A relativistic coupled-channel wave-equation with $$\mathcal{N}$$ and Δ degrees of freedomand Δ degrees of freedom

This work systematically analyzed the fusion dynamics of the projectile-target combinations involving stable and loosely bound systems within the view of the energy-dependent Woods–Saxon potential model (EDWSP model) and the coupled channel approach. The different projectiles are bombarded onto series of Sm-isotopes, which possess the dominance of the different kinds of the nuclear structure degrees of freedom and with the increase of the neutron richness, the Sm-isotopes gradually shift from spherical shape to a statically deformed shape. In the fusion of [Formula: see text] reaction, the impacts of vibrational degrees of freedom of the colliding nuclei are dominant while in the case of [Formula: see text] systems, the rotational states of the deformed target isotopes have a strong impression on the below-barrier fusion data. The heavier target isotopes ([Formula: see text] also exhibit the higher order deformation such as [Formula: see text], [Formula: see text]-deformation parameter in its ground state and couplings to such channels must be incorporated in theoretical calculations in order to achieve close agreement with the sub-barrier fusion data. However, in the case of the loosely bound systems, the projectile breakup channel significantly affects the fusion excitation functions in the domain of the Coulomb barrier. To ensure the role of the projectile breakup channel, the fusion of the different loosely bound projectiles ([Formula: see text] and [Formula: see text] with Sm-isotopes are investigated, wherein the above-barrier fusion data of these reactions are suppressed with reference to the coupled channel calculations. This hindrance is the result of the projectile breakup effects that occur as a consequence of the breakup of the projectile before reaching the fusion barrier due to its low binding energy. However, in the EDWSP model calculations the magnitude of the hindrance of the above-barrier fusion data of [Formula: see text] and [Formula: see text] reactions is reduced by a factor varying from 7% to 13% with respect to a value reported in the literature. In contrast to this, the sub-barrier fusion enhancement of [Formula: see text] and [Formula: see text] reactions is the result of the dominance of the nuclear structure degrees of freedom of the colliding systems.

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Propagating Degrees of Freedom in f(R) Gravity

Advances in High Energy Physics ◽

10.1155/2016/3901734 ◽

2016 ◽

Vol 2016 ◽

pp. 1-6 ◽

Cited By ~ 9

Author(s):

Yun Soo Myung

Keyword(s):

Wave Equation ◽

Gravitational Waves ◽

Degrees Of Freedom ◽

Ricci Scalar ◽

Metric Tensor ◽

Breathing Mode

We have computed the number of polarization modes of gravitational waves propagating in the Minkowski background in f(R) gravity. These are three of two from transverse-traceless tensor modes and one from a massive trace mode, which confirms the results found in the literature. There is no massless breathing mode and the massive trace mode corresponds to the Ricci scalar. A newly defined metric tensor in f(R) gravity satisfies the transverse-traceless (TT) condition as well as the TT wave equation.

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Some solutions of the Lanczos vacuum wave equation

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1994.0156 ◽

1994 ◽

Vol 447 (1931) ◽

pp. 577-585 ◽

Cited By ~ 18

Keyword(s):

Wave Equation ◽

Degrees Of Freedom ◽

Vector Fields ◽

Spin Coefficient ◽

Independent Components ◽

Conformal Curvature ◽

Conformal Curvature Tensor ◽

Non Local ◽

Weyl Conformal Curvature Tensor ◽

Gauge Conditions

In general relativity the non-local part of the gravitational field is described by the 10 degrees of freedom of the Weyl conformal curvature tensor C abcd . In every space-time the Weyl field C abcd is derivable from a potential L abc which has at most 16 algebraically independent components reducing to 10 degrees of freedom when the six gauge conditions L ab s ; s = 0 are imposed. The potential L abc discovered by Lanczos was shown by Illge to have an extremely simple vacuum wave equation, namely, □ L abc ≡ g sm L abc ; s ; m = 0. Using tensor, spinor and spin-coefficient methods we give some solutions of this new vacuum wave equation in some spacetimes containing one or more preferred vector fields.

