# New experimental determination of L shell fluorescence yields and Coster-Kronig transition factors of platinum

Ablaihan Utepov, Marie-Christine Lépy, Y. Ménesguen

► To cite this version:

Ablaihan Utepov, Marie-Christine Lépy, Y. Ménesguen. New experimental determination of L shell fluorescence yields and Coster-Kronig transition factors of platinum. X-Ray Spectrometry, 2026, 55, pp.190-201. 10.1002/xrs.70035 . cea-05526171

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Submitted on 24 Feb 2026

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# Experimental Determination of *L* Shell Fluorescence Yields and Coster-Kronig Transition Probabilities of Platinum

Ablaihan Utepov ID |

Marie-Christine Lépy ID |

Yves Ménesguen ID |

CEA, LIST, Laboratoire National Henri Becquerel (LNE-LNHB), Université Paris-Saclay, Palaiseau, France

**Correspondence:** Ablaihan Utepov (ablaihan.utepov@cea.fr)

**Received:** 24 October 2024 |

**Revised:** 23 July 2025 |

**Accepted:** 2 September 2025

**Funding:** This work was supported by INSNU project (CEA-DES/IRESNE).

**Keywords:** Coster-Kronig transition probabilities | *L* shell fluorescence yields | platinum | reference-free XRF measurements

## ABSTRACT

An accurate database of atomic fundamental parameters (FPs) is crucial for quantitative material analysis based on x-ray fluorescence (XRF). Given the wide range of applications and the limited reliability of existing experimental FPs for the *L* subshells of platinum, we determined its partial *L* fluorescence yields and Coster-Kronig transition probabilities using transmission and reference-free XRF measurements. The determined values are $\omega_{L3}=0.289$ (11), $\omega_{L2}=0.326$ (13), $\omega_{L1}=0.0820$ (34), $f_{23}=0.130$ (39), $f_{12}=0.158$ (40), and $f_{13}=0.37$ (18). These results show good agreement with certain tabulated values, and systematic trends are observed across atomic number *Z* for $\omega_{L3}$, $\omega_{L2}$, $f_{12}$, and $f_{13}$. The relative standard uncertainties for $\omega_{L2}$, $\omega_{L1}$, and $f_{12}$ have been significantly reduced compared to previous experimental studies. The use of tunable monochromatic photon beams and high-precision instrumentation allowed us to establish a reliable uncertainty budget for the determined results.

## 1 | Introduction

Reliable knowledge of atomic fundamental parameters (FPs), such as mass attenuation coefficients, photoionization cross-sections, fluorescence yields, and Coster-Kronig (CK) transition probabilities, is crucial for quantitative material analysis based on x-ray fluorescence (XRF). To date, a number of databases of the FPs exist [1–4] and are frequently used in many fields of physics and industrial applications. Most of the available FPs, however, date back to experimental and theoretical investigations performed more than 50 years ago and, due to technological limitations, their uncertainties are only estimated or are not quoted at all. Furthermore, although the available FPs represent good agreement at high photon energies ($>20$ keV), they exhibit significant differences at low photon energies and around absorption edges of most elements [5]. In addition, for some

elements, there are no available experimental data, forcing databases to rely solely on interpolated or theoretical values [6–9].

To improve the availability and the reliability of the FPs, the International Initiative on Fundamental Parameters (IIFP) [10] was created to encourage a series of new measurements, which are intended to provide an accurate database, benefiting primarily from the advent of tunable monochromatic photon beams of high spectral purity and high precision instrumentation. Over the past decade, a number of high precision measurements of FPs were conducted for different elements, particularly in the *K* shell [11–13] and *L* shell [14, 15] regions. For medium and heavy elements, experimental determinations of FPs were carried out for Sn [16], Sb [17], Dy [18], Hf [19], W [20], Re [21], Os [20], Th [22, 23], and U [22]. For the region of $75 \le Z \le 85$ of our interest, Kolbe et al. [24] and Ménesguen et al. [25] focused on the measurement of *L* shell

<footnote>This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.</footnote>

<footnote>© 2025 The Author(s). *X-Ray Spectrometry* published by John Wiley & Sons Ltd.</footnote>
fluorescence yields and CK transition probabilities for Au and Pb, and Bi, respectively. These studies were carried out using a monochromatic photon beam, radiometrically calibrated detectors, advanced analysis techniques, and provided a reliable uncertainty budget and enhanced our understanding of the FPs.

Despite these advancements, significant gaps remain, particularly for Pt, where reliable experimental data are still scarce. Platinum is one of the most valuable metals that has various applications in catalytic converters, medical equipment, fuel cells, electrical contacts, and electrodes; therefore, it is of high interest to be able to quantify its presence by non-destructive techniques such as XRF-based analysis. As a high-Z element, its quantification relies mostly on the measurement of the L lines. However, the reliability of the Pt FPs of the L shell leaves much to be desired. Especially, for partial L fluorescence yields and CK factors, rather limited experimental data are known, and their associated uncertainties are poorly studied for most of them: only one value for the CK transition probability $f_{12}$ [26], three for $f_{23}$ [26–28] and four for $f_{13}$ [26, 29–31] and for the partial fluorescence yield $\omega_{L1}$ [26, 32–34]. Therefore, as part of the IIFP, the LNE-LNHB, the French metrology institute for ionizing radiation, carried out a dedicated experiment. It includes transmission and reference-free XRF measurements to redetermine the Pt L subshell fluorescence yields as well as CK factors, providing a reliable uncertainty budget for the determined values.

