KOPECKY.readme
Contents of the present readme:
Description of kopecky.dat
Attachment A
Attachment B
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Description of kopecky.dat
Contents
--------
The actual data file, kopecky.dat, contains global systematics
derived from experimental strength function data for f(E1), f(M1)
and f(E1)/f(M1). Recommended experimental data base of f(E1) and
f(M1) is included in a tabular form.
Format
------
Each entry consists of 3 lines:
======================================================================
Nucleus [Ref] Reac #Res/E1/M1 <EgE1/EgM1> D0[eV] from [1-4]
D0[eV] fE1(a) fM1(a)
.................................................
Comment Corr.factor Revised values
======================================================================
Notation in the 1-st line:
Nucleus final nucleus for which the entry is given (e.g. Nb-94)
[Ref] reference to the source
Reac reaction used to determine gamma resonances:
(n,g) stands for (n,gamma),
(n,g)th stands for,gamma) with thermal neutrons
#Res/E1/M1 number of considered resonances/number of E1 transitions/
number of M1 transitions
<EgE1/EgM1> mean energy of E1 transitions/mean energy of M1 transitions
D0 from [1-4] resonance spacing values from 4 major sources:
BNL Brookhaven [1], CNDC Beijing [2],
IPPE Obninsk [3], ENEA Bologna [4].
Notation in the 2-nd line:
D0 actually adopted resonance spacing value
fE1(a) gamma-ray strength function f(E1):
in 10**(-8) MeV**(-3) units based on s-(p-) wave neutron
capture and photonuclear data,
with (a) being in quadrature added statistical,
normalizations (20%) and Porter-Thomas uncertainty
fM1(a) gamma-ray strength function f(M1), otherwise see above
In the 3-rd line of data sections a comment is given on the quality
of data treatment in original references (if doubts exist). If a revi-
sion is executed (based on strong arguments), the correction factor and
the revised f(E1) and f(M1) values are presented, respectively.
Throughout the tables,
- stands for no data of this type
NA stands for Not Applicable (or Not Available)
and the data with their errors use conventional way of notation,
that the uncertainties are given in parentheses in units of
the last given place (e.g. 10.47(157) means 10.47 +- 1.57).
References
----------
[1] S.F. Mughabghab, M. Divadeenam and N.E. Holden, "Neutron
Capture Cross Sections", (Academic Press, New York, 1981 and
1984), Volume 1, Part A and B.
[2] Huang Zhongfu and Su Zongdi, Com. of Nuclear Data Progress,
16, 84 (1993).
[3] A.V. Ignatyuk et al., INDC(CCP)-320 (1990) 25 and private
communication.
[4] G. Reffo, private communication.
[5] C.M. McCullagh, M. Stelts and R.E. Chrien, Phys. Rev.
C23, 1394 (1981).
[6] C. Coceva et al., in "Capture Gamma Ray Spectroscopy" 1987,
(Inst. of Physics Conference Series 88, Institute of
Physics, Bristol, 1988) p.676.
[7] C. Coceva et al., Phys. Rev. C30, 679 (1984).
[8] C. Coceva, Radiative transitions from neutron capture in
Cr-53 resonances, to be published in Il Nuovo Cimento A.
[9] C. Coceva, private communication.
[10] M.A. Islam, T.J. Kennett and W.V. Prestwich, Z.Physik
A335, 173 (1990).
[11] M.A. Islam, T.J. Kennett and W.V. Prestwich, Phys. Rev.
C42, 207 (1990).
[12] F. Becvar et al., Journal of Nuclear Physics (Russian),
46, 3 (1987).
[13] F. Becvar, in "Capture Gamma Ray Spectroscopy 1987",
(Institute of Physics Conference Series 88, Institute
of Physics, Bristol, 1988) p.649 and private communication.
[14] F. Becvar et al., Proc. of the International Conference on
Neutron Physics, Kiev (USSR), 2-6 October, 1983, p.8.
[15] S. Pospisil et al., Annual Report 1995, Frank Laboratory of
Neutron Physics JINR Dubna, p.84.
[16] S. Kahane, S. Raman, G.G. Slaughter, C. Coceva and M. Stefa-
non, Phys. Rev. C30, 807 (1984).
[17] H.H. Schmidt et al., Nucl. Phys. A504, 1 (1989).
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Attachment A.
