-Börnstein editorial staff who
have made major contributions to the successful production of this volume.
Geneva, June 2004 The Editor
Contents
1 Introduction.......................................... 1
1.1 General remarks........................................ 1
1.2 Data collection and presentation................................ 3
1.3 List of notations........................................ 6
1.4 The astrophysical aspect of resonance parameters....................... 11
1.5 Data from high-resolution measurements ........................... 11
1.6 Investigations of iosobar-analog resonances.......................... 15
1.7 Standards and material testing................................. 18
1.8 Conclusions.......................................... 19
1.9 Acknowledgements ...................................... 19
2 Tables............................................. 20
2-Helium 6-Carbon 9-Fluorine
He-5 ........ 20 C-9 ......... 34 F-15 ........ 81
C-10 ........ 34 F-16 ........ 81
3-Lithium
C-11 ........ 34 F-17 ........ 81
Li-5......... 20
C-12 ........ 36 F-18 ........ 85
Li-6......... 20
C-13 ........ 40 F-19 ....... 102
Li-7......... 21
C-14 ........ 43
10-Neon
4-Beryllium C-15 ........ 44
Ne-18....... 114
Be-6 ........ 21 C-16 ........ 44
Ne-19....... 115
Be-7 ........ 21
7-Nitrogen Ne-20....... 119
Be-8 ........ 22
N-11 ........ 45 Ne-21....... 128
Be-9 ........ 24
N-12 ........ 45 Ne-22....... 132
Be-10........ 25
N-13 ........ 45
11-Sodium
5-Boron N-14 ........ 48
Na-19....... 136
B-8......... 26 N-15 ........ 54
Na-20....... 136
B-9......... 26 N-16 ........ 59
Na-21....... 136
B-10 ........ 27 N-17 ........ 60
Na-22....... 139
B-11 ........ 30 N-18 ........ 61
Na-23....... 145
B-12 ........ 33 N-19 ........ 61
B-13 ........ 33 12-Magnesium
8-Oxygen
B-14 ........ 33 Mg-22 ...... 157
O-14 ........ 62
Mg-23 ...... 159
O-15 ........ 62
Mg-24 ...... 160
O-16 ........ 67
Mg-25 ...... 176
O-17 ........ 75
Mg-26 ...... 181
O-18 ........ 78
O-19 ........ 80
VIII Contents
13-Aluminium 15-Phosphorus 17-Chlorine
Al-23....... 188 P-27 ....... 254 Cl-31 ....... 310
Al-24....... 188 P-28 ....... 254 Cl-32 ....... 310
Al-25....... 189 P-29 ....... 255 Cl-33 ....... 311
Al-26....... 193 P-30 ....... 258 Cl-34 ....... 314
Al-27....... 206 P-31 ....... 265 Cl-35 ....... 322
Cl-37 ....... 332
14-Silicon 16-Sulfur
Si-25 ....... 223 S-30 ....... 284 18-Argon
Si-26 ....... 223 S-31 ....... 285 Ar-36....... 346
Si-27 ....... 224 S-32 ....... 286 Ar-38....... 360
Si-28 ....... 226 S-33 ....... 299 Ar-40....... 383
Si-29 ....... 242 S-34 ....... 304
Si-30 ....... 246
3 References ............................................ 388
Supplement (complete sets of resonance parameters)...................... CD-ROM
Ref. p. 388] Proton and α-particle resonance parameters 1
1 Introduction
1.1 General remarks
This report is a compilation of resonance parameters of nuclear reactions induced by protons,
α-particles, as well as deuterons, tritons, and 3He-ions. It is called for simplicity PRF - Proton
ResonanceparametersFile. ThematerialofPRFiscontainedintwobooks: fornucleiwithZ ≤18
and Z ≥19. PRF includes also additional data not contained in the books. The full text of PRF
is given on CD-ROM (as Supplement). The data of PRF are presented in tables which format is
analogoustothatofthecompilationofneutronresonanceparameters(NRF)publishedasvolumes
I/16B [98Sc0A] and I/16C of Springer’s Landoldt-Bo¨rnstein New Series.