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Static and energy dependent nucleus–nucleus potential for description of near and sub-barrier fusion data

Canadian Journal of Physics ◽

10.1139/cjp-2015-0133 ◽

2015 ◽

Vol 93 (11) ◽

pp. 1343-1351 ◽

Cited By ~ 16

Author(s):

Manjeet Singh Gautam

Keyword(s):

Degrees Of Freedom ◽

Saxon Potential ◽

Model Calculations ◽

One Dimensional ◽

A Value ◽

Fusion Data ◽

The One ◽

Energy Dependent ◽

Coupled Channel

This article analyzes the validity of static Woods–Saxon potential and the energy-dependent Woods–Saxon potential (EDWSP) to explore the specific features of fusion dynamics of [Formula: see text] and [Formula: see text] systems. The intrinsic degrees of freedom, such as inelastic surface excitations, play a crucial role in the enhancement of sub-barrier fusion excitation functions over the expectations of the one-dimensional barrier penetration model. Role of dominant intrinsic degrees of freedom of collision partners are entertained within the context of coupled channel calculations. Furthermore, the one-dimensional Wong formula using static Woods–Saxon potential fails miserably to describe the fusion enhancement of [Formula: see text] and [Formula: see text] systems. However, the Wong formula along with the EDWSP model accurately explains the observed fusion enhancement of [Formula: see text] reactions. In the fusion of [Formula: see text] reaction, the above-barrier fusion data are suppressed by a factor of 0.66 with reference to the EDWSP model calculations while the below-barrier fusion data are adequately addressed by the EDWSP model and the coupled channel calculations. Therefore, the coupled channel calculations and the EDWSP model calculations reasonably describe the observed fusion mechanism of [Formula: see text] and [Formula: see text] reactions. This suggests that the energy dependence in the Woods–Saxon potential model introduces similar kinds of barrier modification effects (barrier height, barrier position, and barrier curvature) as reflected from the coupled channel calculations. In the EDWSP model calculations, significantly larger values of diffuseness ranging from a = 0.86 to 0.94 fm, which is much larger than a value extracted from the elastic scattering analysis, are needed to address the sub-barrier fusion data.

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GRAVITATIONAL POTENTIALS AND THE EXISTENCE OF GRAVITATIONAL GREEN'S TENSORS

Modern Physics Letters A ◽

10.1142/s0217732398002497 ◽

1998 ◽

Vol 13 (29) ◽

pp. 2347-2353 ◽

Cited By ~ 1

Author(s):

P. DOLAN ◽

B. MURATORI

Keyword(s):

Wave Equation ◽

Gravitational Field ◽

Degrees Of Freedom ◽

Tensor Potential ◽

Non Local ◽

Relationship Of ◽

Tensor Formula ◽

The Relationship ◽

Insight Into ◽

Gauge Conditions

The non-local part of the gravitational field Cabcd can be generated by the 16-component Lanczos tensor potential Labc. When six gauge conditions are imposed, Labe;e=0, its ten degrees of freedom match those of the Weyl tensor. The Penrose wave equation for Cabcd can be independently derived from that for Labc. The consistency between Labc and Cabcd is also shown by the compatibility of their algebraic classifications. An unexpected insight into the relationship of Labc and Cabcd is found in "Euclidean gravity" which in turn leads to the introduction of a gravitational Green's tensor [Formula: see text] corresponding to the potential Labc.