RECOMMENDED EXPERIMENTAL LORENTZIAN GIANT RESONANCE PARAMETERS OR
FORMULAS FOR THEIR CALCULATION FOR E1, M1, E2 MULTIPOLARITIES
E1: GIANT DIPOLE RESONANCE
==========================
Giant resonance parameters (GRP) can be obtained
i. from the analysis of experimental photoabsorption cross
sections of the compound nucleus,
ii. interpolated from neighbouring nuclei assuming small
dependence of these parameters on A,
iii. if no experimental information is available, global syste-
matics of all parameters can be applied. It should, however,
be noted, that no systematic is reliable for nuclei with
A < 50. The shape of their excitation functions reveals
quite complicated structure for every nucleus due to exci-
tations in unbound individual E1 states.
For more information on this subject see:
* Liu Jianfeng, Su Zongdi and Zuo Yixin, "The Giant
Dipole Resonance Parameters for A < 50 and Sub-
Library of GRP for Gamma-ray (CENPL-GDP 1.1)",
contribution to the 2nd CR Meeting on Development
of Reference Input Parameter Library for Nuclear
Model Calculations of Nuclear Data, INDC(NDS)-350,
March 1996.
Experimental data
-----------------
Recommended compilations of GRP derived from experimental
data:
* S.S. Dietrich and B.L. Berman, At. Nucl. Data Tables,
38, 199 (1988).
* Sub-library of Giant Dipole Resonance Parameters
(BEIJING-GDP.DAT;1), described in
Zuo Yixin, Liu Jianfeng, Zhang Xizhi, Ge Zhigang and
Su Zongdi,"The Sub-library of GDR Parameters for
Gamma-Ray", Com. of Nuclear Data Progress, 11, 95 (1996).
* T. Asami and T. Nakadawa,"Bibliographic Index to Photo-
nuclear Reaction Data (1955-1992)", INDC(JPN)-167/L
or JAERI-M 93-195 (October 1993).
Global parameterization
-----------------------
(applied symbols have the following meaning:
Er, Gr and sigr - the energy, the width and the peak cross sections
of the giant resonance, respectively; B - the quadrupole deformation
parameter).
Spherical targets ( A > 50 )
=============================
Er = 31.2*A**(-0.333) + 20.6*A**(-0.167) [MeV] [1]
Gr = 0.026*Er**1.91 [MeV] [2]
sigr = 0.166*A**1.54 [mb] [3]
(fit to exp. data)
sigr = 1.2*120*N*Z/(A*pi*Gr) [mb] [2]
(adjusted classical sum rule)
Deformed targets ( A > 50 )
=============================
Er1 = Er/(1 + 0.666*B) [MeV] [4]
Er2 = Er/(1 - 0.333*B) [MeV] [4]
Gr1 = 0.026*Er1**1.91 [MeV] [2]
Gr2 = 0.026*Er2**1.91 [MeV] [2]
sigr1 = 1.2*120*N*Z/(A*pi*Gr1) [mb] [2]
sigr2 = 1.2*120*N*Z/(A*pi*Gr2) [mb] [2]
Recently a comprehensive study (D'Arigo et al. [5]) has been com-
leted, in which the following global expressions have been derived,
based on fits to experimental data of Dietrich and Berman:
Global parameterization
-----------------------
Spherical targets ( A > 50 )
=============================
(applied symbols have the usual meaning)
(B = quadrupole deformation parameter)
Er = (49.336 + 7.34*B)*A**0.2409 [MeV]
Gr = 0.3*Er [MeV]
sigr = 10.6*A/Gr [mb]
Deformed targets ( A > 50 )
=============================
Er2 = 50*A**-0.232 [MeV]
ln(Er2/Er1) = 0.946*B [MeV]
Gr1 = (0.283-0.263*B)*Er1 [MeV]
Gr2 = (0.35-0.14*B)*Er2 [MeV]
sigr1 = 3.48*A/Gr1 [mb]
sigr2 = 1.464*A/Gr2 [mb]
Other references of systematic treatment:
* D.G. Gardner in "Neutron Radiative Capture", (Pergamon Press,
Editor R.E. Chrien, 1985), p.62.
* D.G. Gardner, M.A. Gardner and R.W. Hoff,"Detailed Photonuclear
Cross-Section Calculations and Astrophysical Applications",
UCRL-100547 Supplement (1989).
* G. Reffo see Ref. [6]
----------------------------------------------------------------------
M1: SPIN-FLIP GIANT RESONANCE
=============================
Spin-flip giant resonance mode, as proposed by Bohr and Mottel-
son [7], is recommended (see e.g. Refs. [8,9,10]).