## 2 | Partial L Fluorescence Yields and CK Transition Probabilities

The probability of XRF emission following ionization is described by the fluorescence production factor ($\sigma$). It combines the photoelectric cross-section ($\tau$), that is, the probability that an incident photon will ionize a specific atomic subshell, and the fluorescence yield ($\omega$), that is, the relative probability that fluorescence x-rays will be emitted when a vacancy of the given subshell is filled. The fluorescence production factor $\sigma$ depends on the energy of the incident photon, and for each $L_i$ subshell, it is defined as:

$$ \sigma_{Li}(E_0) = \omega_{Li} \tau_{eff,Li}(E_0) \quad (1) $$

where $\tau_{eff,Li}(E_0)$ is the effective partial photoelectric cross-section at incident photon energy $E_0$, and, depending on where $E_0$ lies relative to the absorption edges $E_{L1}$ of the respective $L_i$ subshells, $\tau_{eff,Li}(E_0)$ can be written as follows

For $E_{L3} \le E_0 \le E_{L2}$:

$$ \tau_{eff,L3}(E_0) = \tau_{L3}(E_0) \quad (2) $$

For $E_{L2} \le E_0 \le E_{L1}$:

$$ \tau_{eff,L3}(E_0) = \tau_{L3}(E_0) + \tau_{L2}(E_0)f_{23} \quad (3) $$

$$ \tau_{eff,L2}(E_0) = \tau_{L2}(E_0) \quad (4) $$

For $E_{L1} \le E_0$:

$$ \tau_{eff,L3}(E_0) = \tau_{L3}(E_0) + \tau_{L2}(E_0)f_{23} + \tau_{L1}(E_0)(f_{13} + f_{12}f_{23}) \quad (5) $$

$$ \tau_{eff,L2}(E_0) = \tau_{L2}(E_0) + \tau_{L1}(E_0)f_{12} \quad (6) $$

$$ \tau_{eff,L1}(E_0) = \tau_{L1}(E_0) \quad (7) $$

where the terms $f_{23}$, $f_{12}$ and $f_{13}$ stand for CK transition probabilities which characterize transitions occurring as a motion of vacancies from (more bound) inner to (less bound) outer L subshells. These transitions take place due to a transfer of small amount of energy to outer subshell electrons which then move to unoccupied states of inner subshells. The CK factors are irrelevant for $E_0$ below the absorption edge energy of the respective subshell. Using a monochromatic photon beam with a selected incident energy $E_0$, it is possible to excite a specific subshell and derive the partial fluorescence yield $\omega_{subshell}$. The CK factors can be then derived, for $E_0$ above the absorption edge energy of the respective subshell, by keeping the partial fluorescence yield $\omega_{subshell}$, determined previously without the presence of CK transitions, and by substituting the effective photoelectric cross-section $\tau_{eff,subshell}$ in Equation (1) depending on the considered subshell.

The fluorescence production factor $\sigma$ can be calculated thanks to the theoretical basis provided by Sherman [35], which describes the production and the emission of fluorescence x-ray lines from a thin single-elemental foil irradiated by a beam of monochromatic photons $E_0$:

$$ \sigma_{Li}(E_0) = \omega_{Li} \tau_{eff,Li}(E_0) = \sum_{j=1}^{n} \frac{4\pi I_j}{\Omega \epsilon_j I_0} \frac{\mu_0 + \mu_j \frac{\cos(\alpha_m)}{\cos(\alpha_{out})}}{1 - \exp\left(-\frac{M}{A}\left(\frac{\mu_0}{\cos(\alpha_m)} + \frac{\mu_j}{\cos(\alpha_{out})}\right)\right)} \quad (8) $$

where $I_j$ are the intensities for fluorescence x-rays with energy $E_j$, and $\epsilon_j$ is the detection efficiency at photon energy $E_j$, $\Omega$ is the detection solid angle considering a narrow beam, that is, the detector is far enough from the volume source to consider that all points of its entrance side are seen with the same solid angle, $I_0$ is the number of photons in the beam per unit time, $\mu_0$ and $\mu_j$ are the mass attenuation coefficients at photon energy $E_0$ and $E_j$, respectively, A is the area of the target and M is its mass, $\alpha_{in}$ and $\alpha_{out}$ are the angles of the incoming beam photons and the outgoing fluorescence x-rays, respectively, relative to the normal of the target, see Figure 1 (left). The subscript j denotes the XRF emission. By summing the contributions over the all n XRF emission lines corresponding to a given subshell $L_i$, one can obtain the total fluorescence production factor $\sigma_{Li}$.

## 3 | Experimental Procedure

### 3.1 | Beam Characteristics

The experiment was carried out in a vacuum chamber installed on the hard x-rays branch [36] of the Metrology beamline [36, 37] of the SOLEIL synchrotron facility, France. This branch is equipped with a double Si(111) crystal monochromator. It was tuned to provide a beam of monochromatic x-ray radiation in the energy range from 12.2 to 20 keV, around the L subshell absorption edges of platinum. Its energy calibration
<figure><img src="image_3.png" /><figcaption>**FIGURE 1** | Left: Schematic view of the experimental setup. Right: Design layout of the chamber and the target holder (view from the direction of the beam). The target is placed at $\theta_t = 45^\circ$ and $\phi_t = 45^\circ$ relative to the beam direction and, thus, the angle of the incoming monochromatic X-ray radiation is $\alpha_{in} = 60^\circ$ with respect to the normal incidence $\vec{l}_t$ of the target. The holder was designed and prepared in-house specially for this experiment to use the Pt target in such a configuration allowing a simultaneous measurement of outgoing XRF photons with two energy-dispersive detectors: SDD and HPGe detectors at $\alpha_{out}^{SDD} = 45^\circ$ and $\alpha_{out}^{HPGe} = 60^\circ$ relative to the normal incidence $\vec{l}_t$ of the target, respectively. The data of the latter are not discussed in the analysis (see text for details). [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

involves establishing the relationship between its (Bragg) angle and the photon energy. This is performed by scanning around the absorption edge energies of several pure elements, with energy reference values taken from tables in Reference [38]. The relative difference between the tabulated and the calibrated values is less than 0.04%. The fluctuation of the synchrotron beam current is less than 0.4% thanks to its “top-up” mode operation during which electron bunches are regularly injected [5]. The beam spot size of $0.2 \times 0.2 \text{ mm}^2$ was kept throughout the measurement using horizontal and vertical slits upstream of the vacuum chamber.

