PHENOMENOLOGICAL POTENTIAL, MODEL WAVEFUNCTION AND DIFFRACTIVE INTERACTION OF THREE-NUCLEON-NUCLEI WITH HEAVY NUCLEI

2000 ◽  
Vol 09 (06) ◽  
pp. 449-458
Author(s):  
V. YU. KORDA
Keyword(s):  
Relative Motion ◽  
Cross Sections ◽  
Ground State ◽  
Potential Model ◽  
Heavy Nuclei ◽  
Interaction Processes ◽  
Phenomenological Potential ◽  
Three Body ◽  
Analytical Expressions

On the basis of the simple strict three-body analysis the hyperspherical phenomenological potential and model wavefunction of the three-nucleon ground-state relative motion are built to be permutationally invariant. The analytical expressions for the integrated cross-sections of different three-nucleon-nuclei–nuclei diffraction interaction processes are derived with the new wavefunction presented.

scholarly journals Energy Correlations of α-Particles in the 8Be-Nucleus Ground-State Formation Channel of the 12C(γ,3α) and 16O(γ,4α) Reactions

2019 ◽  
Vol 64 (9) ◽  
pp. 787
Author(s):  
S. N. Afanasyev
Keyword(s):  
Magnetic Field ◽  
Photon Energy ◽  
Relative Motion ◽  
Cross Sections ◽  
Ground State ◽  
Diffusion Chamber ◽  
Mechanism Of Interaction ◽  
The Magnetic Field ◽  
Maximum Photon ◽  
Α Particles

The method of diffusion chamber in the magnetic field making use of a bremsstrahlung beam with a maximum photon energy of 150 MeV is applied to study the 12C(y,3a) and 16O(y,4a) reactions. A resonance identified as the ground state of 8Be nucleus is found in the distribution of events over the energy of the relative motion of two a-particles. The partial cross-sections of the 8Be nucleus formation channels are measured. It is shown that the mechanism of interaction between a y-quantum and a virtual a-particle pair takes place in this case.

Nuclear structure properties of spin-1/2 heavy nuclei within the relativistic cluster model

2020 ◽  
Vol 29 (05) ◽  
pp. 2050026
Author(s):  
Keivan Darooyi Divshali ◽  
Mohammad Reza Shojaei
Keyword(s):  
Nuclear Structure ◽  
Beta Decay ◽  
Ground State ◽  
Cluster Model ◽  
Heavy Nuclei ◽  
Core Cluster ◽  
Phenomenological Potential ◽  
The Stability ◽  
Uvarov Method ◽  
Structure Properties

[Formula: see text]C is a beta decay isotope, its beta decay is very slow reflecting the stability of this nucleus and emitted from medium and heavy mass nuclei. The [Formula: see text]C result is in excellent agreement with the favored ground-state-to-ground-state transition according to the cluster model of Blendowske et al. We study nuclear structure properties of spin-1/2 heavy nuclei in the relativistic core-cluster model, that its cluster is [Formula: see text]C. According to this model for spin-1/2 heavy nuclei and for obtaining its wave function, we solve the Dirac equation with the new phenomenological potential by parametric Nikiforov–Uvarov method and then calculate the binding energy and charge radius.

Integrated Cross-Sections of 3H- and 3He-Nuclei-Nuclei Interaction Processes

1997 ◽  
Vol 06 (01) ◽  
pp. 161-175 ◽  
Author(s):  
Yu. A. Berezhnoy ◽  
V. Yu. Korda
Keyword(s):  
Closed Form ◽  
Cross Sections ◽  
Diffraction Theory ◽  
Nucleus Interaction ◽  
Intermediate Energies ◽  
Interaction Processes ◽  
Analytical Expressions

On the basis of general diffraction theory we present a closed-form description that enables us to obtain the analytical expressions for the integrated cross-sections of different 3 H - and 3 He -nucleus interaction processes at intermediate energies.

scholarly journals Helium-like ions in d-dimensions: analyticity and generalized ground state Majorana solutions

2021 ◽  
Author(s):  
Adrian Mauricio Escobar ◽  
Horacio Olivares-Pilón ◽  
Norberto Aquino ◽  
Salvador Antonio Cruz-Jimenez
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Dimensional Space ◽  
Algebraic Function ◽  
Approximate Solutions ◽  
Algebraic Expression ◽  
Three Body ◽  
First Time ◽  
Analytical Expressions

Abstract Non-relativistic Helium-like ions (−e, −e, Ze) with static nucleus in a d−dimensional space (d > 1) are considered. Assuming r−1Coulomb interactions, a 2-parametric correlated Hylleraas-type trial function is used to calculate the ground state energy of the system in the domain Z ≤ 10. For odd d = 3, 5, the variational energy is given by a rational algebraic function of the variational parameters whilst for even d = 2, 4 it is shown for the first time that it corresponds to a more complicated non-algebraic expression. This twofold analyticity will hold for any d. It allows us to construct reasonably accurate approximate solutions for the ground state energy E0(Z, d) in the form of compact analytical expressions. We call them generalized Majorana solutions. They reproduce the first leading terms in the celebrated 1Z expansion, and serve as generating functions for certain correlation-dependent properties. The (first) critical charge Zc vs d and the Shannon entropy S(d)r vs Z are also calculated within the present variational approach. In the light of these results, for the physically important case d = 3 a more general 3-parametric correlated Hylleraas-type trial is used to compute the finite mass effects in the Majorana solution for a three-body Coulomb system with arbitrary charges and masses. It admits a straightforward generalization to any d as well. Concrete results for the systems e− e− e+, H+2 and H− are indicated explicitly. Our variational analytical results are in excellent agreement with the exact numerical values reported in the literature.