Global parameterization
-----------------------
Er = 41*A**(-1/3) [MeV] [7]
Gr = 4 MeV [8]
sigr = adjusted to:
1. experimental f(M1) value
2. f(M1) = 1.58*A**0.47 at +-7 MeV [9]
3. f(E1)/f(M1) = 0.0588*A**0.878 at +-7 MeV [3,10]
---------------------------------------------------------------------
E2: ISOSCALAR GIANT RESONANCE
=============================
The description of E2 excitations in neutron capture as the
isoscalar giant resonance mode are discussed in Refs. [8,10,11].
Global parameterization
----------------------
Er = 63*A**(-1/3) [MeV] [1]
Gr = 6.11 - 0.021*A [MeV] [11]
sigr = 0.00014*Z**2*Er/(A**1/3*Gr) [mb] [11]
---------------------------------------------------------------------
References:
===========
[1] J. Speth and A. van de Woude, Rep. Prog. Phys. 44, 719 (1981).
[2] N. Kishida, "Methods used in photonuclear data evaluation at JNDC"
in Symposium on Nuclear Data Evaluation Methodology, (World Sci.
Publishing Co., Singapore, 1993) p.598.
[3] J. Kopecky, unpublished data base.
[4] A. Ignatyuk, private communication.
[5] A.D'Arigo, G. Giardina, A. Lamberto, G.F. Rappazzo, R. Sturiale,
A. Taccone, M. Herman and G. Reffo, "Influence of the Nuclear
Deformation on Photon Emission Spectra", private communication
and to be published in Journal of Physics.
[6] G. Reffo, "Parameter Systematics for Statistical Theory
Calculations of Neutron Capture Cross Sections",
ENEA Report RT/FI (78) 11;
and
G. Reffo, M. Blann, T. Komoto and R.J. Howerton, Nucl. Instr.
Methods A267, 408 (1988).
[7] A. Bohr and B. Mottelson, Nuclear Structure, Vol II (Benjamin,
London, 1975).
[8] J. Kopecky and R.E. Chrien, Nucl. Phys. A468, 285 (1987).
[9] J. Kopecky and M. Uhl, NEA/NSC/Doc (95) 1, 119.
[10] M. Uhl and J. Kopecky, "Gamma-Ray Strength Function Models and
their Parameterization", INDC(NDS)-335 (May 1995) p. 157 and
ECN Report, ECN-RX--94-099.
[11] W.V. Prestwich et al., Z. Phys. A315, 103 (1984).
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Attachment B.
RECOMMENDED MODELS AND FORMULAE FOR CALCULATION OF GAMMA-RAY STRENGTH
FUNCTIONS FOR E1, M1 AND E2 MULTIPOLARITIES
Traditional models, used to describe radiative E1, M1 and E2 strength,
namely the standard Lorentzian for E1 and the single-particle model
for M1 and E2, result in a strong overestimation of all pertinent
experimental quantities (such as the gamma-ray strength functions,
total radiative widths, capture cross-sections and gamma-ray spectra).
However, a strong support has been found for the generalised lorent-
zian representation (GLO) for E1, and a standard lorentzian represen-
tation (SLO) for M1 and E2 strength (for details see Refs. [1-10,11].
An overview of practical conclusions is given in Refs. [10,12]. Very
recently Plujko has presented a new model [13] for E1 radiative
strength function, based on microcanonical ensemble of initial states.
The resulting formula has the same features as approaches in Refs.
[10,11,14,15], namely the energy and temperature dependence of the E1 giant
resonance width and the non-zero limit for Eg -> 0. This work forms an
independent theoretical support for the GLO formalism of Refs.[10-13].
For the compilation of the experimental gamma-ray strength functions
the user is referred to Ref. [16].
Recent experiments with Two-Step Cascade (TSC) method [18-25] reveal
additional information on the strength function predictions. This
method is sensitive, not only to primary transitions, but also to
secondary transitions via intermediate states.
Recommended practical models:
-----------------------------
E1 -- in terms of a Generalized Lorentzian (GLO) with an energy de-
pendent spreading width and a non-zero limit as the gamma ray
energy tends to zero. Such features are founded in theoretical
works by Kadmenskij et al. [14], Sirotkin [15] and applied to
(n,g) reactions by Kopecky and Chrien [11].
The GLO model reproduces experimental data (strength functions,
total radiative width, capture cross section and spectra)
rather well for spherical and transitional nuclei in the mass
region A=50-200. This has been tested by many calculations (see
Refs. [1,2,10]). However, GLO fails for strongly deformed nuc-
clei with masses between 150 and 165, as shown in Refs. [3-9].