## 3.2 | Target Characteristics

A platinum foil target, purchased from Goodfellow [39], with a purity of about 99.95%, a surface area of $12 \times 25 \text{ mm}^2$ and a nominal thickness of $12.5 \text{ µm}$ was used. The selection of the thickness was based on the availability of materials at the time of the experiment. In the present work, the target was mounted inside the vacuum chamber on the holder at $\theta_t = 45^\circ$ and $\phi_t = 45^\circ$ with respect to the beam axis. This configuration differs from the conventional geometry ($\alpha_{in} = 45^\circ$ and $\alpha_{out} = 45^\circ$) as the angle of the incoming beam is $\alpha_{in} = 60^\circ$ with respect to the normal incidence ($\vec{l}_t$) of the target and it enables a simultaneous detection of outgoing XRF photons with two energy-dispersive detectors. The target holder was specifically designed and fabricated in-house for the present experiment, see Figure 1 (right).

## 3.3 | Detection Setup

The detection setup consisted of two photodiodes, placed upstream and downstream the target, for transmission measurements, and of two energy-dispersive detectors for XRF measurements: a silicon drift detector (SDD) and a high-purity germanium detector (HPGe) installed inside the vacuum chamber at $\alpha_{out}^{SDD} = 45^\circ$ and $\alpha_{out}^{HPGe} = 60^\circ$ relative to the normal incidence $\vec{l}_t$ of the target, respectively, and perpendicular to the beam axis.

The use of two energy-dispersive detectors, measuring XRF photons at the same time, was intended to cross-validate the results. However, the x-ray peaks recorded by the HPGe detector was saturated by a high count rate, possibly caused by its close proximity to the target, which degraded its energy resolution and prevented from unambiguously quantifying the peaks of interest. Consequently, only the data from the SDD detector are discussed in the following analysis. All the photodiodes and the energy-dispersive detectors have reference-free radiometrically calibrated intrinsic efficiencies provided with a relative standard uncertainty of about 1% [40, 41] in the region of interest. Figure 1 shows a schematic illustration and a design layout of the setup.

## 3.4 | Transmission Measurements

Transmission measurements were performed in order to determine the mass attenuation coefficients ($\mu$) of Pt with well-controlled uncertainty. It represents the probability of interaction of a photon beam in matter, which is essential for the determination of partial L fluorescence yields and CK factors, as described in Equation (8). It depends on the energy of the photon beam and on the material composition. It incorporates significant interaction processes such as photoelectric absorption, Compton and Rayleigh scattering. The total attenuation of a collimated monochromatic photons under normal incidence at the surface of a target material is governed by Beer-Lambert law:

$$ \frac{\mu}{\rho}(E_0) = - \frac{1}{\rho l_{\text{eff}}} \times \ln\left(\frac{I_t}{I_0}\right) = - \frac{A}{M} \times \ln\left(\frac{I_t}{I_0}\right) \quad (9) $$

where $\mu(E_0)$ is the energy-dependent mass attenuation coefficient, $l_0$ and $l_t$ are the incident and the transmitted photon intensities, respectively, $\rho$ and $l_{\text{eff}}$ are the target density and its effective thickness, A and M being the area and the mass of the target material. In the present experiment, the thickness of the Pt target, on the order of $\mu m$, posed a challenge for direct measurement with high precision (<<0.1%). Instead, the mass of the
<table><caption>**TABLE 1** | Platinum target characteristics. The effective thickness $l_{\text{eff}}$ is equal to 26.8 (7) µm ($l_{\text{eff}} = \frac{l}{\cos(\alpha_{\text{in}})}$), accounting for the thickness homogeneity.</caption><thead><tr><th>Nominal thickness (µm)</th><th>Mass (mg)</th><th>Area (mm²)</th><th>Derived mean thickness (l) (µm)</th></tr></thead><tbody><tr><td>12.5</td><td>90.76 (9)</td><td>315.23 (6)</td><td>13.422 (14)</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>**FIGURE 2** | Left: Comparison of the experimental mass attenuation coefficients obtained in this work and in 2017 [42]. A closer view of the region of interest is shown in the inset. The *L* subshell absorption edges are indicated. Right: Comparison of the experimental results from 2017 and database values (DB) from XCOM [3], CXRO [8], and EPDL97 [43]. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

target was measured using a calibrated microbalance, while the area was determined using a calibrated vision machine, which included a microscope and a dedicated picture analyzer. This approach enabled precise determination of both mass and area, with relative uncertainties of about 0.1% and 0.02%, respectively, allowing to derive the mean thickness of the target with a relative standard uncertainty of about 0.1%. To verify the homogeneity of the thickness, measurements were carried out using a vertical thickness gauge over the whole target area. The measured values reveal the homogeneity of the thickness is 2.6%. The measured characteristics of the Pt target are given in Table 1.

The absorption edge energies of the *L* subshells of Pt are 11.56, 13.27, and 13.88 keV for $L_3$, $L_2$, and $L_1$, respectively [38]. In this experiment, the energy of the beam was selected to cover the region around these absorption edges. At each energy, the incident photon intensity $I_0$ was measured using the calibrated photodiode placed upstream of the target. This photodiode was then removed, and the transmitted photon intensity $I_t$ was measured using another calibrated photodiode placed downstream of the target. Each of the $I_0$ and $I_t$ values was obtained as the mean over 10 acquisitions. Therefore, in addition to about 1% of the relative standard uncertainty associated with the photodiode efficiency, we acknowledged the standard deviation resulting from the statistics associated with the $I_0$ and $I_t$ values introduced by their respective photodiodes: no more than 0.98% and 31% for the $I_0$ and $I_t$ intensities, respectively. The high uncertainties in $I_t$ are attributed to the measured intensities approaching the lower detection limit of the photodiode at several beam energies. In contrast, $I_0$ measurements remained well within the optimal range of the photodiode, resulting in significantly lower uncertainties.