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Electromagnetic breakup of the deuteron in the Δ resonance region

Canadian Journal of Physics ◽

10.1139/p84-141 ◽

1984 ◽

Vol 62 (11) ◽

pp. 1036-1045 ◽

Cited By ~ 14

Author(s):

W. Leidemann ◽

H. Arenhövel

Keyword(s):

Cross Section ◽

Degrees Of Freedom ◽

Impulse Approximation ◽

Resonance Region ◽

Final State ◽

Channel Calculation ◽

Main Emphasis ◽

Coupled Channel Calculation ◽

Final State Interactions ◽

Coupled Channel

The processes d(γ, p)n and d(e, e′p)n have been studied in the Δ resonance region with explicit Δ degrees of freedom in a coupled channel treatment that includes all final state interactions. In particular, the dependence on the model for the potential and the Δ parametrization has been investigated. The main emphasis has been put on the photodisintegration. The total cross section for this process is considerably reduced by inclusion of the Δ interactions, resulting in better agreement with a recent experiment. The angular distribution up to the resonance region shows a stronger forward and backward peaking than experimental results do, while above the resonance the agreement is better. Whereas the γ asymmetry is affected very little by the coupled channel calculation compared with the impulse approximation, the proton polarization is quite sensitive to the proper treatment of the Δ degrees of freedom.

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Interplay of neutron transfer and collective degrees of freedom in the fusion dynamics of 16O +76Ge and 18O +74Ge reactions

International Journal of Modern Physics E ◽

10.1142/s021830131950006x ◽

2019 ◽

Vol 28 (01n02) ◽

pp. 1950006 ◽

Cited By ~ 2

Author(s):

Manjeet Singh Gautam ◽

Hitender Khatri ◽

K. Vinod

Keyword(s):

Degrees Of Freedom ◽

Channel Model ◽

Fusion Cross Section ◽

Fusion Process ◽

Neutron Transfer ◽

Saxon Potential ◽

One Dimensional ◽

Fusion Data ◽

Coupled Channel ◽

Transfer Channels

This work examined the fusion dynamics of [Formula: see text] and [Formula: see text] reactions within the framework of the static Woods–Saxon potential model, the energy dependent Woods–Saxon potential (EDWSP) model and coupled channel formulation. The effects of inelastic surface excitations, static deformation of colliding pairs and /or neutron transfer channels on fusion process are investigated through the coupled channel method. The calculations based upon static Woods–Saxon potential in conjunction with one-dimensional Wong formula strongly under predict the fusion data of [Formula: see text] and [Formula: see text] reactions at sub-barrier energies. However, such discrepancies are removed if one uses couplings to nuclear structure degrees of freedom of reacting nuclei. The coupled channel calculations obtained by considering the vibrational nature of the colliding nuclei fairly reproduce the fusion data of [Formula: see text] reactions. For this reaction, the neutron transfer channels, which are expected to influence strongly the fusion yields at below barrier energies, in reality contribute very weakly to fusion process. While in case of [Formula: see text] reaction, the consideration of vibrational couplings as well as the rotational couplings for target provides a reasonable explanation to the fusion cross-section data at near and above barrier energies. In distinction, the energy dependence in the nucleus–nucleus potential causes barrier modulation effects and subsequently modifies the barrier profile of the interaction barrier in such a way that the effective fusion barrier between the colliding pair reduces. This ultimately brings larger fusion cross-sections over the outcomes of one-dimensional barrier penetration model and the EDWSP model based calculations appreciably explained the fusion dynamics of chosen reaction at energy spanning around the Coulomb barrier. Both models (EDWSP and coupled channel model) lead to barrier lowering effects and modeled quantum tunneling in different way, henceforth, adequately explore the fusion dynamics of the studied reactions in near and above barrier energy regions.

