Binding energy of the alpha particle with tensor forces and a velocity-dependent potential

S. C. Jain

doi:10.1139/p70-002

Binding energy of the alpha particle with tensor forces and a velocity-dependent potential

Canadian Journal of Physics ◽

10.1139/p70-002 ◽

1970 ◽

Vol 48 (1) ◽

pp. 7-8

Author(s):

S. C. Jain

Keyword(s):

Wave Function ◽

Binding Energy ◽

Excellent Agreement ◽

Alpha Particle ◽

Variational Calculation ◽

Dependent Potential

The results of a variational calculation for the binding energy of the alpha particle with the tensor velocity-dependent potential of Werner and the Irving wave function, containing a mixture of the principal 1S0 and 5D0(1) states are presented. A binding energy of 28.03 MeV for the alpha particle is found, which is in excellent agreement with experiments, but the r.m.s. radius obtained in this way is about 88% of the experimental value.

Photodisintegration of the alpha particle with tensor forces and a velocity-dependent potential

Canadian Journal of Physics ◽

10.1139/p69-172 ◽

1969 ◽

Vol 47 (13) ◽

pp. 1343-1347

Author(s):

S. C. Jain

Keyword(s):

Wave Function ◽

Cross Section ◽

Alpha Particle ◽

Ground State ◽

Reasonable Agreement ◽

Sum Rules ◽

Variational Calculation ◽

Dependent Potential ◽

Integrated Cross Section ◽

Tensor Part

We calculate the integrated cross section (σint) and the bremsstrahlung-weighted cross section (σb) for the photodisintegration of the alpha particle by applying the sum rules of Levinger and Bethe. The two-body interaction is assumed to be a mixture of a central part, having a velocity-dependent term, and a tensor part. The ground-state wave function of the alpha particle is taken to be a mixture of the principal 1S0 and 5D0(1) states, whose parameters are obtained from a variational calculation of the binding energy of the alpha particle with the above potential. We find our results for σint and σb to be in reasonable agreement with the experiments.

The binding energy of the alpha particle with a velocity-dependent potential containing a tensor component

Journal of Physics A: General Physics ◽

10.1088/0305-4470/4/1/007 ◽

1971 ◽

Vol 4 (1) ◽

pp. 44-48

Author(s):

D Mahanti ◽

H L Yadav ◽

B K Srivastava

Keyword(s):

Binding Energy ◽

Alpha Particle ◽

Tensor Component ◽

Dependent Potential

POSITRONIUM DECAY: GAUGE INVARIANCE AND ANALYTICITY

International Journal of Modern Physics A ◽

10.1142/s0217751x02009606 ◽

2002 ◽

Vol 17 (10) ◽

pp. 1355-1398 ◽

Cited By ~ 6

Author(s):

J. PESTIEAU ◽

C. SMITH ◽

S. TRINE

Keyword(s):

Wave Function ◽

Form Factor ◽

Binding Energy ◽

Gauge Invariance ◽

Dispersion Relations ◽

Decay Rates ◽

Effective Form ◽

Theoretical Predictions ◽

Positronium Decay ◽

Analysis Of Binding Energy

The construction of positronium decay amplitudes is handled through the use of dispersion relations. In this way, emphasis is put on basic QED principles: gauge invariance and soft-photon limits (analyticity).A firm grounding is given to the factorization approaches, and some ambiguities in the spin and energy structures of the positronium wave function are removed. Nonfactorizable amplitudes are naturally introduced. Their dynamics are described, especially regarding the enforcement of gauge invariance and analyticity through delicate interferences. The important question of the completeness of the present theoretical predictions for the decay rates is then addressed. Indeed, some of those nonfactorizable contributions are unaccounted for by NRQED analyses. However, it is shown that such new contributions are highly suppressed, being of [Formula: see text].Finally, a particular effective form factor formalism is constructed for parapositronium, allowing a thorough analysis of binding energy effects and analyticity implementation.

Spinless relativistic particle in energy-dependent potential and normalization of the wave function

Open Physics ◽

10.2478/s11534-014-0457-8 ◽

2014 ◽

Vol 12 (6) ◽

Cited By ~ 1

Author(s):

Amar Benchikha ◽

Lyazid Chetouani

Keyword(s):

Wave Function ◽

Spectral Decomposition ◽

Relativistic Particle ◽

Wave Functions ◽

Integral Approach ◽

Normalizing Constant ◽

Klein Gordon ◽

Dependent Potential ◽

Energy Dependent ◽

Coulomb Potentials

AbstractThe problem of normalization related to a Klein-Gordon particle subjected to vector plus scalar energy-dependent potentials is clarified in the context of the path integral approach. In addition the correction relating to the normalizing constant of wave functions is exactly determined. As examples, the energy dependent linear and Coulomb potentials are considered. The wave functions obtained via spectral decomposition, were found exactly normalized.

