S-wave scattering

For pure S-wave scattering, the difFerential cross section (DCS) is isotropic. For pure P-wave scattering, tlie DCS is symmetric about 0 = n/2, where it vanishes the DCS rises to equal maxima at 0 = 0, ti. For combined S- and P-wave scattering, the DCS is asynnnetric with forward-backward asynnnetry. 

For small scatterers the expression of the multi-scattering matrix simplifies, since only s-wave scattering is important... 

Therefore for the regular part of the s-wave scattering length we have... 

Sigg D. et al. Electromagnetic correction to the s-wave scattering lengths in pionic hydrogen, Nucl. Phys. A 609, 310, (1996)... 

Because the orbital angular momentum of the positron-hydrogen system is zero for s-wave scattering, the total wave function is spherically symmetric and depends only on the three internal coordinates which specify the shape of the three-body system. The kinetic energy operator... 

When the constituent two-body interactions in a three-body system produce an s-wave scattering length a of much larger magnitude a than... 

Interactions between neighboring atoms shift and broaden the line. This can be described from a many-body picture as a result of the mean field energy shift, AEe = (Anh2aeyg/ m) rig, where ae,g is the s-wave scattering length of atoms in state e and g, m is the atomic mass, and ng is the density of g-state atoms. From the an atomic standpoint it is equal to a cold collision frequency shift which we... 

A k as a source of model-independent data on nK S-wave scattering lengths... 

S-wave scattering is the only practical outcome since P-wave final neutron states are not accessible to thermal neutrons, because these wave functions have negligible amplitude at the small radial values that are typical of atomic nuclei. It is convenient to rewrite the equation as a dynamical structure factor (or Scattering Law), which emphasises the dynamics of the sample. 

Figure 2. The Bogoliubov dispersion relation (scaled by the recoil energy of an emitting atom) for short-range s-wave scattering (dashed line) can be modified by the dipole-dipole interaction to the extent that is displays a roton minimum (solid line). Parameters laser wavelength and scaled intensity Al = 795 nm, I = 0.057, BEC radius and density wr = 3.5 Al, 8.1020 atoms.m-3, s-wave scattering length due to van der Waals interaction 5.5 nm.

We calculate the roton [Steinhauer 2004] in atomic vapor BEC using a Jas-trow wavefunction, which allows us to calculate beyond mean-field correlations in the quantum state, giving rise to a roton peak in the structure factor at a momentum k oc a-1 (where a is the s-wave scattering length of the atoms). The relevant parameter e = J i t a (n is the density of the atoms in the BEC), is calculated over a range of values from e < 1 up to e 1. 

Only when the neutron is at an atomic position, r - ri = 0, does it encounter the scattering potential of strength bi. In the Bom approximation only this form for Vf(r ) can successfully reproduce S-wave scattering from bound nuclei. 

Fig. 6. Charge transfer cross section for s-wave scattering of the process K + I - K+ + I as a function of the initial relative kinetic energy. Notice the sharp onset at threshold. (De Vries and Kuppermann, 1971).

Low-energy S-wave scattering parameters as predicted by some meson-theoretic NN potentials. In the last row, the f /datum is given for the fit of the 4 empirical data given in the last column... 

The s-wave scattering length OQ k) (or often just a k)) is particularly important because the s-wave elastic cross-section is given simply by... 

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