Resonance parameters of reactions with protons and other charged particles never were the
subject of a general compilation despite the fact that properties of resonances induced by protons
andα-particlesformasolidpartofnuclearspectroscopy. Well-knownevaluationsoftheproperties
of light nuclei by F. Ajzenberg-Selove [88Aj01, 90Aj01, 91Aj01], D. Tilley et al. [93Ti07, 95Ti07,
98Ti06,97Ch0A],and P. Endt and C. Van der Leun [67En05,73EnVA, 78En02,90En08,98En04]
aredevotedmainlyto relativelylow-lyingexcitedstatesandcontaininmanycasesonlyreferences
to papers where resonance parameters are given. Data on heavy nuclei (A > 44) are included in
the Evaluated Nuclear Structure Data File (ENSDF) [98Bu0A, 02Nu0A].
Observationof proton and neutron resonanceswas explained by Niels Bohr who suggested the
presence of the compound nucleus stage in nuclear reactions. A great number of resonance pa-
rametersinreactionsinducedbyneutronsandchargedparticlesmeasuredindifferentlaboratories
throughout the world was successfully used in the study of the properties of highly excited com-
pound states of many nuclei. These data were widely used in several specific applications as well.
Reviews by E. Bilpuch [72Bi0A, 76Bi0A] and G.E. Mitchell [72Mi0A, 85Mi0A] were devoted to
results obtained in the 70s in TUNL (Triangle University Nuclear Laboratory).
Problemsofnuclearphysicsweretheprincipalobjectivesofresonanceparametermeasurements
from the 60s up to the 80s. Now an important application of charged-particles resonance data is
provided by Nuclear Astrophysics [84Fo0A, 84Ya0A, 52Sa0A, 88Ba0A, 92Ro0A, 87Ro0A]. Ther-
monuclear calculations are connected with charged-particle resonance spectroscopy in the same
wayascalculationsofnuclearreactors–withneutronresonancespectroscopy. Mostofthecapture
parameters for light nuclei were taken from the recent evaluation of astrophysical reaction rates
NACRE [99An35, 00Co0A]. Compilations of resonance parameters data could fulfil their role in
maintaining of the world-wide experimental data (irrespective of their specific applications) on
conditionthatthey containallpublished dataandthe data arepresentedina PC-friendlyformat.
Wehavecollectedtheoriginaldataoncharged-particleresonancesofnucleiwithZ >3including
proton resonances in heavy nuclei (A > 100) which in fact are the positions of gross-structure
resonancescorrespondingtothepositionsoftheanalogstate. ValuesE∗ giveninthePRFshow
analog
corresponding excitations of the analog state in the neighbor parent nucleus. Data on resonances
induced by protons, deuterons, tritons (3H), 3He-particles (frequently called in the literature as
τ) and α-particles are collected together with the parameters of resonance states derived from
inelastic scattering and γ-decay (branching ratios, partial radiative widths, reaction amplitudes,
energies of bound levels). For presentation of these data special formats were used. All data were
grouped according to the common Z and A of the compound nuclei formed in different reactions.
The datafornucleiwith atomicnumberslessthanZ =19arecontainedinthe firstbook(part
1 of PRF). In Tables 1 and 2 the numbers of resonances and branching ratios contained in this
partofPRFaregiven. InTable2thenumbersofresonances(Np,Nα)aregiventogetherwiththe
numberofγ-transitions(Nγ)fromeachresonance. These pairscorrespondto the two-dimensional
format of the tables used for presentation of branching ratios and partial widths.
Landolt-Bo¨rnstein
New Series I/19A1
2 Proton and α-particle resonanceparameters [Ref. p. 388
Table 1. Contents of the volume I/19A1, compound nuclei with Z ≤18:
AZ – compound nucleus,
Np, Nd, Nt, Nh, Nα – number of data-lines for (p,d,t,h,α) projectile, respectively.