The determined mass attenuation coefficients as a function of selected beam energies are shown in Figure 2 (left). The combined standard uncertainties were derived using the uncertainty propagation procedure specified in the Guide to the Expression of Uncertainty in Measurement (GUM) [44]. The relative standard uncertainties remain below 3% for most of the values, with some increasing up to 6.7%, which is dominated by the aforementioned $I_t$ and target thickness homogeneity contributions. The results of the present experiment, conducted with an effective target thickness $l_{\text{eff}}$ of 26.8 (7) µm, are compared with those obtained by our group in 2017 [42] using thinner targets ($l_{\text{eff}} = 3.1271$ (30) µm and 13.748 (6) µm), as shown in Figure 2 (left). The two datasets are in agreement, except for a few points close to the $L_2$ absorption edge. While the present target thickness leads to low transmission and is therefore not optimized for minimizing the relative uncertainty of transmission measurements, the 2017 dataset, with relative standard uncertainties of less than 1% in the region of interest, provides reliable mass attenuation coefficients. Consequently, the 2017 dataset will be used in further analysis. Although the transmission measurements of the present work are not directly included in the final results, they allow to verify the performance of the photodiodes, ensuring the validity of the data. In particular, the $I_0$ intensity data from this experiment, with a relative standard uncertainty of no more than 1.24%, will be used in further analysis.

Figure 2 (right) shows a comparison of the experimental mass attenuation coefficients from 2017 with database values from XCOM [3], CXRO [8], and EPDL97 [43] by plotting the relative differences ($\mu_{\text{exp}} - \mu_{\text{database}}$)/$\mu_{\text{database}}$×100. Significant discrepancies are observed between the experimental data and the database values for energies below the $L_3$ absorption edge. However, above
<figure><img src="image_5.png" /><figcaption>**FIGURE 3** | Photoelectric cross-sections of Pt, obtained by combining the database cross-section ratios from EPDL97 [43] and the experimental mass attenuation coefficients, as a function of photon energy. Shaded regions indicate the contributions from the *L*<sub>3</sub>, *L*<sub>2</sub>, and *L*<sub>1</sub> subshells via the exponential polynomial extrapolation (see text for details). [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

$L_3$ absorption edge, there is good agreement for the EPDL97 and XCOM data up to 30 keV. In contrast, the CXRO data underestimates the mass attenuation coefficients by about 2% across most of the region. Similar to observations for Cu and Zn [5], large differences are also observed among the three database values near absorption edges relative to the experimental data.

Another essential interaction mechanism required to determine
partial *L* fluorescence yields and CK factors is the photoelectric
cross-section *τ*, as described in Equations (1–8). Unlike mass
attenuation coefficients, photoelectric cross-sections are not
accessible through direct measurement, independently from
the fluorescence yields. Therefore, following the approach de-
scribed in Reference [24], it was derived using database mass
attenuation coefficients and photoelectric cross-sections ratios
taken from EPDL97 [43] combined with the measured mass
attenuation coefficients: $\tau = \mu_{\text{LNHB2017}} \frac{\tau_{\text{EPDL97}}}{\mu_{\text{EPDL97}}}$.
In this way, this
approach ensures that the derived photoelectric cross-sections
rely only on relative, rather than absolute, database values. To
determine contributions of each *L* subshells, the photoelectric
cross-sections were extrapolated using an exponential polyno-
mial function: $\tau_{\text{subshell}} = \exp(a_{\text{subshell}} + b_{\text{subshell}} \ln(E))$, where *E*
is the photon energy, $a_{\text{subshell}}$ and $b_{\text{subshell}}$ are the coefficients
determined by the fitted function. The obtained photoelectric
cross-sections are shown in Figure 3. The relative standard un-
certainties for each *L* subshells are around 2%, which include
relative standard uncertainties of 2% and 1% corresponding to
the database-related cross-sections (see Reference [24]) and to
the experimental mass attenuation coefficients, respectively.

**3.5** | Reference-Free XRF Measurements

In addition to the transmission measurements, XRF photons
emitted from the Pt target were recorded using a reference-free
calibrated SDD detector. The measurements were carried out in-
crementally, increasing the beam energy to perform a selective

ionization of the *L*<sub>3</sub>, *L*<sub>2</sub>, and *L*<sub>1</sub> subshells, allowing for the deter-
mination of partial *L* shell fluorescence yields and CK factors.
The solid angle of the SDD detector was calculated with a rel-
ative standard uncertainty of 1.07%, thanks to the well-defined
target-detector distance and the radiographically determined
diameter of the collimator within the detector [45].

Figure 4 shows the XRF spectra of Pt for three beam energy ranges: between the *L*<sub>3</sub> and *L*<sub>2</sub> edges, between the *L*<sub>2</sub> and *L*<sub>1</sub> edges, and above the *L*<sub>1</sub> edge. In order to extract the intensities, the x-ray peaks for each *L* subshell were fitted by means of Colegram software [46] using Voigt functions. Each of these functions is a convolution of Gaussian and Lorentzian functions accounting for the detector response and x-ray natural linewidths, respectively. Literature values for Pt *L* lines used as input parameters for the fitting are given in Table 2. The x-ray line energies were taken from Reference [38] for all lines except for the ones associated with the *O*<sub>1,2,3,4</sub> final shell vacancies; the energies corresponding to those were determined from the atomic shell binding energy difference given in Reference [47]. The x-ray natural linewidths were obtained as the sum of atomic level widths taken from Reference [48]. Background contributions in each spectrum were processed taking into account the step due to the presence of a peak. The relative standard uncertainty of the extracted intensities is below 1%. It is primarily influenced by counting statistics, while the contribution from spectral deconvolution is negligible (<0.3%). This is thanks to the fitting procedure described in Reference [49], which accounts for the variation of the instrumental width with energy and allows the standard deviation of the Gaussian function for overlapping peaks to be constrained, ensuring accurate determination of individual peak areas.

For beam energies between the *L*<sub>3</sub> and *L*<sub>2</sub> edges, there are eight x-ray lines associated with the *L*<sub>3</sub> subshell, see Figure 4 (top panel). The *L*<sub>1</sub>, *L*α<sub>2,1</sub>, *L*β<sub>6</sub>, *L*β<sub>15,2</sub>, *L*β<sub>7,5</sub> peaks were identified by the fit, along with the *L*α<sub>2,1</sub> escape peak. However, the peaks corresponding to the *L*<sub>1</sub> and *L*<sub>2</sub> lines were not identified as they are overlapped by the *L*<sub>1</sub> and *L*α<sub>2,1</sub> peaks. To account for these unidentified peaks, their intensities were calculated using the measured *L*β<sub>15,2</sub> intensity and tabulated emission rate ratios from Reference [44], see Table 2.

