scholarly journals Compound Nucleus Formulation of Reaction Matrix Theory

1972 ◽  
Vol 25 (5) ◽  
pp. 479
Author(s):  
JL Cook ◽  
WK Bertram
Keyword(s):  
Cross Section ◽  
Compound Nucleus ◽  
Cross Sections ◽  
Matrix Theory ◽  
Complex Reaction ◽  
Resonance Parameters ◽  
Channel Matrix ◽  
Reaction Matrix ◽  
T Matrix ◽  
Additional Constraints

It is shown that multilevel resonance parameters for each element of the reaction matrix cannot be determined from available data. However, additional constraints may be introduced without affecting agreement with experiment. The Bohr compound nucleus hypothesis, which states that the modes of formation and decay of a compound nucleus are independent, is applied to the T-matrix and it is found, as in Newton's model, that the channel matrix can be inverted analytically to provide simple formulae for cross sections, for both the real Wigner?Eisenbud reaction matrix and Moldauer's complex reaction matrix. Wigner?Eisenbud theory leads directly to Newton's strong correlation model and its unacceptable consequences. Moldauer's theory does not, however, and can explain cross section behaviour adequately while being consistent with Bohr's hypothesis. Cross sections can be written as a sum of single level contributions, as in the Adler?Adler formulation. Finally, Moldauer's statistical theory is shown to be applicable, and expressions are derived for the �averaged cross sections as functions of the complex Moldauer resonance parameters.

scholarly journals Testing Compound Nucleus Hypothesis Across the 17O Nucleus Excitation

2019 ◽  
Vol 211 ◽  
pp. 02001 ◽  
Author(s):  
Aloys Nizigama ◽  
Pierre Tamagno ◽  
Olivier Bouland
Keyword(s):  
Cross Section ◽  
Compound Nucleus ◽  
Cross Sections ◽  
Center Of Mass ◽  
Ground States ◽  
Mass System ◽  
Resonance Parameters ◽  
Second Stage ◽  
Reference Framework ◽  
Kinetic Transformation

The excited compound nucleus 17O* has been studied over (n,α) and (α,n) cross sections modelling, respectively for 16O and 13C targets in their ground states. The modelling is fulfilled within the Reich-Moore formalism. We were able to calculate the (α,n) cross section by two separate ways: the direct kinematic standard route and by inversion of the (n,α) cross section using the compound nucleus hypothesis. Resonance parameters of the resolved resonance range (0 to 6 MeV) were borrowed from the CIELO project. In a first stage, the modelling is carried out in the referential of the incident particle (either way neutron or α) requesting conversion of the CIELO neutron-type resonance parameters to the α-type. In a second stage, the implementation is uniquely designed in the center of mass system of the excited compound nucleus. The resonance parameters are thus converted in that unique reference framework. The present investigation shows the consistency of the kinetic transformation that relies on the compound nucleus hypothesis.

MEASURING CAPTURE CROSS SECTIONS FOR HEAVY-ELEMENT PRODUCTION

2004 ◽  
Vol 13 (01) ◽  
pp. 293-300
Author(s):  
NEIL ROWLEY ◽  
NABILA GRAR
Keyword(s):  
Cross Section ◽  
Compound Nucleus ◽  
Cross Sections ◽  
Reaction Path ◽  
Superheavy Element ◽  
Evaporation Residue ◽  
Capture Cross ◽  
Total Capture ◽  
Capture Cross Sections

The creation of the nucleus of a superheavy element follows an extremely complex reaction path starting with the crossing of an external potential barrier (or distribution of barriers). This is followed by the evolution towards an equilibrated compound nucleus, which takes place in competition with pre-compound-nucleus fission (quasi-fission). Once formed the equilibrated compound nucleus must still survive against true fusion to yield a relatively long-lived evaporation residue. Much of this path is poorly understood, though recently, progress has been made on the role of the entrance-channel in quasi-fission. This will be briefly reported and a method proposed to measure the total capture cross section for such systems directly.

COLD FUSION REACTIONS USING NEUTRON-RICH PROJECTILES

2013 ◽  
Vol 22 (08) ◽  
pp. 1350061 ◽  
Author(s):  
A. SULAKSONO
Keyword(s):  
Cross Section ◽  
Compound Nucleus ◽  
Cross Sections ◽  
Estimation Method ◽  
Cold Fusion ◽  
Evaporation Residue ◽  
Fusion Reactions ◽  
Fusion Barrier ◽  
The Cross ◽  
Evaporation Residues

