Zero-Energy Feshbach Resonances

Consider the case of a zero-energy Feshbach resonance as a function of magnetic field B. At constant the phase shift follows a form similar to Equation 1.63,... 

Gonzalez-Martmez, M.L. and Hutson, J.M., Ultracold atom—molecule collisions and bound states in magnetic fields zero-energy Feshbach resonances in He—NH ( E ), Phys. Rev. A, 15, 022702, 2007. 

Fig. 10.24. Feshbach resonance in the case of ground state scattering from atoms. The entrance channel wave function Uinit R) couples to a quasibound sate with wave function Ures R)- The energy level of the quasibound state is brought into a zero-energy resonance by tuning a magnetic field. Here the resonance is detected by enhancement of the photoassociation rate to a specific u, J level of the 0 excited state 7l-...

Vibrational Feshbach resonances (VFRs) in a vibrational Feshbach resonance, the interaction of a slow electron takes the form of a virtual excitation of a vibrational level of the neutral molecule with capture of the electron (ffotop et al. 2003 Dessent et al. 2000). For the zero point vibration, the maximum probability of interaction of the electron with parent molecule occurs at zero energy, if the dipole moment of the neutral molecule exceeds the critical value of approximately 2 Debye, the impinging electron maybe trapped into the diffuse bound state, which provides a much longer timescale for the electron to stay near the molecule (fiotop et al. 2003 Dessent et al. 2000 lllenberger 1992), and VFRs may appear as shown in O Fig. 34-5. 

Figure 1 2 10. The reduced Lifshitz parameter"z" - (ET - EF)/(EA- ET), where (EA- Er) is the full energy band dispersion in the c-axis direction, as a function of the number of holes in the G subband in A1 doped MgB2. The quantum uncertainty in the z value is indicated by the error bars that are given by D (

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