Z. Phys. D 33, 171-175 (1995) ZEITSCHRIFT FORPHYSIK D © Springer-Verlag t995 Gauge parameters for extrapolation of oscillator strengths of E1 transitions along the Boron isoelectronic sequence A. Agrawal, K.L. Baluja Department of Physics and Astrophysics, University of Delhi, Delhi 110 007, India Received: 20 September 1994/Final version: 17 November 1994 Abstract. The oscillator strengths f for E1 transitions along an isoelectronic sequence can be written as f= aK 2 + bK + c where K is a gauge parameter repres- enting the gauge condition of the electromagnetic field. The coefficients a, b, and c are functions of length (fl) and velocity (f~) values of the oscillator strengths at the Har- tree-Fock level. We have shown by making a perturba- tion expansion of oscillator strengths f, fl and f~ that the gauge parameter K is independent of the nuclear charge. This property has been exploited to extrapolate f values along the isoelectronic sequence of Boron for some repre- sentative E1 transitions within the n = 2 complex. We obtain good agreement between the extrapolated results with the configuration interaction results. PACS: 32.70 1 Introduction A knowledge of the optical oscillator strengths is required in various fields like astrophysics [1] and fusion research [21 . These oscillator strengths are related to other atomic properties like the refractive index, the dipole polarisabil- ity and the diamagnetic susceptibility through the sum rules [3 5]. The sum rules check the quality of the oscil- lator strengths. The optical oscillator strength can also be used to test the accuracy of the generalised oscillator strength [6]. The latter yields an optical oscillator strength in the limit of vanishing of momentum transfer. The computation of opacity of stellar envelopes [7] also requires the knowledge of such radiative data. On the experimental side, the oscillator strengths can be extracted from the measurements of transition prob- abilities by beam-foil [8] and beam-laser [9, 101 methods. Theoretical methods can yield accurate values of oscil- lator strengths by including the effects of electron correla- tions [11-14]. In the present work, we propose a novel method of extrapolating oscillator strengths along an isoelectronic sequence by employing the gauge condition of the electro- magnetic field [15]. We only need to know the length and velocity values of oscillator strengths along the isoelec- tronic sequence at the Hartree-Fock level; and an accurate value of oscillator strength near the neutral end of the isoelectronic sequence. In the present work we have studied the Boron isoelectronic sequence. 2 Theory The first-order quantumlelectrodynamical relativistic expression for the transition probability is [16, 17] WE~ 2(L+1)(2L+l)(~) zr+l ,-~2= L[(2L+I)!!] 2 + K,/L/(L + 1) x where K is an arbitrary gauge parameter which represents the gauge condition of the electromagnetic field potential, co is the frequency of the emitted photon of electric multi- polarity L, ~bx and ~b2 are the relativistic wavefunctions. The operators IQ~'~ and ~Q~ are defined as [16, 171 l~-qt~(L) __ (2Lco_ + 1) {jL (z) C (L)_q /2L+3 } + is/~JL +I (z) [C (L+ I) X 0C(I) I (_L)q (2) + ~L(-2L - l)jL-,(z) [C (L- ')x ~(I)I(L;} (3)