This paper studies the formation cross-sections of super heavy (SH) nuclei in some cold fusion reactions of radioactive neutron-rich projectiles with double-magic 208 Pb target. In this study, the cross-sections of capture, fusion and evaporation residues in one- and two-neutron (1n and 2n) channels are calculated by using neutron-rich Fe , Ni and Zn projectiles are compared to the cross-sections calculated using stable Fe , Ni and Zn projectiles. The heights of fusion barrier and their positions in all reactions considered in this study are also compared to the heights and positions calculated using the estimation method proposed by Dutt and Puri. For cold fusion reactions with stable Fe , Ni and Zn projectiles, the heights of fusion barrier and the cross-sections of evaporation residues in 1n and 2n channels are compared to their corresponding experimental data. In general, for reactions using projectiles with the same proton number, the neutron-rich projectile is found to yield relatively-heavier mass of SH nucleus and larger evaporation residue cross-section, compared to those of the corresponding stable projectiles. However, in certain reactions, the cross-sections of neutron-rich projectile can be slightly larger or slightly smaller than that of the corresponding stable projectile. This behavior is highly affected by the charge of projectile and the fission barrier of the formed compound nucleus (CN). In addition, the 292114 is found to be the heaviest compound nucleus formed in cold fusion reaction by using neutron-rich nuclei as the projectile, but the cross-section of evaporation residue in one-neutron channel is still around few pico barns (pb).

CALCULATIONS OF CROSS SECTIONS FOR THE SYNTHESIS OF SUPER-HEAVY NUCLEI IN COLD FUSION REACTIONS

2004 ◽  
Vol 13 (01) ◽  
pp. 261-267 ◽  
Author(s):  
W. J. ŚWIATECKI ◽  
K. SIWEK-WILCZYŃSKA ◽  
J. WILCZYŃSKI
Keyword(s):  
Cross Section ◽  
Compound Nucleus ◽  
Cross Sections ◽  
Free Parameter ◽  
Cold Fusion ◽  
One Dimension ◽  
Brownian Diffusion ◽  
Heavy Nuclei ◽  
Fusion Reactions ◽  
Super Heavy Nuclei

The fusion cross sections are considered to be given by the product of three factors: the cross section to overcome the Coulomb barrier, the probability for the resulting system to reach the compound nucleus configuration by diffusion, and the probability for the compound nucleus to survive fission. The first and third factors are treated by more or less conventional equations, and the second by Brownian diffusion in one dimension. Adjusting one free parameter in the theory one can reproduce the twelve measured cross sections to within a factor of two.

scholarly journals Statistical model calculations of the 7Li +11 Β reaction

2019 ◽  
Vol 10 ◽  
pp. 165
Author(s):  
C. Tsabaris ◽  
C. T. Papadopoulos ◽  
R. Vlastou ◽  
A. A. Pakou ◽  
P. A. Assimakopoulos ◽  
...  
Keyword(s):  
Experimental Data ◽  
Statistical Model ◽  
Energy Range ◽  
Cross Section ◽  
Compound Nucleus ◽  
Cross Sections ◽  
Coulomb Barrier ◽  
Reaction Channel ◽  
Model Calculations ◽  
The Individual

The 7Li + 11 Β reaction has been studied in the energy range from a little below to about three times the Coulomb barrier by measuring the cross section of the 7- ray transitions in the residual nuclei produced. Statistical compound nucleus calculations have been performed in order to interpret the experimental data as well as to extract cross sections of the individual exit channels. The statistical compound nucleus theory can reproduce rather well the absolute j - ray and the various reaction channel excitation functions.

scholarly journals Monte Carlo simulation of γ and fission transfer reactions using extended ℛ-matrix theory

2020 ◽  
Vol 239 ◽  
pp. 03013
Author(s):  
Olivier Bouland
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Matrix Theory ◽  
Transfer Reactions ◽  
Test Case ◽  
Compound System ◽  
Reaction Method ◽  
Average Cross Section ◽  
Special Cases ◽  
Induced Fission

This paper comes back on the accuracy of the surrogate-reaction method (SRM) historically used for neutron-induced average partial cross sections inference from measured surrogate-reaction probabilities. The SRM level of performance is examined in relation to a reasonably accurate reference calculation performed with the 𝒜𝒱𝒳𝒮ℱ-ℒ𝒩𝒢 code [1] through a challenging test case : the 240Pu* compound system. This paper argues on some ingredients of the reference calculation [2] and returns some hints about the failure now well-known of the neutron-induced γ average cross section inference. It shows also that in some special cases, the SRM can be poorly accurate also in terms of neutron-induced fission average cross section inference.

