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Register a new userFast & accurate emulation of two-body scattering observables without wave functions
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Added by
Christian Drischler
Publication date
2021
fields
Physics
and research's language is
English
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We combine Newtons variational method with ideas from eigenvector continuation to construct a fast & accurate emulator for two-body scattering observables. The emulator will facilitate the application of rigorous statistical methods for interactions that depend smoothly on a set of free parameters. Our approach begins with a trial $K$ or $T$ matrix constructed from a small number of exact solutions to the Lippmann--Schwinger equation. Subsequent emulation only requires operations on small matrices. We provide several applications to short-range potentials with and without the Coulomb interaction and partial-wave coupling. It is shown that the emulator can accurately extrapolate far from the support of the training data. When used to emulate the neutron-proton cross section with a modern chiral interaction as a function of 26 free parameters, it reproduces the exact calculation with negligible error and provides an over 300x improvement in CPU time.
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The meson-baryon molecular components for the $N^{ast}$ and $Delta ^{ast}$ resonances are investigated in terms of the compositeness, which is defined as the norm of the two-body wave function from the meson-baryon scattering amplitudes. The scattering amplitudes are constructed in a $pi N$-$eta N$-$sigma N$-$rho N$-$pi Delta$ coupled-channels problem in a meson exchange model together with several bare $N^{ast}$ and $Delta ^{ast}$ states, and parameters are fitted so as to reproduce the on-shell $pi N$ partial wave amplitudes up to the center-of-mass energy 1.9 GeV with the orbital angular momentum $L le 2$. As a result, the Roper resonance $N (1440)$ is found to be dominated by the $pi N$ and $sigma N$ molecular components while the bare-state contribution is small. The squared wave functions in coordinate space imply that both in the $pi N$ and $sigma N$ channels the separation between the meson and baryon is about more than 1 fm for the $N (1440)$ resonance. On the other hand, dominant meson-baryon molecular components are not observed in any other $N^{ast}$ and $Delta ^{ast}$ resonances in the present model, although they have some fractions of the meson-baryon clouds.
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We present the 2-point function from Fast and Accurate Spherical Bessel Transformation (2-FAST) algorithm for a fast and accurate computation of integrals involving one or two spherical Bessel functions. These types of integrals occur when projecting the galaxy power spectrum $P(k)$ onto the configuration space, $xi_ell^ u(r)$, or spherical harmonic space, $C_ell(chi,chi)$. First, we employ the FFTlog transformation of the power spectrum to divide the calculation into $P(k)$-dependent coefficients and $P(k)$-independent integrations of basis functions multiplied by spherical Bessel functions. We find analytical expressions for the latter integrals in terms of special functions, for which recursion provides a fast and accurate evaluation. The algorithm, therefore, circumvents direct integration of highly oscillating spherical Bessel functions.
The standard approach to nuclear physics encodes phase shift information in an NN potential, then decodes that information in forming an effective interaction, appropriate to a low-momentum Hilbert space. Here we show that it is instead possible to construct the effective interaction directly from continuum phase shifts and mixing angles, eliminating all reference to a high momentum potential. The theory is rapidly convergent and well behaved, yielding sub-keV accuracy.
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