We study three-body recombination in two dimensions for systems interacting via short-range two-body interactions in the regime of large scattering lengths. Using the adiabatic hyperspherical representation, we derive semianalytical formulas for three-body recombination in both weakly and deeply bound diatom states. Our results demonstrate the importance of long-range corrections to the three-body potentials by showing how they alter the low-energy and scattering-length dependence of the recombination rate for both bosonic and fermionic systems, which exhibit suppressed recombination if compared to the three-dimensional case. We verify these results through numerical calculations of recombination for systems with finite-range interactions and supporting a few two-body bound states. We also study finite-range effects for the energies of the universal three-identical-bosons states and find a slow approach to universal predictions as a function of the scattering length.We study three-body recombination in two dimensions for systems interacting via short-range two-body interactions in the regime of large scattering lengths. Using the adiabatic hyperspherical representation, we derive semianalytical formulas for three-body recombination in both weakly and deeply bound diatom states. Our results demonstrate the importance of long-range corrections to the three-body potentials by showing how they alter the low-energy and scattering-length dependence of the recombination rate for both bosonic and fermionic systems, which exhibit suppressed recombination if compared to the three-dimensional case. We verify these results through numerical calculations of recombination for systems with finite-range interactions and supporting a few two-body bound states. We also study finite-range effects for the energies of the universal three-identical-bosons states and find a slow approach to universal predictions as a function of the scattering length.

arXiv:1411.2321Physical Review AJun 23, 201517 citations

A New Feature of the Efimov-Like Structure in the Hadron System: Long-Range Force as a Recoil Effect

S. Oryu

On the three-body kinematics, we investigate the threshold behavior which appears not only at the three-body break-up threshold (3BT), but also at the quasi two-body threshold (Q2T) for the reactions: $A+(BC)\rightarrow A+B+C$ , and $(ABC)\rightarrow A+(BC)$ , respectively. Recently, the author proposed a general particle ${transfer}$ (GPT) potential which appears, not only at the 3BT, but also at the Q2T between A and (BC). The new potential indicates a Yukawa-type potential for short range, but a $1/r^n$ -type potential for long range. The long range part of the GPT potential for $n=1$ indicates an attractive Coulomb-like or a gravitation-like potential. While, $n=2$ indicates the Efimov-like potential between A and (BC). The three-body binding energy: $E_n=\epsilon +\zeta _n$ with the two-body binding energy $\epsilon$ , and the separation energy $\zeta _n$ for $(ABC)\rightarrow A+(BC)$ satisfies $E_n/E_{n+1}=\zeta _n/\zeta _{n+1}$ =const for $\epsilon =0$ or the two-body scattering length: $a\rightarrow \infty$ (i.e. the two-body unitary limit). At the Q2T, the condensation of the three-body binding energy is given by the GPT-potential in the form of $E_n/E_{n+1}=(\zeta _n+\epsilon )/(\zeta _{n+1}+\epsilon )\rightarrow 1$ (const) for $n\rightarrow \infty$ (with $\zeta _n\rightarrow 0$ ) which implies the existence of Efimov-like states at the Q2T in the hadron systems, thereby the possibility of “ultra low energy nuclear transformation”, where the three-body binding energies degenerate at zero energy. Finally, the origin of such a long range potential will be clarified.On the three-body kinematics, we investigate the threshold behavior which appears not only at the three-body break-up threshold (3BT), but also at the quasi two-body threshold (Q2T) for the reactions: $$A+(BC)\rightarrow A+B+C$$ , and $$(ABC)\rightarrow A+(BC)$$ , respectively. Recently, the author proposed a general particle $$ {transfer}$$ (GPT) potential which appears, not only at the 3BT, but also at the Q2T between A and (BC). The new potential indicates a Yukawa-type potential for short range, but a $$1/r^n$$ -type potential for long range. The long range part of the GPT potential for $$n=1$$ indicates an attractive Coulomb-like or a gravitation-like potential. While, $$n=2$$ indicates the Efimov-like potential between A and (BC). The three-body binding energy: $$E_n=\epsilon +\zeta _n$$ with the two-body binding energy $$\epsilon $$ , and the separation energy $$\zeta _n$$ for $$(ABC)\rightarrow A+(BC)$$ satisfies $$E_n/E_{n+1}=\zeta _n/\zeta _{n+1}$$ =const for $$\epsilon =0$$ or the two-body scattering length: $$a\rightarrow \infty $$ (i.e. the two-body unitary limit). At the Q2T, the condensation of the three-body binding energy is given by the GPT-potential in the form of $$E_n/E_{n+1}=(\zeta _n+\epsilon )/(\zeta _{n+1}+\epsilon )\rightarrow 1$$ (const) for $$n\rightarrow \infty $$ (with $$\zeta _n\rightarrow 0$$ ) which implies the existence of Efimov-like states at the Q2T in the hadron systems, thereby the possibility of “ultra low energy nuclear transformation”, where the three-body binding energies degenerate at zero energy. Finally, the origin of such a long range potential will be clarified.

Few-Body SystemsApr 9, 20189 citations

Long-range many-body scattering

Israel Michael Sigal, Avy Soffer

Inventiones mathematicaeDec 1, 199091 citations

A+(BC)\rightarrow A+B+C

, and

(ABC)\rightarrow A+(BC)

, respectively. Recently, the author proposed a general particle

{transfer}

(GPT) potential which appears, not only at the 3BT, but also at the Q2T between A and (BC). The new potential indicates a Yukawa-type potential for short range, but a

1/r^n

-type potential for long range. The long range part of the GPT potential for

n=1

indicates an attractive Coulomb-like or a gravitation-like potential. While,

n=2

indicates the Efimov-like potential between A and (BC). The three-body binding energy:

E_n=\epsilon +\zeta _n

with the two-body binding energy

\epsilon

, and the separation energy

\zeta _n

for

(ABC)\rightarrow A+(BC)

satisfies

E_n/E_{n+1}=\zeta _n/\zeta _{n+1}

=const for

\epsilon =0

or the two-body scattering length:

a\rightarrow \infty

(i.e. the two-body unitary limit). At the Q2T, the condensation of the three-body binding energy is given by the GPT-potential in the form of

E_n/E_{n+1}=(\zeta _n+\epsilon )/(\zeta _{n+1}+\epsilon )\rightarrow 1

(const) for

n\rightarrow \infty

(with

\zeta _n\rightarrow 0

) which implies the existence of Efimov-like states at the Q2T in the hadron systems, thereby the possibility of “ultra low energy nuclear transformation”, where the three-body binding energies degenerate at zero energy. Finally, the origin of such a long range potential will be clarified.