For beam energies between the *L*₂ and *L*₁ edges, in addition
to the *L*₃ subshell lines, six x-ray lines are present belonging
to the *L*₂ subshell, see Figure 4 (middle panel). The *L*η, *L*β₁,
*L*γ₅, *L*γ₁, *L*γ₈,₆ peaks were identified by the fit. The latter was
distinctly identified only in the spectrum for the beam energy
close to the *L*₁ edge. At lower beam energies, the peak cor-
responding to Rayleigh scattered beam overlapped the one of
*L*γ₈,₆. In such cases, the *L*γ₈,₆ intensity was deduced based on
the measured *L*η intensity and their intensity ratio from the
aforementioned distinctly identified spectrum. The fit could
not distinguish the peak belonging to the *L*β₁₇ line. Its con-
tribution was therefore determined using the measured *L*γ₅
intensity and their tabulated emission rates ratio. Concerning
the *L*₃ subshell lines, the same procedure as mentioned ear-
lier was applied for all the peaks apart from the *L*β₆ and *L*β₁₅,₂
ones. These two were not identified and their intensities were
obtained thanks to the averaged ratio of the previously mea-
sured *L*β₆/*L*α₂,₁ and *L*β₁₅,₂/*L*α₂,₁ intensities as well as the mea-
sured intensity of *L*α₂,₁.
<figure><img src="image_6.png" /><figcaption>**FIGURE 4** | Pt XRF spectra, measured using the SDD detector, at three beam energies exciting the lines contributing from the *L*<sub>3</sub> (top panel), *L*<sub>3</sub> and *L*<sub>2</sub> (middle panel), and *L*<sub>3</sub>, *L*<sub>2</sub> and *L*<sub>1</sub> (bottom panel) subshells. The x-ray lines belonging to each subshell are indicated with different colors. The peaks indicated in gray correspond to the x-ray lines of the chamber materials. The peaks corresponding to Rayleigh scattered beam are indicated with solid lines. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

For beam energies above the *L*₁ edge, there are six x-ray lines corresponding to the *L*₁ subshell, along with the ones of the *L*₃ and *L*₂ subshells, see Figure 4 (bottom panel). Only the *L*γ₄ peak could be clearly identified. Peaks for *L*β₄, *L*β₃, *L*β₁₀,₉, *L*γ₂, and *L*γ₃ were indistinguishable due to overlap with *L*₃ and *L*₂ subshell lines. In particular, the *L*β₄, *L*β₃, and *L*γ₂ peaks were completely masked by *L*β₀, *L*β₁₅,₂, and *L*γ₈,₆, respectively. The contributions of these overlapping peaks were determined by subtracting the intensity of the latter peaks. The intensities of *L*β₁₀,₉ and *L*γ₃ were obtained using their tabulated emission rate ratios relative to that of *L*γ₄ together with the measured intensity of *L*γ₄. For the *L*₃ and *L*₂ subshell lines, the only notable changes were in the intensities of the *L*β₇,₅, *L*β₁, and *L*γ₅ peaks, which were determined using the measured intensities of *L*α₂,₁ and *L*η, combined with the average ratios of *L*β₇,₅/*L*α₂,₁, *L*β₁/*L*η, and *L*γ₅/*L*η intensities measured at beam energies below the *L*₁ edge.

In all spectra, regardless of beam energy, several peaks below 8 keV were identified as x-ray lines from the chamber materials such as Ni, Fe, Mn, and Cr. The contribution of the *K*β₃,₁ line of Ni was subtracted from the Pt peaks by calculating its intensity using the measured *K*α₂,₁ intensity and the ratio of their tabulated emission rates from Reference [7], see Table 2. For the intensities of lines extracted by means of the tabulated emission ratios, an additional 1% of uncertainty was added. However, these lines are less intense compared to others of the respective subshell and therefore have a negligible impact on the final results.

**4 | Results and Discussion**

To derive the fluorescence yield of each line, the extracted intensities for the corresponding *L* subshell x-ray line were normalized using the detection efficiency, solid angle of detection, incident photon intensity, Pt target thickness, mass attenuation coefficients, effective partial photoelectric cross-sections, and the angles of incidence and detection, as described in Equation (8). For the fluorescence production factor without CK transitions, the fluorescence yields of all corresponding lines were summed to obtain the total fluorescence yield for that subshell. For the fluorescence production factor with CK transitions, the CK factors were determined by using the obtained fluorescence yields and adjusting the effective partial photoelectric cross-section in Equation (8) according to the specific CK transition: for *f*<sub>23</sub>, *f*<sub>12</sub>, and *f*<sub>13</sub>, the effective partial photoelectric cross-sections from Equations (3), (6), and (5), respectively, were applied.

