تقرير
Two Particles in a Trap
| العنوان: | Two Particles in a Trap |
|---|---|
| المؤلفون: | Kohler, H. S. |
| سنة النشر: | 2011 |
| المجموعة: | Nuclear Theory Quantum Physics |
| مصطلحات موضوعية: | Nuclear Theory, Quantum Physics |
| الوصف: | The Busch-formula relates the energy-spectrum of two point-like particles interacting in a 3-D isotropic Harmonic Oscillator trap to the free scattering phase-shifts of the particles. This formula is used to find an expression for the \it shift \rm in the spectrum from the unperturbed (non-interacting) spectrum rather than the spectrum itself. This shift is shown to be approximately $\Delta=-\delta(k)/\pi\times dE$, where $dE$ is the spacing between unperturbed energy levels. The resulting difference from the Busch-formula is typically 1/2% except for the lowest energy-state and small scattering length when it is 3%. It goes to zero when the scattering length $\rightarrow \pm \infty$. The energy shift $\Delta$ is familiar from a relatedproblem, that of two particles in a spherical infinite square-well trap of radius $R$ in the limit $R\rightarrow \infty$. The approximation ishowever as large as 30% for finite values of $R$, a situation quite different from the Harmonic Oscillator case. The square-well results for $R\rightarrow \infty$ led to the use ofin-medium (effective) interactions in nuclear matter calculations that were $\propto \Delta$ and known as the \it phase shift approximation \rm.Our results indicate that the validity of this approximation depends on the trapitself, a problem already discussed by DeWitt more than 50 years ago for acubical vs spherical trap. Comment: 7 pages 4 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1110.0039 |
| رقم الأكسشن: | edsarx.1110.0039 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |