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It is shown that the effective interaction strength of three bosons at small collision energies can be extracted from their wave function at zero energy.
N. N. Bogoliubov, J. Phys. (U.S.S.R.) 11
1947
Earlier work this paper cites.
T. D. Lee and C. N. Yang, Phys. Rev. 105
1957
Earlier work this paper cites.
T. D. Lee, K. Huang, and C. N. Yang, Phys. Rev. 106
1957
Earlier work this paper cites.
The first term in this expansion was first found by P. Price, thesis, Cambridge University, Cambridge, 1951 (unpublished); the second and third terms found by Huang and Yang for 𝒩 \mathcal{N} particles Huang and Yang 1957 , although numerical coefficients were inexact; the term ∝ L − 6 ln L \propto L^{-6}\ln L was discovered by Wu Wu 1959 . O ( L − 6 ) O(L^{-6}) corrections were recently computed independently by Beane, Detmold, and Savage Sav for 𝒩 \mathcal{N} particles
1957
Earlier work this paper cites.
K. Huang and C. N. Yang, Phys. Rev. 105
1957
Earlier work this paper cites.
T. T. Wu, Phys. Rev. 115
1959
Earlier work this paper cites.
N. Hugenholtz and D. Pines, Phys. Rev. 116
1959
Earlier work this paper cites.
K. Sawada, Phys. Rev. 116
1959
Cited alongside, same era.
C. N. Yang, Rev. Mod. Phys. 34
1962
Cited alongside, same era.
R. D. Amado and M. H. Rubin, Phys. Rev. Lett. 25
1970
Cited alongside, same era.
1974
Cited alongside, same era.
E. Braaten and A. Nieto, Eur. Phys. J. B 11
1999
Cited alongside, same era.
S. Giorgini, J. Boronat, and J. Casulleras, Phys. Rev. A 60
1999
Cited alongside, same era.
E. Braaten, H.-W. Hammer, and S. Hermans, Phys. Rev. A 63
E. Braaten, H.-W. Hammer, and T. Mehen, Phys. Rev. Lett. 88
2002
Later among the works it cites.
A. Bulgac, Phys. Rev. Lett. 89
2002
Later among the works it cites.
J. O. Andersen, Rev. Mod. Phys. 76
2004
Later among the works it cites.
D. S. Petrov, C. Salomon, and G. V. Shlyapnikov, Phys. Rev. Lett. 93
2004
Later among the works it cites.
S. Stringari, Europhys. Lett. 65
2004
Later among the works it cites.
S. Tan and K. Levin, Phys. Rev. A 74
2006
Later among the works it cites.
S. R. Beane, W. Detmold, and M. J. Savage, arXiv:0707.1670 (2007)
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2001
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The | a | \lvert a\rvert in ln ( q i | a | ) \ln(q_{i}\lvert a\rvert) ensures that Eq. ( 3
Cited in the paper.
For any two-body potential V ( r ) V(r) , U 𝐤 1 𝐤 2 𝐤 3 𝐤 4 = 1 2 ∑ i = 1 2 ∑ j = 3 4 V ~ 𝐤 i − 𝐤 j U_{\mathbf{k}_{1}\mathbf{k}_{2}\mathbf{k}_{3}\mathbf{k}_{4}}=\frac{1}{2}\sum_{i=1}^{2}\sum_{j=3}^{4}\widetilde{V}_{\mathbf{k}_{i}-\mathbf{k}_{j}} , where 𝐤 1 + 𝐤 2 ≡ 𝐤 3 + 𝐤 4 \mathbf{k}_{1}+\mathbf{k}_{2}\equiv\mathbf{k}_{3}+\mathbf{k}_{4} , and V ~ 𝐤 = ∫ d 3 r V ( r ) e i 𝐤 ⋅ 𝐫 \widetilde{V}_{\mathbf{k}}=\int\mathrm{d}^{3}rV(r)\mathrm{e}^{\mathrm{i}\mathbf{k}\cdot\mathbf{r}}
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These functions can be obtained from the wave function of the two-body l l -wave scattering state at energy E → 0 E\rightarrow 0 : ϕ 𝐧 ^ 𝐤 ( l , E ) = ϕ 𝐧 ^ 𝐤 ( l ) + E f 𝐧 ^ 𝐤 ( l ) + E 2 g 𝐧 ^ 𝐤 ( l ) + O ( E 3 ) \phi^{(l,E)}_{\hat{\mathbf{n}}\mathbf{k}}=\phi^{(l)}_{\hat{\mathbf{n}}\mathbf{k}}+Ef^{(l)}_{\hat{\mathbf{n}}\mathbf{k}}+E^{2}g^{(l)}_{\hat{\mathbf{n}}\mathbf{k}}+O(E^{3}) , whose amplitude is defined by ∫ d 3 k ( 2 π ) 3 ϕ 𝐧 ^ 𝐤 ( l , E ) e i 𝐤 ⋅ 𝐫 = ( − 1 ) l + 1 a l Q 𝐧 ^ ( l ) ( ∇ r ) [ sin ( E r + δ l ) / r sin δ l ] \int\frac{\mathrm{d}^{3}k}{(2\pi)^{3}}\phi^{(l,E)}_{\hat{\mathbf{n}}\mathbf{k}}\mathrm{e}^{\mathrm{i}\mathbf{k}\cdot\mathbf{r}}=(-1)^{l+1}a_{l}Q^{(l)}_{\hat{\mathbf{n}}}(\nabla_{r})\big[\sin(\sqrt{E}r+\delta_{l})/r\sin\delta_{l}\big] for r r greater than the range of the interaction. Expanding the latter expression in powers of E E , and using Eq. ( 9
Cited in the paper.
Note that Q 𝐧 ^ ( l ) ( ∇ k ) ( 2 π ) 3 δ ( 𝐤 ) Q^{(l)}_{\hat{\mathbf{n}}}(\nabla_{k})(2\pi)^{3}\delta(\mathbf{k}) scales with k k like k − 3 − l k^{-3-l}
Cited in the paper.
It can be shown that a a and r s r_{s} are real
Cited in the paper.
2007
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