The energy E_j can be expressed in terms of interaction parameters-(Slater-Condon) F_k, and ξ_4f (Lande) by Taylor

ZnLiBiB (UD)―Represents undoped Zinc Lithium Bismuth Borate glass specimens ZnLiBiB (PR)―Represents Pr³⁺ doped Zinc Lithium Bismuth Borate glass specimens.

series expansion for a small variation of energies ∆E_j. In the first order approximation, the energy E_j of the j^th level is given by [19] [20] .

where, E_oj is the zero order energy of j^th level and ΔF_k and Δξ_4f are the small changes in the corresponding parameters and these values have been calculated by partial regression method.

The value of F_k and ξ_4f are then evaluated using equations.

where, and are zero order values of the parameters F_k and ξ_4f, respectively.

The Racah parameters E^k (k = 1, 2, 3) can be expressed as linear combination of F_k (k = 2, 4, 6) given by

The intensity of spectral lines are expressed in terms of oscillator strengths using the relation [21] .

where, ε(ν) is molar absorption coefficient at a given energy ν (cm⁻¹), to be evaluated from Beer-Lambert law.

Under Gaussian Approximation, using Beer-Lambert law, the observed oscillator strengths of the absorption bands have been experimentally calculated, using the modified relation [22] .

where c is the molar concentration of the absorbing ion per unit volume, I is the optical path length, is absorbtivity or optical density and is half band width.

According to Judd [23] and Ofelt [24] theory, independently derived expression for the oscillator strength of the induced forced electric dipole transitions between an initial J manifold level and the terminal J' manifold is given by:

where, the line strength is given by the equation

In the above equation m is the mass of an electron, c is the velocity of light, ν is the wave number of the transition, h is Planck’s constant, n is the refractive index, J and J' are the total angular momentum of the initial and final level respectively, Ω_λ (λ = 2, 4 and 6) are known as Judd-Ofelt intensity parameters which contain the effect of the odd-symmetry crystal field terms, radial integrals and energy denominators. are the matrix elements of the doubly reduced unit tensor operator calculated in intermediate coupling approximation. Ω_λ pa-

rameter can be obtained from least square fitting method [25] . The matrix element that are insensitive to the environment of rare earth ions were taken from the literature [26] .

The Ω_λ parameters obtained using the absorption spectral results have been used to predict radiative properties such as spontaneous emission probability (A) and radiative life time (τ_R), and laser parameters like fluorescence branching ratio (β_R) and stimulated emission cross section (σ_p).

The spontaneous emission probability from initial manifold to a final manifold is given by:

where,

The fluorescence branching ratio for the transitions originating from a specific initial manifold to a final many fold is given by

where, the sum is over all terminal manifolds.

The radiative life time is given by

where, the sum is over all possible terminal manifolds. The stimulated emission cross -section for a transition from an initial manifold to a final manifold

is expressed as

where, the peak fluorescence wavelength of the emission band and is the effective fluorescence line width.

The nature of the R-O bond is known by the Nephelauxetic Ratio and Bonding Parameter (b^1/2), which are computed by using following formulae [27] . The Nephelauxetic Ratio is given by

where, ν_a and ν_g refer to the energies of the corresponding transition in the glass and free ion, respectively. The values of bonding parameter b^1/2 are given by

where is the average value of

The absorption spectra of these glasses were recorded between wavelengths range 400 - 900 nm with a Spctro Scan 80D/80DV Spectrophotometer and 900 - 2250 nm with a Perkin-Elmer Lambda 750 UV/VIS/NIR Spectrophotometer at room temperature.

The absorption spectra of Pr³⁺ doped ZnLiBiB glass specimens have been represented in Figure 2 in terms of relative absorption (I/I₀) versus wavelength (nm), where I and I₀ are intensities of the radiation transmitted through doped specimens and undoped specimens of equal thickness. Eight absorption bands UV-VIS and NIR region have been observed from the ground state ³H₄to excited states ³P₂, ³P₁, ³P₀, ¹D₂, ¹G₄, ³F₄, ³F₃ and ³F₂ for Pr³⁺ doped ZnLiBiB glasses.

The optical absorption bands around the ³P₂ (446 nm), ³P₁ (469 nm), ³P₀ (485 nm), ¹D₂ (592 nm), ¹G₄ (1010 nm), ³F₄ (1442 nm), ³F₃ (1527 nm) and ³F₂ (1936 nm), are assigned from the ground state, ³H₄, Assignment have been made by published article [28] . From the absorption spectra, experimental oscillator strengths have been calculated for all the absorption bands.

The experimental and calculated oscillator strengths for Pr³⁺ ions in zinc lithium bismuth borate glasses are given in Table 2. Racah parameters (E^k) have been deduced from F_k parameters [29] (Table 3). The ratio of Racah parameters E¹/E³ and E²/E³ are about 10 and 0.05 respectively. Which are almost equal to the hydrogenic ratio [30] . This implies that Pr³⁺ ions at different doping concentrations are subjected.

Further Judd-Ofelt intensity parameters Ω_λ (λ = 2, 4 and 6) were calculated by using the fitting approximation of the experimental oscillator strengths to the calculated oscillator strengths with respect to their electric dipole contributions. In the present case the three Ω_λ parameters follow the trend Ω₂ < Ω₄ < Ω₆. The spectroscopic quality factor (Ω₄/Ω₆) related with the rigidity of the glass system has been found to lie between 0.4 and 0.7 in the

present glasses. The values of Judd-Ofelt intensity parameters are given in Table 4.

A comparison of calculated σ values for bismuth borate glasses with those reported [31] for borate, silicate, fluoroberyllate, phosphate and tellurite glasses (Figure 3) shows that bismuth borate glasses are best and tellurite glasses the next best. However, tellurite glasses have low transmission in the desired region (NIR) due to high value of refractive index.

Computed values of Slater-Condon, Lande, Racah, nephelauexetic ratio and bonding parameter for Pr³⁺ doped ZnLiBiB glass specimens are given in Table 3.

The fluorescence spectrum of Pr³⁺doped in zinc lithium bismuth borate glass is shown in Figure 4. There are four broad bands (³P₀ → ³H₄), (³P₀ → ³H₅), (³P₀ → ³H₆) and (³P₀ → ³F₂), respectively for glass specimens. Out of four emission transition observed from³P₀level, only three (³P₀ → ³H₄, ³H₆ and ³F₂) are included in the fit. The transition ³P₀ → ³H₅ is excluded since the matrix elements for this transition are zero and the β is too weak to measure.

The value of stimulated emission cross-section (σ_p) is found to be maximum for the transition (³P₀ → ³F₂) for glass ZnLiBiB PR 01, suggesting that glass ZnLiBiB PR01 is better compared to the other two glass systems (ZnLiBiB PR1.5 and ZnLiBiB PR02). The wavelengths of these bands along with their assignments are given in Table 5.