CALCULATION OF SCATTERING WAVE FUNCTIONS FOR METASTABLE STATES OF A DIATOMIC BERYLLIUM MOLECULE

Lê Hải Lương 1, , Minh Nhựt Nguyễn , Kim Liên Lưu , Alexander Alexandrovich Gusev
1 Khoa Vật lý, Trường Đại học Sư phạm TPHCM

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Abstract

 

 

In this paper, the computational scheme and calculation results of scattering functions for metastable states of a diatomic beryllium molecule in laser spectroscopy are presented. The solution to the problem is performed using the authors' software package with the high-accuracy finite element method. The procedure of matching tabulated potential functions with van der Waals asymptotic potential using Hermite interpolation polynomials which provides continuity of both the function itself and its derivative is presented. The efficiency of the proposed approach is demonstrated by the spectrum of rotational-vibrational metastable states with complex-valued energy eigenvalues in the diatomic beryllium molecule. For selected metastable states, the corresponding scattering states with real-values resonance energies are calculated and shown in graphs.

 

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References

Derbov, V. L., Chuluunbaatar, G., Gusev, A. A., Chuluunbaatar, O., Vinitsky, S. I., Gozdz, A., Krassovitskiy, P. M., & Mitin, A. V. (2020). On calculations of metastable and Rydberg states of diatomic beryllium molecule and antiprotonic helium atom. In: Proc. of SPIE., 11458, 114580.
Derbov, V. L., Chuluunbaatar, G., Gusev, A. A., Chuluunbaatar, O., Vinitsky, S. I., Gozdz, A., Krassovitskiy, P. M., Filikhin, I., & Mitin, A. V. (2021). Spectrum of beryllium dimer in ground X1Σ+g state. J. Quant. Spectrosc. Radiat. Transf, 262, 107529–1-10.
Gusev, A., Vinitsky, S., Gerdt, V., Chuluunbaatar, O., Chuluunbaatar, G., Hai L. L., & Zima, E. (2021). A maple implementation of the finite element method for solving boundary problems of the systems of ordinary second order differential equations. Springer Nature Switzerland AG. CCIS., (1414), 152-166.
Gusev, A. A., Luong, L. L., Chuluunbaatar, O., Vinitsky S. I., KANTBP 4M – program for solving boundary problems of the self-adjoint system of ordinary second order differential equations. JINRLIB; 2015. Retrieved from http://wwwinfo.jinr.ru/programs/jinrlib/kantbp4m/indexe
Gusev, A., Chuluunbaatar, O., Vinitsky, S., Derbov, V. L., Gozdz, A., Krassovitskiy, P. M., Filikhin, I., Mitin A. V., Luong, L., H., & Tran, T., L. (2019). On rotational-vibrational spectrum of diatomic beryllium molecule. In: Proceedings of SPIE., 11066(1), 1106619.
Gusev, A. A., Gerdt, V. P., Luong L. H., Derbov, V. L., Vinitsky, S. I. & Chuluunbaatar, O. (2016). Symbolic-Numeric Algorithms for Solving BVPs for a System of ODEs of the Second Order: Multichannel Scattering and Eigenvalue Problems. CASC, Springer International Publishing Switzerland, LNCS., 9890(1), 212-227.
Gusev, A. A., Luong, L., H., Chuluunbaatar, O., Ulziibayar, V., Vinitsky, S. I., Derbov, V. L., Gozdz, A., & Rostovtsev, V. A. (2015). Symbolic-numeric solution of boundary-value problems for the Schrodinger equation using the finite element method: scattering problem and resonance states. CASC, Springer International Publishing Switzerland, LNCS., 9301(1), 182-197.
Koput, J. (2011). The ground-state potential energy function of a beryllium dimer determined using the single-reference coupled-cluster approach. PCCP., 13(45), 20311.
Lesiuk, M., Przybytek, M., Balcerzak, J. G., Musial, M., & Moszynski, R. (2019). Ab initio potential energy curve for the ground state of beryllium dimer. J. Chem. Theory Comput, (15),
2470-2480.
Merritt, J. M., Bondybey, V. E., & Heaven, M. C. (2009). Beryllium dimer caught in the act of bonding. Science, 324(5934), 1548-1551.
Meshkov, V. V., Stolyarov, A. V., Heaven, M. C., Haugen, C., & LeRoy, R. J. (2014). Direct-potential-fit analyses yield improved empirical potentials for the ground X1 σg+ state of Be2. J. Chem. Phys., 6(140), 064315.
Mitin, A. V. (2011). Ab initio calculations of weakly bonded He2 and Be2 molecules by MRCI method with pseudonatural molecular orbitals. Int. J. Quantum Chem., (111), 2560-2567.
Mitin, A. V. (2017). Unusual chemical bonding in the beryllium dimer and its twelve vibrational levels. Chem Phys Lett., (682), 30-3.
NIST. Physical Measurement Laboratory. Atomic spectroscopy databases. Retrieved from https://www.nist.gov/pml/atomic-spectroscopy-databases
Patkowski, K., Spirko, V., & Szalewicz, K. (2009). On the elusive twelfth vibrational state of beryllium dimer. Science, (326), 1382-1384.
Porsev, S. G., & Derevianko, A. (2006). High-accuracy calculations of dipole, quadrupole, and octupole electric dynamic polarizabilities and van der Waals coefficients C6, C8, and C10 for alkaline-earth dimers. JETP., (102), 195-205.
Sheng, X. W., Kuang, X. Y., Li, P., & Tang, K. T. (2013). Analyzing and modeling the interaction potential of the ground-state beryllium dimer. Phys. Rev. A, (88), 022517.
Streng, G., & Fics, G. (1977). Theory of finite element method. Moscow: World.