Binding energy of the alpha particle and the velocity-dependent potentials

Physics Letters ◽

10.1016/s0375-9601(63)92700-2 ◽

1963 ◽

Vol 5 (2) ◽

pp. 175-176 ◽

Cited By ~ 1

Author(s):

J. Borysowicz ◽

M. Zielińska

Keyword(s):

Binding Energy ◽

Alpha Particle

The interaction of alpha-particles and the binding energy of 8Be

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s030500410007643x ◽

1952 ◽

Vol 48 (4) ◽

pp. 652-664 ◽

Cited By ~ 13

Author(s):

S. F. Edwards

Keyword(s):

Binding Energy ◽

Yukawa Potential ◽

Variational Calculation ◽

Alpha Particles ◽

Particle Model ◽

Heavy Nuclei ◽

Single Particles ◽

Body Type ◽

Gaussian Potential ◽

Direct Use

AbstractA calculation of the binding energy of 8Be is given, based upon the separation of the eight nucleons into two groups of four, using Gaussian functions and a Yukawa central force. The calculation is considerably simplified by the use of an integral identity between the Gaussian potential and the Yukawa potential. The energy is calculated with a Gaussian potential, and the identity used to convert the result to that which would have been obtained by direct use of the Yukawa potential. The results of the variational calculation show that unless the saturation conditions usually adopted in the theory of heavy nuclei are abandoned, there can be no binding, confirming an earlier result of Margenau, obtained with a Gaussian potential. The results do not depend essentially on the range of the force, nor on the central two-body type of force adopted. When the old saturation conditions are abandoned, quite reasonable results are obtained. The magnitude of the energies due to the exchange of single particles and pairs of particles indicates that the force between alpha-particles is not additive. A discussion of the saturation conditions and of the alpha-particle model in the light of the results is given.

ENERGY-DEPENDENT POTENTIAL AND NORMALIZATION OF WAVE FUNCTION

Modern Physics Letters A ◽

10.1142/s021773231350079x ◽

2013 ◽

Vol 28 (18) ◽

pp. 1350079 ◽

Cited By ~ 12

Author(s):

A. BENCHIKHA ◽

L. CHETOUANI

Keyword(s):

Wave Function ◽

Hydrogen Atom ◽

Harmonic Oscillator ◽

Path Integral ◽

Spectral Decomposition ◽

Wave Functions ◽

Integral Approach ◽

Path Integral Approach ◽

Dependent Potential ◽

Energy Dependent

The problem of normalization related to energy-dependent potentials is examined in the context of the path integral approach, and a justification is given. As examples, the harmonic oscillator and the hydrogen atom (radial) where, respectively the frequency and the Coulomb's constant depend on energy, are considered and their propagators determined. From their spectral decomposition, we have found that the wave functions extracted are correctly normalized.

Variational calculations on the binding energy of the alpha particle (I)

Nuclear Physics ◽

10.1016/0029-5582(63)90717-x ◽

1963 ◽

Vol 42 ◽

pp. 95-112 ◽

Cited By ~ 37

Author(s):

E.W. Schmid ◽

Y.C. Tang ◽

R.C. Herndon

Keyword(s):

Binding Energy ◽

Alpha Particle ◽

Variational Calculations

Analytic Variational Calculation of the Ground-State Binding Energy of Hydrogen in Intermediate and Intense Magnetic Fields

The Astrophysical Journal ◽

10.1086/152723 ◽

1974 ◽

Vol 188 ◽

pp. 349 ◽

Cited By ~ 6

Author(s):

Lance W. Wilson

Keyword(s):

Binding Energy ◽

Magnetic Fields ◽

Ground State ◽

Variational Calculation ◽

Ground State Binding Energy

Hydrogenic-Donor Impurity Binding Energy Dependence of the Electric Field in GaAs/AlxGa1−xAs Quantum Rings

Journal of Nanomaterials ◽

10.1155/2013/240563 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Guangxin Wang ◽

Xiuzhi Duan ◽

Wei Chen

Keyword(s):

Wave Function ◽

Binding Energy ◽

Electric Field ◽

Applied Electric Field ◽

Donor Impurity ◽

Electronic Wave ◽

Hydrogenic Donor Impurity ◽

Hydrogenic Donor ◽

Electronic Wave Function ◽

Radial Thickness

Using a variational method with two-parameter trial wave function and the effective mass approximation, the binding energy of a donor impurity in GaAs/AlxGa1−xAs cylindrical quantum ring (QR) subjected to an external field is calculated. It is shown that the donor impurity binding energy is highly dependent on the QR structure parameters (radial thickness and height), impurity position, and external electric field. The binding energy increases inchmeal as the QR parameters (radial thickness and height) decrease until a maximum value for a central impurity and then begins to drop quickly. The applied electric field can significantly modify the spread of electronic wave function in the QR and shift electronic wave function from the donor position and then leads to binding energy changes. In addition, results for the binding energies of a hydrogenic donor impurity as functions of the impurity position and applied electric field are also presented.