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Volumn 77, Issue 4, 2008, Pages

Three fully polarized fermions close to a p -wave Feshbach resonance

Author keywords

[No Author keywords available]

Indexed keywords

DIMERS; INELASTIC SCATTERING; MATHEMATICAL MODELS; NUMERICAL METHODS; RESONANCE;

EID: 42149194444     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.77.043611     Document Type: Article
Times cited : (125)

References (82)
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    • One can equivalently consider a dimer wavefunction of a well defined angular moment component m=0,±1 along the quantization axis z, by replacing (3/4π) 1/2 rγ /r in Eq. 7 by Y1m (θ,).
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    • In the resonant limit | Vs | →+, on the side αres Vs <0 of the resonance, there is a so-called quasibound state in the two-body problem, which was studied experimentally in Ref.: From Eq. 4 and using the fact that αres >0, one finds that the scattering amplitude f (k) has a complex pole with a real part k00 1/ (αres | Vs |) 1/2 much larger than its imaginary part - (k00) 2 / (2 αres). Physically this is related to the existence of a centrifugal barrier when the two particles approach with non-zero relative momentum, here l=1. This quasibound state does not play an important role in the present work: in the exceptional case where we consider a negative rather than positive scattering volume (see end of Sec. 5), the total energy E in the three-body problem is still assumed to be much smaller than 2 (k00) 2 /m so that the relative momentum krel appearing in the three-body problem, as defined in Eq. 39, cannot reach the value k00.
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    • This reasoning extends to an arbitrary, everywhere finite envelope function f (k) such that χ (k) =kf (k).
    • This reasoning extends to an arbitrary, everywhere finite envelope function f (k) such that χ (k) =kf (k).
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    • This arbitrary normalization is 0 + dK K2 | b (K) | 2 =1.
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    • We shall also assume that the first order derivative of E (K) with respect to K is uniformly bounded as a function of K and Ktrim.
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    • From the low- K expansion of the matrix elements in the second line of M (K,k), we get BL=2 (K) =O (1/ K2 + K trim 2), so that K | BL=2 (K) | is uniformly bounded in K and Ktrim, similarly to what happens in the even sector. The crossed terms in BL=0 BL=2 give at most a logarithmic divergence in the normalization integrals.
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    • We use here the convention that, in the two-body calculation of the dimer wave function (r), β= p closed 1/2 ez.
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    • note
    • The infinite Vs bg pure single channel model is equivalent to an infinite Vs two channel model with no open channel interaction and with Λ→+, since both models have the same scattering amplitude in these limits.
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    • note
    • More precisely, if one assumes that v0 (K) diverges as 1/ Kγ for low K, γ<3 to ensure convergence in the integral, one sees that the integral in the limit K→0 either diverges as 1/ Kγ-1, for γ>1, or does not diverge, for γ<1. Since α th even >0, this leads to a contradiction in the integral equation α th even v0 (K) /4= I0† [v0] (K), the left-hand side diverging more rapidly than the right-hand side.


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