AZ Np Nd Nt Nh Nα AZ Np Nd Nt Nh Nα AZ Np Nt Nα AZ Np Nα
5He 2 12N 3 22Ne 9 56 29Si 37
5Li 1 13N 38 6 20Na 11 30Si 69
6Li 4 14N 48 83 33 21Na 52 29P 77
7Li 4 15N 44 16 24 50 22Na 60 30P 97
6Be 1 16N 7 23Na 149 115 31P 256 246
7Be 1 7 14O 5 22Mg 4 7 30S 6
8Be 11 4 9 15O 60 28 23Mg 21 32S 165 69
9Be 4 4 16O 51 29 22 104 24Mg 144 217 33S 156
10Be 5 17O 4 6 60 25Mg 67 34S 103
8B 1 18O 33 26Mg 155 32Cl 4
9B 2 2 15F 2 24Al 4 33Cl 57
10B 31 4 17 17F 89 25Al 47 34Cl 193
11B 4 7 22 18F 58 245 4 187 26Al 147 35Cl 142 92
12B 5 19F 145 18 91 27Al 212 91 37Cl 419
11C 25 4 18Ne 8 5 25Si 1 36Ar 178 16
12C 32 2 7 5 19Ne 14 10 24 26Si 7 38Ar 530 48
13C 10 24 20Ne 93 189 27Si 24 40Ar 59
11N 7 21Ne 7 65 28Si 254 58
Table 2. Radiative decay data in the volume I/19A1, compound nuclei with Z ≤18:
Np, Nα – number of the proton or α-particle resonances, respectively,
Nγ – number of γ–transitions to low-lying levels.
AZ Np/Nγ Nα/Nγ AZ Np/Nγ Nα/Nγ AZ Np/Nγ Nα/Nγ AZ Np/Nγ Nα/Nγ
10Be (7/5) 18O 7/11 23Mg 8/7 31P 65/28 17/24
10B 4/5 19O (7/6) 24Mg 34/24 30S (5/2)
11B 3/6 17F 6/3 25Mg (71/27) 31S (6/3)
11C 7/8 18F 24/23 26Mg 6/25 32S 63/23 12/11
12C 5/6 19F 17/25 31/25 25Al 13/9 33S 6/24
13C 2/3 18Ne (4/2) 26Al 87/26 34S 12/23
14C (7/3) 19Ne 6/6 27Al 120/21 20/21 32Cl (3/4)
14N 13/10 20Ne 30/7 26Si (9/3) 33Cl 14/8
15N 5/10 21Ne (43/12) 27Si 7/11 34Cl 49/25
16N (3/4) 22Ne 13/23 28Si 110/23 28/23 35Cl 48/24
17N (16/7) 21Na 11/6 29Si (99/22) 37Cl 79/23
18N (4/4) 22Na 43/20 30Si (135/26) 36Ar 87/20
15O 20/7 23Na 32/23 2/9 28P (7/6) 38Ar 64/24 32/12
16O (20/6) 2/6 22Mg 4/6 29P 9/7 40Ar 17/21
17O 1/7 30P 28/26
Comments: For several nuclei only branching ratios for γ-transitions between low-lying levels
are known, their numbers are given here in parentheses. Level schemes of the following 11 nuclei
aregiveninthebookLBI/19A1forthesakeofthecompleteness: 13B,14B,9C,10C,15C,16C,19N,
16F, 19Na, 27P and 31Cl. Energy levels of 8Li, 9Li, 11Be, 12Be and 13O are given in Supplement.
Landolt-Bo¨rnstein
New Series I/19A1
Ref. p. 388] Proton and α-particle resonance parameters 3
1.2 Data collection and presentation
TheinternationalfileENSDF[02Nu0A]andinternationalNuclearScienceReferencesystem(NSR)
werewidely used during collection of the PRF-file. We have selected data from the originalworks
mentioned in NSR and corresponding numbers of papers in this reference system are preserved.
