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Abstract

In this work a new scheme is proposed to accurately calculate the rotational energy level of the rigid symmetric-top molecule subjected to the external electric field, and also to obtain the corresponding analytical wave functions. For this purpose, first we use the different forms of function transformation and variable substitution to transform the differential equation of the polar angle θinto a confluent Heun differential equation, and then we use the characteristics of the confluent Heun differential equation and the confluent Heun function to find two linearly dependent solutions of the same eigenstates, which are used to construct the Wronskian determinant to obtain the exact energy spectrum equation. Finally, with the aid of the Maple software, we calculate the eigenvalues for different quantum states, and then substitute the obtained eigenvalues into the unnormalized eigenfunction to obtain the analytical normalized eigenfunction expressed by the confluent Heun function. These results are conducive to the in-depth study of the Stark effect of symmetric-top molecules.

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Authors and contacts

Corresponding author:Chen Chang-Yuan,chency@yctu.edu.cn; Dong Shi-Hai,dongsh2@yahoo.com

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 11975196) and the SIP, Instituto Politécnico Nacional (IPN), Mexico (Grant No. 20210414)

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References

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Cited By

DownLoad: Full-Size Img PowerPoint

J	K	(K,M)	n	b= 1	b= 5	b= 10	b= 20
0	0	(0, 0)	0	–0.15766348	–2.36561388	–6.04507511	–14.18676623
1	0	(0, 0)	1	2.09076065	2.63874703	1.72333341	–2.64067155
	0	(0, 1) (0, –1)	0	1.95033391	0.90475071	–1.52336944	–7.83391897
	1	(1, 1) (–1, –1)	0	1.46550429	–1.13615048	–4.90088894	–13.09274467
		(1, 0) (–1, 0)	0	1.95033391	0.90475071	–1.52336944	–7.83391897
		(1, –1) (–1, 1)	0	2.45930791	3.25240982	2.28859798	–2.10241580
2	0	(0, 0)	2	6.02403166	6.64546248	7.87932729	7.59702750
		(0, 1) (0, –1)	1	6.01157793	6.14932334	5.86920589	3.21233397
		(0, 2) (0, –2)	0	5.97623080	5.42770799	3.91145991	–0.75028417
	1	(1, 2) (–1, –2)	0	5.64610143	3.87965848	1.11394605	–5.42557601
		(1, 1) (–1, –1)	1	5.83444799	5.02308599	3.42628660	–1.26151418
		(1, 0) (–1, 0)	1	6.01157793	6.14932334	5.86920589	3.21233397
		(1, –1) (–1, 1)	1	6.17303459	7.17694539	8.52241501	8.17688040
		(1, –2) (–1, 2)	0	6.31159733	7.08037678	6.95972394	4.30076661
	2	(2, 2) (–2, –2)	0	5.32080726	2.40921111	–1.50915355	–9.82205218
		(2, 1) (–2, –1)	0	5.64610143	3.87965848	1.11394605	–5.42557601
		(2, 0) (–2, 0)	0	5.97623080	5.42770799	3.91145991	–0.75028417
		(2, –1) (–2, 1)	0	6.31159733	7.08037678	6.95972394	4.30076661
		(2, –2) (–2, 2)	0	6.65266958	8.89010555	10.43690550	9.90220896
3	0	(0, 0)	3	12.01112256	12.28609326	13.23851702	16.01072933
		(0, 1) (0, –1)	2	12.00832614	12.20185604	12.68109763	13.00122422
		(0, 2) (0, –2)	1	11.99996510	11.98051777	11.76516026	10.12548434
		(0, 3) (0, –3)	0	11.98611962	11.65790586	10.68518379	7.32389600
	1	(1, 3) (–1, –3)	0	11.73714675	10.44710964	8.38487920	3.22650134
		(1, 2) (–1, –2)	1	11.83176701	11.08791249	9.87421333	6.36151132
		(1, 1) (–1, –1)	2	11.92226344	11.68117484	11.32510413	9.60625434
		(1, 0) (–1, 0)	2	12.00832614	12.20185604	12.68109763	13.00122422
		(1, –1) (–1, 1)	2	12.08964046	12.60886369	13.77998811	16.66271656
		(1, –2) (–1, 2)	1	12.16589908	12.84075061	13.66336275	14.14238561
		(1, –3) (–1, 3)	0	12.23682184	12.90821524	13.10954794	11.68530530
	2	(2, 3) (–2, –3)	0	11.48984080	9.26997167	6.18154889	–0.66884422
		(2, 2) (–2, –2)	1	11.66163328	10.18131826	8.01132314	2.77663392
		(2, 1) (–2, –1)	1	11.83176701	11.08791249	9.87421333	6.36151132
		(2, 0) (–2, 0)	1	11.99996510	11.98051777	11.76516026	10.12548434
		(2, –1) (–2, 1)	1	12.16589908	12.84075061	13.66336275	14.14238561
		(2, –2) (–2, 2)	1	12.32917589	13.62647723	15.47989534	18.60143861
		(2, –3) (–2, 3)	0	12.48932036	14.20615704	15.70403035	16.41950037
	3	(3, 3) (–3, –3)	0	11.24414341	8.12208069	4.05742691	–4.40185593
		(3, 2) (–3, –2)	0	11.48984080	9.26997167	6.18154889	–0.66884422
		(3, 1) (–3, –1)	0	11.73714675	10.44710964	8.38487920	3.22650134
		(3, 0) (–3, 0)	0	11.98611962	11.65790586	10.68518379	7.32389600
		(3, –1) (–3, 1)	0	12.23682184	12.90821524	13.10954794	11.68530530
		(3, –2) (–3, 2)	0	12.48932036	14.20615704	15.70403035	16.41950037
		(3, –3) (–3, 3)	0	12.74368721	15.56368561	18.56353300	21.76261674

DownLoad: CSV

b	Perturbation	Maergoiz^[7]	This work	b	Maergoiz^[7]	This work
0.1	20.00006494		20.00006494	100	15.696	15.69559837
1	20.00649351		20.00649533	200	–31.200	–31.20010397
5	20.16233766	20.164	20.16352072	300	–90.598	–90.59767902
10	20.64935065	20.671	20.67080282	400	–156.41	–156.40991571
20	22.59740260	22.975	22.97522235	500	–226.31	–226.30840320
50	36.23376623	27.681	27.68132358	750	–412.26	–412.26234718

DownLoad: CSV

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Vol. 70, Issue 18 - 2021-09-20

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