arXiv subjects

I. R. Afnan

Publications and source records attributed to I. R. Afnan.

32 records · Page 2Linked to original sources

arXiv1997

$^{6}_{ΛΛ}$He as a $ΛΛ$ interaction constraint

The Nijmegen OBE potential D is SU(3) rotated to model the strangeness -2 sector of the baryon-baryon force. Soft core repulsion is introduced to regularize the singular nature of the OBE functions. The strength of the $^1$S$_0$ $t=0$ interaction is adjusted to model three scenarios: (1) a bound state, (2) a narrow virtual, or antibound, state, and (3) an unbound state in which the force is weakly attractive. Using a separable approximation to these potentials, the binding energy of $^{6}_{ΛΛ}$He is calculated in an $ΛΛα$ model. The resultant binding energies suggest that the strength of the $^1$S$_0$ $t=0$ $ΛΛ$ and the $nn$ interactions should be similar, if the coupling between the $ΛΛ$ and $ΞN$ channels is taken into consideration.

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arXiv1997

The $λΛ$ interaction and the reaction $Ξ^- + d \to n + Λ+ Λ$

The $ΛΛ$ interaction resulting from the SU(3) rotation of the S-wave component of the Nijmegen OBE potential $D$ is used to calculate the binding energy of $^{ 6}_{ΛΛ}$He as a $ΛΛα$ three-body system, and the neutron differential energy spectrum for the reaction $Ξ^- + d \to n + Λ+ Λ$.

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arXiv1997

Role of retardation in 3-D relativistic equations

Equal-time Green's function is used to derive a three-dimensional integral equation from the Bethe-Salpeter equation. The resultant equation, in the absence of anti-particles, is identical to the use of time-ordered diagrams, and has been used within the framework of $ϕ^2σ$ coupling to study the role of energy dependence and non-locality when the two-body potential is the sum of $σ$-exchange and crossed $σ$ exchange. The results show that non-locality and energy dependence make a substantial contribution to both the on-shell and off-shell amplitudes.

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arXiv1996

Solving the four-dimensional $NN-πNN$ equations for scalars below meson-production threshold

The four-dimensional $NN-πNN$ equations are adapted to the case of scalar particles with a $ϕ^2σ$ interaction Lagrangian, and solved for energies below the $σ$-production threshold. This is achieved in the approximation where $ϕσ$ scattering is dominated by the $s$-channel $ϕ$-pole term. The importance of the removal of double-counting is investigated, and a detailed comparison of the results of a covariant coupled-channels formulation and the Bethe-Salpeter equation in the ladder and ladder plus crossed-box approximations is presented. A brief discussion of the extension of the method to energies above the $σ$-production threshold is given.

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arXiv1996

The role of the $S_{31}$ $πN$ partial wave in the three-nucleon force

We re-examine the contribution of the $πN$ $S_{31}$ channel to the three-nucleon force for an energy dependent separable potential. Despite the lack of cancellation between the $S_{31}$ and the $P_{11}$ and $P_{33}$ channels, the total contribution of the three-nucleon force to the triton binding is still small.

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arXiv1995

Covariant four-dimensional scattering equations for the $NN-πNN$ system

We derive a set of coupled four-dimensional integral equations for the $NN-πNN$ system using our modified version of the Taylor method of classification-of-diagrams. These equations are covariant, obey two and three-body unitarity and contain subtraction terms which eliminate the double-counting present in some previous four-dimensional $NN-πNN$ equations. The equations are then recast into a from convenient for computation by grouping the subtraction terms together and obtaining a set of two-fragment scattering equations for the amplitudes of interest.

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arXiv1994

The energy dependence of the $πN$ amplitude and the three-nucleon interaction

By calculating the contribution of the $π-π$ three-body force to the three-nucleon binding energy in terms of the $πN$ amplitude using perturbation theory, we are able to determine the importance of the energy dependence and the contribution of the different partial waves of the $πN$ amplitude to the three-nucleon force. A separable representation of the non-pole $πN$ amplitude allows us to write the three-nucleon force in terms of the amplitude for $NN\rightarrow NN^*$, propagation of the $NNN^*$ system, and the amplitude for $NN^*\rightarrow NN$, with $N^*$ being the $πN$ quasi-particle amplitude in a given state. The division of the $πN$ amplitude into a pole and non-pole gives a procedure for the determination of the $πNN$ form factor within the model. The total contribution of the three-body force to the binding energy of the triton for the separable approximation to the Paris nucleon-nucleon potential (PEST) is found to be very small mainly as a result of the energy dependence of the $πN$ amplitude, the cancellation between the $S$- and $P$-wave $πN$ amplitudes, and the soft $πNN$ form factor.

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arXiv1994

How important is the three-nucleon force?

By calculating the contribution of the $π-π$ three-body force to the three-nucleon binding energy in terms of the $πN$ amplitude using perturbation theory, we are able to determine the contribution of the different $πN$ partial waves to the three-nucleon force. The division of the $πN$ amplitude into a pole and nonpole gives a unique procedure for the determination of the $πNN$ form factor in the model. The total contribution of the three-body force to the binding energy of the triton is found to be very small.