scholarly journals Interaction of Be4+ and Ground State Hydrogen Atom—Classical Treatment of the Collision

Atoms ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 27
Author(s):  
I. Ziaeian ◽  
K. Tőkési
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Hydrogen Atom ◽  
Cross Sections ◽  
Ground State ◽  
Bound States ◽  
Classical Trajectory ◽  
Projectile Energy ◽  
Three Body ◽  
Classical Trajectory Monte Carlo

The interaction between Be4+ and hydrogen atom is studied using the three-body classical trajectory Monte Carlo method (CTMC) and the quasiclassical trajectory Monte Carlo method of Kirschbaum and Wilets (QTMC-KW). We present total cross sections for target ionization, target excitation, and charge exchange to the projectile bound states. Calculations are carried out in the projectile energy range between 10 and 1000 keV/au, relevant to the interest of fusion research when the target hydrogen atom is in the ground state. Our results are compared with previous theoretical results. We found that the classical treatment describes reasonably well the cross sections for various final channels. Moreover, we show that the calculations by the QTMC-KW model significantly improve the obtained cross sections.

scholarly journals Closed analytical solutions of Bohr Hamiltonian with Manning-Rosen potential model

2015 ◽  
Vol 24 (11) ◽  
pp. 1550089 ◽  
Author(s):  
M. Chabab ◽  
A. Lahbas ◽  
M. Oulne
Keyword(s):  
Potential Model ◽  
Heavy Nuclei ◽  
Axially Symmetric ◽  
Eigenvalues And Eigenfunctions ◽  
Unstable Nuclei ◽  
Unstable Case ◽  
Two Parameters ◽  
Rosen Potential ◽  
Analytical Expressions ◽  
Good Agreement

In the present paper, we have obtained closed analytical expressions for eigenvalues and eigenfunctions of the Bohr Hamiltonian with the Manning–Rosen potential for [Formula: see text]unstable nuclei as well as exactly separable rotational ones with [Formula: see text]. Some heavy nuclei with known [Formula: see text] and [Formula: see text] bandheads have been fitted by using two parameters in the [Formula: see text]unstable case and three parameters in the axially symmetric prolate deformed one. A good agreement with experimental data has been achieved.

ELECTROMAGNETIC STRENGTH IN HEAVY NUCLEI – EXPERIMENTS AND A GLOBAL FIT

2011 ◽  
Vol 20 (02) ◽  
pp. 431-442 ◽  
Author(s):  
R. BEYER ◽  
E. BIRGERSSON ◽  
A. R. JUNGHANS ◽  
R. MASSARCZYK ◽  
G. SCHRAMM ◽  
...  
Keyword(s):  
Cross Sections ◽  
Ground State ◽  
Level Density ◽  
Strength Function ◽  
Model Parameters ◽  
Heavy Nuclei ◽  
Dipole Strength ◽  
Dipole Resonance ◽  
Radiative Neutron ◽  
Radiative Neutron Capture

A global parameterization is presented for the electromagnetic strength in heavy nuclei which gives a rather good fit to respective data in nuclei with mass numbers A between 50 and 240. It relies on a Lorentzian description of the isovector giant dipole resonance and it needs only a very small number of parameters to describe the electric dipole strength down to low excitation energy of importance for radiative capture processes. The resonance energies are chosen to be in accordance to liquid drop model parameters adjusted to ground state masses and to rotation invariant determinations of ground state deformation and triaxiality. By a straightforward use of this information a surprisingly smooth variation of the GDR width with A and Z is found and a full agreement to the predictions of the electromagnetic sum rule is assured. Predictions for radiative neutron capture cross sections compare well to respective data, when the proposed photon strength function is combined with standard prescriptions for the level density in the product nuclei.

Formation of α clusters in dilute neutron-rich matter

Science ◽  
2021 ◽  
Vol 371 (6526) ◽  
pp. 260-264 ◽  
Author(s):  
Junki Tanaka ◽  
Zaihong Yang ◽  
Stefan Typel ◽  
Satoshi Adachi ◽  
Shiwei Bai ◽  
...  
Keyword(s):  
Cross Sections ◽  
Cluster Formation ◽  
Reaction Cross ◽  
Skin Thickness ◽  
Neutron Skin ◽  
Heavy Nuclei ◽  
Α Decay ◽  
Neutron Skin Thickness ◽  
Reaction Cross Sections ◽  
Α Particles

The surface of neutron-rich heavy nuclei, with a neutron skin created by excess neutrons, provides an important terrestrial model system to study dilute neutron-rich matter. By using quasi-free α cluster–knockout reactions, we obtained direct experimental evidence for the formation of α clusters at the surface of neutron-rich tin isotopes. The observed monotonous decrease of the reaction cross sections with increasing mass number, in excellent agreement with the theoretical prediction, implies a tight interplay between α-cluster formation and the neutron skin. This result, in turn, calls for a revision of the correlation between the neutron-skin thickness and the density dependence of the symmetry energy, which is essential for understanding neutron stars. Our result also provides a natural explanation for the origin of α particles in α decay.

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