We havetriedto find so-called”bestvalues” andmade the comparisonwith the values adoptedin
the evaluations presented in the so-called Master Tables. Modern PC-capacities and the Nuclear
ScienceReferencefileavailablefromBrookhavenNationalNuclearDataCenterpermittedtocollect
andrepresentinthecommonformatalldatascatteredintheliterature,indissertationsandreviews
for all regions of atomic masses A and numbers Z.
Theproblemsofresonancedatainterpretationsandapplicationswerediscussedinreviewsand
reportsinaseriesofinternationalMeetings: ConferenceonNuclearDataforScienceandTechnol-
ogy[02Sh0A](1997,2001),SymposiumsonNucleiintheCosmos[98Pr0A](1992,1994,1996,1998,
2000, 2002), Symposiums on Capture Gamma-Ray Spectroscopy [00We0B, 03Kv0A] (1993, 1996,
1999,2002),ConferenceonExperimentalNuclearPhysicsinEurope[99Ru0A](Sevilla,1999),Con-
ference on Exotic Nuclei and Atomic Masses[98Sh0A] (1998,2001),IUPAP InternationalNuclear
Physics Conferences [02No0A] (Berkeley, 2001).
Parameters given in the PRF tables are the results of fitting treatments of measured cross-
sections, γ-ray yield, or other effects, by means of several kinds of resonance formulas and usually
the R-matrix formalism is used in such a fitting. A general theory of resonance reactions is given
inseveralmonographs[47Wi0A,52Bl0A,56Kr0A,57Bl0A,58La0A,60Fe0A].Resonanceformulas
in proton resonance spectroscopy routinely used to analyze experimental data are given in the
original papers. In Wigner’s R-matrix formalism all scattering quantities are parametrized in
terms of real, energy-independent quantities for each resonance λ: the reduced-width amplitudes
γλc, and energy eigenvalues Eλ, which are somewhat arbitrary due to their dependence on the
boundary-condition numbers Bc, and channel of specific reaction radii ac (serving to divide space
intoouterandinnervolumes). Resonanceparametersarereflectingtheinner propertiesofnuclear
states,determinedbytheunderlyingnucleardynamics. Thisdynamicsinfluencesthedistributions
ofphysicalquantities suchas eigenvalues(energyof resonance),spectroscopicfactors(overlapping
between the wave-functions of different configurations of the nucleons), transitions between the
states (acting of operators of different nucleon interactions on initial nuclear states), mean life of
the state or the total Γ-width of the state and the widths corresponding to the specific modes of
decay, etc. Different applications of resonance data use the same common theoretical quantities.
The relations between specific parametersused in applications and common(general) parame-
tersinresonanceformulasareusuallysimpleandwerediscussedintheoriginalpapersandreviews.
For example, resonance parameter ωγ frequently used in thermonuclear reaction rate calculations
isacombinationofresonancewidths andspinJ ofthe compoundnucleus(togetherwiththe spins
of target-nucleus and proton, I◦ and s, respectively),
(2J +1) ΓiΓj
ωγ = . (1)
(2I◦+1)(2s+1) Γ
Part of this expression, namely the parameter Sij,
ΓiΓj
Sij =(2J +1) , (2)
Γ
is called the resonance strength and is given in many original papers and compilations. The
resonancestrength is usually derived from the step in the thick-targetyield curve of any reaction,
for example, the γ-yield curve in (p,γ), (α,γ) reactions, or neutron yield-curve in (α,n) reaction
[74Wh03]. Itsdeterminationrequiresknowledgeofmanyfactorsinthegeneralexpression(written
here for the neutron yield under charged-particle bombardment)
Sin = ωγin = mi (cid:8)(Ei)eEiY(∞), (3)
(2I◦+1)(2si+1) π2¯h2 Q
Landolt-Bo¨rnstein
New Series I/19A1
4 Proton and α-particle resonanceparameters [Ref. p. 388
where Y(∞) is the step in the integrated yield curve, (cid:8)(Ei) is the stopping cross section of the
(isotopically composed) target, e is the electronic charge, Q is the total charge collected. An
estimation of the detector efficiency and some minor corrections should be taken into account in
the determination of resonance strengths. If I◦π is known, ωγ can be recalculated from Sij. The
parameters ωγ and Sij obtained in different works could be given separately.