A reasonably good description is achieved with an enhanced GLO
(EGLO), proposed and discussed in Refs. [3-9], with purely
empirical enhancement factor. A global enhancement of the total
radiative width, of a nonstatistical nature, was proposed in
Ref. [16,12] to explain this effect. For lighter nuclei (A<50)
the GLO model can be applied as well, however, contributions
from nonstatistical mechanisms complicate comparisons with
experimental data.
Thus the EGLO formula can be generally applied for all nuclei
with A=50-200 by setting the enhancement factor to unity for
targets outside the range A=150-165.
The general formula reads as
f(E1) = k0(A)*GLO,
where k0(A) is for the enhancement factor, as empirically
formulated and adjusted to experimental data in Ref.[10]) for
level density formulation employing the backshifted Fermi gas
model
k0(A)= 1 + 0.09*(A-148)**2*exp[-0.18*(A-148)].
The constants may change using another level density model or
considering more nuclei (e.g. with A<140). Further for cal-
lation of a particular target, the factor k0(A) can be consi-
dered as a free adjustable parameter to match the particular
experimental data.
The generalized Lorentzian model, using the approximation of
Ref. [11] (see Eq. (2.4) in [1]), reads as
f(E1) = 8.68*10**(-8)*sigr*Gr*
[Eg*G(Eg)/((Eg**2-Er**2)**2+Eg**2*G(Eg)**2)+
0.7*4*pi**2*Gr*T**2],
where Er, Gr and sigr are usual Lorentzian giant resonance pa-
rameters and the energy dependent spreading width â(Eg) and
the nuclear temperature T are taken from Ref. [14] as
G(Eg) = Gr*(Eg**2+4*pi**2*T**2)/Er**2 and
T = SQRT((Ex-Eg)/a),
with the level density parameter "a".
For details and more rigorous treatment see Refs. [1,10,12].
------------------------------------------------------------
M1 -- the spin-flip M1 giant resonance [16] represented by a stan-
dard Lorentzian shape. The role of this excitation in the
neutron capture has been postulated by Kopecky and Chrien [11]
and later extensively studied in Refs. [1-10]. Values of the
standard Lorentzian parameters, Er, âr, år, are extracted
from systematics or experiments (see above).
The standard Lorentzian model (see Eq. (2.1) in [1]), reads as
f(M1) = 8.68*10**(-8)*sigr*Eg*Gr**2
/((Eg**2-Er**2)**2+Eg**2*Gr**2).
E2 -- the isoscalar quadrupole giant resonance represented by a stan-
dard Lorentzian shape. Values of the standard Lorentzian
parameters, Er, âr, år, are extracted again from systematics
(see above).
The standard Lorentzian model (see Eq. (2.5) in [1]), reads as
f(E2) = 5.22*10**(-8)*sigr*Gr**2
/Eg*((Eg**2-Er**2)**2+Eg**2*Gr**2).
References:
===========
[1] J. Kopecky and M. Uhl, Phys. Rev. 41, 1941 (1990).
[2] M. Uhl and J. Kopecky, "Calculations of Capture Cross Sections
and Gamma-Ray Spectra as a Tool for Testing Strength Function
Models", INDC(NDS)-238 (1990) p.113.
[3] J. Kopecky, "Calculations of Capture Cross Sections and Gamma-Ray
Spectra with Different Strength Function Models", Proc. VII. Int.
Symposium on Capture Gamma-ray Spectroscopy and Related Topics,
(AIP Conf. Proc. Np. 238, AIP, New York, 1991) p. 607.
[4] M. Uhl and J. Kopecky, "The Sensitivity of Statistical Model
Capture Calculations to Model Assumptions", Proc. Int. Conf.
Nuclear Data for Science and Technology, Juelich, 1991 (Spring
Verlag, Berlin/Heidelberg, 1992) p. 977.
[5] J. Kopecky, M. Uhl and R.E. Chrien, "Distribution of Radiative
Strength in Gd-156, 157 and 158 Nuclei, ECN-RX--92-011 (April
1992).
[6] J. Kopecky and M. Uhl, "Status of Statistical Model Capture
Calculations", Proc. Int. Symposium on Nuclear Data Evaluation
Methodology, Brookhaven, 1992 (World Scientific, Singapore, 1993)
p.381.
[7] M. Uhl and J. Kopecky, "Neutron Capture Cross-sections and
Gamma-ray Strength Functions", Proc. Int. Symp. on Nuclear Astro-
physics, Karlsruhe, 1992 (IOP Publishing Company Ltd., 1993)
p. 259.
