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Chin. Phys. B, 2019, Vol. 28(2): 023201    DOI: 10.1088/1674-1056/28/2/023201

Quantum photodetachment of hydrogen negative ion in a harmonic potential subjected to static electric field

Azmat Iqbal1, Kiran Humayun1, Sana Maqsood1, Saba Jawaid1, Afaq Ahmad2, Amin Ur Rahman1,3, Bakht Amin Bacha4
1 Department of Physics, The University of Lahore, Raiwind Road Campus, Lahore, Pakistan;
2 Center of Excellence in Solid State Physics, University of the Punjab, Lahore, Pakistan;
3 Department of Physics, RIPHAH International University Islamabad, Pakistan;
4 Department of Physics, University of Malakand Chakdara Dir(L), Pakistan

Photodetachment of negative ions has attracted immense interest owing to its fundamental nature and practical implications with regard to technology. In this study, we explore the quantum dynamics of the photodetachment cross section of negative ion of hydrogen H- in the perturbed one dimensional linear harmonic potential via static electric field. To this end, the quantum formula for total photodetachment cross section of the H- ion is derived by calculating the dipole matrix element in spherical coordinates. In order to obtain the detached electron wave function, we have solved the time-independent Schrödinger wave equation for the perturbed Hamiltonian of the harmonic oscillator in momentum representation. To acquire the corresponding normalized final state detached electron wave function in momentum space, we have employed an approach analogous to the WKB (Wenzel-Kramers-Brillouin) approximation. The resulting analytical formula of total photodetachment cross section depicts interesting oscillator structure that varies considerably with incident-photon energy, oscillator potential frequency, and electric field strength as elucidated by the numerical results. The current problem having close analogy with the Stark effect in charged harmonic oscillator may have potential implications in atomic and molecular physics and quantum optics.

Keywords:  photodetachment cross section      harmonic oscillator potential      Stark effect      time-independent Schrödinger equation      WKB approximation  
Received:  30 September 2019      Revised:  29 October 2018      Accepted manuscript online: 
PACS:  32.80.Gc (Photodetachment of atomic negative ions)  
  32.60.+i (Zeeman and Stark effects)  
Corresponding Authors:  Azmat Iqbal     E-mail:

Cite this article: 

Azmat Iqbal, Kiran Humayun, Sana Maqsood, Saba Jawaid, Afaq Ahmad, Amin Ur Rahman, Bakht Amin Bacha Quantum photodetachment of hydrogen negative ion in a harmonic potential subjected to static electric field 2019 Chin. Phys. B 28 023201

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