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Abstract

The renormalized Numerov algorithm is applied to solving time-independent Schrödinger equation relating to atom-atom collisions at ultralow temperature. The proprieties of Feshbach resonance in ³⁹K- ¹³³Cs collisions are investigated as an example. The results show that the renormalized Numerov method can give excellent results for ultracold colliding process. In contrast to improved log derivative method, the renormalized Numerov method displays a certain weakness in computational efficiency under the same condition. However, it is much stable in a wide range of grid step size. Hence a new propagating method is proposed by combining renormalized Numerov and logarithmic derivative method which can save computational time with a better accuracy. This algorithm can be used to solve close-coupling Schrödinger equation at arbitrary temperature for two-body collisions.

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Authors and contacts

Bai Jing¹,
Xie Ting²

Corresponding author:Xie Ting,tingxie1113@dicp.ac.cn

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	RN			LOGD
	B₀/G	ΔB/G	a_bg	B₀/G	ΔB/G	a_bg
$ \begin{gathered} \left\| {{f_{\text{K}}} = 1, \;{m_{f{\text{K}}}} = 1} \right\rangle + \\ \left\| {{f_{{\text{Cs}}}} = 3, \;{m_{f{\text{Cs}}}} = 3} \right\rangle \\ \end{gathered} $	341.89	4.8	79.1a₀	341.90	4.8	79.0a₀
	421.35	0.4	74.7a₀	421.36	0.4	74.7a₀
	831.14	4 × 10^–4	80.9a₀	831.14	3 × 10^–4	81.0a₀
	860.50	0.05	82.1a₀	860.52	0.05	82.0a₀
	915.57	1.2	80.2a₀	915.56	1.2	80.1a₀

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ΔR	N_RN	N_LOGD	$ B_0^{\rm error} $/G
0.004a₀	4251	1990	0.02
0.006a₀	2834	1990	0.11
0.008a₀	2126	1990	0.57
0.010a₀	1701	1990	2.31

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Vol. 71, Issue 3 - 2022-02-05

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