Figure 5 shows the partial L shell fluorescence yields $\omega_{L3}$, $\omega_{L2}$, $\omega_{L1}$ and the CK transition probabilities $f_{23}$, $f_{12}$, $f_{13}$ of Pt measured at different beam energies. It is evident that CK factors play a crucial role in determining $\omega_{L3}$ and $\omega_{L2}$ at energies above the $L_2$ and $L_1$ edges, respectively. The omission of CK factors leads to incorrect values for $\omega_{L3}$ and $\omega_{L2}$. The final values were obtained by taking the mean of the results from measurements at different beam energies. The derived fluorescence yields and CK
<table><caption>**TABLE 2** | Literature energies, natural linewidths and emission rates for the L shell x-ray lines of platinum (see text for details).</caption><thead><tr><th>Line</th><th>Transition</th><th>Energy (keV)</th><th>Natural linewidth (eV)</th><th>Emission rates (eV/ħ)</th></tr></thead><tbody><tr><td>Ll</td><td>L<sub>3</sub>M<sub>1</sub></td><td>8.2682 (16)</td><td>20.29</td><td>0.0632</td></tr><tr><td>Lt</td><td>L<sub>3</sub>M<sub>2</sub></td><td>8.5329 (17)</td><td>14.59</td><td>0.0007</td></tr><tr><td>Ln</td><td>L<sub>3</sub>M<sub>3</sub></td><td>8.9228 (19)</td><td>13.69</td><td>0.00063</td></tr><tr><td>Lα<sub>2</sub></td><td>L<sub>3</sub>M<sub>4</sub></td><td>9.36196 (21)</td><td>7.47</td><td>0.1299</td></tr><tr><td>Lα<sub>1</sub></td><td>L<sub>3</sub>M<sub>5</sub></td><td>9.44239 (32)</td><td>7.47</td><td>1.145</td></tr><tr><td>Lη</td><td>L<sub>2</sub>M<sub>1</sub></td><td>9.9752 (24)</td><td>20.28</td><td>0.0397</td></tr><tr><td>Lβ<sub>17</sub></td><td>L<sub>2</sub>M<sub>3</sub></td><td>10.6268 (13)</td><td>13.68</td><td>0.00147</td></tr><tr><td>Lβ<sub>6</sub></td><td>L<sub>3</sub>N<sub>1</sub></td><td>10.84188 (70)</td><td>13.64</td><td>0.01537</td></tr><tr><td>Lβ<sub>4</sub></td><td>L<sub>1</sub>M<sub>2</sub></td><td>10.85441 (70)</td><td>18</td><td>0.348</td></tr><tr><td>Lβ<sub>1</sub></td><td>L<sub>2</sub>M<sub>4</sub></td><td>11.07084 (29)</td><td>7.46</td><td>1.471</td></tr><tr><td>Lβ<sub>3</sub></td><td>L<sub>1</sub>M<sub>3</sub></td><td>11.23089 (75)</td><td>17.1</td><td>0.409</td></tr><tr><td>Lβ<sub>15</sub></td><td>L<sub>3</sub>N<sub>4</sub></td><td>11.2334 (24)</td><td>9.49</td><td>0.02351</td></tr><tr><td>Lβ<sub>2</sub></td><td>L<sub>3</sub>N<sub>5</sub></td><td>11.25066 (45)</td><td>9.34</td><td>0.2117</td></tr><tr><td>Lβ<sub>7</sub></td><td>L<sub>3</sub>O<sub>1</sub></td><td>11.4621</td><td>5.39</td><td>0.00303</td></tr><tr><td>Lβ<sub>5</sub></td><td>L<sub>3</sub>O<sub>4</sub></td><td>11.5617</td><td>5.39</td><td>0.01785</td></tr><tr><td>Lβ<sub>6</sub></td><td>L<sub>3</sub>O<sub>5</sub></td><td>11.5617</td><td>5.39</td><td>0.01785</td></tr><tr><td>Lβ<sub>10</sub></td><td>L<sub>1</sub>M<sub>4</sub></td><td>11.6763 (11)</td><td>10.88</td><td>0.0113</td></tr><tr><td>Lβ<sub>9</sub></td><td>L<sub>1</sub>M<sub>5</sub></td><td>11.75679 (22)</td><td>10.88</td><td>0.01692</td></tr><tr><td>Lγ<sub>5</sub></td><td>L<sub>2</sub>N<sub>1</sub></td><td>12.5526 (38)</td><td>13.63</td><td>0.01003</td></tr><tr><td>Lγ<sub>1</sub></td><td>L<sub>2</sub>N<sub>4</sub></td><td>12.94219 (38)</td><td>9.48</td><td>0.2871</td></tr><tr><td>Lγ<sub>8</sub></td><td>L<sub>2</sub>O<sub>1</sub></td><td>13.1709</td><td>5.38</td><td>0.00199</td></tr><tr><td>Lγ<sub>6</sub></td><td>L<sub>2</sub>O<sub>4</sub></td><td>13.2705</td><td>5.38</td><td>0.02293</td></tr><tr><td>Lγ<sub>2</sub></td><td>L<sub>1</sub>N<sub>2</sub></td><td>13.2705 (11)</td><td>15.05</td><td>0.0876</td></tr></tbody></table>

(Continues)

<table><caption>**TABLE 2** | (Continued)</caption><thead><tr><th>Line</th><th>Transition</th><th>Energy (keV)</th><th>Natural linewidth (eV)</th><th>Emission rates (eV/ħ)</th></tr></thead><tbody><tr><td>Lγ<sub>3</sub></td><td>L<sub>1</sub>N<sub>3</sub></td><td>13.3615 (11)</td><td>13.7</td><td>0.1104</td></tr><tr><td rowspan="2">Lγ<sub>4</sub></td><td>L<sub>1</sub>O<sub>2</sub></td><td>13.8152</td><td>8.8</td><td>0.01528</td></tr><tr><td>L<sub>1</sub>O<sub>3</sub></td><td>13.8295</td><td>8.8</td><td>0.01867</td></tr></tbody></table>

factors are $ω_{L3}=0.289$ (11), $ω_{L2}=0.326$ (13), $ω_{L1}=0.0820$ (34), $f_{23}=0.130$ (39), $f_{12}=0.158$ (40), and $f_{13}=0.37$ (18).

The results of this work are compared with literature values for Pt in Table 3 and Figure 6. The derived values for $ω_{L3}$, $ω_{L2}$, $f_{23}$, and $f_{13}$ show agreement with most published data, although some discrepancies are present, which could arise due to limitations of theoretical models, as well as due to lower accuracy of experimental instrumentation used in earlier studies. The values of $ω_{L1}$ and $f_{12}$, while being different from previously reported experimental data, align well with certain theoretical calculations and compilations. In particular, the $ω_{L1}$ value is significantly lower than those reported in References [26, 32–34], while the CK factor $f_{12}$ is higher than the only other reported value in Reference [26].