For an isolated resonance the simplified Breit–Wigner formula for the energy dependence of
the cross-section of a certain reaction, say, the dependence on the particle energy E of elastic
(p,p) and inelastic (p,p(cid:3)) proton scattering, or capture cross-section σγ, can be approximated by
an expression similar to that used for the description of the neutron capture cross-section:
(cid:1)
σres =σ◦ΓΓγ EE◦ 1+1y2, y =2E−ΓE◦, σ◦ =4πλ2◦ gΓΓn. (4)
In this case the Breit-Wignerformula for a crosssection with a sum of isolatedresonancesλ is
(cid:2)
π ΓiΓj 2Jλ+1
σres(E)= k2 gλ(E−Eλ)2+(Γ/2)2, gλ = (2s+1)(2I◦+1). (5)
λ
The notation in this simplified formula (an isolatedresonancewith one entrancechanneli and
one outgoing channel j) is the same as in the PRF tables. This formula comes from an element of
the scattering matrix S expressed for a resonance with definite parity [52Bl0A] as
ig(s(cid:11))g(s(cid:3)(cid:11)(cid:3))
Sα(cid:1)s(cid:1)(cid:5)(cid:1);αs(cid:5) =exp[i(ξ(cid:5)+ξ(cid:5)(cid:1))]Eo−E−iΓ/2. (6)
Here E◦ is the resonance energy, Γ is the total width of the level, and ξ(cid:5),ξ(cid:5)(cid:1) are energy-
dependent phase shifts which include both Coulomb and hard sphere phase shifts. The quantities
g(s(cid:11)) are the real numbers given by gi(s(cid:11)) = ±[Γi]1/2, where i denotes all appropriate quantum
numbersandΓi isthe partialwidthinchanneli[85Mi0A].Thereducedwidthinchanneliisgiven
by γi2 = Γi/2Pi, where Pi is the penetrability in that channel. Expression for the cross section
with many interfering resonances is more complicated [85Ne0A].
The statisticalweight factor gλ (equ. 5) is frequently used in combinationwith severalwidths.
Inthecaseoftheprotonwithintrinsicspin(s=1/2)itsvaluebecomesg =(2J+1)/2(2I◦+1)and,
for example, for the low energy ((cid:11)=0) proton resonances of even-even target nuclei the statistical
factor g =1. In the case of the α-particle s=0 and it gives for an even-eventarget-nuclei ωγ=Sij.
For each resonance of a certain isotope all available data were collected and the values of
resonance parameters selected out of them are forming a single data-line. Each data-line starts
with the energy of the resonance E◦ in the laboratory frame and ends with the energy of the
compoundstateE∗ followedbythereference-codestoshowwherethe datagivenweretakenfrom.
The direct referencing to the original papers at the end of each data-line could be used by the
interested reader for his own judgement. Additional references given at the end of the tables, and
references in comments, could serve for a better orientationin the material. Some important data
are taken from unpublished theses (dissertations) which were also included in the Reference List:
their references were formatted as NSR with 0 and a letter in the last two (out of 6) characters.
New references were introduced only for those works which were not included in the NSR file
previously. In all cases the first two columns are reserved to E◦, and spin J and parity, of the
compound nucleus state (resulting from interaction with the incoming proton or α-particle). The
isotopicspinT isgiveninthethirdcolumn. Asinmanyothercompilationswegivevalues2Jπ and
2T for all A-odd nuclei ( 2J =1+ instead of J =1/2+, etc.). The double spin notation 1−, 3− or
3+, 5+ usually corresponds to (cid:11)=1 or (cid:11)=2 in the case of an even-even target (A-odd compound
nucleus). Notations”odd”and”even”aswellas”not2”,NorN+ onthe secondplace correspond
to the J-values (with N – Normal sequence J = 0+,1−,2+,3−, etc., N+ – positive-parity part of
this sequence J =0+,2+, etc.).
Landolt-Bo¨rnstein
New Series I/19A1