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arXiv1994

Importance of Baryon-Baryon Coupling in Hypernuclei

The $ΛN - ΣN$ coupling in $Λ$--hypernuclei and $ΛΛ- ΞN$ coupling in $ΛΛ$--hypernuclei produce novel physics not observed in the conventional, nonstrange sector. Effects of $Λ\leftrightarrow Σ$ conversion in $^3_Λ$H are reviewed. The role of $ΛN - ΣN$ coupling suppression in the $A=4,5$ $Λ$--hypernuclei due to Pauli blocking is highlighted, and the implications for the structure of $^{10}_{\;\, Λ}$B are explored. Suppression of $ΛΛ- ΞN$ conversion in $^{\;\;\, 6}_{ΛΛ}$He is hypothesized as the reason that the $< V_{ΛΛ} >$ matrix element is small. Measurement of $^{\;\;\, 4}_{ΛΛ}$H is proposed to investigate the full $ΛΛ- ΞN$ interaction. The implication for $ΛΛ$ analog states is discussed.

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arXiv1994

The classification of diagrams in perturbation theory

The derivation of scattering equations connecting the amplitudes obtained from diagrammatic expansions is of interest in many branches of physics. One method for deriving such equations is the classification-of-diagrams technique of Taylor. However, as we shall explain in this paper, there are certain points of Taylor's method which require clarification. Firstly, it is not clear whether Taylor's original method is equivalent to the simpler classification-of-diagrams scheme used by Thomas, Rinat, Afnan and Blankleider (TRAB). Secondly, when the Taylor method is applied to certain problems in a time-dependent perturbation theory it leads to the over-counting of some diagrams. This paper first restates Taylor's method, in the process uncovering reasons why certain diagrams might be double-counted in the Taylor method. It then explores how far Taylor's method is equivalent to the simpler TRAB method. Finally, it examines precisely why the double-counting occurs in Taylor's method, and derives corrections which compensate for this double-counting.

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arXiv1994

A gauge invariant unitary theory for pion photoproduction

The Ward-Takahashi identities are central to the gauge invariance of the photoproduction amplitude. Here we demonstrate that unitarity and in particular the inclusion of both the $πN$ and $γπN$ thresholds on equal footing yields a photoproduction amplitude that satisfies both two-body unitarity and the generalized Ward-Takahashi identities. The final amplitude is a solution of a set of coupled channel integral equations for the reactions $πN\rightarrowπN$ and $γN\rightarrowπN$. % Figures available from the authors upon request, % e-mail: phchv@pippin.cc.flinders.edu.au % Submitted to Physical Review C

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arXiv1993

Perturbation schemes for systems of nucleons and pions: The relationship of covariant perturbation theory, the convolution integral and time-ordered perturbation theory

This paper is the first in a series of three which attempt to resolve the difficulties that have plagued the $NN-πNN$ problem for the past ten years. Various theoretical inconsistencies in the current formulation have been pointed out and this work aims to eliminate these inconsistencies and so, we hope, produce agreement with experiment. This is to be done by using covariant perturbation theory, in which these inconsistencies are not present. The covariant perturbation theory is developed starting from a model Lagrangian, in order to fix notation and phases. It is shown that both old-fashioned "time-ordered" perturbation theory and the convolution integral of Kvinikhidze and Blankleider may be recovered from the covariant perturbation theory when certain approximations are made. The connection of these results with the work of Klein, Lévy, Macke and Kadyshevsky is discussed. Two forthcoming papers will pursue this covariant calculation in the $NN-πNN$ system using the model and perturbation scheme developed in this paper and derive fully covariant $NN-πNN$ equations without the double counting problems present in previous covariant equations.

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arXiv1993

A Gauge Invariant Unitary Theory for Pion Photoproduction

A covariant, unitary and gauge invariant theory for pion photoproduction on a single nucleon is presented. To achieve gauge invariance at the operator level one needs to include both the $πN$ and $γπN$ thresholds. The final amplitude can be written in terms of a distorted wave in the final $πN$ channel provided one includes additional diagrams to the standard Born term in which the photon is coupled to the final state pion and nucleon. These additional diagrams are required in order to satisfy gauge invariance.

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arXiv1992

Resonances in $Λd$ Scattering and the $Σ$-hypertriton

Using separable $NN$ and $ΛN$-$ΣN$ potentials in the Faddeev equations, we have demonstrated that the predicted enhancement in the $Λd$ cross section near the $Σd$ threshold is associated with resonance poles in the scattering amplitude. The positions of these poles, on the second Riemann sheet of the complex energy plane, are determined by examining the eigenvalues of the kernel of the Faddeev equations. This suggests that for a certain class of $ΛN$-$ΣN$ potentials we can form a $Σ$-hypertriton with a width of about 8 MeV.

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