Figure 7 shows a comparison of the results of the present work with those obtained for adjacent elements, particularly Au and Pb [24] and Bi [25]. It illustrates that the determined partial L shell fluorescence yields and CK transition probabilities for Pt follow the expected trends across atomic number Z indicated by experimental data, theoretical calculations, and compilations. In particular, the values of $ω_{L3}$ and $ω_{L2}$ for Pt align well with the systematic decrease observed from Bi to Au. It supports the consistency of the results of the present work with established trends in high-Z elements. For the CK factors, the measured values for $f_{12}$ and $f_{13}$ exhibit continuity with the existing experimental data, reflecting the expected increase and decrease, respectively, in CK transition probabilities as atomic number decreases. However, for $ω_{L1}$, a slightly larger deviation is observed compared to Au, Pb, and Bi, while for $f_{23}$, a systematic trend is not evident. For the latter, it is required to reduce the associated uncertainties to draw definitive conclusions. Thus, a further investigation of these values as a function of atomic number could provide deeper insight into their behavior and improve the accuracy of FP data for high-Z elements.

The contributions of individual relative standard uncertainties to the combined standard uncertainty budget, as shown in Figure 8 and Table 4, were evaluated using the GUM's uncertainty propagation procedure. This study has significantly reduced the relative standard uncertainties compared to previous investigations. In particular, for the partial fluorescence yields $ω_{L2}$, $ω_{L1}$ and for CK factor $f_{12}$ the uncertainties have been improved from 4.97% [28], 6% [26], and 30.3% [26] to 3.99%, 4.15%, and 25.32%, respectively. For $ω_{L3}$, the uncertainty (3.81%) in this work is comparable to the previously achieved value of 2.45%
<figure><img src="image_7.png" /><figcaption>**FIGURE 5** | Partial *L* shell fluorescence yields *ω*<sub>L3</sub>, *ω*<sub>L2</sub>, *ω*<sub>L1</sub> and CK factors *f*<sub>23</sub>, *f*<sub>12</sub>, and *f*<sub>13</sub> of Pt at different beam energies. The mean of the values and the associated uncertainties are indicated with horizontal dashed lines and shaded regions, respectively. CK On or CK Off refer to whether CK factors are applied or not, respectively, in Equations (1–8). The *L*<sub>2</sub> and *L*<sub>1</sub> absorption edges are indicated. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

[28]. However, for the CK factors *f*<sub>23</sub> and *f*<sub>13</sub>, the relative standard uncertainties (30% and 48.65%, respectively) are higher than those reported in earlier studies (5.36% [28] and 3.56% [26]). It is important to point out that one of the dominant contributions, up to 2.14% of uncertainties, arises from the partial photoelectric cross-sections because, as previously mentioned, they cannot be measured directly, forcing the reliance on relative values of tabulated data. In addition, the large uncertainties in the CK factors are primarily due to those of partial photoelectric cross-sections contributing from different subshells to the uncertainty budget. Despite these larger uncertainties, this work presents the first uncertainty budget for Pt *L* shell FPs that rigorously adheres to the GUM, thereby ensuring greater reliability. Future progress in reducing CK factor uncertainties could be made by using the novel holistic approach recently employed by Hönicke [15], which has demonstrated the ability to lower CK factor uncertainties for Ru from the range of 17%–42% to below 4%–13% when compared to conventional methods. Applying this approach to our data is a subject for potential future analysis.

**5 | Conclusion**

In this paper, we present the fluorescence yields and CK transition probabilities for the *L* subshell of platinum determined primarily using tunable monochromatic photon beams and high precision instrumentation. The measurements were carried out via transmission and XRF techniques using a detection setup with reference-free radiometrically calibrated detection efficiencies. It should be emphasized that the results were obtained without reliance on any absolute atomic FPs from the literature.

Our findings indicate good agreement between most of the tabulated values for $\omega_{L3}$, $\omega_{L2}$, $f_{23}$, and $f_{13}$ of Pt, while for its $\omega_{L1}$ and $f_{12}$, although deviations from existing experimental data were observed, the results align well with certain theoretical and compiled values. It is important to note that this work marks only the second time that the CK factor $f_{12}$ has been experimentally determined.

By comparing our determined values with those of adjacent elements, we observed systematic trends for $\omega_{L3}$, $\omega_{L2}$, $f_{12}$, and $f_{13}$ across atomic number *Z*, reinforcing the reliability of our measurements. However, a slightly larger deviation was found for $\omega_{L1}$, while the trend for $f_{23}$ is less clear, suggesting that further studies with reduced uncertainties are needed to confirm its scaling behavior.