[8] J. Kopecky, M. Uhl and R.E. Chrien, Phys. Rev. 47, 312 (1993).
[9] M. Uhl and J. Kopecky, "The Impact of Models for E1 Gamma-ray
Strength Functions in the Mass Region A=140-200, Proc. Int. Conf.
Nuclear Data for Science and Technology, Gatlinburg, 1994 (Ameri-
can Nuclear Soc., La Grange Park, 1994) p. 438.
[10] M. Uhl and J. Kopecky, "Gamma-ray Strength Function Models and
their Parameterization", INDC(NDS)-335 (May 1995) p. 157.
[11] J. Kopecky and R.E. Chrien, Nucl. Phys. A468, 285 (1987).
[12] J. Kopecky, "Gamma-ray Strength Function Models and their Parame-
terization", to be published as INDC(NDS) report in 1998.
[13] J. Plujko, "Radiative Strength Functions as a Tool in Studying
of mechanisms of Nuclear Dissipation", Contr. Int. Conf. Nuclear
Data for Science and Technology, Trieste, May 1997, to be publi-
shed.
[14] S.G. Kadmenskij, V.P. Markushev and V.I. Furman, Sov. J. Nucl.
Phys. 37, 165 (1983).
[15] V.K. Sirotkin, Sov. J. Nucl. Phys. 43, 362 (1986).
[16] A. Bohr and B. Mottelson, Nuclear Structure, Vol II
(Benjamin, London, 1975).
[16] J. Kopecky and M. Uhl, Present Status of Experimental Gamma Ray
Strength Functions, ENEA/NSC/Doc (95) 1, 119 and ECN-RX--94-103.
and to be published as INDC(NDS) report in 1998.
[18] F.Becvar, P.Cejnar, R.E. Chrien and J.Kopecky, "Distribution of
Photon Strength in Nuclei by a Method of Two-Step Cascades",
in Proc. of the 7th International Symposium on Capture Gamma-Ray
Spectroscopy and Related Topics, ed. R.W. Hoff, AIP Conf.Proc.
No.238 (AIP, New York, 1991), p.287.
[19] F.Becvar, P.Cejnar, R.E. Chrien and J.Kopecky, "Test of Photon
Strength by a Method of Two-Step Cascades", Phys.Rev. C46, 1276
(1992).
[20] J.Honzatko, K.Konecny, I.Tomandl, F.Becvar, P.Cejnar and
R.E.Chrien, "Photon Strength Functions Studied from Two-Step
Cascades Following Neutron Capture in 145Nd and 152Dy",
in Proc. of the 8th International Symposium on Capture Gamma-Ray
Spectroscopy and Related Topics, ed.J.Kern (World Scientific,
Singapore, 1994) p.572.
[21] J.Honzatko, K.Konecny, I.Tomandl, F.Becvar and P.Cejnar,
"The Use of a Method of Two-Step Cascades for Studying Photon
Strength Functions at Intermediate Gamma-Ray Energies",
in Proc. of the 8th International Symposium on Capture Gamma-Ray
Spectroscopy and Related Topics, ed.J.Kern (World Scientific,
Singapore, 1994) p.590.
[22] J.Honzatko, K.Konecny, I.Tomandl, F.Becvar and P.Cejnar,
"The Use of a Method of Two-Step Gamma-Cascades for Studying
Photon Strength Functions of Heavy Nuclei", in Proc. of the 2nd
International Seminar on Interaction of Neutrons with Nuclei,
JINR Report No. E3-94-419 (Dubna, 1994) p.154.
[23] J.Honzatko, I.Tomandl, F.Becvar and P.Cejnar, "Study of Photon
Strength Functions in 116In", in Proc. of the 3rd International
Seminar on Interaction of Neutrons with Nuclei, JINR Report No.
E3-95-307 (Dubna, 1995) p.109.
[24] J.Honzatko, K.Konecny, I.Tomandl, F.Becvar and P.Cejnar,
"Two-Step Gamma Cascades Following Thermal-Neutron Capture in
143,145Nd", Physica Scripta T56, 253 (1995).
[25] F.Becvar, P.Cejnar, J.Honzatko, K.Konecny, I.Tomandl and
R.E.Chrien, "E1 and M1 Strengths Studied from Two-Step Gamma
Cascades Following Capture of Thermal Neutrons in 162Dy",
Phys.Rev. C52, 1278 (1995).
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