arXiv subjects
Publications and source records attributed to A. B. Balantekin.
We introduce a new class of exactly solvable boson pairing models using the technique of Richardson and Gaudin. Analytical expressions for all energy eigenvalues and first few energy eigenstates are given. In addition, another solution to Gaudin's equation is also mentioned. A relation with the Calogero-Sutherland model is suggested.
We analyze the cumulative data from the latest SNO, KamLAND and other solar neutrino experiments in the standard scenario of three oscillating active neutrinos. We determine the solar neutrino oscillation parameters and obtain new bounds on $θ_x$. We also place constraints on the fraction of oscillating solar neutrinos that transform to sterile neutrinos with the $^8$B flux normalization left free. Concomitantly, we assess the sensitivity of future data from the SNO and KamLAND experiments to $θ_x$ and to the sterile neutrino content of the solar flux.
A simple description of core-collapse supernovae is given. Properties of the neutrino-driven wind, neutrino fluxes and luminosities, reaction rates, and the equilibrium electron fraction in supernova environments are discussed. Neutrino mixing and neutrino interactions that are relevant to core-collapse supernovae are briefly reviewed. The values of electron fraction under several evolution scenarios that may impact rapid neutron capture process (r-process) nucleosynthesis are calculated.
Recent high precision experimental data for heavy-ion fusion reactions at subbarrier energies systematically show that a surprisingly large surface diffuseness parameter for a Woods-Saxon potential is required in order to fit the data. We point out that experimental data for quasi-elastic scattering at backward angles also favor a similar large value of surface diffuseness parameter. Consequently, a double folding approach fails to reproduce the experimental excitation function of quasielastic scattering for the $^{16}$O + $^{154}$Sm system at energies around the Coulomb barrier. We also show that the deviation of the ratio of the quasielastic to the Rutherford cross sections from unity at deep subbarrier energies offers an unambiguous way to determine the value of the surface diffuseness parameter in the nucleus-nucleus potential.
We consider the counter-term describing isoscalar axial two-body currents in the nucleon-nucleon interaction, L1A, in the effective field theory approach. We determine this quantity using the solar neutrino data. We investigate the variation of L1A when different sets of data are used.
Fusion reactions below the Coulomb barrier provide new insights into multidimensional quantum tunneling, nuclear reaction dynamics and nuclear structure. These reactions are also of considerable interest to nuclear astrophysics. In this summary recent developments in the field are reviewed and open questions related to subbarrier fusion are presented.
Generalized coherent states for shape invariant potentials are constructed using an algebraic approach based on supersymmetric quantum mechanics. We show this generalized formalism is able to: a) supply the essential requirements necessary to establish a connection between classical and quantum formulations of a given system (continuity of labeling, resolution of unity, temporal stability, and action identity); b) reproduce results already known for shape-invariant systems, like harmonic oscillator, double anharmonic, Poschl-Teller and self-similar potentials and; c) point to a formalism that provides an unified description of the different kind of coherent states for quantum systems.
We introduce a class of exactly solvable boson models. We give explicit analytic expressions for energy eigenvalues and eigenvectors for an sd-boson Hamiltonian, which is related to the SO(6) chain of the Interacting Boson Model Hamiltonian.
Using a method of local transmission matrix, we generalize the well-known WKB formula for a barrier penetrability to multi-channel systems. We compare the WKB penetrability with a solution of the coupled-channels equations, and show that the WKB formula works well at energies well below the lowest adiabatic barrier. We also discuss the eigen-channel approach to a multi-channel tunneling, which may improve the performance of the WKB formula near and above the barrier.
Recent developments in solar, reactor, and accelerator neutrino physics are reviewed. Implications for neutrino physics, solar physics, nuclear two-body physics, and r-process nucleosynthesis are briefly discussed.
We discuss the physics potential of the solar neutrino experiments i) To explore the parameter space of neutrino mass and mixings; ii) To probe the physics of the Sun; iii) To explore nuclear physics of the neutrino-target interactions. Examples are given for these three classes.
Recent developments in the study of shape-invariant Hamiltonians are briefly summarized. Relations between certain exactly solvable problems in many-body physics and shape-invariance are explored. Connection between Gaudin algebras and supersymmetric quantum mechanics is pointed out.
A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show these new ladder operators satisfy new q-deformed commutation relations. In this context we construct an alternative q-deformed model that preserve the shape-invariance property presented by primary system. q-deformed generalizations of Morse, Scarf, and Coulomb potentials are given as examples.
In this brief review we explore the role of neutrino-nucleus interactions in core-collapse supernovae and discuss open questions. In addition implications of neutrino mass and mixings in such environments are summarized.
Algebraic approach to the integrability condition called shape invariance is briefly reviewed. Various applications of shape-invariance available in the literature are listed. A class of shape-invariant bound-state problems which represent two-level systems are examined. These generalize the Jaynes-Cummings Hamiltonian. Coherent states associated with shape-invariant systems are discussed. For the case of quantum harmonic oscillator the decomposition of identity for these coherent states is given. This decomposition of identity utilizes Ramanujan's integral extension of the beta function.
We generalize the pull approach to define the $χ^2$ function to the analysis of the data with correlated statistical errors. We apply this method to the analysis of the Sudbury Neutrino Collaboration data obtained in the salt-phase. In the global analysis of all the solar neutrino and KamLAND data we find the best fit (minimum $χ^2$) values of neutrino parameters to be $\tan^2 θ_{12} \sim 0.42$ and $δm_{12}^2 \sim 7.1 \times 10^{-5}$ eV$^2$. We confirm that the maximal mixing is strongly disfavored while the bounds on $δm_{12}^2$ are significantly strengthened.
We briefly review recent calculations of neutrino deuteron cross sections within the effective field theory and traditional potential model approaches. We summarize recent efforts to determine the counter term describing axial two-body currents, L_{1A}, in the effective field theory approach. We determine the counter term directly from the solar neutrino data and find several, slightly different, ranges of L_{1A} under different sets of assumptions. Our most conservative fit value with the largest uncertainty is L_{1A} = 4.5 +18/-12 fm^3. We show that the contribution of the uncertainty of L_{1A} to the analysis and interpretation of the solar neutrino data measured at the Sudbury Neutrino Observatory is significantly less than the uncertainty coming from the lack of having a better knowledge of θ_{13}.
We study the effect of virtual Coulomb break-up, commonly known as the dipole polarizability, of the deuteron projectile on the astrophysical fusion reaction 3He(d,p)4He. We use the adiabatic approximation to estimate the potential shift due to the E1 transition to the continuum states in the deuteron, and compute the barrier penetrability in the WKB approximation. We find that the enhancement of the penetrability due to the deuteron break-up is too small to resolve the longstanding puzzle observed in laboratory measurements that the electron screening effect is surprisingly larger than theoretical prediction based on an atomic physics model. The effect of the 3He break-up in the 3He(d,p)4He reaction, as well as the 7Li break-up in the 7Li(p,alpha)4He reaction is also discussed.