We achieved significant improvements in the relative standard uncertainties for the experimental partial *L* fluorescence yields $\omega_{L2}$, $\omega_{L1}$ and for the CK factor $f_{12}$, while for $\omega_{L3}$ the obtained uncertainty is comparable to the previously achieved value. However, this was not the case for the CK factors $f_{23}$ and $f_{13}$, where large uncertainties remain. The uncertainties for CK factors primarily arise from contributions of partial photoelectric cross-sections from different subshells, which propagate through the uncertainty budget. A potential improvement in the relative uncertainties of the CK factors could be realized by applying the recently employed novel holistic approach [15], which may be explored in future analysis. Nevertheless, the uncertainty budget presented in this work is the first to be rigorously derived for the Pt *L* shell FPs in accordance with the GUM, enhancing in this way the overall reliability of the results.
<table><caption>**TABLE 3** | Partial *L* shell fluorescence yields *ω*<sub>*L*3</sub>, *ω*<sub>*L*2</sub>, *ω*<sub>*L*1</sub>, and CK factors *f*<sub>23</sub>, *f*<sub>12</sub>, and *f*<sub>13</sub> of platinum derived in the present work compared with values from the literature.</caption><thead><tr><th>Author (year)</th><th>Origin</th><th>ω<sub>L3</sub></th><th>ω<sub>L2</sub></th><th>ω<sub>L1</sub></th><th>f<sub>23</sub></th><th>f<sub>12</sub></th><th>f<sub>13</sub></th></tr></thead><tbody><tr><td>Küstner (1935) [32]</td><td>Lit. Exp</td><td>0.262</td><td>0.274</td><td>0.392</td><td></td><td></td><td></td></tr><tr><td>Roos (1959) [33]</td><td>Lit. Exp</td><td>0.275 (3)</td><td>0.31 (4)</td><td>0.35 (8)</td><td></td><td></td><td></td></tr><tr><td>Listengarten (1960) [291]</td><td>Lit. Exp</td><td></td><td></td><td></td><td></td><td></td><td>0.58 (12)</td></tr><tr><td>Jopson (1964) [50]</td><td>Lit. Exp</td><td>0.31 (4)</td><td>0.46 (7)</td><td></td><td></td><td></td><td></td></tr><tr><td>Ferreira (1965) [30]</td><td>Lit. Exp</td><td></td><td></td><td></td><td></td><td></td><td>0.50 (5)</td></tr><tr><td>Price (1968) [51]</td><td>Lit. Exp</td><td>0.317 (29)</td><td>0.341 (53)</td><td></td><td></td><td></td><td></td></tr><tr><td>Mohan (1972) [27]</td><td>Lit. Exp</td><td>0.309 (20)</td><td>0.318 (22)</td><td></td><td>0.126 (21)</td><td></td><td></td></tr><tr><td>McGhee (1988) [28]</td><td>Lit. Exp</td><td>0.286 (7)</td><td>0.342 (17)</td><td></td><td>0.112 (6)</td><td></td><td></td></tr><tr><td>Werner (1988) [26]</td><td>Lit. Exp</td><td>0.294 (12)</td><td>0.349 (21)</td><td>0.130 (8)</td><td>0.104 (20)</td><td>0.066 (20)</td><td>0.562 (20)</td></tr><tr><td>Xu (1991) [34]</td><td>Lit. Exp</td><td>0.284 (11)</td><td>0.341 (17)</td><td>0.112 (11)</td><td></td><td></td><td></td></tr><tr><td>Singh (2002) [31]</td><td>Lit. Exp</td><td></td><td></td><td></td><td></td><td></td><td>0.527 (27)</td></tr><tr><td>McGuire (1971) (interpolated) [52]</td><td>Lit. Th.</td><td>0.3152</td><td>0.343</td><td>0.107</td><td>0.1302</td><td>0.1054</td><td>0.5816</td></tr><tr><td>Chen (1981) (interpolated) [53]</td><td>Lit. Th.</td><td>0.301</td><td>0.342</td><td>0.10033</td><td>0.131</td><td>0.10767</td><td>0.58667</td></tr><tr><td>Puri (1993) [54]</td><td>Lit. Th.</td><td>0.303</td><td>0.344</td><td>0.074</td><td>0.132</td><td>0.067</td><td>0.716</td></tr><tr><td>Krause (1979) [55]</td><td>Lit. Comp.</td><td>0.306 (15)</td><td>0.321 (16)</td><td>0.114 (17)</td><td>0.124 (19)</td><td>0.140 (28)</td><td>0.50 (5)</td></tr><tr><td>Hanke (1985) [56]</td><td>Lit. Comp.</td><td>0.284</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Fink (1991) (fitted values) [57]</td><td>Lit. Comp.</td><td>0.301</td><td>0.317</td><td></td><td></td><td></td><td></td></tr><tr><td>Perkins (1991) [58]</td><td>Lit. Comp.</td><td>0.30704</td><td>0.34905</td><td>0.07942</td><td></td><td></td><td></td></tr><tr><td>Xraylib (2011) [4]</td><td>Lit. Comp.</td><td>0.306</td><td>0.321</td><td>0.114</td><td>0.126</td><td>0.075</td><td>0.545</td></tr><tr><td><strong>This work (2025)</strong></td><td><strong>Exp</strong></td><td><strong>0.289 (11)</strong></td><td><strong>0.326 (13)</strong></td><td><strong>0.0820 (34)</strong></td><td><strong>0.130 (39)</strong></td><td><strong>0.158 (40)</strong></td><td><strong>0.37 (18)</strong></td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>**FIGURE 6** | Partial *L* shell fluorescence yields *ω*<sub>*L*3</sub>, *ω*<sub>*L*2</sub>, *ω*<sub>*L*1</sub> and CK factors *f*<sub>23</sub>, *f*<sub>12</sub>, and *f*<sub>13</sub> for Pt derived in the present work compared with values from the literature. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>**FIGURE 7** | Partial *L* shell fluorescence yields *ω*<sub>*L*3*</sub>, *ω*<sub>*L*2*</sub>, *ω*<sub>*L*1*</sub> and CK factors *f*<sub>23</sub>, *f*<sub>12</sub>, and *f*<sub>13</sub> of Pt, derived in the present work, compared with those of adjacent elements from the literature. The dashed lines are drawn to guide the eye over the experimental values, illustrating systematic trends observed across atomic number *Z* for *ω*<sub>*L*3*</sub>, *ω*<sub>*L*2*</sub>, *f*<sub>12</sub>, and *f*<sub>13</sub> (see text for details). [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**FIGURE 8** | Individual relative standard uncertainties contributing to the combined standard uncertainty budget. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

<table><caption>**TABLE 4** | Individual relative standard uncertainties contributing to the combined standard uncertainty budget.</caption><thead><tr><td>Origin</td><td>Relative standard uncertainty (k = 1)</td></tr></thead><tbody><tr><td>Mass (M)</td><td>0.1%</td></tr><tr><td>Area (A)</td><td>0.019%</td></tr><tr><td>Mass attenuation coefficients (μ)</td><td>&lt; 0.77%</td></tr><tr><td>XRF intensity (I<sub>XRF</sub>)</td><td>&lt; 1%</td></tr><tr><td>Solid angle (Ω)</td><td>1.07%</td></tr><tr><td>Monochromatic photon beam intensity (I<sub>0</sub>)</td><td>&lt; 1.24%</td></tr><tr><td>SDD intrinsic efficiency (ε<sub>SDD</sub>)</td><td>&lt; 1.3%</td></tr><tr><td>Photoelectric cross-sections (τ)</td><td>2.14%</td></tr><tr><td>Target thickness inhomogeneity (l)</td><td>2.60%</td></tr></tbody></table>
Acknowledgments

This work has been funded by the INSNU project (CEA-DES/IRESNE).
We wish to thank SOLEIL for providing the synchrotron radiation facil-
ities, and Pascal Mercère and Paulo da Silva for assistance in using the
Metrology beamline.

Conflicts of Interest

The authors declare no conflicts of interest.

Data Availability Statement

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

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