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The wave equation for the Lanczos potential. I

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1994.0155 ◽

1994 ◽

Vol 447 (1931) ◽

pp. 557-575 ◽

Cited By ~ 23

Keyword(s):

Wave Equation ◽

Degrees Of Freedom ◽

Wave Equations ◽

Conformal Curvature ◽

Lanczos Potential ◽

Conformal Curvature Tensor ◽

Radiation Theory ◽

Non Local ◽

Spinor Wave ◽

Gauge Conditions

The non-local part of the gravitational field in general relativity is described by the 10 component conformal curvature tensor C abcd of Weyl. For this field Lanczos found a tensor potential L abc with 16 independent components. We can make L abc have only 10 effective degrees of freedom by imposing the 6 gauge conditions L ab s :s = 0. Both fields C abcd , L abc satisfy wave equations. The wave equation satisfied by C abcd is nonlinear, even in vacuo . However, a linear spinor wave equation for the Lanczos potential has been found by Illge but no correct tensor wave equation for L abc has yet been published. Here, we derive a correct tensor wave equation for L abc and when it is simplified with the aid of some four-dimensional identities it is equivalent to Illge’s wave equation. We also show that the nonlinear spinor wave equation of Penrose for the Weyl field can be derived from Illge’s spinor wave equation. A set of analogues of well-known results of classical electromagnetic radiation theory can now be given. We indicate how a Green’s function approach to gravitational radiation could be based on our tensor wave equation, when a global study of space-time is attempted.

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N* Experiments and what they tell us about Strong QCD Physics

EPJ Web of Conferences ◽

10.1051/epjconf/202024101004 ◽

2020 ◽

Vol 241 ◽

pp. 01004

Author(s):

V. D. Burkert

Keyword(s):

Excited States ◽

Degrees Of Freedom ◽

Full Employment ◽

Light Quark ◽

Experimental Studies ◽

Form Factors ◽

Negative Parity ◽

Helicity Amplitudes ◽

Coupled Channel ◽

Electromagnetic Beams

I give an overview on experimental studies of the spectrum and the structure of the excited states of the nucleon and what we can learn about their in ternal structure. One focus is on the efforts to obtain a more complete picture of the light-quark baryon exci tation spectrum employing electromagnetic beams that will allow us to draw some conclusions on the symme tries underlying the spectrum. For the higher mass ex citations, the full employment of coupled channel ap proaches is essential when searching for new excited states in the large amounts of data already accumulated in different channels involving a variety of polarization observables. The other focus is on the study of transition form factors and helicity amplitudes and their de pendences on Q2, especially on some of the more promi nent resonances, especially Δ(1232)3/2+, N(1440)1/2+, and negative parity states N(1535)1/2-, and N(1675)5/2-.These were obtained in pion and eta electroproduction experi ments off proton targets and have already led to further insights in the active degrees-of-freedom as a function of the distance scale involved.

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Wave zone in the Hořava–Lifshitz theory at the kinetic-conformal point in the low energy regime

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09720-6 ◽

2021 ◽

Vol 81 (10) ◽

Author(s):

J. Mestra-Páez ◽

J. M. Peña ◽

A. Restuccia

Keyword(s):

Wave Equation ◽

Gravitational Radiation ◽

Degrees Of Freedom ◽

Low Energy ◽

Linear Wave ◽

Wave Zone ◽

Linear Wave Equation ◽

Asymptotically Flat ◽

Energy Regime ◽

Lifshitz Theory

AbstractWe show that in the Hořava–Lifshitz theory at the kinetic-conformal point, in the low energy regime, a wave zone for asymptotically flat fields can be consistently defined. In it, the physical degrees of freedom, the transverse traceless tensorial modes, satisfy a linear wave equation. The Newtonian contributions, among which there are terms which manifestly break the relativistic invariance, are non-trivial but do not obstruct the free propagation (radiation) of the physical degrees of freedom. For an appropriate value of the couplings of the theory, the wave equation becomes the relativistic one in agreement with the propagation of the gravitational radiation in the wave zone of General Relativity. Previously to the wave zone analysis, and in general grounds, we obtain the physical Hamiltonian of the Hořava–Lifshitz theory at the kinetic-conformal point in the constrained submanifold. We determine the canonical physical degrees of freedom in a particular coordinate system. They are well defined functions of the transverse-traceless modes of the metric and coincide with them in the wave zone and also at linearized level.

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