Systematic decay analysis of 202Po∗ compound nucleus using Dynamical Cluster-decay Model

2019 ◽  
Vol 28 (12) ◽  
pp. 1950105 ◽  
Author(s):  
Pooja Kaushal ◽  
Manoj K. Sharma
Keyword(s):  
Cross Section ◽  
Compound Nucleus ◽  
Cross Sections ◽  
Degrees Of Freedom ◽  
Cluster Decay ◽  
Channel Cross Section ◽  
Decay Model ◽  
Cross Section Formula ◽  
Collective Clusterization ◽  
Mechanical Fragmentation

The decay analysis of [Formula: see text]Po[Formula: see text] compound nucleus (CN), formed via [Formula: see text]Ca+[Formula: see text]Gd reaction, with inclusion of additional degrees-of-freedom, i.e., the higher multipole deformations, the octupole ([Formula: see text]) and hexadecupole ([Formula: see text]), the corresponding “compact” orientations ([Formula: see text]), and noncoplanarity degree-of-freedom ([Formula: see text]0), is investigated within the collective clusterization approach. The Quantum Mechanical Fragmentation Theory (QMFT)-based Dynamical Cluster-decay Model (DCM), wherein the point of penetration [Formula: see text], fixed via the in-built neck-length parameter [Formula: see text] in [Formula: see text] (equivalently, the “barrier lowering” [Formula: see text]), is used to best fit the channel cross-section ([Formula: see text]) and predict the quasi-fission (qf)-like nCN cross-section [Formula: see text], if any, and the fusion–fission ([Formula: see text]) cross-sections. We also look for other target-projectile (t-p) combinations for the synthesis of CN [Formula: see text]Po[Formula: see text].

Neutron Activation Resonance Integral of 74Ge and 76Ge and Evaluation of the 74Ge keV Neutron Radiative Capture Cross Section and Resonance Integral

1972 ◽  
Vol 50 (17) ◽  
pp. 1978-1986
Author(s):  
M. D. Ricabarra ◽  
R. Turjanski ◽  
G. H. Ricabarra
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Capture Cross Section ◽  
Radiative Capture ◽  
Resonance Integral ◽  
Neutron Resonance ◽  
Capture Cross ◽  
Resonance Parameters ◽  
Radiative Capture Cross Section ◽  
Average Resonance

Values of the reduced activation resonance integral relative to the thermal cross section I′/σ0 of 74Ge and 76Ge were determined relative to gold by measuring cadmium ratios in a reactor spectrum.A lithium-drifted germanium γ-ray spectrometer was used to resolve the activities of the samples.The results for 74Ge are I′/σ0 = 1.514 ± 0.031 and I′ = 0.681 ± 0.123 b with an assumed σ0 = 0.45 ± 0.08 b; for 76GeI′/σ0 = 12.00 ± 0.16 and I′ = 1.992 ± 0.359 with an assumed σ0 = 0.166 ± 0.030 b.The values obtained for I′ are in serious disagreement with the values calculated with neutron resonance parameters and confirm previous results obtained in similar keV average resonance spacing isotopes.Due to this fact a careful evaluation of the keV neutron radiative capture cross section and resonance integral for 74Ge was undertaken.The evaluation and comparison with the experimental value of the resonance integral shows first that for nuclides with an average resonance spacing of keV the unresolved resonance integral has been seriously underestimated in many evaluations, and second that between 10 and 100 keV, resonance integrals calculated with smooth low resolution activation cross sections give a better calculation of neutron captures than that obtained with neutron resonance parameters.

Measurements of the 107Ag neutron capture cross sections with PHWT at the CSNS Back-n facility

2022 ◽  
Author(s):  
X. X. Li ◽  
L. X. Liu ◽  
W. Jiang ◽  
J. Ren ◽  
H. W. Wang ◽  
...  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Nuclear Power ◽  
Power Plants ◽  
Nuclear Astrophysics ◽  
Reaction Cross ◽  
Pressurized Water ◽  
Resonance Parameters ◽  
Control Rod ◽  
The Cross

Abstract Silver indium cadmium (Ag-In-Cd) control rod is widely used in pressurized water reactor nuclear power plants, and which is continuously consumed in a high neutron flux environment. The mass ratio of 107Ag in Ag-In-Cd control rod is 41.44%. To accurately calculate the consumption value of the control rod, a reliable neutron reaction cross section of the 107Ag is required. Meanwhile, 107Ag is also an important weak r nuclei. Thus, the cross sections for neutron induced interactions with 107Ag are very important both in nuclear energy and nuclear astrophysics. The (n, γ) cross section of 107Ag has been measured in the energy range of 1-60 eV using a back streaming white neutron beam line at China spallation neutron source. The resonance parameters are extracted by an R-matrix code. All the cross section of 107Ag and resonance parameters are given in this paper as datasets. The datasets are openly available at https://www.scidb.cn/s/aaUJbu.

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